THE 

ARCHITECT'S  AND  BUILDER'S 
POCKET-BOOK 

A  HANDBOOK  FOR  ARCHITECTS,  STRUCTURAL 

ENGINEERS,  BUILDERS,  AND 

DRAUGHTSMEN. 


BY 


ERANK  E.  KIDDER,  C.E.,  PH.D., 

Author  of  "  Building  'Construction  and  Superintendence.' 


tmtff   1000  latgrauutga,  maatlg 
frnm  GDrujural 


FIFTEENTH  EDITION,   REVISED. 
TOTAL    ISSUE,    THIRTY-FIVE    THOUSAND. 


~>  x 

EW   YORK: 

JOHN  WILEY  &  SONS. 

LONDON:  CHAPMAN   &  HALL,  LIMITED. 

1908. 


GENERAL 


Copyright,  1884,  1892,  1897,  1904, 


BY 


FRANK  E.   KIDDER. 


Copyright,  1908, 

BY 
KATHER1NE  E-  KIDDER. 


PRESS  OF 

BRAUNWORTH  &  CO. 

BOOKBINDERS  AND  PRINTERS 

BROOKLYN,   N.  Y. 


i$  HBoofe 


IS    RESPECTFULLY    DEDICATED    TO    THOSE    WHOSE    KINDNESS 
HAS  ENABLED  ME  TO  PRODUCE  IT. 

TO  MY  PARENTS, 
WHO    GAVE    ME    THE    EDUCATION  UPON    WHICH    IT    IS    BASED; 

TO   MY  WIFE, 

FOR  HER  LOVING  SYMPATHY,  ENCOURAGEMENT, 
AND  ASSISTANCE; 

TO  ORLANDO  W.  NORCROSS 

OF  WORCESTER,    MASS., 

WHOSE  SUPERIOR  PRACTICAL  KNOWLEDGE  OF  ALL  THAT 

PERTAINS  TO  BUILDING  HAS  GIVEN  ME  A  MORE 

INTELLIGENT  AND  PRACTICAL  VIEW  OF 

THE    SCIENCE  OF  CONSTRUCTION 

THAN  I  SHOULD  OTHERWISE 

HAVE    OBTAINED.* 


Dedication  to  First  Edition. 

189726 


THE  publishers  and  the  author  will  be  grateful  to  any  of 
the  readers  of  this  volume  who  will  kindly  call  their  attention 
to  errors,  typographical  or  otherwise,  discovered  therein,  in  order 
that  these  may  be  corrected  before  the  next  edition  goes  to 
press,  also  for  suggestions  towards  making  the  index  more  com- 
plete. 

JOHN  WILEY  &  SONS. 

43  &  45  EAST  NINETEENTH  STREET, 
NEW  YORK. 


PREFACE  TO  FIFTEENTH  EDITION. 


THE  changes  in  this  edition  consist  of  the  correction  of  all 
typographical  errors  reported  to  the  publishers,  and  the  re- 
writing of  Chapters  XXIII  and  XXIV.  This  work  has  been 
done  by  Rudolph  P.  Miller,  who  was  for  ten  years  connected 
with  the  Department  of  Buildings,  New  York  City,  and  for 
the  last  five  years  as  its  Chief  Engineer.  During  his  con- 
nection with  the  Department  of  Buildings  he  had  large  oppor- 
tunities for  studying  fire-proof  construction  particularly,  and 
gave  the  subject  of  Reinforced  Concrete  much  study,  drafting 
the  first  regulations  ever  promulgated  in  this  country  regard- 
ing its  use.  These  regulations  have  formed  the  basis  of  the 
regulations  since  adopted  by  the  cities  of  this  country,  in  many 
instances  the  major  part  of  them  being  copied  verbatim. 

Chapter  XXIII  has  been  revised,  one  half  of  the  matter  in 
the  old  edition  having  been  used  again.  The  new  matter  has 
been  substituted  for  such  parts  as  have  been  found  unneces- 
sary or  out  of  date. 

Chapter  XXIV,  on  Reinforced  Concrete,  is  entirely  new, 
the  whole  manuscript  being  original  and  Mr.  Miller's  own 
work. 

At  the  time  of  Mr.  Kidder's  revision  for  the  fourteenth  edi- 
tion, he  was  not  altogether  satisfied  with  the  chapters  on  fire- 
proofing  and  reinforced  concrete,  and  had  he  lived,  would 
have  revised  them  personally;  and  we  believe  that  the  chap- 
ters as  they  now  stand  would  meet  with  his  approval  were 
he  living. 

Professor  Alvah  H.  Sabin  has  also  kindly  brought  the  section 
on  Paints  and  Varnishes  up  to  date. 

v 


PREFACE  TO  FOURTEENTH  EDITION. 


IT  is  now  nearly  twenty  years  since  the  author,  then  quite 
a  young  man,  completed  the  first  edition  of  this  work,  which, 
although  containing  but  586  pages,  had  required  about  three 
years  for  its  preparation.  At  that  time  the  author  thought  he 
had  covered  all  of  those  practical  details  relating  to  the  planning 
and  construction  of  buildings,  with  which  the  architect  was 
concerned,  tolerably  well,  and  it  would  appear  as  though  the 
-  purchasers  of  the  book  thought  so  too,  but  as  the  years  have 
come  and  gone,  so  many  and  such  great  improvements  have 
taken  place  in  the  building  world,  so  many  articles  invented, 
new  methods  of  construction  developed,  higher  standards  estab- 
lished, that  the  present  edition,  although  containing  nearly 
three  times  as  many  pages,  is  perhaps  not  more  complete,  for 
the  times,  than  was  the  first  edition. 

When  preparing  the  first  edition,  it  was  the  aim  of  the  author 
to  give  to  architects  and  builders  a  handbook  which  shguld  be, 
in  its  field,  as  useful  and  reliable  as  Trautwine's  had  been  to 
civil  engineers;  and  with  that  object  constantly  in  view,  the 
book  has  been  revised  from  time  to  time  to  meet  the  changed 
conditions  in  building  construction  and  equipment. 

About  three  years  ago  it  was  thought,  by  the  publishers  and 
the  author,  that  a  thorough  and  complete  revision  of  the  book 
should  be  undertaken,  and  although  the  re-Avriting  of  a  work  of 
this  character,  even  with  the  thirteenth  edition  to  work  from, 
involved  many  months  of  close  and  constant  application,  the 
utilization  of  those  hours  which  one  ordinarily  takes  for  recrea- 
tion, and  at  the  best  more  or  less  interruption  to  his  regular 
business,  and  consequent  reduction  in  income,  the  writer  under- 

vi 


PREFACE  TO  FOURTEENTH  EDITION.  vii 

took  to  prepare  a  work  of  a  still  wider  scope,  and  which  should 
be  thoroughly  up-to-date  in  every  particular,  or  at  least  as  far 
as  is  practicable,  in  a  work  requiring  a  period  of  three  years  in 
its  preparation,  and  from  that  time  to  this  he  has  spared  no 
labor  or  expense  to  make  the  book  as  useful  and  complete  as 
he  possibly  could,  without  making  it  too  bulky. 

In  this  revision  the  author  has  had  in  view : 

1st.  A  reference-book  which  should  contain  some  informa- 
tion on  every  subject  (except  design)  likely  to  come  before  an 
architect,  structural  engineer,  draughtsman,  or  master-builder, 
including  data  for  estimating  the  approximate  cost. 

2d.  To  as  thoroughly  cover  the  subject  of  architectural  engi- 
neering as  is  practicable  in  a  handbook. 

3d.  To  present  all  information  in  as  simple  and  convenient  a 
form  for  immediate  application  as  is  consistent  with  accuracy. 
To  this  end  a  great  many  new  tables,  arranged  and  computed 
by  the  author,  have  been  inserted. 

At  the  time  the  first  edition  was  written,  the  term  "Archi- 
tectural Engineering"  had  not  been  used  in  its  present  applica- 
tion, and  the  term  "  Structural  Engineering,"  when  used, 
referred  almost  exclusively  to  bridge  work. 

To-day,  structural  and  architectural  engineers  are  concerned 
almost  exclusively  with  building  construction,  and  their  work 
is  more  closely  allied  to  that  of  the  architect  than  to  that  of 
the  civil  engineer;  hence  the  author  has  had  in  mind  the  needs 
of  the  structural  engineer  and  draughtsman  as  well  as  those  of 
the  architect  and  builder,  and  the  book  should  be  of  nearly 
equal  value  to  both. 

Where  it  was  impossible,  for  lack  of  space,  to  go  extensively 
into  any  subject,  references  to  other  books  or  sources  of  infor- 
mation have  been  given,  so  that  in  this  way  the  book  may 
serve  as  a  general  index  to  the  many  lines  of  work,  materials, 
and  manufactured  products  entering  into  the  planning,  con- 
struction, and  equipment  of  buildings. 

To  attain  the  objects  in  view,  it  has  been  necessary  to  add 
considerably  to  the  number  of  pages,  but  as  experience  has 
shown  that  the  book  is  used  principally  at  the  desk  or  draught- 
ing-table,  and  is  seldom  carried  in  the  pocket,  it  is  believed 
that  the  convenience  of  having  everything  in  one  book  will 
more  than  offset  any  disadvantage  resulting  from  increase  in 
bulk. 

Nearly  the  entire  book  has  been  re-written,  and  great  pains 


Via          PREFACE   TO   FOURTEENTH   EDITION. 

have  been  taken  to  furnish  reliable  data.  A  large  number  of 
experts  in  various  lines  have  assisted  the  author,  as  is  manifest 
by  the  foot-notes  and  references.  To  all  of  such,  and  to  the 
many  authors  of  technical  works,  and  to  the  publishers  of 
technical  journals,  who  have  kindly  consented  to  the  use  of 
cuts  and  data,  the  author  takes  pleasure  in  acknowledging  his 
•indebtedness.  Also  to  Mr.  E.  S.  Hand,  of  New  York,  who,  for 
many  years,  has  rendered  material  assistance  in  collecting  data 
along  the  line  of  manufactured  products. 

The  names  and  addresses  of  manufacturers  have  been  given 
solely  for  the  convenience  of  the  u^ers  of  the  book,  and  not  for 
any  pecuniary  considerations;  in  fact,  if  money  considerations 
had  solely  appealed  to  the  writer,  this  book  would  never  have 
been  re-written,  because  a  technical  work  of  this  character  can 
never  adequately  compensate,  in  money,  for  the  time,  labor, 
and  thought  required  in  its  preparation.  The  many  words  of 
appreciation  which  have  come  to  the  author  from  hundreds  of 
those  who  have  found  the  book  useful  have  been  a  great  stim- 
ulus to  further  increase  its  usefulness. 

As  in  the  former  prefaces,  the  author  requests  that  any  one 
discovering  errors  in  the  work  or  who  may  have  any  sugges- 
tions looking  to  the  further  improvement  of  the  book,  will  com- 
municate the  same  to  him,  that  the  book  may  be  made  as 
complete  and  reliable  as  possible. 

Finally,  the  author  desires  to  acknowledge  his  indebtedness 
to  the  publishers,  who  have  heartily  seconded  his  efforts  in 
every  particular,  and  who  have  spared  no  pains  or  expense  to 
make  a  perfect  handbook. 

F.  E.   KlDDER. 
DENVER,  COLO.,  July  18th,  1904. 


PREFACE  TO  FIRST  EDITION,   1884. 


IN  preparing  the  following  pages,  it  has  ever  been  the  aim  of 
the  author  to  give  to  the  architects  and  builders  of  this  country 
a  reference  book  which  should  be  for  them  what  Trautwine's 
"Pocket-Book"  is  to  engineers, — a  compendium  of  practical 
facts,  rules,  and  tables,  presented  in  a  form  as  convenient  for 
application  as  possible/and  as  reliable  as  our  present  knowledge 
will  permit.  Only  so  much  theory  has  been  given  as  will  render 
the  application  of  the  formulas  more  apparent,  and  aid  the 
student  in  understanding,  in  some  measure,  the  principles  upon 
which  the  formulas  are  based.  It  is  believed  that  nothing  has 
been  given  in  this  book  but  what  has  been  borne  out  in  practice- 

As  this  book  was  not  written  for  engineers,  the  more  intricate 
problems  of  building  construction,  which  may  fairly  be  said  to 
come  within  the  province  of  the  civil  engineer,  have  been  omitted. 

Desiring  to  give  as  much  information  as  possible  likely  to  be  of 
service  to  architects  and  builders,  the  author  has  borrowed  and 
quoted  from  many  sources,  in  most  cases  with  the  permission  of 
the  authors.  Much  practical  information  has  been  derived  from 
the  various  handbooks  published  by  the  large  manufacturers  of 
rolled-iron  beams,  bars,  etc. ;  and  the  author  has  always  found 
the  publishers  willing  to  aid  him  whenever  requested. 

Although  but  very  little  has  been  taken  from  Trautwine's 
' 'Pocket-Book  for  Engineers,"  yet  this  valuable  book  has  served 
the  author  as  a  model,  which  he  has  tried  to  imitate  as  well  as 
the  difference  in  the  subjects  would  permit;  and  if  his  work 
shall  prove  of  as  much  value  to  architects  and  builders  as  Mr. 
Trautwine's  has  to  engineers,  he  will  feel  amply  rewarded  for 
his  labor. 

As  it  is  impossible  for  the  author  to  verify  all  of  the  dimensions 

ix 


x  PREFACE  TO   FIRST  EDITION. 

and  miscellaneous  information  contained  in  Part  III.,  he  cannot 
speak  for  their  accuracy,  except  that  they  were  in  all  cases  taken 
from  what  were  considered  reliable  sources  of  information.  The 
tables  in  Part  II.  have  been  carefully  computed,  and  it  is  believed 
are  free  from  any  large  errors.  There  are  so  many  points  of 
information  often  required  by  architects  and  builders,  that  it  is 
difficult  for  one  person  to  compile  them  all;  and  although  the 
present  volume  is  by  no  means  a  small  one,  yet  the  author  desires 
to  make  his  work  as  useful  as  possible  to  those  for  whom  it  has 
been  prepared,  and  he  will  therefore  be  pleased  to  receive  any 
information  of  a  serviceable  nature  pertaining  to  architecture  or 
building,  that  it  may  be  inserted  in  future  editions  should  such 
become  necessary,  and  for  the  correction  of  any  errors  that  may 
be  found. 

The  author,  while  compiling  this  volume,  has  consulted  a  great 
number  of  works  relating  to  architecture  and  building ;  and  as  he 
has  frequently  been  asked  by  students  and  draughtsmen  to  refer 
them  to  books  from  which  they  might  acquire  a  better  knowledge 
of  construction  and  building,  the  following  list  of  books  is  given 
as  valuable  works  on  the  various  subjects  indicated  by  the 
titles : — 

"  Notes  on  Building  Construction,"  compiled  for  the  use  of  the 
students  in  the  science  and  art  schools,  South  Kensington,  Eng- 
land. 3  vols.  Rivingtons,  publishers,  London. 

"Building  Superintendence,"  by  T.  M.  Clark,  architect  and 
professor  of  architecture,  Massachusetts  Institute  of  Technology. 
J.  R.  Osgood  &  Co.,  publishers,  Boston. 

"The  American  House  Carpenter"  and  "The  Theory  of 
Transverse  Strains,"  both  by  Mr.  R.  G.  Hatfield,  architect, 
formerly  of  New  York. 

"Graphical  Analysis  of  Roof-Trusses,"  by  Professor  Charles 
E.  Green  of  the  University  of  Michigan. 

"The  Fire  Protection  of  Mills,"  by  C.  J.  H.  Woodbury,  in- 
spector for  the  Factory  Mutual  Fire  Insurance  Companies.  John 
Wiley  &  Sons,  publishers,  New  York. 

"House  Drainage  and  Water  Service,"  by  James  C.  Bayles, 
editor  of  "The  Iron  Age"  and  "The  Metal  Worker."  David 
Williams,  publisher,  New  York. 

"The  Builders'  Guide  and  Estimators'  Price-Book,"  and  "Plas- 
ter and  Plastering,  Mortars,  and  Cements,"  by  Fred.  T.  Hodgson, 
editor  of  "The  Builder  and  Wood  Worker."  Industrial  Publi- 
cation Company,  New  York. 


PREFACE   TO   FIRST  EDITION.  XI 

"Foundations  and  Concrete  Works,"  and  "Art  of  Building," 
by  E.  Dobson.  Weale's  Series,  London. 

It  would  be  well  if  all  of  the  above  books  might  be  found  in 
every  architect's  office;  but  if  the  expense  prevents  that,  the 
ambitious  student  and  draughtsman  should  at  least  make  him- 
self acquainted  with  their  contents.  These  works  will  also  be 
found  of  great  value  to  the  enterprising  builder. 


CONTENTS. 


PART    I. 

PAGE 

ARITHMETICAL  SIGNS  AND  CHARACTERS 

-INVOLUTION 4 

EVOLUTION,  SQUARE  AND  CUBE  ROOT,  RULES,  AND  TABLES  4 

WEIGHTS  AND  MEASURES 25 

THE  METRIC  SYSTEM 31 

METRIC  CONVERSION  TABLES 34,  36a 

SCRIPTURE  AND  ANCIENT  MEASURES  AND  WEIGHTS 36 

MENSURATION 37 

GEOMETRICAL  PROBLEMS 70 

TABLE  OF  CHORDS 88 

HIP  AND  JACK  RAFTERS 97 

TRIGONOMETRY,  FORMULAS  AND  TABLES 98 


PART    II. 

STRENGTH  OF  MATERIALS  AND  STABILITY  OF 
STRUCTURES. 

INTRODUCTION 127 

EXPLANATION  OF  SIGNS  AND  TERMS 128 

CHAPTER  I. 
DEFINITIONS  OF  TERMS  USED  IN  MECHANICS 130 

CHAPTER  II. 

FOUNDATIONS  AND  SPREAD  FOOTINGS 135 

xiii 


xiv  CONTENTS. 

CHAPTER  III. 

PAGE 

MASONRY    WALLS    AND    FOOTINGS  —  CEMENTS    AND    CON- 

CRETES .........................................     178 

CHAPTER  IV. 
RETAINING  WALLS  —  VAULT  WALLS  ....................     206 

CHAPTER  V. 

STRENGTH   OF   BRICK   AND    STONE   MASONRY   AND    CON- 

CRETE ..........................................     212 

CHAPTER  VI. 

COMPOSITION  AND  RESOLUTION  OF  FORCES  —  CENTRE   OF 

GRAVITY  ........................................     231 

CHAPTER  VII. 
STABILITY  OF  PIERS  AND  BUTTRESSES  ..............  .....     242 

CHAPTER  VIII. 
THE  STABILITY  OF  ARCHES  ............................ 


CHAPTER  IX. 
BENDING  MOMENTS  AND  SUPPORTING  FORCES  ...........     266 

CHAPTER  X. 

MOMENTS  OF  INERTIA  AND  RESISTANCE,  RADIUS  OF 
GYRATION.  DIMENSIONS  AND  PROPERTIES  OF  STRUC- 
TURAL SHAPES  ......  .  ............................  278 

CHAPTER  XI. 

RESISTANCE     TO     TENSION  —  PHYSICAL     PROPERTIES     OF 

IRON  AND  STEEL  .................................     321 

CHAPTER  XII. 
RESISTANCE  TO  SHEARING  —  RIVETED  JOINTS  ............     360 

CHAPTER  XIII. 
PROPORTIONS  OF  CAST-IRON  AND  STEEL   BEARING-PLATES 

AND  FOR  BRACKETS  ON  CAST-IRON  COLUMNS  ........     398 


CONTENTS.  xv 

CHAPTER  XIV. 

PAGE 

STRENGTH    OF   POSTS,  STRUTS,  AND    COLUMNS.     DETAILS 

OF  COLUMN  CONNECTIONS 407 

CHAPTER  XV. 

GENERAL  PRINCIPLES  OF  THE  STRENGTH  OF  BEAMS  AND 
STRENGTH  OF  STEEL  BEAMS.  STANDARD  CONNEC- 
TIONS FOR  STEEL  BEAMS 497 

CHAPTER  XVI. 
STRENGTH  OF  CAST-IRON,  WOODEN,  AND  STONE   BEAMS  . .     554 

CHAPTER  XVII. 

STRENGTH  OF  BUILT-UP  WOODEN  BEAMS,  FLITCH- 
PLATES,  AND  TRUSSED  GIRDERS 579 

CHAPTER  XVIIL 
STIFFNESS  AND  DEFLECTION  OF  BEAMS 595 

CHAPTER  XIX. 
STRENGTH  AND  STIFFNESS  OF  CONTINUOUS  GIRDERS.  . .  .      608 

CHAPTER  XX. 
RIVETED  STEEL-PLATE  AND  Box  GIRDERS 618 

CHAPTER  XXI. 
STRENGTH  AND  STIFFNESS  OF  WOODEN  FLOORS 651 

CHAPTER  XXII. 
MILL  AND  WAREHOUSE  CONSTRUCTION 687 

CHAPTER  XXIII. 
FIRE-PROOFING  OF  BUILDINGS 726 

By  RUDOLPH   P.  MILLER,  C.E. 

CHAPTER   XXIV. 

REINFORCED  CONCRETE 851 

By  RUDOLPH  P.   MILLER,  C.E. 

CHAPTER  XXV. 
ROOF-TRUSSES — TYPES  OF  WOODEN  AND  STEEL  TRUSSES.      883 


xvi  CONTENTS. 

CHAPTER  XXVI. 

PAGE 

STRESSES  IN  ROOF-TRUSSES 941 

CHAPTER  XXVII. 

ROOF-TRUSSES;   PROPORTIONING   MEMBERS    OF,   AND  DE- 
TAILS OF  JOINTS 1037 

CHAPTER  XXVIII. 
WIND    STRESSES    AND    BRACING    IN    TOWERS    AND    HIGH 

BUILDINGS 1075 

PART   III. 

HEAT,  FUEL,  WATER,  STEAM,  AND  AIR 1107 

DRYING  BY  STEAM 1117 

COMPARISON  OF  THERMOMETERS 1118 

GRAVITY  SYSTEMS  OF  STEAM  HEATING 1121 

SYSTEMS  OF  PIPING  FOR  STEAM  HEATING 1146 

STEAM-PIPE  FITTINGS  AND  VALVES 1153 

RULES  FOR  PROPORTIONING  RADIATING  SURFACE 1158 

HOT-WATER  HEATING 1168 

FURNACE  HEATING 1 174 

SPECIFICATIONS  FOR  HEATING  APPARATUS 1188 

TABLES  OF  HOT-AIR  STACKS,  REGISTERS,  STEAM  PIPING, 

ETC 1197 

SMOKE  PREVENTION 1207 

VENTILATION 1208 

CHIMNEYS 1220 

HYDRAULICS 1231 

PRIVATE  WATER-SUPPLY,  PUMPS,  WINDMILLS,  ETC 1244 

FIRE  STREAMS 1251 

CONSTRUCTION  OF  CYLINDRICAL  WOODEN  TANKS 1252 

CAPACITY  OF  TANKS 1258 

PLUMBING  DEFINITIONS  AND  REQUIREMENTS 1262 

PLUMBING  MATERIALS  AND  DETAILS 1269 

PLUMBING  SPECIALTIES 1281 

PLUNGE-BATHS 1283 

ILLUMINATING-GAS,  VARIETIES  OF 1285 

PIPING  A  HOUSE  FOR  GAS 1287 

NOTES  ON  LIGHTING  AND  ILLUMINATION 1294 

THE  DIFFUSION  OF  LIGHT  THROUGH  WINDOWS 1300 


CONTENTS.  xvn 

PAGE 

ELECTRICITY 1305 

ELECTRIC  LIGHTING  AND  WIRING 1311 

SPECIFIC  GRAVITIES  AND  WEIGHTS  OF  SUBSTANCES 1341 

WIRE  AND  SHEET-METAL  GAUGES 1345 

WEIGHTS  OF  WROUGHT  IRON,  STEEL,  COPPER,  AND  BRASS 

SHEETS 1347 

WEIGHT  OF  LEAD,  COPPER,  AND  BRASS 1348 

SIZE,  WEIGHT,  AND  KINDS  OF  SMOOTH  STEEL  WIRE 1349 

WEIGHTS  AND  AREAS  OF  ROUND  AND  SQUARE  BARS 1350 

WEIGHTS  OF  FLAT-ROLLED  STEEL  BARS 1353 

[DATA  FOR  ESTIMATING  WEIGHT  OF  CAST  IRON,  WROUGHT 

IRON,  AND  STEEL 1357 

WEIGHT  OF  CAST-IRON  COLUMNS 1358 

WEIGHT  OF  CAST-IRON  PLATES 1360 

i  SCREW-THREADS,  NUTS  AND  BOLT-HEADS,  DIMENSIONS 

AND  WEIGHT 1361 

WEIGHT  OF  RIVETS  AND  ROUND-HEADED  BOLTS 1364 

NAILS,  KINDS,  VARIETIES,  SIZES,  ETC.,  HOLDING  POWER  OF  1365 

SCREWS  AND  EXPANSION  BOLTS 1370 

EXCAVATING 1371 

STONEWORK 1373 

BRICKS  AND  BRICKWORK 1376 

LIME 1387 

SAND  AND  GRAVEL 1388 

LATHING  AND  PLASTERING .- 1389 

LUMBER  AND  CARPENTERS'  WORK. 1394 

BUILDING  PAPERS  FELTS  AND  INSULATING  QUILTS 1401 

PAINT  AND  VARNISH 1403 

GLASS  KINDS  AND  PRICE  LISTS 1415 

TRANSLUCENT  FABRIC — MIRRORS 1424 

MEMORANDA  ON  ROOFING — SHINGLES,  SLATES,  TILES,  TIN, 

AND  GRAVEL 1425 

CORRUGATED  IRON  AND  STEEL  SHEETS — ROOFING  AND 

SIDING 1437 

GALVANIZED  IRON 1443 

FLOOR  AND  WALL  TILING 1443 

ASPHALTUM,  ROCK  ASPHALT 1448 

MINERAL  WOOL 1450 

ESTIMATING  THE  COST  OF  STRUCTURAL  STEEL 1451 

STANDARD  STEEL  CLASSIFICATION 1455 

COST  OF  BUILDINGS  PER  CUBIC  FOOT  .  .  1457 


xvin  CONTENTS. 

PAGE 

COST  OF  BUILDINGS  PER  SQUARE  FOOT 1467 

DEPRECIATION  OF  BUILDINGS 1468 

DIMENSIONS  OF  FURNITURE,  PLUMBING  FIXTURES,  CAR- 

RIAGES,  FIRE-WAGONS,  LOCOMOTIVES,  AND  CARS 1470 

DIMENSIONS    FOR    HORSE-STALLS,    FLAG-POLES,    SCHOOL-  . 

ROOMS,  SCHOOL-SEATS,  ETC 1474 

STAIRS 1476 

SASH  WEIGHTS 1477 

SEATING  SPACE  IN  CHURCHES  AND  THEATRES 1478 

CAPACITY  OF  CHURCHES,  THEATRES,  AND  OPERA-HOUSES.  .  1479 

DIMENSIONS  OF  THEATRES  AND  OPERA-HOUSES 1480 

PROPORTIONING  GUTTERS  AND  CONDUCTORS  TO  HOOF  SUR- 
FACE   1481 

ELEVATORS .  1482 

MAIL  CHUTES 1491 

REFRIGERATORS 1492 

TOWER  CLOCKS 1494 

LIBRARY  STACKS,  CAPACITY  OF  SHELVING 1494 

CLASSICAL  MOULDINGS 1496 

THE  CLASSICAL  ORDERS 1497 

LIGHTNING  CONDUCTORS 1505 

ADHESIVE  STRENGTH  OF  SULPHUR,  LEAD,  AND  PORTLAND 

CEMENT  FOR  ANCHORING  BOLTS 1507 

EFFLORESCENCE  ON  BRICKWORK 1508 

RELATIVE   HARDNESS   OF  WOODS.     WEIGHT     OF  ROUGH 

LUMBER r 1509 

FORCE  OF  THE  WIND 1510 

To  MAKE  BLUE-PRINT  COPIES  OF  TRACINGS 1510 

HORSE-POWER,  PULLEYS,  GEARS,  BELTING,  AND  SHAFTING  1512 

CHAIN  BLOCKS 1516 

PROPORTION  OF  HOOKS 1518 

THE  LONGEST  BRIDGES  IN  THE  WORLD 1519 

OTHER  NOTABLE  BRIDGES 1521 

DIMENSIONS  AND  WEIGHTS  OF  CHURCH  BELLS 1522 

LARGEST  RINGING  BELLS  IN  THE  WORLD 1523 

SYMBOLS  OF  THE  APOSTLES  AND  SAINTS 1524 

HEIGHTS  OF  COLUMNS,  TOWERS,  DOMES,  SPIRES,  ETC.  . . .  1525 

PRINCIPAL  DIMENSIONS  OF  THE  ENGLISH  CATHEDRALS.  .  .  1527 

DIMENSIONS  OF  THE  VARIOUS  OBELISKS 1528 

DIMENSIONS  OF  SOME  WELL-KNOWN  EUROPEAN  BUILDINGS.  1529 


CONTENTS.  xix 

PAGE 

HEIGHT  OF   SOME   OF  THE  TALLEST  BUILDINGS   IN   THE 

UNITED  STATES.  . 1531 

DESCRIPTION  OF  NOTABLE  AMERICAN  BUILDINGS 1533 

ARCHITECTS  OF  NOTED  PUBLIC  AND  SEMI-PUBLIC  BUILD- 
INGS IN  THE  UNITED  STATES 1537 

LIST  OF  NOTED  ARCHITECTS 1540 

PROFESSIONAL  PRACTICE  OF  ARCHITECTS, — A. I. A.  SCHED- 
ULE OF  CHARGES 1552 

CONTRACT  BETWEEN  ARCHITECT  AND  OWNER 1553 

[THE  UNIFORM  CONTRACT 1555 

'ARCHITECTS'  LICENSE  LAW — STATE  OF  ILLINOIS 1558 

COLLEGES  AND  SCHOOLS  OF  ARCHITECTURE  IN  THE  UNITED 

STATES 1562 

(TRAVELLING  FELLOWSHIPS  AND  SCHOLARSHIPS 1565 

LIST   OF    BOOKS    FOR    ARCHITECTS,    DRAUGHTSMEN,    AND 

BUILDERS 1566 

TRADE  REFERENCES 1570 

GLOSSARY  OF  TECHNICAL  TERMS,  ANCIENT  AND  MODERN, 

USED  BY  ARCHITECTS,  BUILDERS,  AND  DRAUGHTSMEN.    1575 
LEGAL  DEFINITION  OF  ARCHITECTURAL  TERMS 1628 


PART  I. 


PRACTICAL 

ARITHMETIC,  GEOMETRY,  AND  TRIGONOMETRY. 


RULES,  TABLES,  AND  PROBLEMS. 


PRACTICAL 

AEITHMETIC  AND  GEOIETEY. 


SIGNS  AND  CHARACTERS. 

THE  following  signs  and  characters  are  generally  used  to  denote 
and  abbreviate  the  several  mathematical  operations: — 
The  sign=  means  equal  to,  or  equality. 

—  means  minus  or  less,  or  subtraction. 

+  means  plus,  or  addition. 

X  means  multiplied  by,  or  multiplication. 

-f-  means  divided  by,  or  division. 

2  (   Index  or   power,   meaning  that  the  number  to 

3  J       which  they  are  added  is  to  be  squared  (2)  or 
(        cubed  (3). 

:  is  to  } 

::  so  is  >•  Signs  of  proportion. 
:to      ) 
\Xmeans  that  the  square  root  of  the  number  before 

which  it  is  placed  is  required. 

-sj/means  that  the   cube   root  of  the  number  before 
which  it  is  placed  is  required. 

the  bar  indicates  that  all  the  numbers  under  it  are 

to  be  taken  together. 
( )  the  parenthesis  means  that  all  the  numbers  between 

are  to  be  taken  as  one  quantity. 
.  means  decimal  parts;    thus,  2.5  means  2T5T5,  0.46 

means  T4o%. 

0  means  degrees,  '  minutes,  "  seconds. 
.'.  means  hence. 

3 


4  INVOLUTION.— EVOLUTION. 

INVOLUTION. 

To  square  a  number,  multiply  the  number  by  itself,  and 
the  product  will  be  the  square;  thus,  the  square  of!8=18Xl8= 
324. 

The  cube  of  a  number  is  the  product  obtained  by  multi- 
plying the  number  by  itself,  and  that  product  by  the  number 
again;  thus,  the  cube  of  14=14X14X14=2744. 

The  fourth  power  of  a  number  is  the  product  obtained 
by  multiplying  the  number  by  itself  four  times;  thus,  the  fourth 
power  of  10=10X10X10X10=10000. 

EVOLUTION. 

Square  Root. — Rule  for  determining  the  square  root  of  a 
number. 

1st,  Divide  the  given  number  into  periods  of  two  figures  each, 
commencing  at  the  right  if  it  is  a  whole  number,  and  at  the 
decimal-point  if  there  are  decimals;  thus,  10236.8126. 

2d,  Find  the  largest  square  in  the  left-hand  period,  and  place 
its  root  in  the  quotient;  subtract  the  said  square  from  the  left- 
hand  period,  and  to  the  remainder  bring  down  the  next  period 
for  a  new  dividend. 

3d,  Double  the  root  already  found,  and  annex  one  cipher  for  a 
trial  divisor,  see  how  many  times  it  will  go  in  the  dividend,  and 
put  the  number  in  the  quotient,  also,  in  place  of  the  cipher  in  the 
divisor ; — multiply  this  final  divisor  by  the  number  in  the  quotient 
just  found,  and  subtract  the  product  from  the  dividend,  and  to 
the  remainder  bring  down  the  next  period  for  a  new  dividend, 
and  proceed  as  before.  If  it  should  be  found  that  the  trial  divisor 
cannot  be  contained  in  the  dividend,  bring  down  the  next  period 
for  a  new  dividend,  and  annex  another  cipher  to  the  trial  divisor, 
and  put  a  cipher  in  the  quotient,  and  proceed  as  before. 

EXAMPLE  i0236.8i26  ( 101.17  square  root. 

1 

20  f)  0236 
201 


2021 )  3581 
2021 


20227)  156026 

141589 

14437 


CUBE  ROOT. 


Cube  Root. — To  extract  the  cube  root  of  a  number,  point 
off  the  number  from  right  to  left  into  periods  of  three  figures 
each,  and,  if  there  is  a  decimal,  commence  at  the  decimal-point, 
and  point  off  into  periods,  going  both  ways. 

Ascertain  the  highest  root  of  the  first  period,  and  place  to  right 
of  number,  as  in  long  division;  cube  the  root  thus  found,  and 
subtract  from  the  first  period ;  to  the  remainder  annex  the  next 
period;  square  the  root  afready  found,  and  multiply  by  three, 
and  annex  two  ciphers  for  the  trial  divisor.  Find  how  often  this 
trial  divisor  is  contained  in  the  dividend,  and  write  the  result 
in  the  root. 

Add  together  the  trial  divisor,  three  times  the  product  of  the 
first  figure  of  the  root  by  the  second  with  one  cipher  annexed,  and 
the  square  of  the  second  figure  in  the  root ;  multiply  the  sum  by 
the  last  figure  in  the  root,  and  subtract  from  the  dividend;  to 
the  remainder  annex  the  next  period,  and  proceed  as  before. 

When  the  trial  divisor  is  greater  than  the  dividend,  write  a 
cipher  in  the  root,  annex  the  next  period  to  the  dividend,  and 
proceed  as  before. 

Desired  the  i/493039. 

493039  (79  cube  root. 

7X7X7=343 


7X7X3-14700 

7X9X3=    1890 

9X9=       81 


16671 


150039 


150039 


Desired  the  ^/403583.419. 

403583.419  ( 73.9  cube  root. 

7X7X7=343 


7X7X3=14700 

7X3X3=      630 

3X3=         9 

15339 


73X73X3=1598700 

73X   9X3=      19710 

9X9=  81 


1618491 


60583 


46017 


14566419 


14566419 


CUBE   ROOT. 

Desired  the  ^/l  58252.632929. 

158252.632929  (  54.09  cube  root 
5X5X5=125 


5X5X3-7500 
5X4X3=   600 
4X4=      16 

33252 
32464 

8116 

540  X  540  X  3  =  87480000 
540  X     9X3=      145800 
9X9=             81 

788632929 
788632929 

87625881 

TABLE 


SQUARES,  CUBES,  SQUARE  ROOTS,  CUBE  ROOTS, 
AND  RECIPROCALS, 


1    -bo   ±054. 


The  following  table,  taken  from  Searle's  "Field  Engineering/ 
will  be  found  of  great  convenience  in  finding  the  square,  cube, 
square  root,  cube  root,  and  reciprocal  of  any  number  from  1  to 
1054.  The  reciprocal  of  a  number  is  the  quotient  obtained  by 
dividing  1  by  the  number.  Thus  the  reciprocal  of  8  is  l-f-8= 
0.125. 

7 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals 

1 

1 

1 

1.0000000 

1  .  0000000 

1.000000000 

2 

4 

8 

1.4142136 

1.2599210 

.  500000000 

3 

9 

27 

1  .  7320508 

1.4422496 

.333333333 

4 

16 

64 

2.0000000 

1.5874011 

.250000000 

5 

25 

125 

2  .  2360680 

1.7099759 

.200000000 

6 

36 

216 

2.4494897 

1.8171206 

.166666667 

7 

49 

343 

2.6457513 

1.9129312 

.142857143 

8 

64 

512 

2.8284271 

2  .  0000000 

.  125000000 

9 

81 

729 

3.0000000 

2.0800837 

.111111111 

10 

100 

1000 

3.1622777 

2.1544347 

.  100000000 

11 

121 

1331 

3.3166248 

2.2239801 

.090909091 

12 

144 

1728 

3.4641016 

2  .  2894286 

.083333333 

13 

169 

2197 

3.6055513 

2.3513347 

.076923077 

14 

196 

2744 

3.7416574 

2.4101422 

.071428571 

15 

225 

3375 

3.8729833 

2.4662121 

.066666667 

16 

256 

4096 

4  .  0000000 

2.5198421 

.062500000 

17 

289 

4913 

4.1231056 

2.5712816 

.058823529 

18 

324 

5832 

4  .  2426407 

2.6207414 

.055555556 

19 

361 

6859 

4.3588989 

2.6684016 

.052631579 

20 

400 

8000 

4.4721360 

2.7144177 

.050000000 

21 

441 

9261 

4  .  5825757 

2  .  7589243 

.047619048 

22 

484 

10648 

4.6904158 

2  .  8020393 

.045454545 

23 

529 

12167 

4.7958315 

2.8438670 

.043478261 

24 

576 

13824 

4.8989795 

2.8844991 

.041666667 

25 

625 

15625 

5.0000000 

2.9240177 

.040000000 

26 

676 

17576 

5.0990195 

2.9624960 

.038461538 

27 

729 

19683 

5.1961524 

3.0000000 

.037037037 

28 

784 

21952 

5.2915026 

3.0365889 

.035714286 

29 

841 

24389 

5.3851648 

3.0723168 

.034482759 

30 

900 

27000 

5.4772256 

3.1072325 

.033333333 

31 

961 

29791 

5  .  5677644 

3.1413806 

.032258065 

32 

1024 

32768 

5.6568542 

3.1748021  ' 

.031250000 

33 

1089 

35937 

5.7445626 

3.2075343 

.030303030 

34 

1156 

39304 

5.8309519 

3.2396118 

.029411765 

35 

1225 

42875 

5.9160798 

3.2710663 

.028571429 

36 

1296 

46656 

6.0000000 

3.3019272 

.027777778 

37 

1369 

50653 

6  .  0827625 

3.3322218 

.027027027 

38 

1444 

54872 

6.1644140 

3.3619754 

.026315789 

39 

1521 

59319 

6.2449980 

3.3912114 

.025641026 

40 

1600 

64000 

6  .  3245553 

3.4199519 

.025000000 

41 

1681 

68921 

6.4031242 

3.4482172 

.024390244 

42 

1764 

74088 

6.4807407 

3.4760266 

.023809524 

43 

1849 

79507 

6  .  5574385 

3.5033981 

.023255814 

44 

1936 

85184 

6.6332496 

3.5303483 

.022727273 

45 

2025 

91125 

6.7082039 

3.5568933 

.022222222 

46 

2116 

97336 

6  .  7823300 

3.5830479 

.021739130 

47 

2209 

103823 

6.8556546 

3.6088261 

.021276600 

48 

2304 

110592 

6.9282032 

3.6342411 

.020833333 

49 

2401 

117649 

7.0000000 

3.6593057 

.020408163 

50 

2500 

125000 

7.0710678 

3.6840314 

.020000000 

51 

2601 

132651 

7.1414284 

3.7084298 

.019607843 

52 

2704 

140608 

7.2111026 

3.7325111 

.019230769 

53 

2809 

148877 

7.2801099 

3.7562858 

.018867925 

54 

2916 

157464 

7.3484692 

3.7797631 

.018518519 

55 

3025 

166375 

7.4161985 

3.8029525 

.018181818 

56 

3136 

175616 

7.4833148 

3.8258624 

.017857143 

57 

3249 

185193 

7.5498344 

3.8485011 

.017543860 

58 

3364 

195112 

7.6157731 

3.8708766 

.017241379 

59 

3481 

205379 

7.6811457 

3.8929965 

.016949153 

60 

3600 

216000 

7.7459667 

3.9148676 

.016666667 

61 

3721 

226981 

7.8102497 

3.9364972 

.016393443 

62 

3844 

238328 

7.8740079 

3.9578915 

.016129032 

CUBE  ROOTS,  AND  RECIPROCALS. 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

63 

3969 

250047 

7.9372539 

3.9790571 

.015873016 

64 

4096 

262144 

8.0000000 

4  .  0000000 

.015625000 

65 

4225 

274625 

8.0622577 

4.0207256 

.015384615 

66 

4356 

287496 

8.1240384 

4.0412401 

.015151515 

67 

4489 

300763 

8.1853528 

4.0615480 

.014925373 

68 

4624 

314432 

8.2462113 

4.0816551 

.014705882 

69 

4761 

328509 

8.3066239 

4.1015661 

.014492754 

70 

4900 

343000 

8.3666003 

4.1212853 

.014285714 

71 

6041 

357911 

8.4261498 

4.1408178 

.014084507 

72 

5184 

373248 

8.4852814 

4.1601676 

.013888889 

73 

5329 

389017 

8.5440037 

4.1793390 

.013698630 

74 

5476 

405224 

8.6023253 

4.1983364 

.013513514 

75 

5625 

421875 

8.6602540 

4.2171633 

.013333333 

76 

5776 

438976 

8.7177979 

4.2358236 

.013157895 

77 

5929 

456533 

8  .  7749644 

4.2543210 

.012987013 

78 

6084 

474552 

8.8317609 

4.2726586 

.012820513 

79 

6241 

493039 

8.8881944 

4.2908404 

.012658228 

80 

6400 

512000 

8.9442719 

4  .  3088695 

.012500000 

81 

6561 

531441 

9.0000000 

4  .  3267487 

.012345679 

82 

6724 

551368 

9.0553851 

4.3444815 

.012195122 

83 

6889 

571787 

9.1104336 

4  .  3620707 

.012048193 

84 

7056 

592704 

9.1651514 

4.3795191 

.011904762 

85 

7225 

614125 

9.2195445 

4  .  3968296 

.011764706 

86 

7396 

636056 

9.2736185 

4.4140049 

.011627907 

87 

7569 

658503 

9.3273791 

4.4310476 

.011494253 

88 

7744 

681472 

9.3808315 

4.4479602 

.011363636 

89 

7921 

704969 

9.4339811 

4.4647451 

.011235955 

90 

8100 

729000 

9.4868330 

4.4814047 

.011111111 

91 

8281 

753571 

9  .  5393920 

4.4979414 

.010989011 

92 

8464 

778688 

9.5916630 

4.5143574 

.010869565 

93 

8649 

804357 

9.6436508 

4  .  5306549 

.010752688 

94 

8836 

830584 

9.6953597 

4.5468359 

.010638298 

95 

9025 

857375 

9.7467943 

4.5629026 

.010526316 

96 

9216 

884736 

9  .  7979590 

4  .  5788570 

.010416667 

97 

9409 

'  912673 

9.8488578 

4  .  5947009 

.010309278 

98 

9604 

941192 

9.8994949 

4.6104363 

.010204082 

99 

9801 

970299 

9.9498744 

4.6260650 

.010101010 

100 

10000 

1000000 

10.0000000 

4.6415888 

.010000000 

101 

10201 

1030301 

10.0498756 

4.6570095 

.009900990 

102 

10404 

1061208 

10.0995049 

4.6723287 

.009803922 

103 

10609 

1092727 

10.1488916 

4.6875482 

.009708738 

104 

10816 

1124864 

10.1980390 

4.7026694 

.009615385 

105 

11025 

1157625 

10.2469508 

4.7176940 

.009523810 

106 

11236 

1191016 

10  .  2956301 

4.7326235 

.009433962 

107 

11449 

1225043 

10.3440804 

4.7474594 

.009345794 

108 

11664 

1259712 

10.3923048 

4.7622032 

.009259259 

109 

11881 

1295029 

10.4403065 

4.7768562 

.009174312 

110 

12100 

1331000 

10.4880885 

4.7914199 

.009090909 

111 

12321 

1367631 

10  .  5356538 

4.8058955 

.009009009 

112 

12544 

1404928 

10.5830052 

4  .  8202845 

.008928571 

113 

12769 

1442897 

10.6301458 

4.8345881 

.008849558 

114 

12996 

1481544 

10.6770783 

4  .  8488076 

.008771930 

115 

13225 

1520875 

10.7238053 

4.8629442 

.008695652 

116 

13456 

1560896 

10.7703296 

4.8769990 

.008620690 

117 

13689 

1601613 

10.8166538 

4.8909732 

.008547009 

118 

13924 

1643032 

10.8627805 

4.9048681 

.008474576 

119 

14161 

1685159 

10.9087121 

4.9186847 

.008403361 

120 

14400 

1728000 

10.9544512 

4.9324242 

.008333333 

121 

14641 

1771561 

11.0000000 

4.9460874 

.008264463 

122 

34884 

1815848 

11.0453610 

4.9596757 

.008196721 

123 

15129 

1860867 

11.0905365 

4.9731898 

.008130081 

124 

15376 

1906624 

11.1355287 

4.9866310 

.008064516 

10 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

125 

15625 

1953125 

11.1803399 

5.0000000 

.008000000 

126 

15876 

2000376 

11.2249722 

5.0132979 

.007936508 

127 

16129 

2048383 

11.2694277 

5.0265257 

.007874016 

128 

16384 

2097152 

11.3137085 

5.0396842 

.007812500 

129 

16641 

2146689 

11.3578167 

5.0527743 

.007751938 

130 

16900 

2197000 

11.4017543 

5.0657970 

.007692308 

131 

17161 

2248091 

11.4455231 

5.0787531 

.007633588 

132 

17424 

2299968 

11.4891253 

5.0916434 

.007575758 

133 

17689 

2352637 

11.5325626 

5  .  1044687 

.007518797 

134 

17956 

2406104 

11.5758369 

5.1172299 

.007462687 

135 

18225 

2460375 

11.6189500 

5.1299278 

.007407407 

136 

18496 

2515456 

11.6619038 

5.1425632 

.007352941 

137 

18769 

2571353 

11.7046999 

5.1551367 

.007299270 

138 

19044 

2628072 

11.7473401 

5.1676493 

.007246377 

139 

19321 

2685619 

11.7898261 

5.1801015 

.007194245 

140 

19600 

2744000 

11.8321596 

5.1924941 

.007142857 

141 

19881 

2803221 

11.8743421 

5  .  2048279 

.007092199 

142 

20164 

2863288 

11.9163753 

5.2171034 

.007042254 

143 

20449 

2924207 

11.9582607 

5.2293215 

.006993007 

144 

20736 

2985984 

12.0000000 

5.2414828 

.  006944444 

145 

21025 

3048625 

12.0415946 

5.2535879 

.006896552 

146 

21316 

3112136 

12.0830460 

5.2656374 

.006849315 

147 

21609 

3176523 

12.1243557 

5.2776321 

.006802721 

148 

21904 

3241792 

12.1655251 

5  .  2895725 

.006756757 

149 

22201 

3307949 

12.2065556 

5.3014592 

.006711409 

150 

22500 

3375000 

12.2474487 

5.3132928 

.006666667 

151 

22801 

3442951 

12.2882057 

5  .  3250740 

.006622517 

152 

23104 

3511808 

12.3288280 

5.3368033 

.006578947 

153 

23409 

3581577 

12.3693169 

5.3484812 

.006535948 

154 

23716 

3652264 

12.4096736 

5.3601084 

.006493506 

155 

24025 

3723875 

12.4498996 

5.3716854 

.006451613 

156 

24336 

3796416 

12.4899960 

5.3832126 

.006410256 

157 

24649 

3869893 

12.5299641 

5  .  3946907 

.006369427 

158 

24964 

3944312 

12.5698051 

5.4061202 

.006329114 

159 

25281 

4019679 

12.6095202 

5.4175015 

006289308 

160 

25600 

4096000 

12.6491106 

5  .  4288352 

.006250000 

161 

25921 

4173281 

12.6885775 

5.4401218 

.006211180 

162 

26244 

4251528 

12.7279221 

5.4513618 

.006172840 

163 

26569 

4330747 

12.7671453 

5.4625556 

.006134969 

164 

26896 

4410944 

12.8062485 

5.4737037 

.006097561 

165 

27225 

4492125 

12.8452326 

5.4848066 

.006060606 

166 

27556 

4574296 

12.8840987 

5.4958647 

.  006024096 

167 

27889 

4657463 

12.9228480 

5  .  5068784 

.  005988024 

168 

28224 

4741632 

12.9614814 

5.5178484 

.005952381 

169 

28561 

4826809 

13.0000000 

5.5287748 

.005917160 

170 

28900 

4913000 

13.0384048 

5.5396583 

.005882353 

171 

29241 

5000211 

13.0766968 

5.5504991 

.  005847953 

172 

29584 

5088448 

13.1148770 

5.5612978 

.005813953 

173 

29929 

5177717 

13.1529464 

5  .  5720546 

.  005780347 

174 

30276 

5268024 

13.1909060 

5  .  5827702 

.005747126 

175 

30625 

5359375 

13.2287566 

5  .  5934447 

.005714286 

176 

30976 

5451776 

13.2664992 

5.6040787 

.005681818 

177 

31329 

5545233 

13.3041347 

5.6146724 

.005649718 

178 

31684 

5639752 

13.3416641 

5.6252263 

.005617978 

179 

32041 

5735339 

13.3790882 

5.6357408 

.005586592 

180 

32400 

5832000 

13.4164079 

5.6462162 

.005555556 

181 

32761 

5929741 

1  3  .  4536240 

5  .  6566528 

.005524862 

182 

33124 

6028568 

13.4907376 

5.6670511 

.005494505 

183 

33489 

6128487 

13.5277493 

5.6774114 

.005464481 

184 

33856 

6229504 

13.5646600 

5.  6877340 

.005434783 

185 

34225 

6331625 

13.6014705 

5.6980192 

.005405405 

186 

34596 

6434856 

13.6381817 

5  .  70S2G75 

.O0537r.;m 

CUBE  ROOTS,  AND  RECIPROCALS. 


11 


i 
;  No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

187 

34969 

6539203 

13.6747943 

5.7184791 

.005347594 

188 

35344 

6644672 

13.7113092 

5  .  7286543 

.005319149 

189 

35721 

6751269 

13.7477271 

5.7387936 

.005291005 

190 

36100 

6859000 

13.7840488 

5.7488971 

.005263158 

191 

36481 

6967871 

13.8202750 

5.7589652 

.005235602 

192 

36864 

7077888 

13.8564065 

5.7689982 

.005208333 

193 

37249 

7189057 

13.8924440 

5.7789966 

.005181347 

194 

37636 

7301384 

13.9283883 

5.7889604 

.005154639 

195 

38025 

7414875 

13.9642400 

5.7988900 

.005128205 

196 

38416 

7529536 

14.0000000 

5.8087857 

.005102041 

197 

38809 

7645373 

14.0356688 

5.8186479 

.005076142 

198 

39204 

7762392 

14.0712473 

5.8284767 

.005050505 

199 

39601 

7880599 

14.1067360 

5.8382725 

.005025126 

200 

40000 

8000000 

14.1421356 

5.8480355 

.005000000 

201 

40401 

8120601 

14.1774469 

5.8577660 

.004975124 

202 

40804 

8242408 

14.2126704 

5.8674643 

.004950495 

203 

41209 

8365427 

14.2478068 

5.8771307 

.004926108 

204 

41616 

8489664 

14.2828569 

5.8867653 

.004901961 

205 

42025 

8615125 

14.3178211 

5.8963685 

.004878049 

206 

42436 

8741816 

14.3527001 

5.9059406 

.  004854369 

207 

42849 

8869743 

14.3874946 

5.9154817 

.004830918 

208 

43264 

8998912 

14.4222051 

5.9249921 

.004807692 

209 

43681 

9129329 

14.4568323 

5.9344721 

.004784689 

210 

44100 

9261000 

14.4913767 

5.9439220 

.004761905 

211 

44521 

9393931 

14.5258390 

5.9533418 

.004739336 

212 

44944 

9528128 

14.5602198 

5.9627320 

.004716981 

213 

45369 

9663597 

14.5945195 

5.9720926 

.004694836 

214 

45796 

9800344 

14.6287388 

5.9814240 

.004672897 

215 

46225 

9938375 

14.6628783 

5.9907264 

.004651163 

216 

46656 

10077696 

14.6969385 

6.0000000 

.004629630 

217 

47089 

10218313 

14.7309199 

6.0092450 

.004608295 

218 

47524 

10360232 

14.7648231 

6.0184617 

.004587156 

219 

47961 

10503459 

14.7986486 

6.0276502 

.004566210 

220 

48400 

10648000 

14.8323970 

6.0368107 

.004545455 

221 

48841 

10793861 

14.8660687 

6.0459435 

.004524887 

222 

49284 

10941048 

14.8996644 

6.0550489 

.  004504505 

223 

49729 

11089567 

14.9331845 

6.0641270 

.004484305 

224 

50176 

11239424 

14.9666295 

6.0731779 

.  004464286 

225 

50625 

11390625 

15.0000000 

6.0822020 

.004444444 

226 

51076 

11543176 

15.0332964 

6.0911994 

.004424779 

227 

51529 

11697083 

15.0665192 

6.1001702 

.  004405286 

228 

51984 

11852352 

15.0996689 

6.1091147 

.004385965 

229 

52441 

12008989 

15.1327460 

6.1180332 

.004366812 

230 

52900 

12167000 

15  .  1657509 

6.1269257 

.004347826 

231 

53361 

12326391 

15.1986842 

6.1357924 

.004329004 

232 

53824 

12487168 

15.2315462 

6.1446337 

.004310345 

233 

54289 

12649337 

15.2643375 

6.1534495 

.004291845 

234 

54756 

12812904 

15.2970585 

6.1622401 

.004273504 

235 

55225 

12977875 

15.3297097 

6.1710058 

.004255319 

236 

55696 

13144256 

15.3622915 

6.1797466 

.004237288 

237 

56169 

13312053 

15.3948043 

6.1884628 

.004219409 

238 

56644 

13481272 

15.4272486 

6.1971544 

.004201681 

239 

57121 

13651919 

15.4596248 

6.2058218 

.004184100 

240 

57600 

13824000 

15.4919334 

6.2144650 

.004166667 

241 

58081 

13997521 

15.5241747 

6  .  2230843 

.004149378 

242 

58564 

14172488 

15.5563492 

6.2316797 

.004132231 

243 

59049 

14348907 

15.5884573 

6.2402515 

.004115226 

244 

59536 

14526784 

15.6204994 

6.2487998 

.004098361 

245 

60025 

14706125 

15.6524758 

6.2573248 

.004081633 

246 

60516 

14886936 

15.6843871 

6  .  2658266 

.004065041 

247 

61009 

15069223 

15.7162336 

6  .  2743054 

.  004048583 

248 

61504 

15252992 

15.7480157 

6.2827613 

.004032258 

12 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 

Hoots. 

Cube  Roots. 

Reciprocals. 

249 

62001 

15438249 

15.7797338 

6.2911946 

.004016064 

250 

62500 

15625000 

15.8113883 

6.2996053 

.004000000 

251 

63001 

15813251 

15.8429795 

6.3079935 

.003984064 

252 

63504 

16003008 

15.8745079 

6.3163596 

.  003968254 

253 

64009 

16194277 

15.9059737 

6  .  3247035 

.003952569 

254 

64516 

16387064 

15.9373775 

6  .  3330256 

.  003937008 

255 

65025 

16581375 

15.9687194 

6.3413257 

.003921569 

256 

65536 

16777216 

16.0000000 

6.3496042 

.003906250 

257 

66049 

16974593 

16.0312195 

6.3578611 

.003891051 

258 

66564 

17173512 

16.0623784 

6  .  3660968 

.  003875969 

259 

67081 

17373979 

16.0934769 

6.3743111 

.003861004 

260 

67600 

17576000 

16.1245155 

6  .  3825043 

.003846154 

261 

68121 

17779581 

16.1554944 

6  .  3906765 

.003831418 

262 

68644 

17984728 

16.1864141 

6.3988279 

.003816794 

263 

69169 

18191447 

16.2172747 

6.4069585 

.003802281 

264 

69696 

18399744 

16.2480768 

6.4150687 

.003787879 

265 

70225 

18609625 

16.2788206 

6.4231583 

.003773585 

266 

70756 

18821096 

16.3095064 

6.4312276 

.  003759398 

267 

71289 

19034163 

16.3401346 

6.4392767 

.003745318 

268 

71824 

19248832 

16.3707055 

6.4473057 

.003731343 

269 

72361 

19465109 

16.4012195 

6.4553148 

.003717472 

270 

72900 

19683000 

16.4316767 

6.4633041 

.003703704 

271 

73441 

19902511 

16.4620776 

6.4712736 

.003690037 

272 

73984 

20123648 

16.4924225 

6.4792236 

.003676471 

273 

74529 

20346417 

16.5227116 

6.4871541 

.003663004 

274 

75076 

20570824 

16.5529454 

6.4950653 

.003649635 

275 

75625 

20796875 

16.5831240 

6.5029572 

.  003636364 

276 

76176 

21024576 

16.6132477 

6.5108300 

.003623188 

277 

76729 

21253933 

16.6433170 

6.5186839 

.003610108 

278 

77284 

21484952 

16.6733320 

6.5265189 

.003597122 

279 

77841 

21717639 

16.7032931 

6.5343351 

.003584229 

280 

78400 

21952000 

16.7332005 

6.5421326 

.003571429 

281 

78961 

22188041 

16  .  7630546 

6.5499116 

.003558719 

282 

79524 

22425768 

16.7928556 

6.5576722 

.003546099 

283 

80089 

22665187 

16.8226038 

6.5654144 

.003533569 

284 

80656 

22906304 

16.8522995 

6.5731385 

.003521127 

285 

81225 

23149125 

16.8819430 

6.5808443 

.003508772 

286 

81796 

23393656 

16.9115345 

6.5885323 

.003496503 

287 

82369 

23639903 

16.9410743 

6  .  5962023 

.003484321 

288 

82944 

23887872 

16.9705627 

6.6038545 

.003472222 

289 

83521 

24137569 

17.0000000 

6.6114890 

.003460208 

290 

84100 

24389000 

17.0293864 

6.6191060 

.003448276 

291 

84681 

24642171 

17.0587221 

6.6267054 

.003436426 

292 

85264 

24897088 

17.0880075 

6  .  6342874 

.003424658 

293 

85849 

25153757 

17.1172428 

6.6418522 

.003412969 

294 

86436 

25412184 

17.1464282 

6.6493998 

.003401361 

295 

87025 

25672375 

17.1755640 

6.6569302 

.003389831 

296 

87616 

25934336 

17.2046505 

6.6644437 

.003378378 

297 

88209 

26198073 

17.2336879 

6.6719403 

.003367003 

298 

88804 

26463592 

17.2626765 

6.6794200 

.003355705 

299 

89401 

26730899 

17.2916165 

6.6868831 

.003344482 

300 

90000 

27000000 

17.3205081 

6.6943295 

.003333333 

301 

90601 

27270901 

17.3493516 

6.7017593 

.003322259 

302 

91204 

27543608 

17.3781472 

6.7091729 

.003311258 

303 

91809 

.  27818127 

17.4068952 

6.7165700 

.003300330 

304 

92416 

28094464 

17.4355958 

6.7239508 

.003289474 

305 

93025 

28372625 

17.4642492 

6.7313155 

.003278689 

306 

93636 

28652616 

17.4928557 

6.7386641 

.003267974 

307 

94249 

28934443 

17.5214155 

6.7459967 

.003257329 

308 

94864 

29218112 

17.5499288 

6.7533134 

.003246753 

309 

95481 

29503629 

17.5783958 

6.7606143 

.003236246 

310 

96100 

29791000 

17.6068169 

6.7678995 

.  003225806 

CUBE  ROOTS,  AND  RECIPROCALS. 


13 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

311 

96721 

30080231 

17.6351921 

6.7751690 

.003215434 

312 

97344 

30371328 

17.6635217 

6.7824229 

.003205128 

313 

97969 

30664297 

17.6918060 

6.7896613 

.003194888 

314 

98596 

30959144 

17.7200451 

6  .  7968844 

.003184713 

315 

99225 

31255875 

17.7482393 

6.8040921 

.003174603 

316 

99856 

31554496 

17.7763888 

6.8112847 

.003164557 

317 

100489 

31855013 

17.8044938 

6.8184620 

.003154574 

318 

101124 

32157432 

17.8325545 

6.8256242 

.003144654 

319 

101761 

32461759 

17.8605711 

6.8327714 

.003134796 

320 

102400 

32768000 

17.8885438 

6.8399037 

.003125000 

321 

103041 

33076161 

17.9164729 

6.8470213 

.003115265 

322 

103684 

33386248 

17.9443584 

6.8541240 

.003105590 

323 

104329 

33698267 

17.9722008 

6.8612120 

.003095975 

324 

104976 

34012224 

18.0000000 

6  .  8682855 

.  003086420 

325 

105625 

34328125 

18.0277564 

6.8753443 

.003076923 

326 

106276 

34645976 

18.0554701 

6  .  8823888 

.003067485 

327 

106929 

34965783 

18.0831413 

6.8894188 

.003058104 

328 

107584 

35287552 

18.1107703 

6.8964345 

.003048780 

329 

108241 

35611289 

18.1383571 

6.9034359 

.003039514 

330 

108900 

35937000 

18.1659021 

6.9104232 

.003030303 

331 

109561 

36264691 

18.1934054 

6.9173964 

.003021148 

332 

110224 

36594368 

18.2208672 

6.9243556 

.003012048 

333 

110889 

36926037 

18.2482876 

6.9313008 

.003003003 

334 

111556 

37259704 

18.2756669 

6.9382321 

.002994012 

335 

112225 

37595375 

18.3030052 

6.9451496 

.002985075 

336 

112896 

37933056 

18.3303028 

6.9520533 

.002976190 

337 

113569 

38272753 

18.3575598 

6.9589434 

.002967359 

338 

114244 

38614472 

18.3847763 

6.9658198 

.002958580 

339 

114921 

38958219 

18.4119526 

6.9726826 

.002949853 

340 

115600 

39304000 

18.4390889 

6.9795321 

.002941176 

341 

116281 

39651821 

18.4661853 

6.9863681 

.002932551 

342 

116964 

40001688 

18.4932420 

6.9931906 

.002923977 

343 

117649 

40353607 

18.5202592 

7.0000000 

.002915452 

344 

118336 

40707584 

18.5472370 

7.0067962 

.002906977 

345 

119025 

41063625 

18.5741756 

7.0135791 

.002898551 

346 

119716 

41421736 

18.6010752 

7.0203490 

.002890173 

347 

120409 

41781923 

18.6279360 

7.0271058 

.002881844 

348 

121104 

42144192 

18.6547581 

7.0338497 

.002873563 

349 

121801 

42508549 

18.6815417 

7  .  0405806 

.002865330 

350 

122500 

42875000 

18.7082869 

7.0472987 

.002857143 

351 

123201 

43243551 

18.7349940 

7.0540041 

.  002849003 

352 

123904 

43614208 

18.7616630 

7.0606967 

.002840909 

353 

124609 

43986977 

18.7882942 

7.0673767 

.002832861 

354 

125316 

44361864 

18.8148877 

7  .  0740440 

.002824859 

355 

126025 

44738875 

18.8414437 

7.0806988 

.002816901 

356 

126736 

45118016 

18.8679623 

7.0873411 

.002808989 

357 

127449 

45499293 

18.8944436 

7  .  0939709 

.002801120 

358 

128164 

45882712 

18.9208879 

7  .  1005885 

.002793216 

359 

128881 

46268279 

18.9472953 

7.1071937 

.002785595 

360 

129600 

46656000 

18.9736660 

7.1137866 

.002777778 

361 

130321 

47045881 

19.0000000 

7.1203674 

.002770083 

632 

131044 

47437928 

19.0262976 

7.1269360 

.002762431 

363 

131769 

47832147 

19.0525589 

7.1334925 

.002754821 

364 

132498 

48228544 

19.0787840 

7.1400370 

.002747253 

365 

133225 

48627125 

19.1049732 

7.1465695 

.002739726 

366 

133956 

49027896 

19.1311265 

7.1530901 

.002732240 

367 

134689 

49430863 

19.1572441 

7.1595988 

.002724796 

368 

135424 

49836032 

19.1833261 

7  .  1660957 

.002717391 

369 

136161 

50243409 

19.2093727 

7.1725809 

.002710027 

370 

136900 

50653000 

19.2353841 

7.1790544 

.002702703 

371 

137641 

51064811 

19.2613603 

7.1855162 

.002695418 

372 

138384 

51478848 

19.2873015 

7.1919663 

.002688172 

14 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 

Hoots. 

Cube  Roots. 

Reciprocals. 

373 

139129 

51895117 

19.3132079 

7.1984050 

.002680955 

374 

139876 

52313624 

19.3390796 

7.2048322 

.002673/97 

375 

140625 

52734375 

19.3649167 

7.2112479 

.  002060007 

376 

141376 

53157376 

19.3907194 

7.2176522 

.002059574 

377 

142129 

53582633 

19.4164878 

7.2240450 

002652520 

378 

142884 

54010152 

19.4422221 

7  .  2304268 

.  002645503 

379 

143641 

54439939 

19.4679223 

7.2367972 

.  002638522 

380 

144400 

54872000 

19.4935887 

7.2431565 

.002631579 

381 

145161 

55306341 

19.5192213 

7  .  2495045 

.  002624672 

382 

145924 

55742968 

19.5448203 

7.2558415 

.002617801 

383 

146689 

58181887 

19.5703858 

7.2621675 

.002610906 

384 

147456 

56623104 

19.5959179 

7  .  2684824 

.002604167 

385 

148225 

57086625 

19.6214169 

7.2747864 

.002597403 

386 

148996 

57512456 

19.6468827 

7.2810794 

.002590674 

387 

149769 

57960603 

19.6723156 

7.2873617 

.  002583979 

388 

150544 

58411072 

19.6977156 

7  .  2936330 

.002577320 

389 

151321 

58863869 

19.7230829 

7.2998936 

.002570694 

390 

152100 

59319000 

19.7484177 

7.3061436 

.002564103 

391 

152881 

59776471 

19.7737199 

7.3123828 

.0025575!.-, 

392 

153664 

60236288 

19  .  7989899 

7.3186114 

.002551020 

393 

154449 

60698457 

19.8242276 

7  .  3248295 

.002544529 

394 

155236 

61162984 

19  .  8494332 

7.3310369 

.002538071 

395 

156025 

61629875 

19.8746069 

7  .  3372339 

.002531646 

396 

156816 

62099136 

19.8997487 

7  .  3434205 

.002525253 

397 

157609 

62570773 

19.9248588 

7.3495900 

.002518892 

398 

158404 

63044792 

19.9499373 

7.3557024 

.002512503 

399 

159201 

63521199 

19.9749844 

7.3619178 

.002500266 

400 

160000 

64000000 

20  .  0000000 

7.3680630 

.002500000 

401 

160801 

64481201 

20  .  0249844 

7.3741979 

.  002493766 

402 

161604 

64964808 

20.0499377 

7.3803227 

.  002487562 

403 

162409 

65450827 

20.0748599 

7  .  3864373 

.002481390 

404 

163216 

65939264 

20.0997512 

7.3925418 

.002475248 

405 

164025 

66430125 

20.1246118 

7  .  3986363 

.002469136 

406 

164836 

66923416 

20.1494417 

7.4047206 

.002463054 

407 

165649 

67419143 

20.1742410 

7.4107950 

.  002457002 

408 

166464 

67917312 

20.1990099 

7.4168595 

.002450980 

409 

167281 

68417929 

20.2237484 

7.4229142 

.002444988 

410 

168100 

68921000 

20  .  2484567 

7.4289589 

.002439024 

411 

168921 

69426531 

20.2731349 

7.4349938 

.  002433090 

412 

169744 

69934528 

20.2977831 

7.4410189 

.002427184 

413 

170569 

70444997 

20.3224014 

7.4470342 

.002421308 

414 

171396 

70957944 

20  .  3469899 

7  .  4530399 

.002415459 

415 

172225 

71473375 

20.3715488 

7.4590359 

.  002409039 

416 

173056 

71991296 

20.3960781 

7.465022.'1, 

.002403840 

417 

173889 

72511713 

20.4205779 

7.4709991 

.  002398082 

418 

174724 

73034632 

20  .  4450483 

7.47690K1 

.002392344 

419 

175561 

73560059 

20.4694895 

7.4829212 

.002380035 

420 

176400 

74088000 

20.4939015 

7.4888724  • 

.002.380952 

421 

177241 

74618461 

20.5182845 

7.4948113 

.002375297 

422 

178084 

75151448 

20  .  5426380 

7  .  5007400 

.002369608 

423 

178929 

75686967 

20  .  5669638 

7  .  5066607 

.002304006 

424 

179776 

76225024 

20.5912603 

7.5125715 

.002358491 

425 

180625 

76765625 

20.6155281 

7.5184730 

.002352941 

426 

181476 

77308776 

20.6397674 

7  .  5243052 

.002347418 

427 

182329 

77854483 

20.6639783 

7  .  5302482 

.002341920 

428 

183184 

78402752 

20.6881609 

7.5361221 

.002336449 

429 

184041 

78953589 

20.7123152 

7.5419807 

.002331002 

430 

184900 

79507000 

20.7364414 

7  .  547S423  * 

.002325581 

431 

185761 

80062991 

20  .  7605395 

7  .  55308S8 

.002320180 

432 

186624 

80621568 

20.7840007 

7  .  5595203 

.002:;  I  1815 

433 

187489 

81182737 

20  .  8080520 

7.5653548 

.002309409 

434 

188356 

81740501 

20.832(1007 

7.5711743 

.002304147 

CUBE  ROOTS,  AND  RECIPROCALS. 


15 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

435 

189225 

82312875 

20  .  8566536 

7  .  5769849 

.002298851 

436 

190096 

82881856 

20.8806130 

7.5827865 

.002293578 

437 

190969 

83453453 

20  .  9045450 

7.5885793 

.002288330 

438 

191844 

84G27672 

20  .  9284495 

7.5943633 

.002283105 

439 

192721 

84604519 

2^0.9523268 

7.6001385 

.002277904 

440 

193600 

85184000 

20.9761770 

7.6059049 

.002272727 

441 

194481 

85766121 

21.0000000 

7.6116626 

.002267574 

442 

195364 

86350888 

21.0237960 

7.6174116 

.002262443 

443 

196249 

86938307 

21.0475652 

7.6231519 

.002257336 

444 

197136 

87528384 

21.0713075 

7.6288837 

.002252252 

445 

198025 

88121125 

21.0950231 

7.6346067 

.002247191 

446 

198916 

88716536 

21.1187121 

7.6403213 

.002242152 

447 

199809 

89314623 

21-1423745 

7.6460272 

.002237136 

448 

200704 

89915392 

2i.  1660105 

7.6517247 

.002232143 

449 

201601 

90518849 

21  .  1896201 

7.6574138 

.002227171 

450 

202500 

91125000 

21.2132034 

7.6630943 

.002222222 

451 

203401 

91733851 

21.2367606 

7.6687665 

.002217295 

452 

204304 

92345408 

21.2602916 

7.6744303 

.002212389 

453 

205209 

92959677 

21.2837967 

7  .  6800857 

.002207506 

454 

206116 

93576664 

21.3072758 

7.6857328 

.002202643 

455 

207025 

94196375 

21.3307290 

7.6913717 

.002197802 

456 

207936 

94818816 

21.3541565 

7.6970023 

.002192982 

457 

208849 

95443993 

21.3775583 

7.7026246 

.002188184 

458 

209764 

96071912 

21.4009346 

7.7082388 

.002183406 

459 

210681 

96702579 

21.4242853 

7.7138448 

.002178649 

460 

211600 

97336000 

21.4476106 

7.7194426 

.002173913 

461 

212521 

97972181 

21.4709106 

7.7250325 

.002169197 

462 

213444 

98611128 

21.4941853 

7.7306141 

.002164502 

463 

214369 

99252847 

21.5174348 

7.7361877 

.002159827 

464 

215296 

99897344 

21.5406592 

7.7417532 

.002155172 

465 

216225 

100544625 

21.5638587 

7.7473109 

.002150538 

466 

217156 

101194696 

21.5870331 

7.7528606 

.002145923 

467 

218089 

101847563 

21.6101828 

7.7584023 

.002141328 

468 

219024 

102503232 

21.6333077 

7.7639361 

.002136752 

469 

219961 

103161709 

21.6564078 

7.7694620 

.002132196 

470 

220900 

103823000 

21.6794834 

7.7749801 

.002127660 

471 

221841 

104487111 

21.7025344 

7  .  7804904 

.002123142 

472 

222784 

105154048 

21.7255610 

7.7859928 

.002118644 

473 

223729 

105823817 

21.7485632 

7.7914875 

.002114165 

474 

224676 

106496424 

21.7715411 

7  .  7969745 

.002109705 

475 

225625 

107171875 

21.7944947 

7.8024538 

.002105263 

476 

226576 

107850176 

21.8174242 

7  .  8079254 

.002100840 

477 

227529 

108531333 

21.8403297 

7.8133892 

.002096436 

478 

228484 

109215352 

21.8632111 

7.8188456 

.002092050 

479 

229441 

109902239 

21.8860686 

7.8242942 

.002087683 

480 

230400 

110592000 

21.9089023 

7.8297353 

.  002083333 

481 

231361 

111284641 

21.9317122 

7.8351688 

.002079002 

482 

232324 

111980168 

21.9544984 

7.8405949 

.002074689 

483 

233289 

112678587 

21.9772610 

7.8460134 

.002070393 

484 

234256 

113379904 

22.0000000 

5.8514244 

.002066116 

485 

235225 

114084125 

22.0227155 

7.8568281 

.002061856 

486 

236196 

114791256 

22.0454077 

7.8622242 

.002057613 

487 

237169 

115501303 

22.0680765 

7.8676130 

.002053388 

488 

238144 

116214272 

22.0907220 

7.8729944 

.002049180 

489 

239121 

116930169 

22.1133444 

7.8783684 

.002044990 

490 

240100 

117649000 

22.1359436 

7.8837352 

.002040816 

491 

241081 

118370771 

22.1585198 

7.8890946 

.002036660 

492 

242064 

119095488 

22.1810730 

7.8944468 

.002032520 

493 

243049 

119823157 

22  .  2036033 

7.8937917 

.002028398 

494 

244036 

120553784 

22.2261108 

7.9051294 

.002024291 

495 

245025 

121287375 

22  .  2485955 

7.9104599 

.002020202 

496 

246016 

122023936 

22.2710575 

7.9157832 

.002016129 

16 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

497 

247009 

122763473 

22.2934968 

7.9210994 

.002012072 

498 

248004 

123505992 

22.3159136 

7.9264085 

.002008032 

499 

249001 

124251499 

22.3383079 

7.9317104 

.002004008 

500 

250000 

125000000 

22.3606798 

7.9370053 

.002000000 

501 

251001 

125751501 

22  .  3830293 

7.9422931 

.001996008 

502 

252004 

126506008 

22.4053565 

7.9475739 

.001992032 

503 

253009 

127263527 

22.4276615 

7.9528477 

.001988072 

504 

254016 

128024064 

22  .  4499443 

7.9581144 

.001984127 

505 

255025 

128787625 

22.4722051 

7.9633743 

.001980198 

506 

256036 

129554216 

22.4944438 

7.9686271 

.001976255 

507 

257049 

130323843 

22.5166605 

7.9738731 

.001972387 

508 

258064 

131096512 

22  .  5388553 

7.9791122 

.001968504 

509 

259081 

131872229 

22.5610283 

7.9843444 

.001964637 

510 

260100 

132651000 

22.5831796 

7.9895697 

.001960784 

511 

261121 

133432831 

22.6053091 

7.9947883 

.001956947 

512 

262144 

134217728 

22.6274170 

8  .  0000000 

.001953125 

513 

263169 

135005697 

22  .  6495033 

8  .  0052049 

.001949318 

514 

264196 

135796744 

22.6715681 

8.0104032 

.001945525 

515 

265225 

136590875 

22.6936114 

8.0155946 

.001941748 

516 

266256 

137388096 

22.7156334 

8.0207794 

.001937984 

517 

267289 

138188413 

22.7376340 

8.0259574 

.001934236 

518 

268324 

138991832 

22.7596134 

8.0311287 

.001930502 

519 

269361 

139798359 

22.7815715 

8.0362935 

.001926782 

520 

270400 

140608000 

22.8035085 

8.0414515 

.001923077 

521 

271441 

141420761 

22.8254244 

8.0466030 

.001919386 

522 

272484 

142236648 

22.8473193 

8.0517479 

.001915709 

523 

273529 

143055667 

22.8691933 

8  .  0568862 

.001912046 

524 

274576 

143877824 

22.8910463 

8.0620180 

.001908397 

525 

275625 

144703125 

22.9128785 

8.0671432 

.001904762 

526 

276676 

145531576 

22.9346899 

8.0722620 

.001901141 

527 

277729 

146363183 

22.9564806 

8.0773743 

.001897533 

528 

278784 

147197952 

22  .  9782506 

8  .  0824800 

.001893939, 

529 

279841 

148035889 

23.0000000 

8  .  0875794 

.001890359 

530 

280900 

148877000 

23.0217289 

8.0926723 

.001886792 

531 

281961 

149721291 

23  .  0434372 

8.0977589 

.001883239 

532 

283024 

150568768 

23.0651252 

8  .  1028390 

.001879699 

533 

284089 

151419437 

23.0867928 

8.1079128 

.001876173 

534 

285156 

152273304 

23  .  1084400 

8.1129803 

.001872659 

535 

286225 

153130375 

23  .  1300670 

8.1180414 

.001869159 

536 

287296 

153990656 

23.1516738 

8.1230962 

.001865672 

537 

288369 

154854153 

23.1732605 

8.1281447 

.001862197 

538 

289444 

155720872 

23  .  1948270 

8.1331870 

.001858736 

539 

290521 

156590819 

23.2163735 

8.1382230 

.001855288 

540 

291600 

157464000 

23.2379001 

8.1432529 

.001851852 

541 

292681 

158340421 

23  .  2594067 

8.1482765 

.001848429 

542 

293764 

159220088 

23  .  2808935 

8.1532939 

.001845018 

543 

294849 

160103007 

23  .  3023604 

8.1583051 

.001841621 

544 

295936 

160989184 

23  .  3238076 

8.1633102 

.001838235 

545 

297025 

161878625 

23.3452351 

8.1683092 

.001834862 

546 

298116 

162771336 

23  .  3666429 

8.1733020 

.001831502 

547 

299209 

163667323 

23.3880311 

8.1782888 

.001828154 

548 

300304 

164566592 

23  .  4093998 

8.1832695 

.001824818 

549 

301401 

165469149 

23  .  4307490 

8.1882441 

.001821494 

550 

302500 

166375000 

23.4520788 

8.1932127 

.001818182 

551 

303601 

167284151 

23  .  4733892 

8.1981753 

.001814882 

552 

304704 

168196608 

23.4946802 

8.2031319 

.001811594 

553 

305809 

169112377 

23.5159520 

8  .  2080825 

.001808318 

554 

306916 

170031464 

23  .  5372046 

8.2130271 

.001805054 

555 

308025 

170953875 

23  .  5584380 

8.2179657 

.001801802 

556 

309136 

171879616 

23  .  5796522 

8  .  2228985 

.001798561 

557 

310249 

172808693 

23  .  6008474 

8.2278254 

.001795332 

558 

311364 

173741112 

23  .  6220236 

8.2327463 

.001792115 

CUBE  ROOTS,  AND  RECIPROCALS. 


17 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

559 

312481 

174676879 

23.6431808 

8.2376614 

.001788909 

560 

313600 

175616000 

23.6643191 

8.2425706 

.001785714 

561 

314721 

176558481 

23.6854386 

8.2474740 

.001782531 

562 

315844 

177504328 

23  .  7065392 

8.2523715 

.001779359 

563 

316969 

178453547 

23.7276210 

8.2572633 

.001776199 

564 

318096 

179406144 

23  .  7486842 

8.2621492 

.001773050 

565 

319225 

180362125 

23.7697286 

8.2670294 

.001769912 

566 

320356 

181321496 

23  .  7907545 

8.2719039 

.001766784 

567 

321489 

182284263 

23.8117618 

8.2767726 

.001763668 

568 

322624 

183250432 

23.8327506 

8.2816355 

.001760563 

569 

323761 

184220000 

23.8537209 

8.2864928 

.001757469 

570 

324900 

185193000 

23.8746728 

8.2913444 

.001754386 

571 

326041 

186169411 

23.8956063 

8.2961903 

.001751313 

572 

327184 

187149248 

23.9165215 

8.3010304 

.001748252 

573 

328329 

188132517 

23.9374184 

8.3058651 

.001745201 

574 

329476 

189119224 

23.9582971 

8.3106941 

.001742160 

575 

330625 

190109375 

23.9791576 

8.3155175 

.001739130 

576 

331776 

191102976 

24  .  0000000 

8.3203353 

.001736111 

577 

332929 

192100033 

24.0208243 

8.3251475 

.001733102 

578 

334084 

193100552 

24.0416306 

8  .  3299542 

.001730104 

579 

335241 

194104539 

24.0624188 

8.3347553 

.001727116 

580 

336400 

195112000 

24.0831891 

8  .  3395509 

.001724138 

581 

337561 

196122941 

24.1039416 

8.3443410 

.001721170 

582 

338724 

197137368 

24.1246762 

8.3491256 

.001718213 

583 

339889 

198155287 

24.1453929 

8.3539047 

.001715266 

584 

341056 

199176704 

24.1660919 

8.3586784 

.001712329 

585 

342225 

200201625 

24.1867732 

8.3634466 

.001709402 

586 

343396 

201230056 

24  .  2074369 

8  .  3682095 

.001706485 

587 

344569 

202262003 

24  .  2280829 

8.3729668 

.001703578 

588 

345744 

203297472 

24.2487113 

8.3777188 

.001700680 

589 

346921 

204336469 

24.2693222 

8.3824653 

.001697793 

590 

348100 

205379000 

24.2899156 

8.3872065 

.001694915 

591 

349281 

206425071 

24.3104916 

8.3919423 

.001692047 

592 

350464 

207474688 

24.3310501 

8  .  3966729 

.001689189 

593 

351649 

208527857 

24.3515913 

8.4013981 

.001686341 

594 

352836 

209584584 

24.3721152 

8.4061180 

.001683502 

595 

354025 

210644875 

24.3926218 

8.4108326 

.001680672 

596 

355216 

211708736 

24.4131112 

8.4155419 

.001677852 

597 

356409 

212776173 

24.4335834 

8.4202460 

.001675042 

598 

357604 

213847192 

24  .  4540385 

8.4249448 

.001672241 

599 

358801 

214921799 

24.4744765 

8.4296383 

.0*1669449 

600 

360000 

•216000000 

24.4948974 

8.4343267 

.001666667 

601 

361201 

217081801 

24.5153013 

8.4390098 

.001663894 

602 

362404 

218167208 

24.5356883 

8.4436877 

.001661130 

603 

363609 

219256227 

24.5560583 

8.4483605 

.001658375 

604 

364816 

220348864 

24.5764115 

8.4530281 

.001655629 

605 

366025 

221445125 

24  .  5967478 

8.4576906 

.001652893 

606 

367236 

222545016 

24.6170673 

8.4623479 

.001650165 

607 

368449 

223648543 

24  .  6373700 

8.4670001 

.001647446 

608 

369664 

224755712 

24.6576560 

8.4716471 

.001644737 

609 

370881 

225866529 

24.6779254 

8.4762892 

.001642036 

610 

372100 

226981000 

24.6981781 

8.4809261 

.001639344 

611 

373321 

228099131 

24.7184142 

8.4855579 

.001636661 

612 

374544 

229220928 

24.7386338 

8.4901848 

.001633987 

613 

375769 

230346397 

24.7588368 

8.4948065 

.001631321 

614 

376996 

231475544 

24.7790234 

8.4994233 

.001628664 

615 

378225 

232608375 

24.7991935 

8.5040350 

.001626016 

616 

379456 

233744896 

24.8193473 

8.5086417 

.001623377 

617 

380689 

234885113 

24.8394847 

8.5132435 

.001620746 

618 

381924 

236029032 

24.8596058 

8.5178403 

.001618123 

619 

383161 

237176659 

24.8797106 

8  .  5224321 

.001615509 

620 

384400 

238328000 

24.8997992 

8.5270189 

.001612903 

18 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

621 

385641 

239483061 

24.9198716 

8.5316009 

.001610306 

622 

386884 

240641848 

24.9399278 

8.5361780 

.001607717 

623 

388129 

241804367 

24  .  9599679 

8.5407501 

.001605136 

624 

389376 

242970624 

24.9799920 

8.5453173 

.001602564 

625 

390625 

244140625 

25.0000000 

8.5498797 

.001600000 

626 

391876 

245314376 

25.0199920 

8  .  5544372 

.001597444 

627 

393129 

246491883 

25.0399681 

8  .  5589899 

.001594896 

628 

394384 

247673152 

25.0599282 

8.5635377 

.001592357 

629 

395641 

248858189 

25.0798724 

8  .  5680807 

.001589825 

630 

396900 

250047000 

25  .  0998008 

8.5726189 

.001587302 

631 

398161 

251239591 

25.1197134 

8.5771523 

.001584786 

632 

399424 

252435968 

25.1396102 

8.5816809 

.001582278 

633 

400689 

253636137 

25.1594913 

8.5862047 

.001579779 

634 

401956 

254840104 

25.1793566 

8  .  5907238 

.001577287 

635 

403225 

256047875 

25.1992063 

8  .  5952380 

.001574803 

636 

404496 

257259456 

25.2190404 

8.5997476 

.001572,327 

637 

405769 

258474853 

25  .  2388589 

8.6042525 

.001569859 

638 

407044 

259694072 

25.2586619 

8.6087526 

.001567398 

639 

408321 

260917119 

25  .  2784493 

8.6132480 

.001564945 

640 

409600 

262144000 

25.2982213 

8.6177388 

.001562500 

641 

410881 

263374721 

25.3179778 

8.6222248 

.001560062 

642 

412164 

264609288 

25.3377189 

8.6267063 

.001557632 

643 

413449 

265847707 

25.3574447 

8.6311830 

.001555210 

644 

414736 

267089984 

25.3771551 

8.6356551 

.001552795 

645 

416025 

268333125 

25.3968502 

8.6401226 

.001550388 

646 

417316 

269586136 

25.4165301 

8.6445855 

.001547988 

647 

418609 

270840023 

25.4361947 

8  .  6490437 

.001545595 

648 

419904 

272097792 

25.4558441 

8.6534974 

.001543210 

649 

421201 

273359449 

25.4754784 

8.6579465 

.001540832 

650 

422500 

274625000 

25  .  4950976 

8.6623911 

.001538462 

651 

423801 

275894451 

25.5147016 

8.6668310 

.001536098 

652 

425104 

277167808 

25.5342907 

8.6712665 

.001533742 

653 

426409 

278445077 

25.5538647 

8.6756974 

.001531394 

654 

427716 

279726264 

25  .  5734237 

8.6801237 

.001529052 

655 

429025 

281011375 

25  .  5929678 

8.6845456 

.001526718 

656 

430336 

282300416 

25.6124969 

8  .  6889630 

.001524390 

657 

431649 

283593393 

25.6320112 

8.6933759 

.001522070 

658 

432964 

284890312 

25.6515107 

8  .  6977843 

.001519757 

659 

434281 

286191179 

25  .  6709953 

8.7021882 

.001517451 

660 

435600 

287496000 

25  .  6904652 

8  .  7065877 

.001515152 

661 

436921 

288804781 

25  .  7099203 

8.7109827 

.001512859 

662 

438244 

290117528 

25  .  7293607 

8.7153734 

.001510574 

663 

439569 

291434247 

25  .  7487864 

8.7197596 

.001508296 

664 

440896 

292754944 

25.7681975 

8.7241414 

.001506024 

665 

442225 

294079625 

25  .  7875939 

8.7285187 

.001503759 

666 

443556 

295408296 

25.8069758 

8.7328918 

.001501502 

667 

444889 

296740963 

25.8263431 

8.7372604 

.001499250 

668 

446224 

298077632 

25  .  8456960 

8.7416246 

.001497006 

669 

447561 

299418309 

25.8650343 

8  .  7459846 

.001494768 

670 

448900 

300763000 

25.8843582 

8.7503401 

.001492537 

671 

450241 

302111711 

25  .  9036677 

8.7546913 

.001490313 

672 

451584 

303464448 

25.9229628 

8.7590383 

.001488095 

673 

452929 

304821217 

25.9422435 

8  .  7633809 

.001485884 

674 

454276 

306182024 

25.9615100 

8.7677192 

.001483680 

675 

455625 

307546875 

25.9807621 

8.7720532 

.001481481 

676 

456976 

308915776 

26  .  0000000 

8.7763830 

.001479290 

677 

458329 

310288733 

26.0192237 

8  .  7807084 

.001477105 

678 

459684 

311665752 

26.0384331 

8.7850296 

.001474926 

679 

461041 

313046839 

26.0576284 

8.7893466 

.  004472754 

680 

462400 

314432000 

26.0768096 

8  .  7936593 

.001470588 

681 

463761 

315821241 

26.0959767 

8.7979679 

.001468429 

682 

465124 

317214568 

26.1151297 

8.8022721 

.001466276 

CUBE  ROOTS,  AND  RECIPROCALS. 


19 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

683 

466489 

318611987 

26.1342687 

8.8065722 

.001464129 

684 

467856 

320013504 

26.1533937 

8.8108681 

.001461988 

685 

469225 

321419125 

26.1725047 

8.8151598 

.001459854 

686 

470596 

322828856 

26.1916017 

8.8194474 

.001457726 

687 

471969 

324242703 

26.2106848 

8.8237307 

.001455604 

688 

473344 

325660672 

26.2297541 

8.8280099 

.001453488 

689 

474721 

327082769 

26.2488095 

8.8322850 

.001451379 

690 

476100 

328509000 

26.2678511 

8.8365559 

.001449275 

691 

477481 

329939371 

26.2868789 

8.840S227 

.001447178 

692 

478864 

331373888 

26.3058929 

8.8450854 

.001445087 

693 

480249 

332812557 

26  .  3248932 

8.8493440 

.001443001 

694 

481636 

334255384 

26  .  3438797 

8.8535985 

.001440922 

695 

483025 

335702375 

26.3628527 

8.8578489 

.001438849 

696 

484416 

337153536 

26.3818119 

8.8620952 

.001436782 

697 

485809 

338608873 

26.4007576 

8.8663375 

.001434720 

698 

487204 

340068392 

26.4196896 

8.8705757 

.001432665 

699 

488601 

341532099 

26.4386081 

8.8748099 

.001430615 

700 

490000 

343000000 

26.4575131 

8.8790400 

.001428571 

701 

491401 

344472101 

26.4764046 

8.8832661 

.001426534 

702 

492804 

345948408 

26  .  4952826 

8.8874882 

.001424501 

703 

494209 

347428927 

26.5141472 

8.8917063 

.001422475 

704 

495616 

348913664 

26.5329983 

8.8959204 

.001420455 

705 

497025 

350402625 

26.5518361 

8.9001304 

.001418440 

706 

498436 

351895816 

26.5706605 

8  .  9043366 

.001416431 

707 

499849 

353393243 

26.5894716 

8.9085387 

.001414427 

708 

501264 

354894912 

26  .  6082694 

8.9127369 

.001412429 

709 

502681 

356400829 

26.6270539 

8.9169311 

.001410437 

710 

504100 

357911000 

26.6458252 

8.9211214 

.001408451 

711 

505521 

359425431 

26.6645833 

8.9253078 

.001406470 

712 

506944 

360944128 

26.6833281 

8.9294902 

.001404494 

713 

508369 

362467097 

26  .  7020598 

8.9336687 

.001402525 

714 

509796 

363994344 

26.7207784 

8.9378433 

.001400560 

715 

511225 

365525875 

26.7394839 

8.9420140 

.001398601 

716 

512656 

367061696 

26.7581763 

8.9461809 

.001396648 

717 

514089 

368601813 

26'.  7768557 

8.9503438 

.VA,  1394700 

718 

515524 

370146232 

26.7955220 

8.9545029 

.001392758 

719 

516961 

371694959 

26.8141754 

8.9586581 

.001390821 

720 

518400 

373248000 

26.8328157 

8  .  9628095 

.001388889 

721 

519841 

374805361 

26.8514432 

8  .  9669570 

.001386963 

722 

521284 

376367048 

26.8700577 

8.9711007 

.001385042 

723 

522729 

377933067 

26.8886593 

8  .  9752406 

.001383126 

724 

524176 

379503424 

26.9072481 

8.9793766 

.001381215 

725 

525625 

381078125 

26  .  9258240 

8.9835089 

.001379310 

726 

527076 

382657176 

26.9443872 

8.9876373 

.001377410 

727 

528529 

384240583 

26  .  9629375 

8.9917620 

.001375516 

728 

529984 

385828352 

26.9814751 

8  .  9958829 

.001373626 

729 

531441 

387420489 

27  .  0000000 

9.0000000 

.001371742 

730 

532900 

389017000 

27.0185122 

9.0041134 

.001369863 

731 

534361 

390617891 

27.0370117 

9.0082229 

.001367989 

732 

535824 

392223168 

27.0554985 

9.0123288 

.001366120 

733 

537289 

393832837 

27.0739727 

9.0164309 

.001364256 

734 

538756 

395446904 

27  .  0924344 

9.0205293 

.001362398 

735 

540225 

397065375 

27.1108834 

9.0246239 

.001360544 

736 

541696 

398688256 

27.1293199 

9.0287149 

.001358696 

737 

543169 

400315553 

27.1477439 

9.0328021 

.001356852 

738 

544644 

401947272 

27.1661554 

9.0368857 

.001355014 

739 

546121 

403583419 

27.1845544 

9.0409655 

.001353180 

740 

547600 

405224000 

27.2029410 

9.0450419 

.001351351 

741 

549081 

406869021 

27.2213152 

9.0491142 

001349528 

.  742 

550564 

408518488 

27  .  2396769 

9.  0531  S3  1 

001347709 

743 

552049 

410172407 

27  .  2580263 

9.0572482 

001345895 

744 

553536 

411830784 

27.27630.T1 

9.0613098 

001344086 

20 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

745 

555025 

413493625 

27.2946881 

9.0653677 

.001342282 

746 

556516 

415160936 

27.3130006 

9.0694220 

.001340483 

747 

558009 

416832723 

27.3313007 

9.0734726 

.001338688 

748 

559504 

418508992 

27  .  3495887 

9.0775197 

.001336898 

749 

561001 

420189749 

27.3678644 

9.0815631 

.001335113 

750 

562500 

421875000 

27.3861279 

9.0856030 

.001333333 

751 

564001 

423564751 

27.4043792 

9.0896392 

.001331558 

752 

565504 

425259008 

27.4226184 

9.0936719 

.001329787 

753 

567009 

426957777 

27.4408455 

9.0977010 

.001328021 

754 

568516 

428661O64 

27.4590604 

9.1017265 

.001326260 

755 

570025 

430368875 

27.4772633 

9  .  105748^ 

.001324503 

756 

571536 

432081216 

27.4954542 

9.1097669 

.001322751 

757 

573049 

433798093 

27.5136330 

9.1137818 

.001321004 

758 

574564 

435519512 

27.5317998 

9.1177931 

.001319261 

759 

576081 

437245479 

27.5499546 

9.1218010 

.001317523 

760 

577600 

438976000 

27.5680975 

9  .  1258053 

.001315789 

761 

579121 

440711081 

27.5862284 

9.1298061 

.001314060 

762 

580644 

442450728 

27.6043475 

9.1338034 

.001312336 

763 

582169 

444194947 

27  .  6224546 

9.1377971 

.001310616 

764 

583696 

445943744 

27  .  6405499 

9.1417874 

.001308901 

765 

585225 

447697125 

27.6586334 

9.1457742 

.001307190 

766 

586756 

449455096 

27.6767050 

9.1497576 

.001305483 

767 

588289 

451217663 

27  .  6947648 

9.1537375 

.001303781 

768 

589824 

452984832 

27.7128129 

9.1577139 

.001302083 

769 

591361 

454756609 

27.7308492 

9.1616869 

.001300390 

770 

592900 

456533000 

27.7488739 

9.1656565 

.001298701 

771 

594441 

458314011 

27.7668808 

9.1696225 

.001297017 

772 

595984 

460099648 

27  .  7848880 

9.1735852 

.001295337 

773 

597529 

461889917 

27.8028775 

9.1775445 

.001293661 

774 

599076 

463684824 

27.8208555 

9.1815003 

.001291990 

775 

600625 

465484375 

27.8388218 

9  .  1854527 

.001290323 

776 

602176 

467288576 

27.8567766 

9.1894018 

.001288660 

777 

603729 

469097433 

27.8747197 

9.1933474 

.001287Q01 

778 

605284 

470910952 

27.8926514 

9.1972897 

.001285347 

779 

606841 

472729139 

27.9105715 

9.2012286 

.001283697 

780 

608400 

474552000 

27.9284801 

9.2051641 

.001282051 

781 

609961 

476379541 

27.9463772 

9  .  2090962 

.001280410 

782 

611524 

478211768 

27  .  9642629 

9.2130250 

.001278772 

783 

613089 

480048687 

27.9821372 

9.2169505 

.001277139 

784 

614656 

481890304 

28.0000000 

9  .  2208726 

.001275510 

785 

616225 

483736625 

28.0178515 

9.2247914 

.001273885 

786 

617796 

485587656 

28.0356915 

9  .  2287068 

.001272265 

787 

619369 

487443403 

28.0535203 

9.2326189 

.001270648 

788 

620944 

489303872 

28.0713377 

9.2365277 

.001269036 

789 

622521 

491169069 

28.0891438 

9.2404333 

.001267427 

790 

624100 

493039000 

28  .  1069386 

9.2443355 

.001265823 

791 

625681 

494913671 

28.1247222 

9  .  2482344 

.001264223 

792 

627264 

496793088 

28.1424946 

9.2521300 

.001262626 

793 

628849 

498677257 

28.1602557 

9  .  2560224 

.001261034 

794 

630436 

500566184 

28.1780056 

9.2599114 

.001259446 

795 

632025 

502459875 

28.1957444 

9  .  2637973 

.001257862 

796 

633616 

504358336 

28.2134720 

9  .  2676798 

.001256281 

797 

635209 

506261573 

28.2311884 

9.2715592 

.001254705 

798 

636804 

508169592 

28  .  2488938 

9.2754352 

.001253133 

799 

638401 

510082399 

28.2665881 

9.2793081 

.001251564 

800 

640000 

512000000 

28.2842712 

9.2831777 

.001250000 

801 

641601 

513922401 

28.3019434 

9.2870440 

.001248439 

802 

643204 

515849608 

28.3196045 

9.2909072 

.001246883 

803 

644809 

517781627 

28  .  3372546 

9.2947671 

.001245330 

804 

646416 

519718464 

28.3548938 

9.2986239 

.001243781 

805 

648025 

521660125 

28.3725219 

9  .  3024775 

.001242236 

806 

649636 

523606616 

28.3901391 

9  .  3063278 

.001240695 

CUBE  ROOTS,  AND  RECIPROCALS. 


21 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

807 

651249 

525557943 

28.4077454 

9.3101750 

.001239157 

808 

652864 

527514112 

28.4253408 

9.3140190 

.001237624 

809 

654481 

529475129 

28.4429253 

9.3178599 

.001236094 

810 

656100 

531441000 

28.4604989 

9.3216975 

.001234568 

811 

657721 

533411731 

28.4780617 

9.3255320 

.001233046 

812 

659344 

535387328 

28.4956137 

9.3293634 

.001231527 

813 

660969 

537367797 

28.5131549 

9.3331916 

.001230012 

814 

662596 

539353144 

28.5306852 

9.3370167 

.001228501 

815 

664225 

541343375 

28  .  5482048 

9  .  3408386 

.001226994 

816 

665856 

543338496 

28.5657137 

•9  .  3446575 

.001225490 

817 

667489 

545338513 

28.5832119 

9.3484731 

.001223990 

818 

669124 

547343432 

28.6006993 

9.3522857 

.001222494 

819 

670761 

549353259 

28.6181760 

9  .  3560952 

.001221001 

820 

672400 

551368000 

28.6356421 

9.3599016 

.001219512 

821 

674041 

553387661 

28.6530976 

9.3637049 

.001218027 

822 

675684 

555412248 

28  .  6705424 

9.3675051 

.001216545 

823 

677329 

557441767 

28.6879766 

9.3713022 

.001215067 

824 

678976 

559476224 

28.7054002 

9  .  3750963 

.001213592 

825 

680625 

561515625 

28.7228132 

9  .  3788873 

.001212121 

826 

682276 

563559976 

28.7402157 

9  .  3826752 

.001210654 

827 

683929 

565609283 

28.7576077 

9  .  3864600 

.001209190 

828 

685584 

567663552 

28.7749891 

9.3902419 

.001207729 

829 

687241 

569722789 

28.7923601 

9.3940206 

.001206273 

830 

688900 

571787000 

28.8097206 

9  .  3977964 

.001204819 

831 

690561 

573856191 

28.8270706 

9.4015691 

.001203369 

832 

692224 

575930368 

28.8444102 

9.4053387 

.001201923 

833 

693889 

578009537 

28.8617394 

9.4091054 

.001200480 

834 

695556 

580093704 

28.8790582 

9.4128690 

.001199041 

835 

697225 

582182875 

28.8963666 

9.4166297 

.001197605 

836 

698896 

584277056 

28.9136646 

9.4203873 

.001196172 

837 

700569 

586376263 

28.9309523 

9.4241420 

.001194743 

838 

702244 

588480472 

28.9482297 

9.4278936 

.001193317 

839 

703921 

590589719 

28.9654967 

9.4316423 

.001191895 

840 

705600 

592704000 

28.9827535 

9.4353880 

.001190476 

841 

707281 

594823321 

29  .  0000000 

9.4391307 

.001189061 

842 

708964 

596947688 

29.0172363 

9  .  4428704 

.001187648 

843 

710649 

599077107 

29.0344623 

9.4466072 

.001186240 

844 

712336 

601211584 

29.0516781 

9.4503410 

.001184834 

845 

714025 

603351125 

29  .  0688837 

9.4540719 

.001183432 

846 

715716 

605495736 

29.0860791 

9.4577999 

.001182033 

847 

717409 

607645423 

29  .  1032644 

9.4615249 

.001180638 

848 

719104 

609800192 

29.1204396 

9.4652470 

.001179245 

849 

720801 

611960049 

29.1376046 

9.4689661 

.001177856 

850 

722500 

614125000 

29.1547595 

9.4726824 

.001176471 

851 

724201 

616295051 

29.1719043 

9.4763957 

.001175088 

852 

725904 

618470208 

29.1890390 

9.4801061 

.001173709 

853 

727609 

620650477 

29.2061637 

9.4838136 

.001172333 

854 

729316 

622835864 

29  .  2232784 

9.4875182 

.001170960 

855 

731025 

625026375 

29.2403830 

9.4912200 

.001169591 

856 

732736 

627222016 

29.2574777 

9.4949188 

.001168224 

857 

734449 

629422793 

29.2745623 

9.4986147 

.001166861 

858 

736164 

631628712 

29.2916370 

9.5023078 

.001165501 

859 

737881 

633839779 

29.3087018 

9.5059980 

.001164144 

860 

739600 

636056000 

29.3257566 

9.5096854 

.001162791 

861 

741321 

638277381 

29.3428015 

9.5133699 

.001161440 

862 

743044 

640503928 

29.3598365 

9.5170515 

.001160093 

863 

744769 

642735647 

29.3768616 

9.5207303 

.001158749 

864 

746496 

644972544 

29  .  3938769 

9  .  5244063 

.001157407 

865 

748225 

647214625 

29.4108823 

9  .  5280794 

.001156069 

866 

749956 

649461896 

29  .  4278779 

9.5317497 

.001154734 

867 

751689 

651714363 

29.4448637 

9.5354172 

.001153403 

868 

753424 

653972032 

29.4618397 

9.5390818 

.001152074 

22 


SQUARES,  CUBES,  SQUARE  ROOTS, 


No. 

Squares. 

Cubes. 

Square 
Root*. 

Cube  Roots. 

Reciprocals. 

869 

755161 

656234909 

29.4788059 

9.5427437 

.001150748 

870 

756900 

658503000 

29.4957624 

9.5464027 

.001149425 

871 

758641 

660776311 

29.5127091 

9.5500589 

.001148106 

872 

760384 

663054848 

29.5296461 

9.5537123 

.001146789 

873 

762129 

665338617 

29.5465734 

9.5573630 

.001145475 

874 

763876 

667627624 

29.5634910 

9.5610108 

.001144165 

875 

765625 

669921875 

29.5803989 

9.5646559 

.001142857 

876 

767376 

672221376 

29.5972972 

9.5682982 

.001141553 

877 

769129 

674526133 

29.6141858 

9.5719377 

.001140251 

878 

770884 

676836152 

29.6310648 

9.5755745 

.001138952 

879 

772641 

679151439 

29.6479342 

9.5792085 

.001137656 

880 

774400 

681472000 

29  .  6647939 

9.5828397 

.001136364 

881 

776161 

683797841 

29.6816442 

9.5864682 

.001135074 

882 

777924 

686128968 

29.6984848 

9  .  5900939 

.001133787 

883 

779689 

688465387 

29.7153159 

9.5937169 

.001132503 

884 

781456 

690807104 

29.7321375 

9  .  5973373 

.001131222 

885 

783225 

693154125 

29  .  7489496 

9  .  6009548 

.001129944 

886 

784996 

695506456 

29.7657521 

9.6045696 

.001128668 

887 

786769 

697864103 

29.7825452 

9.6081817 

.001127396 

888 

788544 

700227072 

29.7993289 

9.6117911 

.001126126 

889 

790321 

702595369 

29.8161030 

9.6153977 

.001124859 

890 

792100 

704969000 

29.8328678 

9.6190017 

.001123596 

891 

793881 

707347971 

29.8496231 

9.6226030 

.001122334 

892 

795664 

709732288 

29.8663690 

9.6262016 

.001121076 

893 

797449 

712121957 

29.8831056 

9.6297975 

.001119821 

894 

799236 

714516984 

29.8998328 

9.6333907 

.001118568 

895 

801025 

716917375 

29.9165506 

9.6369812 

.001117318 

896 

802816 

719323136 

29.9332591 

9.6405690 

.001116071 

897 

804609 

721734273 

29.9499583 

9.6441542 

.001114827 

898 

806404 

724150792 

29.9666481 

9.6477367 

.001113586 

899 

808201 

726572699 

29.9833287 

9.6513166 

.001112347 

900 

810000 

729000000 

30.0000000 

9.6548938 

.001111111 

901 

811801 

731432701 

30.0166620 

9.6584684 

.001109878 

902 

813604 

733870808 

30.0333148 

9.6620403 

.001108647 

903 

815409 

736314327 

30.0499584 

9.6656096 

.001107420 

904 

817216 

738763264 

30.0665928 

9.6691762 

.001106195 

905 

819025 

741217625 

30.0832179 

9  .  6727403 

.001104972 

906 

820836 

743677416 

30.0998339 

9.6763017 

.001103753 

907 

822649 

746142643 

30.1164407 

9.6798604 

.001102536 

908 

824464 

748613312 

30.1330383 

9.6834166 

.001101322 

909 

826281 

751089429 

30.1496269 

9.6869701 

.001100110 

910 

828100 

753571000 

30.1662063 

9.6905211 

.001098901 

911 

829921 

756058031 

30.1827765 

9.6940694 

.001097695 

912 

831744 

758550528 

30.1993377 

9.6976151 

.001096491 

913 

833569 

761048497 

30.2158899 

9.7011583 

.001095290 

914 

835396 

763551944 

30.2324329 

9.7046989 

.001094092 

915 

837225 

766060875 

30.2489669 

9.7082369 

.001092896 

916 

839056 

768575296 

30.2654919 

9.7117723 

.001091703 

917 

840889 

771095213 

30.2820079 

9.7153051 

.001090513 

918 

842724 

773620632 

30.2985148 

9.7188354 

.001089325 

919 

844561 

776151559 

30.3150128 

9.7223631 

.001088139 

920 

846400 

778688000 

30.3315018 

9.7258883 

.001086957 

921 

848241 

781229961 

30.3479818 

9.7294109 

.001085776 

922 

850084 

783777448 

30  .  3644529 

9.7329309 

.001084599 

923 

851929 

786330467 

30.3809151 

9.7364484 

.001083423 

924 

853776 

788889024 

30.3973683 

9.7399634 

.001082251 

925 

855625 

791453125 

30.4138127 

9.7434758 

.001081081 

926 

857476 

794022776 

30.4302481 

9.7469857 

.001079914 

927 

859329 

796597983 

30.44G(i7l7 

9.7504930 

.001078749 

928 

861184 

799178752 

30.4630924 

9  .  7539979 

.001077586 

929 

863041 

801765089 

30.4795013 

9.7575002 

.001076426 

930 

864900 

804357000 

30.4959014 

9.7610001 

.001075269 

CUBE  ROOTS,  AND  RECIPROCALS. 


23 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

931 

866761 

806954491 

30.5122926 

9  .  7644974 

.001074114 

932 

868624 

809557568 

30.5286750 

9.7679922 

.001072961 

933 

870489 

812166237 

30.5450487 

9.7714845 

.001071811 

934 

872356 

814780504 

30.5614136 

9.7749743 

.001070664 

935 

874225 

817400375 

30.5777697 

9.7784616 

.001069519 

936 

876096 

820025856 

30.5941171 

•  9.7819466 

.001068376 

937 

877969 

822656953 

30.6104557 

9.7854288 

.001067236 

938 

879844 

825293672 

30.6267857 

9.7889087 

.001066098 

939 

881721 

827936019 

30.6431069 

9.7923861 

.001064963 

940 

883600 

830584000 

30.6594194 

9.7958611 

.001063830 

941 

885481 

833237621 

30.6757233 

9.7993336 

.001062699 

942 

887364 

835896888 

30.6920185 

9.8028036 

.001061571 

943 

889249 

838561807 

30.7083051 

9.8062711 

.001060445 

944 

891136 

841232384 

30  .  7245830 

9.8097362 

.001059322 

945 

893025 

843908625 

30.7408523 

9.8131989 

.001058201 

946 

894916 

846590536 

30.7571130 

9.8166591 

.001057082 

947 

896809 

849278123 

30.7733651 

9.8201169 

.001055966 

948 

898704 

851971392 

30.7896086 

9.8235723 

.001054852 

949 

900601 

854670349 

30.8058436 

9.8270252 

.001053741 

950 

902500 

857375000 

30.8220700 

9.8304757 

.001052632 

951 

904401 

860085351 

30.8382879 

9.8339238 

.001051525 

952 

906304 

862801408 

30.8544972 

9.8373695 

.001050420 

953 

908209 

865523177 

30.8706981 

9.8408127 

.001049318 

954 

910116 

868250664 

30.8868904 

9.8442536 

.001048218 

955 

912025 

870983875 

30.9030743 

9.8476920 

.001047120 

956 

913936 

873722816 

30.9192497 

9.8511280 

.001046025 

957 

915849 

876467493 

30.9354166 

9.8545617 

.001044932 

958 

917764 

879217912 

30.9515751 

9.8579929 

.001043841 

959 

919681 

881974079 

30.9677251 

9.8614218 

.001042753 

960 

921600 

884736000 

30.9838668 

9.8648483 

.001041667 

961 

923521 

887503681 

31.0000000 

9.8682724 

.001040583 

962 

925444 

890277128 

31.0161248 

9.8716941 

.001039501 

963 

927369 

893056347 

31.0322413 

9.8751135 

.001038422 

964 

929296 

895841344 

31.0483494 

9.8785305 

.001037344 

965 

931225 

898632125 

31.0644491 

9.8819451 

.001036269 

966 

933156 

901428696 

31.0805405 

9.8853574 

.001035197 

967 

935089 

904231063 

31.0966236 

9.8887673 

.001034126 

968 

937024 

9p7039232 

31.1126984 

9.8921749 

.001033058 

969 

938961 

909853209 

31  .  1287648 

9.8955801 

.001031992 

970 

940900 

912673000 

31  .  1448230 

9.8989830 

.091030928 

971 

942841 

915498611 

31  .  1608729 

9.9023835 

.001029866 

972 

944784 

918330048 

31.1769145 

9.9057817 

.001028807 

973 

946729 

921167317 

31  .  1929479 

9.9091776 

.001027749 

974 

948676 

924010424 

31.2089731 

9.9125712 

.001026694 

975 

950625 

926859375 

31.2249900 

9.9159624 

.001025641 

976 

952576 

929714176 

31.2409987 

9.9193513 

.001024590 

977 

954529 

932574833 

31.2569992 

9.9227379 

.001023541 

978 

956484 

935441352 

31.2729915 

9.9261222 

.001022495 

979 

958441 

938313739 

31.2889757 

9.9295042 

.001021450 

980 

960400 

941192000 

31.3049517 

9.9328839 

.001020408 

981 

962361 

944076141 

31.3209195 

9.9362613 

.001019368 

982 

964324 

946966168 

31  .  3368792 

9.9396363 

.001018330 

983 

966289 

949862087 

31.352830,3 

9.9430092 

.001017294 

984 

968256 

952763904 

31.3687743 

9.9463797 

.001016260 

985 

970225 

955671625 

31.3847097 

9.9497479 

.001015228 

986 

972196 

958585256 

31.4006369 

9.9531138 

.001014199 

987 

974169 

961504803 

31.4165561 

9.9564775 

.001013171 

988 

976144 

964430272 

31.4324673 

9.9598389 

.001012146 

989 

978121 

967361669 

31.4483704 

9.9631981 

.001011122 

990 

980100 

970299000 

31.4642654 

9.9665549 

.001010101 

991 

982081 

973242271 

31.4801525 

9  .  9699095 

.001009082 

992 

984064 

976191488 

31.4960315 

9.9732619 

.001008065 

24          SQUARES,  CUBES,  SQUARE  ROOTS,  ETC. 


No. 

Squares. 

Cubes. 

Square 
Roots. 

Cube  Roots. 

Reciprocals. 

993 

986049 

979146657 

31.5119025 

9.9766120 

.001007049 

994 

988036 

982107784 

31.5277655 

9.9799599 

.001006036 

995 

990025 

985074875 

31.5436206 

9.9833055 

.001005025 

996 

992016 

988047936 

31.5594677 

9.9866488 

.001004016 

997 

994009 

991026973 

31.5753068 

9.9899900 

.001003009 

998 

996004 

994011992 

31.5911380 

9.9933289 

.001002004 

999 

998001 

997002999 

31.6069613 

9.9966656 

.001001001 

1000 

1000000 

1000000000 

31.6227766 

10.0000000 

.001000000 

1001 

1002001 

1003003001 

31.6385840 

10.0033322 

.0009990010 

1002 

1004004 

1006012008 

31.6543836 

10.0066622 

.  0009980040 

1003 

1006009 

1009027027 

31.6701752 

10.0099899 

.0009970090 

1004 

1008016 

1012048064 

31.6859590 

10.0133155 

.0009960159 

1005 

1010025 

1015075125 

31.7017349 

10.0166389 

.0009950249 

1006 

1012036 

1018108216 

31.7175030 

10.0199601 

.0009940358 

1007 

1014049 

1021147343 

31.7332633 

10.0232791 

.0009930487 

1008 

1016064 

1024192512 

31.7490157 

10.0265958 

.0009920635 

1009 

1018081 

1027243729 

31.7647603 

10.0299104 

.0009910803 

1010 

1020100 

1030301000 

31.7804972 

10.0332228 

.0009900990 

1011 

1022121 

1033364331 

31.7962262 

10.0365330 

.0009891197 

1012 

1024144 

1036433728 

31.8119474 

10.0398410 

.0009881423 

1013 

1026169 

1039509197 

31.8276609 

10.0431469 

.0009871668 

1014 

1028196 

1042590744 

31.8433666 

10.0464506 

.0009861933 

1015 

1030225 

1045678375 

31.8590646 

10.0497521 

.0009852217 

1016 

1032256 

1048772096 

31.8747549 

10.0530514 

.0009842520 

1017 

1034289 

1051871913 

31.8904374 

10.0563485 

.0009832842 

1018 

1036324 

1054977832 

31.9061123 

10.0596435 

.0009823183 

1019 

1038361 

1058089859 

31.9217794 

10.0629364 

.0009813543 

1020 

1040400 

1061208000 

31.9374388 

10.0662271 

.0009803922 

1021 

1042441 

1064332261 

31.9530906 

10.0695156 

.0009794319 

1022 

1044484 

1067462648 

31.9687347 

10.0728020 

.0009784736 

1023 

1046529 

1070599167 

31.9843712 

10.0760863 

.0009775171 

1024 

1048576 

1073741824 

32.0000000 

10.0793684 

.0009765625 

1025 

1050625 

1076890625 

32.0156212 

10.0826484 

.0009756098 

1026 

1052676 

1080045576 

32.0312348 

10.0859262 

.0009746589 

1027 

1054729 

1083206683 

32  .  0468407 

10.0892019 

.0009737098 

1028 

1056784 

1086373952 

32.0624391 

10  .  0924755 

.  0009727626 

1029 

1058841 

1089547389 

32.0780298 

10.0957469 

.0009718173 

1030 

1060900 

1092727000 

32.0936131 

10.0990163 

.0009708738 

1031 

1062961 

1095912791 

32.1091887 

10.1022835 

.0009699321 

1032 

1065024 

1099104768 

32.1247568 

10.1055487 

.0009689922 

1033 

1067089 

1102302937 

32.1403173 

10.1088117 

.0009680542 

1034 

1069156 

1105507304 

32.1558704 

10.1120726 

.0009671180 

1035 

1071225 

1108717875 

32.1714159 

10.1153314 

.0009661836 

1036 

1073296 

1111934656 

32.1869539 

10.1185882 

.0009652510 

1037 

1075369 

1115157653 

32  .  2024844 

10.1218428 

.  0009643202 

1038 

1077444 

1118386872 

32.2180074 

10.1250953 

.0009633911 

1039 

1079521 

1121622319 

32  .  2335229 

10.1283457 

.0009624639 

1040 

1081600 

1124864000 

32.2490310 

10.1315941 

.0009615385 

1041 

1083681 

1128111921 

32.2645316 

10.1348403 

.0009606148 

1042 

1085764 

1131366088 

32  .  2800248 

10.1380845 

.0009596929 

1043 

1087849 

1134626507 

32.2955105 

10.1413266 

.0009587738 

1044 

1089936 

1137893184 

32  .  3109888 

10.1445667 

.0009578544 

1045 

1092025 

1141166125 

32  .  3264598 

10.1478047 

.0009569378 

1046 

1094116 

1144445336 

32.3419233 

10.1510406 

.0009560229 

1047 

1096209 

1  147730823 

32  .  3573794 

'10.1542744 

.0009551098 

1048 

1098304 

1151022592 

32.3728281 

10.1575062 

.0009541985 

1049 

1100401 

1154320619 

32  .  3882695 

10.1607359 

.0009532888 

1050 

1102500 

1157625000 

32.4037035 

10.1639636 

.0009523810 

1051 

1104601 

1160935651 

32.4191301 

10.1671893 

.  0009514748 

1052 

1106704 

1164252608 

32  .  4345495 

10.1704129 

.0009505703 

1053 

1108809 

1167575877 

32.4499615 

10.1736344 

.0009496676 

1054 

1110916 

1170905461 

:;  2.1  053662 

10.1768539 

.0009487666 

WEIGHTS  AND  MEASURES. 


25 


WEIGHTS    AND  MEASURES. 
Measures  of  Length. 

12    inches    =  1  foot. 
3  feet          =  1  yard     =       36  inches. 
5i  yards      =  1  rod        =      198  inches=      16J  ft. 
40    rods        =  1  furlong =   7920  inches =   660  ft.  =  220  yds. 
8    furlongs=l  mile      =63360  inches  =5280    ft.  =  1760    yds.= 
1    yard       =0.0005682  of  a  mile.  [320  rods. 

GUNTER'S  CHAIN. 
7.92  inches  =1  link. 

100      links    =  1  chain = 4  rods  =  66  feet. 
80       chains  =1  mile. 

ROPES    AND    CABLES. 

6  feet=  1  fathom.         120  fathoms  =  1  cable's  length. 

TABLE  SHOWING  INCHES  EXPRESSED  IN  DECIMALS 
OF  A  FOOT. 


In. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

0 

Foot 

0833 

1667 

2500 

3333 

4167 

5000 

.5833 

.6667 

.7500 

.8333 

.9167 

1-32 

.0026 

0859 

1693 

2526 

3359 

4193 

5026 

.5859 

.6693 

.7526 

.8359 

.9193 

1-16  0052 

0885 

1719 

2552 

3385 

4219 

5052 

.5885 

.6719 

.7552 

.8385 

.9219 

3-32 

0078 

0911 

1745 

2578 

3411 

4245 

5078 

.5911 

.6745 

.7578 

.8411 

.9245 

1-8 

0104 

0938 

1771 

2604 

3438 

4271 

5104 

.5938 

.6771 

.7604 

.8438 

.9271 

5-32 

0130 

0964 

1797 

2630 

3464 

4297 

5130 

.5964 

.6797 

.7630 

.8464 

.9297 

3-16 

0156 

0990 

1823 

2656 

3490 

4323 

5156 

.5990 

.6823 

.7656 

.8490 

.9323 

7-32 

0182 

1016 

1849 

2682 

3516 

4349 

5182 

.6016 

.6849 

.7682 

.8516 

.9349 

1-4 

0208 

1042 

1875 

2708 

3542 

4375 

5208 

.6042 

.6875 

.7708 

.8542 

.9375 

9-32 

0234 

1068 

1901 

2734 

3568 

4401 

5234 

.6068 

.6901 

.7734 

.8568 

.9401 

5-16 

0260 

1094 

1927 

2760 

3594 

4427 

5260 

.6094 

.6927 

.7760 

.8594 

.9427 

11-32 

0286 

1120 

1953 

2786 

3620 

4453 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

3-8 

0313 

.1146 

.1979 

2813 

3646 

4479 

.5313 

.6146 

.6979 

.7813 

.8646 

.9479 

13-32 

0339 

.1172 

.2005 

2839 

3672 

4505 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

7-16 

0365 

.1198 

.2031 

2865 

3698 

4531 

.5365 

.6198 

.7031 

.7865 

.8698 

.9531 

15-32 

.0391 

.1224 

.2057 

2891 

3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

1-2 

0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

17-32 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

9-16 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

19-32 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

5-8 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

21-32 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

.8047 

.8880 

.9714 

11-16 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

.5573 

.6406 

.7240 

.8073 

.8906 

.9740 

23-32 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

3-4 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

.6458 

.7292 

.8125 

.8958 

.9792 

25-32 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.5651 

.6484 

.7318 

.8151 

.8984 

.9818 

13-16 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

27-32 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

7-8 

.0729 

.1563 

.2396 

.3229 

.4063 

.4896 

.5729 

.6563 

.7396 

.8229 

.9063 

.9896 

29-32 

.0755 

.1589 

.2422 

.3255 

.4089 

.4922 

.5755 

.6589 

.7422 

.8255 

.9089 

.9922 

15-1P 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.7448 

.8281 

.9115 

.9948 

31-32 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

26      DECIMAL   EQUIVALENTS  FOR  FRACTIONS. 
DECIMAL  EQUIVALENTS  FOR  FRACTIONS  OF  AN  INCH. 


Ads. 

Biths. 

Decimal. 

Frac- 
tion. 

Ads. 

Aths. 

Decimal. 

Frac- 
tion. 

1 

.015625 

33 

.515625 

1 

2 

.03125 

17 

34 

.53125 

3 

.046875 

35 

.546875 

2 

4 

.0625 

1/16 

18 

36 

.5625 

9/16 

5 

.078125 

37 

.578125 

3 

6 

.09375 

19 

38 

.59375 

7 

.  109375 

39 

.609375 

4 

8 

.125 

1/8 

20 

40 

.625 

5/8 

9 

.  140625 

41 

.640625 

5 

10 

.15625 

21 

42 

.65625 

11 

.171875 

43 

.671875 

6 

12 

.1875 

3/16 

22 

44 

.6875 

11/16 

13 

.203125 

45 

.703125 

7 

14 

.21875 

23 

46 

.71875 

15 

.234375 

47 

.734375 

8 

16 

.25 

1/4 

24 

48 

.75 

3/4 

17 

.265625 

49 

.765625 

9 

18 

.28125 

25 

50 

.78125 

19 

.296875 

51 

.796875 

10 

20 

.3125 

5/16 

26 

52 

.8125 

13/16 

21 

.328125 

53 

.828125 

11 

22 

.34375 

27 

54 

.84375 

23 

.359375 

55 

.859375 

12 

24 

.375 

3/8 

28 

56 

.875 

7/8 

25 

.390625 

57 

.890625 

13 

26 

.40625 

29 

58 

.90625 

27 

.421875 

59 

.921875 

14 

28 

.4375 

7/16 

30 

60 

.9375 

15/16 

29 

.453125 

61 

.953125 

15 

30 

.46875 

31 

62 

.96875 

31 

.484375 

63 

.984375 

16 

32 

.5 

1/2 

32 

64 

1. 

1 

MEASURES   OF   SURFACE   AND   VOLUME.         27 

NAUTICAL   MEASURE. 

A  nautical  or  sea  mile  is  the  length  of  a  minute  of  longitude 
of  the  earth  at  the  equator  at  the  level  of  the  sea.  It  is  assumed 
at  6086.07  feet  =1.1 52664  statute  or  land  miles  by  the  United 
States  Coast  Survey. 

3  nautical  miles  =1  league. 

MISCELLANEOUS. 

1  palm  =  3  inches.  1  span  =9  inches. 

1  hand=4  inches.  1  meter  =3.2809  feet. 

Measures  of  Surface. 

144  square  inches  =  1  square  foot. 

9  square  feet     =  1  square  yard  =  1296  square  inches. 
100  square  feet     =  1  square  (architects'  measure). 

LAND. 

30J  square  yards      =  1  square  rod. 
40    square  rods         =  1  square  rood    =1210  square  yards. 

4  square  roods    (  =  1  acre  =  4840  square  yards. 
10    square  chains  >  =160  square  rods. 

640    acres  =1  square  mile     =3097600  square  yards = 

208.71  feet  square      =  1  acre.     [102400  sq.  rods=2560  sq.  roods. 
A  section  of  land  is  a  square  mile,  and  a  quarter-section  is  160 
acres. 

Measures  of  Volume, 

1  gallon  liquid  measure  =  231  cubic  inches,  and  contains 
8.339  avoirdupois  pounds  of  distilled  water  at  39.8°  F.,  or  58333 
grains. 

1  cubic  foot  contains  7.48  liquid  gallons,  or  6.428  dry  gallons. 

1  gallon  dry  measure =268.8  cubic  inches. 

1  bushel  (Winchester)  contains  2150.42  cubic  inches,  or  77.627 
pounds  distilled  water  at  39.8°  F. 

A  heaped  bushel  contains  2747.715  cubic  inches. 

DRY. 

2  pints     =  1  quart  =  67.2  cubic  inches. 
4  quarts  =  1  gallon  =    8  pints=                       268.8  cubic  inches. 
2  gallons^  1  peck     =16  pints=    8  quarts=  537.6  cubic  inches. 
4  pecks    =1  bushel  =  64  pints  =  32  quarts  =8  gals.  =  2150.42 
1  cord  of  wood=  128s cubic  feet.  [cu.  in. 


28          MEASURES   OF  VOLUME  AND  WEIGHT. 

LIQUID. 

4  gills     =  l  pint    =  16  fluid  ounces. 
2  pints   =  1  quart  =    8  gills  =  32  fluid  ounces. 
4  quarts  =  1  gallon  ==32  gills  =8  pints  =  128  fluid  ounces. 
In  the  United  States  and  Great  Britain  1  barrel  of  wine  or 
brandy=31J  gallons,  and  contains  4.211  cubic  feet. 

A  hogshead  is  63  gallons,  but  this  term  is  often  applied  to  casks 
of  various  capacities. 

Cubic  Measure. 
1728  cubic  inches  =  1  cubic  foot. 
27  cubic  feet      =  1  cubic  yard. 

In  measuring  wood,  a  pile  of  wood  cut  4  feet  long,  piled  4  feet 
high,  and  8  feet  on  the  ground,  making  128  cubic  feet,  is  called 
a  cord. 

16  cubic  feet  make  one  cord  foot. 

A  perch  of  stone  is  nominally  16J  feet  long,  1  foot  high,  and 
1J  feet  thick,  and  contains  24 f  cubic  feet. 

A  perch  of  stone  is,  however,  often  computed  differently  in 
different  localities;  thus,  in  most  if  not  all  of  the  States  and  Ter- 
ritories west  of  the  Mississippi,  stone  masons  figure  rubble  by 
the  perch  of  16|  cu.  ft.  In  Philadelphia,  22  cu.  ft.  are  called  a 
perch.  In  Chicago,  stone  is  measured  by  the  cord  of  100  cu.  ft. 
A  ton  of  shipping  is  42  cubic  feet  in  Great  Britain  and  40  cubic 
feet  in  the  United  States. 

Fluid  Measure. 
60  minims  =  1  fluid  drachm. 

8  fluid  drachms  =  1  ounce. 
16  ounces  =  1  pint. 

8  pints  =  1  gallon. 

Miscellaneous, 

Butt  of  Sherry  =  108  gals.  Puncheon  of  Brandy,  110  to  120  gals. 
Pipe  of  Port  =115  gals.  Puncheon  of  Rum,  100  to  110  gals. 
Butt  of  Malaga=  105  gals.  Hogshead  of  Brandy,  55  to  60  gals. 
Puncheon  of  Scotch  Whis-  Hogshead  of  Claret,  46  gals, 

key,  110  to  130  gals. 

Measures  of  Weight. 

The  standard  avoirdupois  pound  is  the  weight  of  27.7015  cubic 
inches  of  distilled  water  weighed  in  air  at  39.83°,  the  barometer 
at  30  inches;  it  contains  7000  grains.  One  pound  avoirdupois = 
1.2153  pounds  troy. 


MEASURES  OF  WEIGHT.  29 

Avoirdupois,  or  Ordinary  Commercial  Weight. 

1  drachm  =  27.343  grains. 

16  drachms  =1  ounce  (oz.). 

16  ounces  =1  pound  (lb.). 

100  pounds  =  1  hundred  weight  (cwt.). 

20  hundred  weight  =  1  ton. 

In  collecting  duties  upon  foreign  goods  at  the  United  States 
custom-houses,  and  also  in  freighting  coal,  and  selling  it  by 
wholesale, — 

28  pounds  *=  1  quarter. 

4  quarters,  or  112  lbs.=  1  hundred  weight. 
20  hundred  weight         =  1  long  ton=  2240  pounds. 
A  stone  =  14  pounds. 

A  quintal    *  =100  pounds. 

The  following  measures  are  sanctioned  by  custom  or  law: 
1  bushel  =  1.244  cubic  feet  or  1J  cubic  feet  nearly. 

32  pounds  of  oats  =  1  bushel. 

45  pounds  of  Timothy-seed  =  1  bushel. 
48  pounds  of  barley  =  1  bushel. 

56  pounds  of  rye  =  1  bushel. 

56  pounds  of  Indian  corn  =  1  bushel. 
50  pounds  of  Indian  meal  =  1  bushel. 
60  pounds  of  wheat  =  1  bushel.  ' 

60  pounds  of  clover-seed  =  1  bushel. 
60  pounds  of  potatoes  =  1  bushel. 
56  pounds  of  butter  =  1  firkin. 

100  pounds  of  meal  or  flour  =  1  sack. 
100  pounds  of  grain  or  flour  =  1  cental. 
100  pounds  of  dry  fish  =  1  quintal. 

100  pounds  of  nails  =  1  cask. 

196  pounds  of  flour  =  1  barrel. 

200  pounds  of  beef  or  pork    =  1  barrel. 
80  pounds  of  lime  =  1  bushel. 

Troy  Weight. 

USED    IN    WEIGHING    GOLD    OR    SILVER. 

24  grains  =  1  pennyweight  (pwt.). 

20  penny  weights  =1  ounce  (oz.). 

12  ounces  =1  pound  (lb.). 

A  carat  of  the  jewellers,  for  precious  stones,  is,  in  the  United 
States,  3.2  grains:  in  London,  3.17  grains,  in  Paris,  3.18  grains 


30  MEASURES  OF  VALUE  AND  TIME. 

are  divided  into  4  jewellers'  grains.  In  troy,  apothecaries', 
and  avoirdupois  weights,  the  grain  is  the  same,  one  pound  troy 
being  equal  to  .82286  pound  avoirdupois. 

Apothecaries'  Weight. 

USED  IN  COMPOUNDING  MEDICINES,   AND  IN  PUTTING  UP 
MEDICAL    PRESCRIPTIONS. 


20  grains  (gr.)  =  1  scruple  O ). 
3  scruples       =  1  drachm  (  3  ). 


8  drachms=  1  ounce    (oz.). 
12  ounces    =  1  pound  (lb.). 


•  Measures  of  Value. 

UNITED    STATES    STANDARD. 


10  mills  =1  cent. 
10  cents  =1  dime. 


10  dimes    =  1  dollar. 
10  dollars  =  1  eagle. 


The  standard  of  gold  and  silver  is  900  parts  of  pure  metal  and 
100  of  alloy  in  1000  parts  of  coin. 

The  fineness  expresses  the  quantity  of  pure  metal  in  1000  parts. 

The  remedy  of  the  mint  is  the  allowance  for  deviation  from  the 
exact  standard  fineness  and  weight  of  coins. 

Weight  of  Coin. 

Double  eagle  =516        troy  grains. 

Eagle  =258        troy  grains. 

Dollar  (gold)  =    25 . 8    troy  grains. 

Dollar  (silver)  =412.5    troy  grains. 

Half-dollar  =192        troy  grains. 

5-cent  piece  (nickel)  =  77.16  troy  grains. 
3-cent  piece  (nickel)  =  30  troy  grains. 
Cent  (bronze)  =  48  troy  grains. 

Measure  of  Time. 


60  seconds  =  1  minute. 
60  minutes  =  1  hour. 


365  days=  1  common  }rear. 

366  days=  1  leap  year. 


24  hours      =  1  day. 

A  solar  day  is  measured  by  the  rotation  of  the  earth  upon  its 
axis  with  respect  to  the  sun. 

In  astronomical  computation  and  in  nautical  time  the  day  com- 
mences at  noon,  and  in  the  former  it  is  counted  throughout  the  24 
hours. 

In  civil  computation  the  day  commences  at  midnight,  and  is 
divided  into  two  portions  of  12  hours  each. 

A  solar  year  is  the  time  in  which  the  earth  makes  one  revolution 
around  the  sun;  and  its  average  time,  called  the  mean  solar  year, 


THE  CALENDER,— ANGULAR  MEASURE.    31 

is  365  days,  5  hours,  48  minutes,  49.7  seconds,  or  nearly  365J 
days. 

A  mean  lunar  month,  or  lunation  of  the  moon,  is  29  days,  12 
hours,  44  minutes,  2  seconds,  and  5.24  thirds. 

The  Calendar,  Old  and  New  Style. 

The  Julian  Calendar  was  established  by  Julius  Caesar,  44  B.C., 
and  by  it  one  day  was  inserted  in  every  fourth  year.  This  was 
the  same  thing  as  assuming  that  the  length  of  the  solar  year  was 
365  days,  6  hours,  instead  of  the  value  given  above,  thus  intro- 
ducing an  accumulative  error  of  11  minutes,  12  seconds,  every 
year.  This  calendar  was  adopted  by  the  church  in  325  A.D.,  at 
the  Council  of  Nice.  In  the  year  1582  the  annual  error  of  11  min- 
utes, 12  seconds,  had  amounted  to  a  period  of  10  days,  which,  by 
order  of  Pope  Gregory  XIII.,  was  suppressed  in  the  calendar,  and 
the  5th  of  October  reckoned  as  the  15th.  To  prevent  the  repe- 
tition of  this  error,  it  was  decided  to  leave  out  three  of  the  in- 
serted days  every  400  years,  and  to  make  this  omission  in  the 
years  which  are  not  exactly  divisible  by  400.  Thus,  of  the  years 
1700,  1800,  1900,  2000,  all  of  which  are  leap  years  according  to 
the  Julian  Calendar,  only  the  last  is  a  leap  year  according  to  the 
Reformed  or  Gregorian  Calendar.  This  Reformed  Calendar  was 
not  adopted  by  England  until  1752,  when  11  days  were  omitted 
from  the  calendar.  The  two  calendars  are  now  often  called  the 
Old  Style  and  the  New  Style. 

The  latter  style  is  now  adopted  in  every  Christian  country 
except  Russia. 

Circular  and  Angular  Measures. 

USED    FOR    MEASURING    ANGLES    AND    ARCS.    AND    FOR    DETERMIN- 
ING LATITUDE  AND  LONGITUDE. 

60  seconds  (")  =  1  minute  ('). 

60  minutes        =  1  degree  (°) . 

360  degrees       =  1  circumference     (C.). 

Seconds  are  usually  subdivided  into  tenths  and  hundredths. 
A  minute  of  the  circumference  of  the  earth  is  a  geographical 
mile. 

Degrees  of  the  earth's  circumference  on  a  meridian  average 
69.16  common  miles. 

THE  METRIC  SYSTEM. 

The  metric  system  is  a  system  of  weights  and  measures  based 
upon  a  unit  called  a  meter. 


32  THE  METRIC  SYSTEM. 

The  meter  was  intended  to  be  one  ten-millionth  part  of  the 
distance  from  the  equator  to  either  pole,  measured  on  the  earth's 
surface  at  the  level  of  the  sea. 

The  names  of  derived  metric  denominations  are  formed  by  pre- 
fixing to  the  name  of  the  primary  unit  of  measure — 


Milli  (mill'e),  a  thousandth, 
Centi  (sent'e),  a  hundredth, 
Deci  (des'e),  a  tenth, 


Hecto  (hek'to),  one  hundred, 
Kilo  (kil'o),  a  thousand, 
Myria  (mir'ea),  ten  thousand. 


Deka  (dek'a),  ten. 

This  system,  first  adopted  by  France,  has  been  extensively 
adopted  by  other  countries,  and  is  much  used  in  the  sciences  and 
the  arts.  It  was  legalized  in  1866  by  Congress  to  be  used  in  the 
United  States,  and  is  already  employed  by  the  Coast  Survey,  and, 
to  some  extent,  by  the  Mint  and  the  General  Post-Office. 

Linear  Measures. 

The  meter  is  the  primary  unit  of  lengths. 
TABLE. 

10  millimeters  (mm.)  =  l  centimeter  (cm.)     =   0.3937  in. 

10  centimeters  =  1  decimeter  =     3. 937  in. 

10  decimeters  =  1  METER  =   39 . 37    in. 

10  meters  =  1  dekameter  =  393 .37    in . 

10  dekameters  =1  hectometer  ==328  ft.  1  in. 

10  hectometers  =  1  KILOMETER  (km.)   =0.62137  miles. 

10  kilometers  =  1  myriameter  =6.2137    miles. 

The  meter  is  used  in  ordinary  measurements;  the  centimeter,  or 
millimeter,  in  reckoning  very  small  distances;  and  the  kilometer, 
for  roads  or  great  distances. 

A  centimeter  is  about  f  of  an  inch;  a  meter  is  about  3  feet  3 
inches  and  J ;  a  kilometer  is  about  200  rods,  or  f  of  a  mile  (see  p. 
35). 

Surface  Measures. 

The  square  meter  is  the  primary  unit  of  ordinary  surfaces. 

The  are  (air),  a  square,  each  of  whose  sides  is  ten  meters,  is 
the  unit  of  land  measures. 

TABLE. 
100  square  millimeters  (sq.  mm.)  =  1  square  )  _  .  1    _        .     , 

centimeter  (sq.  cm.)  > 

100  square  centimeters^  1  square  decimeter    =  15.5    sq.  inches. 

100  square  decimeters  =1  square  )       , 

\  =1550sq.  in.,  or  1.196sq.yds. 
METER  (sq.  m.)  ) 


THE  METRIC  SYSTEM.  33 

ALSO 

100  centiares,  or  sq.  meters,  =  1  ARE  (ar,)  = 119 .6  sq.  yds. 

100  ares  =  1  hectare  (ha.)       =2.471  acres. 

A  square  meter,  or  one  centiare,  is  about  lOf  square  feet,  or  1^ 
square  yards,  and  a  hectare  is  about  2J  acres. 

Cubic  Measures. 

The  cubic  meter,  or  stere  (stair),  is  the  primary  unit  of  a  volume. 

TABLE. 

1000  cubic  millimeters  (cu.  mm.)  =  1  cubic  centimeter  (cu.  cm.)  = 

[0.061  cubic  inch. 

1000  cubic  centimeters=l  cubic  decimeter  =61. 022  cubic  inches. 
1000  cubic  decimeters  =  1  cubic  METER  (cu.  m.)  =  35.314  cu.  ft. 

} 

The  stere  is  the  name  given  to  the  cubic  meter  in  measuring 

wood  and  timber,     A  tenth  of  a  stere  is  a  decistere,  and  ten  steres 
are  a  dekastere. 

A  cubic  meter,  or  stere ,  is  about  1 J  cubic  yards,  or  about  2J  cord 
feet. 

Liquid  and  Dry  Measures. 

The  liter  (leeter)  is  the  primary  unit  of  measures  of  capacity, 
and  is  a  cube,  each  of  whose  edges  is  a  tenth  of  a  meter  in  length. 

The  hectoliter  is  the  unit  in  measuring  large  quantities  of  grain, 
fruits,  roots,  and  liquids. 

10  milliliters  (ml.)  =  1  centiliter  (el.)       =0.338  fluid  ounce. 
10  centiliters  =  1  deciliter  =  0 . 845  liquid  gill. 

10  deciliters  =  1  LITER  (1.)  =  1 .0567  liquid  quarts. 

10  liters  =  1  dekaliter  =  2 . 6417  gallons. 

10  dekaliters  =  1  HECTOLITER  (hi.)  =  2  bushels  3 . 35  pecks. 

10  hectoliters          =  1  kiloliter  =28  bushels  1 J  pecks. 

A  centiliter  is  about  J  of  a  fluid  ounce;  a  liter  is  about  lf§- 
liquid  quarts,  or  ^  of  a  dry  quart ;  a  hectoliter  is  about  2f  bushels; 
and  a  kiloliter  is  one  cubic  meter,  or  stere. 

Weights. 

The  gram  is  the  primary  unit  of  weights,  and  is  the  weight  in  a 
vacuum  of  a  cubic  centimeter  of  distilled  water  at  the  tempera- 
ture of  39.2  degrees  Fahrenheit. 


34  THE  METRIC  SYSTEM. 

TABLE. 

10  milligrams  (mg.)    =  1  centigram  =       0.1543  troy  grain. 

10  centigrams  =  1  decigram  =        1.543    troy  grains 

10  decigrams  =  1  GRAM  (g.)  =      15.432    troy  grains 

10  grams  =  1  dekagram  =       0.3527  avoir,  oz. 

10  dekagrams  =  1  hectogram          =       3.5274  avoir,  oz. 

10  hectograms  =  1  KILOGRAM  (k.)   =        2.2046  avoir.  Ibs. 

10  kilograms  =  1  myriagram         =      22.046    avoir.  Ibs. 

10  myriagrams  =  1  quintal  =   220.46      avoir.  Ibs. 

10  quintals.  =  1  TONNEAU  (t.)      =2204.6        avoir,  Ibs. 

1  kilogram  per  kilometer   ==    .67195  pounds  per  1000  feet. 
1  pound  per  thousand  feet=  1.4882  kilogrames  per  kilometer. 
1  kilogram  per  square  millimeter  =  1423  pounds  per  square  inch. 
1  pound  per  square  inch  =  .000743  kilograms  per  square 

[millimeter. 

The  gram  is  used  in  weighing  gold,  jewels,  letters,  and  small 
quantities  of  things.  The  kilogram,  or,  for  brevity,  kilo,  is  used 
by  grocers ;  and  the  tonneau  (tonno) ,  or  metric  ton,  is  used  in  find- 
ing the  weight  of  very  heavy  articles. 

A  gram  is  about  15J  grains  troy;  the  kilo  about  2J  pounds 
avoirdupois;  and  the  metric  ton,  about  2205  pounds. 

A  kilo  is  the  weight  of  a  liter  of  water  at  its  greatest  density; 
and  the  metric  ton,  of  a  cubic  meter  of  water. 

Metric  numbers  are  written  with  the  decimal-point  (.)  at  the 
right  of  the  figures  denoting  the  unit;  thus,  15  meters,  3  centi- 
meters, are  written,  15.03  m. 

When  metric  numbers  are  expressed  by  figures,  the  part  of  the 
expression  at  the  left  of  the  decimal-point  is  read  as  the  number 
of  the  unit,  and  the  part  at  the  right,  if  any,  as  a  number  of  the 
lowest  denomination  indicated,  or  as  a  decimal  part  of  the  unit; 
thus,  46.525  m.  is  read  46  meters  and  525  millimeters,  or  46  and 
525  thousandths  meters. 

In  writing  and  reading  metric  numbers,  according  as  the  scale 
is  10,  100,  or  1000,  each  denomination  should  be  allowed  one, 
two,  or  three  orders  of  figures. 

METRIC  CONVERSION  TABLE. 

The  following  metric  conversion  table  has  been  compiled  by 
Mr.  C.  W.  Hunt,  M.  Am.  Soc.  M.  E.,  President  of  the  C.  W.  Hunt 
Company,  of  New  York  City,  and  is  most  convenient  in  dealing 
with  metric  weights  and  measures : 


METRIC   CONVERSION  TABLE. 


35 


Millimeters  X. 03937 

Millimeters -7- 25.4 

Centimeters  X  .3937 

Centimeters  -r-  2.54 

Meters  X  39. 37 

Meters  X  3.281 

Meters  X  1.094 

Kilometers  X  .621 

Kilometers  -=-1. 6093 

Kilometers  X  3280.7 

Square  millimetersX.0155 

Square  millimeters -r-  645.1 

Square  centimeters  X.I  55 

Square  centimeters  -r- 6. 451 

Square  meters  X  10.764 

Square  kilometers  X  247.1 

Hectares  X  2.471 

Cubic  centime ters-f- 16. 383 

Cubic  centimeters  ^3. 69 

Cubic  centimeters  -h 29.57 

Cubic  meters  X  35.31 5 

Cubic  meters  X  1.308 

Cubic  meters  X  264.2 

Liters  X  61. 022 

Liters  X  33.84 

Liters  X. 2642 

Liters-f-3.78 

Liters  -=-28.316 

HectolitersX3.531 

HectolitersX2.84 

Hectoliters  X. 131 

Hectoliters -f- 26.42 

Grammes  X  15.432 

Grammes  X  981 

Grammes  (water)  -j-  29. 57 

Grammes -r- 28.35 

Grammes  per  cu.  cent.  -*-  27.7 

Joule  X. 7373 

Kilograms  X  2. 2046 

Kilogrammes  X  35,3 

Kilograms -- 1102.3 

Kilograms  per  sq.  cent  .  X  14.223 


==  inches. 

=  inches. 

=  inches. 

=  inches. 

=  ins.     (Act  of  Congress.) 

=  feet. 

=  yards. 

=  miles. 

=  miles. 

=  feet. 

=  square  inches. 
=  square  inches. 
=  square  inches. 

=  square  inches. 

=  square  feet. 

=  acres. 

=  acres. 

=  cubic  inches. 

=  fluid  drachms.  (U.  S.  P.) 

=  fluid  ounce.    (U,  S.  P.) 

=  cubic  feet. 

=  cubic  yards. 

=  gallons  (231  cu.  ins.). 

=  cu  ins.    (Act  of  Congress.) 

=  fluid  ounces.     (U.  S.  P. 

=  gallons  (231  cu.  ins.). 

=  gallons  (231  cu.  ins.). 

=  cubic  feet. 

=  cubic  feet. 

=  bushels  (2150.42  cu.  ins.). 

=  cubic  yards. 

=  gallons  (231  cu.  ins.). 

=  grains.   (Act  of  Congress.) 

=  dynes. 

=  fluid  ounces. 

=  ounces  avoirdupois. 

=  pounds  per  cubic  inch. 

=  foot-pounds. 

=  pounds. 

=  ounces  avoirdupois. 

=  tons  (2000  pounds). 

=  pounds  per  square  inch. 


36 


ANCIENT   MEASURES  AND   WEIGHTS. 


Kilogrammeters  X  7.233  =  foot-pounds. 

Kilograms  per  meter X-672  = pounds  per  square  foot. 

Kilograms  per  cubic  meter  X  .062  =  pounds  per  cubic  foot. 

Kilograms  per  cheval  vapeurX  2. 235=  pounds  per  horse-power. 

Kilo- watts  X 1 .34  =  horse-power. 

Watts  -r-  746  =  horse-power. 

Watts  -r-  .7373  =  foot-pounds  per  second. 

Calorie  X  3.968  =B.  T.  U. 

Cheval  vapeur  X  .9863  =  horse-power. 

(Centigrade  X 1 .8)  +  32  =  degrees  Fahrenheit. 

Francs  X. 193  =  dollars. 

Gravity,  Paris  =980.94  cent,  per  second. 

SCRIPTURE  AND  ANCIENT  MEASURES  AND 

WEIGHTS. 
Scripture  Long  Measures. 

Inches.                                                Feet.  Inches. 

,      =   0.912  Cubit                  =1  9.888 

=   3.648  Fathom             =7  3.552 
=  10.944 


Digit 
Palm 
Span 


Egyptian  JLoiig'  Measures. 

Nahud  cubit=  1  foot  5.71  ins.     Royal  cubit=  1  foot  8.66  ins. 


Digit 

Pous  (foot) 
Cubit  =    1 


Grecian  Long1  Measure. 

Feet.     Inches. 

0.7554  Stadium 

1     0 . 0875  Mile 

5984f 


Feet. 
=    604 

=  4835 


Inches . 
4.5 


Jewish  Long1  Measures, 


Cubit  =1.824  ft. 

Sabbath-day's  journey=   3648  ft. 


Mile  =        7296  feet. 

Day's  journey  =  33 . 164  miles. 


Roman  Long  Measures. 


Digit 

Uncia  (inch) 
Pes  (foot) 


Inches. 
--    0.72575  Cubit 
=    0.967 
=11.604 


Passus  = 

Mile  (millarium)  = 


Feet.  Inches. 

1  5.406 

4  10.02 
=  4842 


Arabian  foot 
Babylonian  foot 
Egyptian  finger 


Roman  Weight. 

Ancient  libbra=  0 . 7094  pound. 

Miscellaneous. 

Feet. 

Hebrew  foot 


= 1 . 095 
=  1.140 
=  0.06145 


Hebrew  cubit 
Hebrew  sacred  cubit 


Feet. 
=  1.212 
=  1.817 
=  2.002 


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l>  W  00  "^ 

§t^  tOCNJ 
CC    (M    rH 

O  CO  CM  00 

o 

rH  CO  TF 

CO  t-  OS   rH 

<N  rtH  tO  I> 

Oi  O  CM  00 
I-H  CM  CM  Cl 

3 

rH 

^^^ 

\2         N2 

H^^\fo|oo«>\ 

N.2      V3 

rHtNO-.  NIC|OCJ5\ 

\  -r        \  (g 
rtH-S^HacSX 

hH 

MENSURATION.— DEFINITIONS. 


37 


MENSURATION. 
Definitions. 

A  point  is  that  which  has  only  position. 

A  plane  is  a  surface  in  -which,  any  two  points  being  taken,  the 
straight  line  joining  them  will  be  wholly  in  the 
surface.  ^     Fig.  I 

A  curved  line  is  a  line  of  which  no  portion  is 
straight  (Fig.  1). 

Parallel  lines  are  such  as  are  wholly  in  the  same  plane,  and  have 
the  same  direction  (Fig.  2). 

A  broken  line  is  a  line  composed  of  a       

series  of  dashes;  thus,  —  — .  Fig. 2 

An  angle  is  the  opening  between  two  Parallel  Lines, 

lines  meeting  at  a  point,  and  is  termed  a  right  angle  when  the  two 
lines  are  perpendicular  to  each  other, 
an  acute  angle  when  it  is  less  or 
sharper  than  a  right  angle,  and  06- 
tuse  when  it  is  greater  than  a  right 
angle.  Thus,  in  Fig.  3, 

A  A  A  A  are  acute  angles, 

o  o  o  o  are  obtuse  angles,  R  R  R  R    AX^ 


Fig.3 


R  R 


are  right  angles. 

Polygons. 

A  polygon  is  a  portion  of  a  plane  bounded  by  straight  lines. 

A  triangle  is  a  polygon  of  three  sides. 

A  scalene  triangle  has  none  of  its  sides  equal;   an  isosceles  tri- 
angle has  two  of  its  sides  equal;    an  equi- 
lateral   triangle   has   all   three    of   its   sides 
equal. 

A  right-angled  triangle  is  one  which  has  a 
right   angle.     The  side   opposite   the   right 
angle  is  called  the  hypothenuse;  the  side  on 
which  the  triangle  is  supposed  to  stand  is  called  its  base,  and  the 
other  side,  its  altitude. 


Fig.  4. 


Fig.  5. 
Scalene  Triangle. 


Fig-  6.  Fig.   7. 

Isosceles  Triangle.   Equilateral  Triangle. 


38 


GEOMETRICAL   TERMS. 


A  quadrilateral  is  a  polygon  of  four  sides. 

Quadrilaterals  are  divided  into  classes,  as  follows, — the  trape- 
zium (Fig.  8),  which  has  no  two  of  its  sides  parallel;  the  trapezoid 
(Fig.  9),  which  has  two  of  its  sides  parallel;  and  the  parallelogram 
(Fig.  10),  which  is  bounded  by  two  pairs  of  parallel  sides. 


"\ 


\ 


Fig.  8.  Fig.  9.  Fig.  10. 

A  parallelogram  whose  sides  are  not  equal,  and  its  angles  not 
right  angles,  is  called  a  rhomboid  (Fig.  11) ;  when  the  sides  are  all 
equal,  but  the  angles  are  not  right  angles,  it  is  called  a  rhombus 
(Fig.  12);  and,  when  the  angles  are  right  angles,  it  is  called  a 
rectangle  (Fig.  13).  A  rectangle  whose  sides  are  all  equal  is 
called  a  square  (Fig.  14).  Polygons  whose  sides  are  all  equal  are 
called  regular. 


Fig-  II.  Fig.  12.  Fig.  13.  Fig.  14. 

Besides  the  square  and  equilateral  triangles,  there  are 
The  pentagon  (Fig.  15),  which  has  five  sides; 
The  hexagon  (Fig.  16),  which  has  six  sides; 
The  heptagon  (Fig.  17),  which  has  seven  sides; 
The  octagon  (Fig.  18),  which  has  eight  sides. 


Fig.  17. 


Fig.  18. 


Fig.  15.  Fig.  16. 

The  enneagon  has  nine  sides. 

The  decagon  has  ten  sides. 

The  dodecagon  has  twelve  sides. 

For  all  polygons,  the  side  upon  which  it  is  supposed  to  stand  is 
called  its  base;  the  perpendicular  distance  from  the  highest  side 
or  angle  to  the  base  (prolonged,  if  necessary)  is  called  the  altitude; 
arid  M  line  joining  any  two  angles  not  adjacent  is  called  a  diagonal. 


GEOMETRICAL  TERMS. 


39 


A  perimeter  is  the  boundary  line  of  a  plane  figure. 

A  circle  is  a  portion  of  a  plane  bounded  by  a  curve,  all  the  points 
of  which  are  equally  distant  from  a  point  within  called  the  centre 
(Fig.  19). 

The  circumference  is  the  curve  which  bounds  the  circle. 

A  radius  is  any  straight  line  drawn  from  the  centre  to  the  cir- 
cumference. 

Any  straight  line  drawn  through  the  centre  to  the  circumfer- 
ence on  each  side  is  called  a  diameter. 

An  arc  of  a  circle  is  any  part  of  its  circumference. 

A  chord  is  any  straight  line  joining  two  points  of  the  circumfer- 
ence, as  bd. 

A  segment  is  a  portion  of  the 
circle  included  bet  ween  the  arc  and 
its  chord,  as  A  in  Fig.  19. 

A  sector  is  the  space  included  be- 
tween an  arc  and  two  radii  drawn 
to  its  extremities,  as  B,  Fig.  19. 
In  the  figure,  ab  is  a  radius,  cd  a 
diameter,  and  db  is  a  chord  sub- 
tending  the  arc  bed.  A  tangent  is 
a  right  line  which  in  passing  a 


Fig.  19. 


curve  touches  without  cutting  it,  as  fg,  Fig.  19. 
Volumes. 

A  prism  is  a  volume  whose  ends  are  equal  and  parallel  poly- 
gons, and  whose  sides  are  parallelograms. 

A  prism  is  triangular,  rectangular,  etc.,  according  as  its  ends 
are  triangles,  rectangles,  etc. 

A  cube  is  a  rectangular  prism  all  of  whose  sides  are  squares. 

A  cylinder  is  a  volume  of  uniform  diameter,  bounded  by  a 
curved  surface  and  two  equal  and  parallel  circles. 

A  pyramid  is  a  volume  whose  base  is  a  poly- 
gon, and  whose  sides  are  triangles  meeting  in  a 
point  called  the  vertex. 

A  pyramid  is  triangular,  quadrangular,  etc., 
according  as  its  base  is  a  triangle,  quadrilateral, 
etc. 

A  cone  is  a  volume  whose  base  is  a  circle, 
from  which  the  remaining  surface  tapers  uni- 
formly to  a  point  or  vertex  (Fig.  20). 

Conic  sections  are  the  figures  made  by  a  plane  cutting  a  cone. 


Fig.  20. 


40 


MENSURATION. 


An  ellipse  is  the  section  of  a  cone  when  cut  by  a  plane  passing 
obliquely  through  both  sides,  as  at  ab,  Fig.  21. 

A  parabola  is  a  section  of  a  cone  cut  by  a  plane  parallel  to  its 
side,  as  at  cd. 

A  hyperbola  is  a  section  of  a  cone  cut  by  a  plane  at  a  greater 
angle  through  the  base  than  is  made  by  the  side  of  the  cone,  as 
at  eh. 

In  the  ellipse,  the  transverse  axis,  or 
long  diameter,  is  the  longest  line  that  ran 
be  drawn  through  it.  The  conjugate  axis, 
or  short  diameter,  is  a  line  drawn  through 
the  centre,  at  right  angles  to  the  long 
diameter. 

A  frustum  of  a  pyramid  or  cone  is  that 
which  remains  after  cutting  off  the  upper 
part  of  it  by  a  plane  parallel  to  the  base. 

A   sphere  is  a  volume    bounded    by  a 
curved   surface,   all  points   of   which  are 
equally  distant  from  a  point  within,  called  the  centre. 

Mensuration  treats  of  the  measurement  of  lines,  surfaces, 
and  volumes. 

RULES. 

To  compute  the  area  of  a  square,  a  rectangle,  a  rhombus,  or  a 

rhomboid. 

RULE. — Multiply  the  length  by  the  breadth  or  height;  thus, 
in  either  of  Figs.  22,  23,  24,  the  area=a&X&c. 


Fig.  20. 


Fig.23 


To  compute  the  area  of  a  triangle. 

c  RULE. — Multiply  the  base  by  the  alti- 

tude, and  divide  by  2;   thus,  in  Fig.  25, 

,,  „     ,        abXcd 

the  area   of   abc=  — 


d 
Fig.25 


-,   To  find  the  length  of  the  hypothenuse  of  a 
right-angled  triangle  when  both  s 
are  known. 


MENSURATION.— POLYGONS. 


41 


RULE. — Square  the  length  of  each  of  the  sides  making  the  right 
angle,  add  their  squares  together,  and  take 
the  square  root  of  their  sum.     Thus  (Fig.  26), 
the  length  of  ac  =  3,  and  of  bc=4;  then 

06=3X3  =  9  + (4X4)  =  9  + 16  =  25. 
\/25=5,     or    ab=5. 


To  find  the  length  of  the  base  or  altitude  of  a  right-angled  triangle 
when  the  length  of  the  hypothenuse  and  one  side  is  known. 

RULE. — From  the  square  of  the  length  of  the  hypothenuse 
subtract  the  square  of  the  length  of  the 
other  side,  and  take  the  square  root  of 
the  remainder. 
To  find  the  area  of  a  trapezium. 

RULE. — Multiply  the  diagonal  by 
the  sum  of  the  two  perpendiculars  fall- 
ing upon  it  from  the  opposite  fxngles, 
and  divide  the  product  by  2.  Or, 

abX(ce+di) 

— -= =  area  (Fig.  27). 


To  find  the  area  of  a  trapezoid  (Fig.  28). 

RULE. — Multiply  the  sum  of  the  two  par- 
allel sides  by  the  perpendicular  distance  be- 
tween them,  and  divide  the  product  by  2. 
To  compute  the  area  of  an  irregular  polygon. 

RULE. — Divide  the  polygon  into  triangles 
by  means  of  diagonal  lines,  and  then  add  to- 
gether the  areas  of  all  the  triangles,  as  A,  B, 
and  C  (Fig.  29). 

To  find  the  area  of  a  regular  polygon. 

RULE. — Multiply  the  length  of  a  side  by 
the  perpendicular  distance  to  the  centre  (as 
ao,  Fig.  30),  and  that  product  by  the  iiunibe 
of  sides,  and  divide  the  result  by  2. 

To  compute  the  area  of  a  regular  polygon  when 

the  length  of  a  side  only  is  given. 
RULE. — Multiply  the  square  of  the  side  by 
the  multiplier  opposite  the  name  of  the  poly- 
gon in  column  .1  of  the  following  table  : 


Fig.30 


42      MENSURATION.— POLYGONS  AND   CIRCLES. 


A. 

B. 

C. 

D. 

Radius  of 

Name  of  Polygon. 

No.  of 

Area. 

circum- 
scribing 

Length  of 
the  sides. 

Radius  of 
inscribed 

circle. 

circle. 

Triangle  

3 

0  433013 

0  5773 

1  732 

0  2887 

Tetragon       • 

4 

1 

0  7071 

1  4142 

0  5 

Pentagon  

5 

1  720477 

0  8506 

1   1756 

0  6882 

Hexagon  

6 

2.598076 

1 

1 

0  .  866 

Heptagon  

7 

3.633912 

1  .  1524 

0.8677 

1.0383 

Octagon 

8 

4  S98427 

1   3066 

0  7653 

1  2071 

Nonagon.  .     .  . 

0 

6  181824 

1  4619 

0  684 

1   3737 

Decagon  

10 

7  .  694209 

1   618 

0  618 

1  5383 

Undecagon  

11 

9  .  36564 

1.7747 

0.5634 

1.7028 

Dodecagon  

12 

11.196152 

1.9319 

0.5176 

1.866 

To  compute  the  radius  of  a  circumscribing  circle  when  the  length 

of  a  side  only  is  given. 

RULE. — Multiply  the  length  of  a  side  of  the  polygon  by  the 
number  in  column  B. 

EXAMPLE. — What  is  the  radius  of  a  circle  that  will  contain  a 
hexagon,  the  length  of  one  side  being  5  inches? 

Ans.  5X1  =  5  inches. 
To  compute  the  length  of  a  side  of  a  polygon  that  is  contained  in 

a  given  circle,  when  the  radius  of  the  circle  is  given. 
RULE. — Multiply  the  radius  of  the  circle  by  the  number  oppo- 
site the  name  of  the  polygon  in  column  C. 

EXAMPLE. — What  is  the  length  of  the  side  of  a  pentagon  con- 
tained in  a  circle  8  feet  in  diameter? 

Ans.  8  ft.  diameter  +  2=  4  ft.  radius,  4X1.1756  =  4.7024  ft. 
To  compute  the  length  of  a  side  of  a  regular  polygon,  when  the  radius 
of  the  inscribed  circle  is  given. 

RULE. — Divide  the  radius  of  "the  inscribed  circle  by  the  num- 
ber opposite  the  name  of  the  polygon  in  column  D. 
To  com.pute  the  radius  of  a  circle  that  can  lie  inscribed  in  a  given 

polygon,  when  the  length  of  a  side  is  given. 

RULE. — Multiply  the  length  of  a  side  of  the  polygon  by  the 
number  opposite  the  name  of  the  polygon  in  column  D. 

EXAMPLE. — What  is  the  radius  of  the  circle  that  can  be  in- 
scribed in  an  octagon,  the  length  of  one  side  being  6  inches. 

Ans.  6X1.2071  =  7.2426  inches. 

Circles. 

To  compute  the  circumference  of  a  circle. 

RULE. — Multiply  the  diameter  by  3.1416;   or,  for  most  pur- 
poses, by  3|  is  sufficiently  accurate. 


MENSURATION.—  CIRCLES.  43 

EXAMPLE.  —  What  is  the  circumference  of  a  circle  7  inches  in 
diameter? 

Ans.    7X3.1416  =  21.9912   inches,    or   7X3^=22   inches,   the 

error  in  this  last  being  0.0088  of  an  inch. 
To  find  the  diameter  of  a  circle  when  the  circumference  is  given. 

RULE.  —  Divide  the  circumference  by  3.1416,  or  for  a  very  close 
approximate  result  multiply  by  7  and  divide  by  22. 
To  find  the  radius  of  an  arc,  when  the  chord  and  rise  or  versed 
sine  are  given. 

RULE.  —  Square  one-half  the  chord,  also  square  the  rise;  divide 
their  sum  by  twice  the  rise  ;   the  result  will 
be  the  radius. 

EXAMPLE.  —  The  length  of  the  'chord  ac, 
Fig.  30-|,  is  48  inches,  and  the  rise,  bo,  is  6 
inches.  What  is  the  radius  of  the  arc? 

' 


t    .  . 

Ans.  Rad=  —  ^  -  =  -~rp>  —  =  51  ms 
2bo  12 

To  find  the  rise  or  versed  sine  of  a  circular  arc,  when  the  chord 
and  radius  are  given. 

RULE.  —  Square  the  radius;  also  square  one-half  the  chord; 
subtract  the  latter  from  the  former,  and  take  the  square  root  of 
the  remainder.  Subtract  the  result  from  the  radius,  and  the 
remainder  will  be  the  rise. 

EXAMPLE.  —  A  given  arc  has  a  radius  of  51  inches,  and  a 
chord  of  48  inches.  What  is  the  rise? 

Ans.  Rise  =  rad  -  Vrac!^-~icriord2=  51  -  \/2601  -  576 

=  51—45=6  inches  =  rise. 
To  compute  the  area  of  a  circle. 

RULE.  —  Multiply  the  square,  of  the  diameter  by  0.7854,  or  mul- 
tiply the  square  of  the  radius  by  3.1416. 

EXAMPLE.  —  What  is  the  area  of  a  circle  10  inches  in  diameter? 

Ans.  10X10X0.7854=78.54  square  inches,  or  5X5X3.1416 
=  78.54  square  inches. 

The  following  tables  will  be  found  very  convenient  for  finding 
the  circumference  and  area  of  circles. 


44  MENSURATION.— CIRCLES. 

AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(For  Diameters  from  j0  to  100,  advancing  by  Tenths.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum  . 

Dia. 

Area. 

Circum. 

0.0 

5.0 

19.6350 

15.7080 

10.0 

78.5398 

31.4159 

.1 

0.007854 

0.31416 

.1 

20.4282 

16.0221 

.1 

80.1185 

31.7301 

.2 

0.031416 

0.62832 

2 

21.2372 

16.3363 

.2 

81.7128 

32.0442 

.3 

0.070086 

0.94248 

!3 

22.0618 

16.6504 

.3 

83.3229 

32.3584 

.4 

0.12566 

1.2566 

.4 

22.9022 

16.9646 

.4 

84.9487 

32.6726 

.5 

0.19635 

1.5708 

.5 

23.7583 

17.2788 

.5 

86.5901 

32.9867 

.6 

0.28274 

1.8850 

.6 

24.6301 

17.5929 

.6 

88.2473 

33.3009 

.7 

0.38485 

2.1991 

.7 

25.5176 

17.9071 

.7 

89.9202 

33.6150 

.8 

0.50266 

2.5133 

.8 

26.4208 

18.2212 

.8 

91.6088 

33.9292 

.9 

0.63617 

2.8274 

.9 

27.3397 

18.5354 

.9 

93.3132 

34.2434 

1.0 

0.7854 

3.1416 

6.0 

28.2743 

18.8496 

11.0 

95.0332 

34.5575 

.1 

0.9503 

3.4558 

.1 

29.2247 

19.1637 

.1 

96.7689 

34.8717 

.2 

1.1310 

3.7699 

.2 

30.1907 

19.4779 

.2 

98.5203 

35.1858 

.3 

1.3273 

4.0841 

.3 

31.1725 

19.7920 

.3 

100.2875 

35.5000 

.4 

1.5394 

4.3982 

.4 

32.1699 

20.1062 

.4 

102.0703 

35.8142 

.5 

1.7671 

4.7124 

.5 

33.1831 

20.4204 

.5 

103.8689 

36.1283 

.6 

2.0106 

5.0265 

.6 

34.2119 

20.7345 

.6 

105.6832 

36.4425 

.7 

2.2698 

5.3407 

.7 

35.2565 

21.0487 

.7 

107.5132 

36.7566 

.8 

2.5447 

5.6549 

.8 

36.3168 

21.3628 

.8 

109.3588 

37.0708 

.9 

2.8353 

5.9690 

.9 

37.3928 

21.6770 

.9 

111.2202 

37.3850 

2.0 

3.1416 

6.2832 

7.0 

38.4845 

21.9911 

12.0 

113.0973 

37.6991 

.1 

3.4636 

6.5973 

.1 

39.5919 

22.3053 

.1 

114.9901 

38.0133 

.2 

3.8013 

6.9115 

.2 

40.7150 

22.6195 

.2 

116.8987 

38.3274 

.3 

4.1548 

7.2257 

.3 

41.8539 

22.9336 

.3 

118.8229 

38.6416 

.4 

4.5239 

7.5398 

.4 

43.0084 

23.2478 

.4 

120.7628 

38.9557 

.5 

4.9087 

7.8540 

.5 

44.1786 

23.5619 

.5 

122.7185 

39.2699 

.6 

5.3093 

8.1681 

.6 

45.3646 

23.8761 

.6 

124.6898 

39.5841 

.7 

5.7256 

8.4823 

.7 

46.5663 

24.1903 

.7 

126.6769 

39.8982 

.8 

6.1575 

8.7965 

.8 

47.7836 

24.5044 

.8 

128.6796 

40.2124 

.9 

6.6052 

9.1106 

.9 

49.0167 

24.8186 

.9 

130.6981 

40,5265 

3.0 

7.0686 

9.4248 

8.0 

50.2655 

25.1327 

13.0 

132.7323 

40.8407 

.1 

7.5477 

9.7389 

.1 

51.5300 

25.4469 

.1 

134.7822 

41.1549 

.2 

8.0425 

10.0531 

.2 

52.8102 

25.7611 

.2 

136.8478 

41.4690 

.3 

8.5530 

10.3673 

.3 

54.1061  ' 

26.0752 

.3 

138.9291 

41.7832 

.4 

9.0792 

10.6814 

.4 

55.4177 

26.3894 

.4 

141.0261 

42.0973 

.5 

9.6211 

10.9956 

.5 

56.7450 

26.7035 

.5 

143.1388 

42.4115 

.6 

10.1788 

11.3097 

.6 

58.0880 

27.0177 

.6 

145.2672 

42.7257 

.7 

10.7521 

11.6239 

.7 

59.4468 

27.3319 

.7 

147.4114 

43.0398 

.8 

11.3411 

11.9381 

.8 

60.8212 

27.6460 

.8 

149.5712 

43.3540 

.9 

11.9459 

12.2522 

.9 

62.2114 

27.9602 

.9 

151.7468 

43.6681 

4.0 

12.5664 

12.5664 

9.0 

63.6173 

28.2743 

14.0 

153.9380 

43.9823 

.1 

13.2025 

12.8805 

.1 

65.0388 

28.5885 

.1 

156.1450 

44.2965 

.2 

13.8544 

13.1947 

.2 

66.4761 

28.9027 

.2 

158.3677 

44.6106 

.3 

14.5220 

13.5088 

.3 

67.9291 

29.2168 

.3 

160.6061 

44.9248 

.4 

15.2053 

13.8230 

.4 

69.3978 

29.5310 

.4 

162.8602 

45.2389 

.5 

15.9043 

14.1372 

.5 

70.8822 

29.8451 

.5 

165.1300 

45.5531 

.6 

16.6190 

14.4513 

.6 

72.3823 

30.1593 

.6 

167.4155 

45.8673 

.7 

17.3494 

14.7655 

.7 

73.8981 

30.4734 

.7 

169.7167 

46.1814 

.8 

18.0956 

15.0796 

.8 

75.4296 

30.7876 

g 

172.0336 

46.4956 

.9 

18.8574 

15.3938 

.9 

76.9769 

31.1018 

]9 

174.3662 

46.8097 

MENSURATION.— CIRCLES. 
AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Tenths.) 


45 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

15.0 

176.7146 

47.1239 

20.0 

314.1593 

62.8319 

25.0 

490.8739 

78.5398 

.1 

179.0786 

47.4380 

.1 

317.3087 

63.1460 

.1 

494.8087 

7S.8540 

.2 

181.4584 

47.7522 

.2 

320.4739 

63.4602 

.2 

498.7592 

79.1681 

.3 

183.8539 

48.0664 

.3 

323.6547 

63.7743 

.3 

502.7255 

79.4823 

.4 

186.2050 

48.3805 

.4 

326.8513 

64.0885 

.4 

506.7075 

79.7965 

.5 

188.6919 

48.6947 

.5 

330.0636 

64.4026 

.5 

510.7052 

80.1106 

.6 

191.1345 

49.0088 

.6 

333.2916 

64.7168 

.6 

514.7185 

80.4248 

.7 

193.5928 

49.3230 

.7 

336.5353 

65.0310 

.7 

518.7476 

80.7389 

.8 

196.0668 

49.6372 

.8 

339.7947 

65.3451 

.8 

522.7924 

81.0531 

.9 

198.5565 

49.9513 

.9 

343.0698 

65.6593 

.9 

526.8529 

81.3672 

16.0 

201.0619 

50.2655 

21.0 

346.3606 

65.9734 

26.0 

530.9292 

81.6814 

.1 

203.5831 

50.5796 

.1 

349.6671 

66.2876 

.1 

535.0211 

81.9956 

.2 

206.1199 

50.8938 

.2 

352.9891 

66.6018 

.2 

539.1287 

82.3097 

.3 

208.6724 

51.2030 

.3 

356.3273 

66.9159 

.3 

543.2521 

82.6239 

.4 

211.2407 

51.5221 

.4 

359.6809 

67,2301 

.4 

547.3911 

82.9380 

.5 

213.8246 

51.8363 

.5 

303.0503 

67.5442 

.5 

551.5459 

83.2522 

.6 

216.4243 

52.1504 

.6 

366.4354 

67.8584 

.6 

555.7163 

83.5664 

.7 

219.0397 

52.4646 

.7 

369.S361 

68.1726 

.7 

559.9025 

83.8805 

.3 

221.6708 

52.7788 

.8 

373.2526 

68.4867 

.8 

564.1044 

84.1947 

.9 

224.3176 

53.0929 

.9 

376.6848 

68.8009 

.9 

568.3220 

84.5088 

17.0 

226.9801 

53.4071 

22.0 

380.1327 

69.1150 

27.0 

572.5553 

84.8230 

.1 

229.6583 

53.7212 

.1 

383.5963 

69.4292 

.1 

576.8043 

85.1372 

.2 

232.3522 

54.0354 

.2 

387.0756 

69.7434 

.2 

581.0690 

85.4513 

.3 

235.0618 

54.3496 

.3 

390.5707 

70.0575 

.3 

585.3494 

85.7655 

.4 

237.7871 

54.6637 

.4 

394.0814 

70.3717 

.4 

589.6455 

86.0796 

.5 

240.5282 

54.9779 

.5 

397.6078 

70.6858 

.5 

593.9574 

86.3938 

.6 

243.2849 

55.2920 

.6 

401.1500 

71.0000 

.6 

598.2849 

86.7080 

.7 

246.0574 

55.6002 

.7 

404.7078 

71.3142 

.7 

602.6282 

87.0221 

.8 

248.8456 

55.9203 

.8 

408.2814 

71.6283 

.8 

606.9871 

87.3363 

.9 

251.6494 

56.2345 

.9 

411.8707 

71.9425 

.9 

611.3618 

87.6504 

18.0 

254.4690 

56.5486 

23.0 

415.4756 

72.2566 

28.0 

615.7522 

87.9646 

1 

257.3043 

56.8628 

.1 

419.0963 

72.5708 

.1 

620.1582 

88.2788 

'.2 

260.1553 

57.1770 

.2 

422.7327 

72.8849 

.2 

624.5800 

88.5929 

.3 

263.0220 

57.4911 

.3 

426.3848 

73.1991 

.3 

629.0175 

88.9071 

.4 

265.9044 

57.8053 

.4 

430.0526 

73.5133 

.4 

633.4707 

89.2212 

.5 

268.8025 

58.1195 

.5 

433.7361 

73.8274 

.5 

637.9397 

89.5354 

.6 

271.7164 

58.4336 

A 

437.4354 

74.1416 

.6 

642.4243 

89.8495 

.7 

274.6459 

58.7478 

.7 

441.1503 

74.4557 

.7 

646.9246 

90.1637 

.8 

277.5911 

59.0619 

.8 

444.8809 

74.7699 

.8 

651.4407 

90.4779 

.9 

280.5521 

59.3761 

.9 

448.6273 

75.0841 

.9 

655.9724 

90.7920 

19.0 

283.5287 

59.6903 

24.0 

452.3893 

75.3982 

29.0 

660.5199 

91.1062 

.1 

286.5211 

60.0044 

.1 

456.1671 

75.7124 

.1 

665.0830 

91.4203 

.2 

289.5292 

60.3186 

.2 

459.9606 

76.0265 

2 

669.6619 

91.7345 

.3 

292.5530 

60.6327 

.3 

463.7698 

76.3407 

!s 

674.2565 

02.0487 

.4 

295.5925 

60.9469 

.4 

467,5947 

76.6549 

.4 

678.8668 

92.3628 

.5 

298.6477 

61.2611 

.5 

471.4352 

76.9690 

.5 

683.4928 

92.6770 

.6 

301.7186 

61.5752 

.6 

475.2916 

77.2832 

.6 

688.1345 

92.9911 

.7 

304.8052 

61.8894 

.7 

479.1636 

77.5973 

.7 

692.7919 

93.3053 

.8 

307.9075 

62.2035 

.8 

483.0513 

77.9115 

.8 

697.4650 

93.6195 

.9 

311.0255 

62.5177 

.9 

486.9547 

78.2257 

.9 

702.1538 

93.9336 

46 


MENSURATION.— CIRCLES. 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Tenths.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

30.0 

706.8583 

94.2478 

35.0 

962.1128 

109.9557 

40.0 

1256.6371 

125.6637 

.1 

711.5786 

94.5619 

.1 

967.6184 

110.2699 

.1 

1262.9281 

125.9779 

.2 

716.3145 

94.8761 

.2 

973.1397 

110.5841 

.2 

1269.2348 

126.2920 

.3 

721.0662 

95.1903 

.3 

978.6768 

110.8982 

.3 

1275.5573 

126.6062 

A 

725.8336 

95.5044 

.4 

984.2296 

111.2124 

.4 

1281.8955 

126.9203 

.5 

730.6167 

95.8186 

.5 

989.7980 

111.5265 

.5 

1288.2493 

127.2345 

.6 

735.4154 

96.1327 

.6 

995.3822 

111.8407 

.61  1294.6189 

127.5487 

.7 

740.2299 

96.4469 

.7 

1000.9821 

112.1549 

.7 

1301.0042 

127.8628 

.8 

745.0601 

96.7611 

.8 

1006.5977 

112.4690 

.8 

1307.4052 

128.1770 

.9 

749.9060 

97.0752 

.9 

1012.2290 

112.7832 

.9 

1313.8219 

128.4911 

31.0 

754.7676 

97.3894 

36.0 

1017.8760 

113.0973 

41.0 

1320.2543 

128.8053 

.1 

759.6450 

97.7035 

.1 

1023.5387 

113.4115 

.1 

1326.7024 

129.1195 

.2 

764.5380 

98.0177 

.2 

1029.2172 

113.7257 

.2 

1333.1663 

129.4336 

.3 

769.4437 

98.3319 

.3 

1034.9113 

114.0398 

.3 

1339.6458 

129.7478 

.4 

774.3712 

98.6460 

.4 

1040.6212 

114.3540 

.4 

1346.1410 

130.0619 

.5 

779.3113 

98.9602 

.5 

1046.3467 

114.6681 

.5 

1352.6520 

130.3761 

.6 

784.2672 

99.2743 

.6 

1052.0880 

114.9823 

.6 

1359.1786 

130.6903 

.7 

789.2388 

99.5885 

.7 

1057.8449 

115.2965 

.7 

1365.7210 

131.0044 

.8 

794.2260 

99.9026 

.8 

1063.6176 

115.610G 

.8 

1372.2791 

131.3186 

.9 

799.2290 

100.2168 

.9 

1069.4060 

115.9248 

.9 

1378.8529 

131.6327 

32.0 

804.2477 

100.5310 

37.0 

1075.2101 

116.2389 

42.0 

1385.4424 

131.9469 

.1 

809.2821 

100.8451 

.1 

1081.0299 

116.5531 

.1 

1392.0476 

132.2611 

.2 

814.3322 

101.1593 

.2 

1086.8654 

116.8672 

.2 

1398.6685 

1S2.5752 

.3 

819.3980 

101.4734 

.3 

1092.7166 

117.1814 

.3 

1405.3051 

132.8894 

.4 

824.4796 

101.7876 

.4 

1098.5835 

117.4956 

.4 

1411.9574 

133.2035 

.5 

829.5768 

102.1018 

.5 

1104.4662 

117.8097 

.5 

1418.6254 

133.5177 

.6 

834.6898 

102.4159 

.6 

1110.3645 

118.1239 

.6 

1425.3092 

133.8318 

.7 

839.8185 

102.7301 

.7 

1116.2786 

118.4380 

.7 

1432.0086 

134.1460 

.8 

844.9628 

103.0442 

.8 

1122.2083 

118.7522 

.8 

1438.7238 

134.4602 

.9 

850.1229 

103.3584 

.9 

1128.1538 

119.0664 

.9 

1445.4546 

134.7743 

33.0 

855.2986 

103.6726 

38.0 

1134.1149 

119.3805 

43.0 

1452.2012 

135.0885 

.1 

860.4902 

103.9867 

.1 

1140.0918 

119.6947 

.1 

1458.9635 

135.4026 

'  .2 

865.6973 

104.3009 

9 

1146.0844 

120.0088 

.2 

1465.7415 

135.7168 

.3 

870.9202 

104.6150 

!3 

1152.0927 

120.3230 

.3 

1472.5352 

136.0310 

.4 

876.1588 

104.9292 

.4 

1158.1167 

120.6372 

.4 

1479.3446 

136.3151 

.5 

881.4131 

105.2434 

.5 

1164.1564 

120.9513 

.5 

1486.1697 

136.6593 

.6 

886.6831 

105.5575 

.6 

1170.2118 

121.2655 

.6 

1493.0105 

'  136.9734 

.7 

891.9688 

105.8717 

.7 

1176.2830 

121.5796 

.7 

1499.8670 

137.2876 

.8 

897.2703 

106.1858 

.8 

1182.3698 

121.8938 

.8 

1506.7393 

137.0018 

.9 

902.5874 

106.5000 

.9 

1188.4724 

122.2080 

.9 

1513.6272 

137.9159 

34.0 

907.9203 

106.8142 

39.0 

1194.5906 

122.5221 

44.0 

1520.5308 

138.2301 

.1 

913.2688 

107.1283 

.1 

1200.7246 

122.8363 

.1 

1527.4502 

138.5442 

.2 

918.6331 

107.4425 

2 

1206.8742 

123.1504 

.2 

1534.3853 

138.8584 

.3 

924.0131 

107.7566 

!3 

1213.0396 

123.4646 

.3 

1541.3360 

139.1726 

.4 

929.4088 

108.0708 

.4 

1219.2207 

123.7788 

.4 

1548.3025 

139.4867 

.5 

934.8202 

108.3849 

.5 

1225.4175 

124.0929 

.5 

1555.247 

139.8009 

.6 

940.2473 

108.6991 

.6 

1231.6300 

124.4071 

.6 

1562.2826 

140.1153 

.7 

945.6901 

109.0133 

.7 

1237.8582 

124.7212 

.7 

1569.2962 

140.4292 

.8 

951.1486 

109.3274 

.8 

1244.1021 

125.035-1 

.8 

1576.3255 

140.7434 

.9 

956.6228 

109.641T 

.9 

1250.3617 

125.3495 

.9 

1583.3706 

141.0575 

MENSURATION.— CIRCLES. 


47 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Tenths.) 


Dia. 

Area. 

Circum 

Dia 

Area. 

Circum 

Dia 

Area. 

Circum. 

45.0 

1590.4313 

141.3717 

50.0 

1963.4954 

157.0796 

55.0 

2375.8294 

172.7876 

.1 

1597.5077 

141.6858 

.1 

1971.3572 

157.3938 

.1 

2384.4767 

173.1017 

.2 

1604.5999 

142.0000 

.2 

1979.2348 

157.7080 

.2 

2393.1396 

173.4159 

3 

1611.7077 

142.3142 

.3 

1987.1280 

158.0221 

.3 

2401.8183 

173.7301 

.4 

1618.8313 

142.6283 

.4 

1995.0370 

158.3363 

.4 

2410.5126 

174.0442 

.5 

1625.9705 

142.9425 

.5 

2002.9617 

158.6504 

.5 

2419.2227 

174.3584 

.6 

1633.1255 

143.2566 

.6 

2010.9020 

158.9646 

.6 

2427.9485 

174.6726 

.7 

1640.2962 

143.5708 

.7 

2018.8581 

159.2787 

.7 

2436.6899 

174.9867 

.8 

1647.4826 

143.8849 

.8 

2026.8299 

159.5929 

.8 

2445.4471 

175.3009 

.9 

1654.6847 

144.1991 

.9 

2034.8174 

159.9071 

.9 

2454.2200 

175.6150 

46.0 

1661.9025 

144.5133 

51.0 

2042.8206 

160.2212 

56.0 

2463.0086 

175.9292 

.1 

1669.1360 

144.8274 

.1 

2050.8395 

160.5354 

.1 

2471.8130 

176.2433 

.2 

1676.3853 

145.1416 

2 

2058.8742 

160.8495 

2 

2480.6330 

176.5575 

.3 

1683.6502 

145.4557 

.*3 

2066.9245 

161.1637 

!3 

2489.4687 

176.8717 

.4 

1690.9308 

145.7699 

.4 

2074.9905 

161.4779 

.4 

2498.3201 

177.1858 

.5 

1698.2272 

146.0841 

.5 

2083.0723 

161.7920 

.5 

2507.1873 

177.5000 

.6 

1705.5392 

146.3982 

.6 

2091.1697 

162.1062 

.6 

2516.0701 

177.8141 

.7 

1712.8670 

146.7124 

.7 

2099.2829 

162.4203 

.7 

2524.9687 

178.1283 

.8 

1720.2105 

147.0265 

.8 

2107.4118 

162.7345 

.8 

2533.8830 

178.4425 

.9 

1727.5697 

147.3407 

.9 

2115.5563 

163.0487 

.9 

2542.8129 

178.7566 

47.0 

1734.9445 

147.6550 

52.0 

2123.7166 

163.3628 

57.0 

2551.7586 

179  0708 

.1 
2 

1742.3351 
1749.7414 

147.9690 
148.2832 

.1 

.2 

2131.8926 
2140.0843 

163.6770 
163.9911 

.1 
.2 

2560.7200 
2569.6971 

179.3849 
179.6991 

!3 

1757.1635 

148.5973 

.3 

2148.2917 

164.3053 

.3 

2578.6899 

180  013, 

.4 

1764.6012 

148.9115 

.4 

2156.5149 

164.6195 

.4 

2587.6985 

180!3274 

.5 

.6 

.7 
.8 
.9 

1772.0546 
1779.5237 
1787.0086 
1794.5091 
1802.0254 

149.2257 
149.5398 
149.8540 
150.1681 
150.4823 

.5 

.6 

.7 
.8 
.9 

2164.7537 
2173.0082 

2181.2785 
2189.5644 
2197.8661 

164.9336 
165.2479 
165.5619 
165.8761 
166.1903 

.5 

.6 
.7 
.8 
.9 

2596.7227 
2605.7626 
2614.8183 
2623.8896 
2632.9767 

180.6416 
180.955? 
181.2699 
181.5841 
181.8982 

48.0 
.1 
.2 
.3 
.4 

1809.5574 
1817.1050 
1824.6684 
1832.2475 
1839.8423 

150.7964 
151.1106 
151.4248 
151.7389 
152.0531 

53.0 
.1 
.2 
.3 
.4 

2206.1834 
2214.5165 
2222.8653 
2231.2298 
2239.6100 

166.5044 
166.8186 
167.1327 
167.4469 
167.7610 

58.0 
.1 
.2 
.3 

.4 

2642.0794 
2651.1979 
2660.3321 
2669.4820 
2678.6476 

182.2124 
182.5265 
182.8407 
183.1549 
183.4690 

.5 

.6 

.7 
.8 
.9 

1847.4528 
1855.0790 
1862.7210 
1870.3786 
1878.0519 

152.3672 
152.6814 
152.9956 
153.3097 
153.6239 

.5 

.6 
.7 
.8 
.9 

2248.0059 
2256.4175 
2264.8448 
2273.2879 
2281.7466 

168.0752 
168.3894 
168.7035 
169.0177 
169.3318 

.5 

.6 

'  .7 
.8 
.9 

2687^8289 
2697.0259 
2706.2386 
2715.4670 
2724.7112 

183.7332 
184.0973 
184.4115 
184.7256 
185.0398 

49.0 
.1 
.2 
.3 
.4 

1885.7409 
1893.4457 
1901.1662 
1908.9024 
1916.6543 

153.9380 
154.2522 
154.5664 
154.8805 
155.1947 

54.0 
.1 
.2 
.3 

.4 

2290.2210 
2298.7112 
2307.2171 
2315.7386 
2324.2759 

169.6460 
169.9602 
170.2743 
170.5885 
170.9026 

59.0 
.1 
.2 
.3 
.4 

2733.9710 
2743.2466 
2752.5378 
2761.8448 
2771.1675 

185.3540 

185.6681 
185.9823 
186.2964 
186.6106 

.5 

.6 
.7 
.8 
.9 

1924.4218 
1932.2051 
1940.0042 
1947.8189 
1955.6493 

155.5088 
155.8230 
156.1372 
156.4513 
156.7655 

.5 

.6 
.7 
.8 
.9 

2332.8289 
2341.3976 
2349.9820 
2358.5821 
2367.1979 

171.2168 
171.5310 
171.8451 
172.1593 
172.4735 

.5 
.6 

.7 
.8 
.9 

2780.5058 
2789.8599 
2799.2297 
2808.6152 
2818.0165 

186.9248 
187.2389 
187.5531 
187.8672 
188.1814 

48 


MENSURATION.— CIRCLES. 


AREAS  AND   CIRCUMFERENCES   OF  CIRCLES. 

(Advancing  by  Tenths.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum 

Dia 

Area. 

Circum. 

GO.O 

2827.4334 

188.4956 

65.0 

3318.3072 

204.2035 

70.0 

3848.4510 

219.9115 

.1 

2836.8660 

188.8097 

.1 

3328.5253 

204.5176 

.1 

3859  4544 

220  2251 

.2 
.3 
.4 

2846.3144 

2855.7784 
2865.2582 

189.1239 
189.4380 

189.7522 

.2 
.3 
.4 

3338.7590 
3349.0085 
3359.273f 

204.8318 
205.1460 
205.4602 

.2 
.3 
.4 

3870.4736 
3881.5084 
3892.5590 

220!5398 
220.8540 
221.1681 

.5 

.6 

.7 

2874.7530 
2884.2648 
2893.7917 

190.0664 
190.3805 
190.6947 

.5 
.6 

.7 

3369.5545 
3379.8510 
3390.1633 

205.7743 
206.0885 
206.4026 

.5 

.6 

.7 

3903.6252 
3914.7072 
3925.8049 

221.4823 
221.7964 
222  1106 

.8 

2903.3343 

191.0088 

.8 

3400.4913 

206.7168 

.8 

3936.9182 

222.4248 

.9 

2912.8926 

191.3230 

.9 

3410.8350 

207.0310 

.9 

3948.0473 

222.7389 

61.0 

2922.4666 

191.6372 

66.0 

3421.1944 

207.3451 

71.0 

3959.1921 

223.0531 

.1 

2932.0563 

191.9513 

.1 

3431.5695 

207.6593 

.1 

3970.3526 

223.3672 

.2 

2941.6617 

192.2655 

.2 

3441.9603 

207.9734 

.2 

3981.5289 

223.6814 

.3 

2951.2828 

192.5796 

.3 

3452.3669 

208.287o 

.3 

3992.7208 

223.9956 

.4 

2960.9197 

192.8938 

.4 

3462.789 

208.6017 

.4 

4003.9284 

224.3097 

.5 

2970.5722 

193.2079 

.5 

3473.227C 

208.9159 

.5 

4015.1518 

224.6239 

.6 

2980.2405 

193.5221 

.6 

3483.6807 

209.2301 

.6 

4026.3908 

224.9380 

.7 

2989.9244 

193.8363 

.7 

3494.1500 

209.5442 

.7 

4037.6456 

225.2522 

.8 

2999.6241 

194.1504 

.8 

3504.635 

209.8584 

.8 

4048.9160 

225.5664 

.9 

3009.3395 

194.4646 

.9 

3515.1359 

210.1725 

.9 

4060.2022 

225.3805 

62.0 

3019.0705 

194.7787 

67.0 

3525.6524 

210.4867 

72.0 

4071.5041 

226.1947 

.1 

3028.8173 

195.0929 

.1 

3536.1845 

210.8009 

.1 

4082.8217 

226.5088 

.2 

3038.5798 

195.4071 

.2 

3546.7324 

211.1150 

.2 

4094.1550 

226.8230 

.3 

3048.3580 

195.7212 

.3 

3557.2960 

211.4292 

.3 

4105.5040 

227.1371 

.4 

3058.1520 

196.0354 

.4 

3567.8754 

211.7433 

.4 

4116.8687 

227.4513 

.5 

3067.9616 

196.3495 

.5 

3578.4704 

212.0575 

.5 

4128.2491 

227.7655 

.6 

3077.7869 

196.6637 

.6 

3589.0811 

212.3717 

.6 

4139.6452 

228.0796 

.7 

3087.6279 

196.9779 

.7 

3599.7075 

212.6858 

.7 

4151.0571 

228.3938 

.8 

3097.4847 

197.2920 

.8 

3610.3497 

213.0000 

.8 

4162.484( 

228.7079 

.9 

3107.3571 

197.6062 

.9 

3621.0075 

213.3141 

.9 

4173.9279 

229.0221 

63.0 

3117.2453 

197.9203 

68.0 

3631.6811 

213.6283 

73.0 

4185.3868 

229.3363 

.1 

3127.1492 

198.2345 

.1 

3642.3704 

213.9425 

.1 

4196.8615 

229.6504 

.2 

3137.0688 

198.548" 

.2 

3653.0754 

214.256( 

2 

4208.3519 

229.9646 

.3 

3147.0040 

198.8628 

.3 

3663.7960 

214.5708 

i3 

4219.8579 

230.2787 

.4 

3156.9550 

199.1770 

.4 

3674.5324 

214.8849 

.4 

4231.3797 

230.5929 

.5 

3166.9217 

199.4911 

.5 

3685.2845 

215.1991 

.5 

4242.9172 

230.9071 

0 

3176.9043 

199.8053 

.6 

3696.0523 

215.5133 

.6 

4254.4704 

231.2212 

.7 

3186^9023 

200.1105 

.7 

3706.8359 

215.8274 

.7 

4266.0394 

231.5354 

g 

3196  9161 

200  4336 

.8 

3717.6351 

216.1416 

.8 

4277.6240 

231.8495 

.'9 

3208.'9456 

200.7478 

.9 

3728.4500 

216.4556 

.9 

4289.2243 

232.1637 

64.0 
1 

3216.9909 
3227.0518 

201.0620 
201.3761 

69.0 
.1 

3739.2807 
3750.1270 

216.7699 
217.0841 

74.0 
.1 

4300.8403 
4312.4721 

232.4779 
232.7920 

%2 

3237.1285 

201.6902 

.2 

3760.9891 

217.3982 

.2 

4324.1195 

233.1062 

3 

3247.2222 

202  0044 

.3 

3771.8668 

217.7124 

.3 

4335.7827 

233.4203 

.'4 

3257.3289 

202.3186 

.4 

3782.7603 

218.0265 

.4 

4347.4616 

233.7345 

5 

3267  4527 

202.6327 

.5 

3793.6695 

218.3407 

.5 

4359.1562 

234.0487 

.6 

7 

3277.5922 
3287.7474 

202.9469 
203.2610 

.6 

.7 

3804.5944 
3815.5350 

218.6548 
218.9690 

.6 

.7 

4370.8664 
4382.5924 

234.3628 
234.6770 

is 

.9 

3297.9183 
3308.1049 

203.5752 
203.889-1 

.8 
.9 

3826.4913 
3837.4633 

219.2832 
219.5973 

.8 
.9 

4394.3341 
4406.0916 

234.9911 
235.3053 

MENSURATION.— CIRCLES. 


40 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Tenths.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

75.0 

4417.8647 

235.6194 

80.0 

5026.5482 

251.3274 

85.0 

5674.5017 

267.0354 

4429.6535 

235.9336 

.1 

5039.1225 

251.6416 

.1 

5687.8614 

267.3495 

]2 

4441.4580 

236.2478 

.2 

5051.7124 

251.9557 

.2 

5701.2367 

267.6637 

.3 

4453.2783 

236.5619 

.3 

5064.3180 

252.2699 

.3 

5714.6277 

267.9779 

.4 

4465.1142 

236.8761 

.4 

5076.9394 

252.5840 

.4 

5728.0345 

268.2920 

.5 

4476.9659 

237.1902 

.5 

5089.5764 

252.8982 

.5 

5741.4569 

26,8.6062 

.6 

448S.S332 

237.5044 

.6 

5102.2292 

253.2124 

.6 

5754.8951 

268.9203 

.7 

4500.7163 

237.8186 

.7 

5114,8977 

253.5265 

.7 

5768.3490 

269.2345 

.8 

4512.6151 

238.1327 

.8 

5127.5819 

253.8407 

.8 

5781.8185 

269.5486 

.0 

4524.5296 

238.4469 

.9 

5140.2818 

254.1548 

.9 

5795.3038 

269.8628 

76.0 

4536.4598 

238.7610 

81.0 

5152.9973 

254.4690 

86.0 

5808.8048 

270.1770 

.1 

4548.4057 

239.0752 

.1 

5165.7287 

254.7832 

.1 

5822.3215 

270.4911 

.2 

4560.3673 

239.3894 

.2 

5178.4757 

255.0973 

.2 

5835.8539 

270.8053 

.3 

4572.3446 

239.7035 

.3 

5191.2384 

255.4115 

.3 

5849.4020 

271.1194 

.4 

4584.3377 

240.0177 

.4 

5204.0168 

255.7256 

.4 

5862.9659 

271.4336 

.5 

4596.3464 

240.3318 

.5 

5216.8110 

256.0398 

.5 

5876.5454 

271.7478 

.6 

4608.3708 

240.6460 

.6 

5229.6208 

256.3540 

.6 

5890.1407 

272.0619 

.7 

4620.4110 

240.9602 

.7 

5242.4463 

256.6681 

.7 

5903.7516 

272.3761 

.8 

4632.4669 

241.2743 

.8 

5255.2876 

256.9823 

.8 

5917.3783 

272.6902 

.9 

4644.5384 

241.5885 

.9 

5268.1446 

257.2966 

.9 

5931.0206 

273.0044 

77.0 

4656.6257 

211.9026 

82.0 

5281.0173 

257.6106 

87.0 

5944.6787 

273.3186 

.1 

4668.7287 

242.2168 

.1 

5293.9056 

257.9247 

.1 

5958.3525 

273.6327 

.2 

4680.8474 

242.5310 

.2 

5306.8097 

258.2389 

.2 

5972.0420 

273.9469 

.3 

4692.9818 

242.8451 

.3 

5319.7295 

258.5531 

.3 

5985.7472 

274.2610 

.4 

4705.1319 

243.1592 

.4 

5332.6650 

258.8672 

.4 

5999.4681 

274.5752 

.5 

4717.2977 

243.4734 

5 

5345.6162 

259.1814 

.5 

6013.2047 

274.8894 

.6 

4729.4792 

243.7876 

.6 

5358.5832 

259.4956 

.6 

6026.9570 

275.2035 

.7 

4741.6765 

244.1017 

.7 

5371.5658 

259.8097 

.7 

6040.7250 

275.5177 

.8 

4753.8894 

244.4159 

.8 

5384.5641 

260.1239 

.8 

6054.5088 

275.8318 

.9 

4766.1181 

244.7301 

.9 

5397.5782 

260.4380 

.9 

6068.3082 

276.1460 

7S.O 

4778.3624 

245.0442 

83.0 

5410.6079 

260.752? 

88.0 

6082.1234 

276.4602 

.1 

4790.6225 

245.3584 

.1 

5423.6534 

261.0663 

.1 

6095.9542 

276.7743 

.2 

4802.8983 

245.6725 

.2 

5436.7146 

261.3805 

.2 

6109.8008 

277.0885 

.3 

4815.1897 

245.9867 

.3 

5449.7915 

261.6947 

.3 

6123.6631 

277.4026 

.4 

4827.4969 

246.3009 

.4 

5462.8840 

262.0088 

.4 

6137.5411 

277.7168 

.5 

4839.8198 

246.6150 

.5 

5475.9923 

262.3230 

.5 

6151.4348 

278.0309 

.6 

4852.1584 

246.9292 

.6 

5489.1163 

262.6371 

.6 

6165.3442 

278.3451 

.7 

4864.5128 

247.2433 

.7 

5502.2561 

262.9513 

.7 

6179.2693 

278.6593 

.8 

4876.8828 

247.5575 

.8 

5515.4115 

263.2655 

.8 

6193.2101 

278.9740 

.9 

4889.2685 

247.8717 

.9 

5528.5826 

263.5796 

.9 

6207.1666 

279.2876 

79.0 

4901  .6699 

248.1858 

84.0 

5541.7694 

263.8938 

89.0 

6221.1389 

279.6017 

.1 

4914.0871 

248.5000 

.1 

5554.9720 

264.2079 

.1 

6235.1268 

279.9159 

.2 

4926.5199 

248.8141 

.2 

5568.1902 

264.5221 

.2 

6249.1304 

280.2301 

.3 

4938.9685 

249.1283 

.3 

5581.4242 

264.8363 

.3 

6263.1498 

280.5442 

.4 

4951.4328 

249.4425 

.4 

5594.6739 

265.1514 

.4 

6277.1849 

280.8584 

.5 

4963.9127 

219.7566 

.5 

5607.9392 

265.4646 

.5 

6291.2356 

281.1725 

.6 

4976.4084 

250.0708 

.6 

5621.2203 

265.7787 

p, 

6305.3021 

281.4867 

.7 

4988.9198 

250.3850 

.7 

5634.5171 

266.0929 

.7 

6319.3843 

281.8009 

.8 

5001.4469 

250.6991 

.8 

5647.8296 

266.4071 

.8 

6333.4822 

282.1150 

.9 

5013.9897 

251.0133 

.9 

5661.  157S 

266.7212 

.9 

6347.5958 

282.4292 

50  MENSURATION.— CIRCLES. 

AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Tenths.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

90.0 

6301.7251 

282.7433 

93.5 

6866.1471 

293.7389 

97.0 

73S9.8113 

304.7345 

.1 

6375.8701 

283.0575 

.6 

6880.8419 

294.0531 

.1 

7405.0559 

305.0486 

.2 

6390.0309 

283.?717 

.7 

6895.5524 

294.3672 

.2 

7420.3102 

305.3628 

.3 

6104.2073 

283.6858 

.8 

6910.2786 

294.6814 

.3 

7435.5922 

305.6770 

.4 

6418.3995 

284.0000 

.9 

6925.0205 

294.9956 

.4 

7450.8839 

305.9911 

.5 

6432.6073 

284.3141 

94.0 

6939.7782 

295.3097 

• 

7466.1913 

306.3053 

.6 

6446.8309 

284.6283 

.1 

6954.5515 

295.6239 

!fi 

7481.5144 

306.6194 

.7 

6461.0701 

284.9425 

.2 

6969.3100 

295.9380 

.7 

7496.8532 

306.9336 

.8 

G475.3251 

285.2560 

.3 

6984.1453 

296.2522 

.8 

7512.2078 

307.2478 

.9 

6489.5958 

285.5708 

.4 

6998.9658 

296.5663 

.9 

7527.5780 

307.5619 

91.0 

6.503.8822 

285.8849 

.5 

7013.8019 

296.8805 

98.0 

7542.9640 

307.8761 

.1 

6518.1843 

286.1991 

.6 

7028.6538 

297.1947 

.1 

7558.3656 

308.1902 

.2 

6532.5021 

286.5133 

.7 

7043.5214 

297.5088 

.2 

7573.7830 

308.5014 

.3 

6546.8356 

286.8274 

.8 

7058.4047 

297.8230 

g 

7589.2161 

308.8186 

.4 

6561.1848 

287.1416 

.9 

7073.3033 

298.1371 

'A 

7604.6648 

309.1327 

.5 

6575.5498 

287.4557 

95.0 

70S8.2184 

298.4513 

.5 

7620.1293 

309.4469 

.6 

6589.9304 

287.7699 

.1 

7103.1488 

298.7655 

.0 

7035.6095 

309.7610 

.7 

6604.3268 

288.0840 

.2 

7118.1950 

299.0796 

.7 

7051.1054 

310.0752 

.8 

6618.7388 

288.3982 

.3 

7133.0568 

299.3938 

.8 

7066.6170 

310.3894 

.9 

6633.1666 

288.7124 

.4 

7148.0343 

299.7079 

.9 

7682.1444 

310.7035 

92.0 

'6647.6101 

289.0265 

.5 

7163.0276 

300.0221 

99.0 

7697.6893 

311.0177 

.1 

6062.0692 

289.3407 

.6 

7178.0366 

300.3363 

.1 

7713.2461 

311.3318 

.2 

6676.5441 

289.6548 

.7 

7193.0012 

300.6504 

.2 

77*8.8206 

311.6460 

.3 

6691.0347 

289.9690 

.8 

7208.1016 

300.9646 

.3 

7744.4107 

311.9602 

.4 

6705.5410 

290.2832 

.9 

7223.1577 

301.2787 

.4 

7760.0166 

312.2743 

.5 

6720.0630 

290.5973 

96.0 

7238.2295 

301.5929 

.5 

7775.6382 

312.5885 

.6 

6734.6008 

290.9115 

.1 

7253.3170 

301.9071 

.6 

7791.2754 

312.9020 

.7 

6749.1542 

291.2256 

.2 

7268.4202 

302.2212 

.7 

7806.9284 

313.2168 

.8 

6763.7233 

291.5398 

.3 

7283.5391 

302.5354 

.8 

7822.5971 

313.5309 

.9 

6778.3082 

291.8540 

.4 

7298.6737 

302.8405 

.9 

7838.2815 

313.8451 

93.0 

6792.9087 

292.1681 

.5 

7313.8240 

303.1637 

100.0 

7853.9816 

314.1593 

.1 

6807.5250 

292.4823 

.6 

7328.9901 

303.4779 

.2 

6822.1569 

292.7964 

.7 

7344.1718 

303.7920 

.3 

68?6.8046 

293.1106 

.8 

7359.3693 

304.1062 

.4 

6851.4680 

293.4248 

.9 

7374.5824 

304.4203 

MENSURATION.— CIRCLES. 


51 


AREAS   OF   CIRCLES. 

(Advancing  by  Eighths.) 
AREAS. 


Dia. 

0.0 

o.J 

o.-i 

o.f 

O.J 

o.f 

o.f 

o.l 

0 

0.0 

0.0122 

0.0490 

0.1104 

.    0.1963 

0.3068 

0.4417 

0.0013 

1 

0.7854 

0.9940 

1.227 

1.484 

1.767 

2.073 

2.405 

2.761 

9 

3.1416 

3.546 

3.976 

4.430 

4.908 

5.411 

5.939 

6.491 

3 

7.068 

7.669 

8.295 

8.946 

9.021 

10.32 

11.04 

11.79 

4 

12.56 

13.36 

14.18 

15.03 

15.90 

16.80 

17.72 

18.60 

5 

19.63 

20.62 

21.64 

22.69 

23.75 

24.85 

25.96 

27.10 

6 

28.27 

29.16 

30.07 

31.91 

S3.18 

34.47 

35.73 

37  12 

7 

38.48 

39.87 

41.28 

42.71 

44.17 

45.66 

47.17 

48.70 

8 

50.26 

51.84 

53.45 

55.08 

56.74 

58.42 

60.13 

61  bG 

9 

63.61 

65.39 

67.20 

69.02 

70.88 

72.75 

74.00 

76.58 

10 

78.54 

80.51 

82.51 

84.54 

86.59 

88.66 

90.76 

92.88 

11 

95.03 

97.20 

99.40 

101.6 

103.8 

106.1 

108.4 

110  7 

12 

113.0 

115.4 

117.8 

120.2 

122.7 

125.1 

127.6 

130.1 

13 

132.7 

135.2 

137.8 

140.5 

143.1 

145.8 

148.4 

151.2 

14 

153.9 

156.6 

159.4 

162.2 

165.1 

167.9 

170.8 

173.7 

15 

176.7 

179.6 

182.6 

185.6 

188.6 

191.7 

194.8 

197.9 

16 

201.0 

204.2 

207.3 

210.5 

213.8 

217.0 

220.3 

223  6 

17 

226.9 

230.3 

233.7 

237.1 

240.5 

243.9 

247.4 

250.9 

18 

254.4 

258.0 

261.5 

265.1 

268.8 

272.4 

276.1 

279  8 

19 

283.5 

287.2 

291.0 

294.8 

298.6 

302.4 

300.3 

310.2 

20 

314.1 

318.1 

322.0 

326.0 

330.0 

334.1 

338.1 

342.2 

21 

316.3 

350.4 

354.6 

358.8 

363.0 

367.2 

371.5 

375  -S 

22 

380.1 

384.4 

388.8 

393.2 

397.6 

402.0 

406.4 

410.9 

23 

415.4 

420.0 

424.5 

429.1 

433.7 

438.3 

443.0 

447.0 

24 

452.3 

457.1 

461.8 

466.6 

471.4 

476.2 

481.1 

4S5  9 

25 

490.8 

495.7 

500.7 

505.7 

510.7 

515.7 

520.7 

525^8 

20 

530.9 

536.0 

541.1 

546.3 

551.5 

5.56.7 

502.0 

507.2 

27 

572.5 

577.8 

583.2 

588.5 

593.9 

599.3 

604.8 

610.2 

2S 

615.7 

621.2 

626.7 

032.3 

P37.9 

043.5 

649.1 

654.8 

29 

660.5 

666.2 

671.9 

677.7 

683.4 

689.2 

695.1 

700  9 

30 

706.8 

712.7 

718.6 

724.6 

730.6 

736.6 

742.6 

748.6 

31 

754.8 

760.9 

767.0 

773.1 

779.3 

785.5 

791.7 

798.0 

32 

804.3 

810.6 

810.9 

823.2 

829.6 

830.0 

842.4 

848.*8 

33 

855.3 

861.8 

868.3 

874.9 

881.4 

888.  0 

894.6 

901  3 

34 

907.9 

914.7 

921.3 

928.1 

934.8 

941.0 

948.4 

05^  3 

35 

962.1 

969.0 

975.9 

982.8 

989.8 

990.8 

1003.8 

1010.8 

30 

1017.9 

1025.0 

1032.1 

1039.2 

1040.3 

1053.5 

1060.7 

1008  0 

37 

1075.2 

1082.5 

1089.8 

1097.1 

1104.5 

1111.8 

1119.2 

1126.7 

38 

1134.1 

1141.6 

1149.1 

1150.6 

1164.2 

1171.7 

1179.3 

1186.9 

39 

1194.6 

1202.3 

1210.0 

1217.7 

1225.4 

1233.2 

1241.0 

1248  8 

40 

1256.6 

1264.5 

1272.4 

1280.3 

1288.2 

1290.2 

1304.2 

1312.2 

41 

1320.3 

1328.3 

1336.4 

1344.5 

1352.7 

1360.8 

1369.0 

1377.2 

42 

1385.4 

1393.7 

1402.0 

1410.3 

1418.6 

1427.0 

1435.4 

1443.8 

43 

1452.2 

1460.7 

1469.1 

1477.6 

1486.2 

1494.7 

1503.3 

1511.9 

44 

1520.5 

1529.2 

1537.9 

1546.6 

1555.3 

1564.0 

1572.8 

1581.6 

45 

1590.4 

1599.3 

1608.2 

1617.0 

1626.0 

1634.9 

1643.9 

1652.  J 

52 


MENSURATION.— CIRCLES. 


CIRCUMFERENCES  OF  CIRCLES. 

(Advancing  by  Eighths.) 

CIRCUMFERENCES. 


Di:i. 

0.0 

o.i 

o.i 

o.i 

O.J 

o.f 

o.i 

o.} 

0 

0.0 

0.3927 

0.7854 

1.178 

1.570 

1.963 

2.350 

2.748 

1 

3.141 

3.534 

3.927 

4.319 

4.712 

5.105 

5.497 

5.890 

•;> 

6.283 

0.075 

7.068 

7.461 

7.854 

8.246 

8.039 

9.032 

3 

9.424 

9.S17 

10.21 

10.00 

10.99 

11.38 

11.78 

12.17 

4 

12.50 

12.95 

13.35 

13.74 

14.13 

14.52 

14.92 

15.31 

5 

15.70 

10.10 

16.49 

10.88 

17.27 

17.67 

18.00 

18.45 

6 

18.84 

19.24 

19.03 

20.02 

20.42 

20.81 

21.20 

21.59 

7 

21.99 

22.38 

22.77 

23.16 

23.50 

23.95 

24.34 

24.74 

8 

25.13 

25.52 

25.91 

20.31 

26.70 

27.09 

27.48 

27.88 

9 

28.27 

28.00 

29.05 

29.45 

29.84 

30.23 

30.03 

31.02 

10 

31.41 

31.80 

32.20 

32.59 

32.98 

33.37 

33.77 

34.16 

11 

34,55 

31.95 

35.34 

35.73 

36.12 

36.52 

36.91 

37.30 

12 

37.09 

38.09 

38.48 

38.87 

39.27 

39.00 

40.05 

40.44 

13 

40.84 

41.23 

41.02 

42.01 

42.41 

42.80 

43.19 

43.58 

14 

43.98 

44.37 

44.76 

45.16 

45.55 

45.94 

46.33 

46.73 

15 

47.12 

47.51 

47.90 

48.30 

48.69 

49.08 

49.48 

49.87 

10 

50.20 

50.05 

51.05 

51.44 

51.83 

52.22 

52.62 

53.01 

17 

53.40 

53.79 

54.19 

54.58 

54.97 

55.37 

55.76 

50.15 

18 

50.54 

50.94 

57.33 

57.72 

58.11 

58.51 

58.90 

59.29 

19 

59.09 

00.08 

00.47 

00.86 

61.20 

61.65 

62.04 

02.43 

20 

02.83 

03.22 

03.61 

64.01 

64.40 

64.79 

65.18 

65.58 

21 

65.97 

66.30 

66.75 

07.15 

67.54 

67.93 

68.32 

68.72 

22 

09.11 

09.50 

69.90 

70.29 

70.08 

71.07 

71.47 

71.80 

23 

72.25 

72.04 

73.01 

73.43 

73.82 

74.22 

74.01 

75.00 

21 

75.39 

75.79 

70.18 

70.57 

76.90 

77.36 

77.75 

78.14 

25 

78.54 

78.93 

79.32 

79.71 

80.10 

80.50 

80.89 

81.28 

26 

81.08 

82.07 

82.46 

82.85 

83.25 

83.04 

84.03 

84.43 

27 

84.82 

85.21 

85.60 

80.00 

80.39 

86.78 

87.17 

87.57 

28 

87.90 

88.35 

88.75 

89.14 

89.53 

89.92 

90.32 

90.71 

29 

91.10 

91.49 

91.89 

92.28 

92.07 

93.06 

93.46 

93.,85 

30 

94.24 

94.01 

95.03 

95.42 

95.81 

96.21 

96.60 

90.99 

31 

97.39 

97.78 

98.17 

98.57 

98.90 

99.35 

99.75 

100.14 

32 

100.53 

100.92 

101.32 

101.71 

102.10 

102.49 

102.89 

103.29 

33 

103.07 

104.07 

104.46 

104.85 

105.24 

105.64 

100.03 

100.42 

34 

100.81 

107.21 

107.00 

107.99 

108.39 

108.78 

109.17 

109.50 

35 

109.90 

110.35 

110.74 

111.13 

111.53 

111.92 

112.31 

112.71 

36 

113.10 

113.49 

113.8S 

114.28 

114.67 

115.06 

115.45 

115.85 

37 

110.24 

110.03 

117.02 

117.42 

117.81 

118.20 

118.00 

118.99 

38 

119.38 

119.77 

120.17 

120.56 

120.95 

121.34 

121.74 

122.13 

39 

122.52 

122.92 

123.31 

123.70 

124.09 

124.49 

124.88 

125.27 

40 

125.00 

120.06 

126.45 

126.84 

127.24 

127.63 

128.02 

128.41 

41 

128.81 

129.20 

127.59 

129.98 

130.38 

130.77 

131.16 

131.55 

12 

131.95 

132.34 

132.73 

133.13 

133.52 

133.91 

134.30 

134.70 

43 

135.09 

135.48 

135.87 

136.27 

130.00 

137.05 

137.45 

137.84 

44 

138.23 

138.02 

139.02 

139.41 

139.80 

140.19 

140.59 

140.98 

45 

141.37 

141.70 

142.16 

142.55 

142.94 

143.34 

143.73 

144.12 

MENSURATION.— CIRCLES. 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES. 

FROM    1    TO    50    FEET. 
(Advancing  by  One  Inch.) 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Oircum  . 

Ft. 

Feet. 

Ft.  In. 

Feet 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

1  0 

0.7854 

3  If 

5  0 

19.635 

15  8i 

9  0 

63.6174 

28  3i 

1 

0.9217 

3  4f 

1 

20.2947 

15  11| 

1 

64.8006 

28  61 

2 

1.009 

3  8 

2 

20.9656 

16  23 

2 

65.9951 

28  9* 

3 

1.2271 

3  11 

3 

21.6475 

16  5-1- 

3 

67.2007 

29   | 

4 

1.3962 

4  2i 

4 

22.34 

16  9 

4 

68.4166 

29  3f 

5 

1.5761 

4  5f 

5 

23.0437 

17   i 

5 

69.644 

29  7 

6 

1.7671 

4  8* 

6 

23.7583 

17  Si 

6 

70.8823 

29.  10| 

7 

1.9689 

4  111 

7 

24.4835 

17  (if 

7 

72.1309 

30  11 

8 

2.1816 

5  23 

8 

25.2199 

17  95- 

8 

73.391 

SO  4| 

9 

2.4052 

5  5| 

9 

25.9672 

18   i 

9 

74.662 

30  7i 

10 

2.6398 

5  9 

10 

26.7251 

18  3* 

10 

75.9433 

30  11| 

11 

2.8852 

6   i 

11 

27.4943 

18  7i 

11 

77.2362 

31  If 

2  0 

3.1416 

6  21 

6  0 

28.2744 

18  10i 

10  0 

78.54 

31  5 

1 

3.4087 

6  6* 

1 

29.0649 

19  li 

1 

79.854 

31  Si 

2 

3.68(>9 

6  y| 

2 

29.8668 

19  41 

2 

81.1795 

31  iii 

3 

3.976 

7   3 

3 

30.6796 

19  7i 

3 

82.516 

32  21 

4 

4.276 

7  3| 

4 

31.5029 

19  10| 

4 

83.8627 

32  5£ 

5 

4.5S69 

7  7 

5 

32.3376 

20  11 

5 

85.2211 

32  8| 

6 

4.9087 

7  lOi 

6 

33.1831 

20  4-| 

6 

86.5903 

32  11| 

7 

5.2413 

8  11 

7 

34.0391 

20  8i 

7 

87.9697 

33  21 

8 

5.585 

8  4£ 

8 

34.9065 

20  Hi 

8 

89.3608 

33  6i 

9 

5.9295 

8  73- 

9 

35.7847 

21  21 

9 

90.7627 

33  9i 

10 

6.3049 

8  10* 

10 

36.6735 

21  5* 

10 

92.1749 

34   1 

11 

6.6813 

0  1| 

11 

37.5736 

21  8f 

11 

93.5986 

34  3i 

3  0 

7.0680 

9  5 

7  0 

38.4846 

21  111 

11  0 

95.0334 

34  61 

1 

7.4666 

9  8i 

1 

39.406 

22  3 

1 

96.4783 

34  9f 

2 

7.8757 

9  HI 

2 

40.3388 

22  Gi 

2 

97.9347 

35   2- 

3 

8.2957 

10  21 

3 

41.2825 

22  9i 

3 

99.4021 

35  4i 

4 

8.7265 

10  54 

4 

42.2367 

23   1 

4 

100.8797 

35  7i 

5 

9.1683 

10  S3- 

5 

43.2022 

23  2i 

R 

102.3689 

35  lOf 

6 

9.6211 

10  11| 

6 

44.1787 

23  63- 

6 

103.8691 

36  H 

7 

10.0S46 

11  3 

7 

45.1656 

23  9£ 

7 

105.3794 

36  4* 

8 

10.5591 

11  6* 

8 

46.1638 

24.  H 

8 

106.9013 

36  7f 

9 

11.0446 

11  91 

9 

47.173 

24  4i 

9 

108.4342 

36  10* 

10 
11 

11.5409 
12.0481 

12   V 
12  3f 

10 
11 

48.1962 
49.2236 

24  7i 
24  101 

10 
11 

109.9772 
111.5319 

37  2| 
37  5i 

4  0 

12.5664 

12  6|- 

8  0 

50.2656 

25  1} 

12  0 

113.0976 

37  F£ 

13.0952 

12  9£ 

1 

51.3178 

25  41 

1 

114.6732 

;-7  m 

2 

13.6353 

13  1 

2 

52.3816 

25  7| 

2 

116.2607 

38  2* 

3 

14.1862 

13  4i 

3 

53.4562 

25  11 

3 

117.859 

38  of 

4 

14.7479 

13  7i 

4 

54.5412 

26  2i 

4 

119.4674 

38  81 

5 

15.3206 

13  10* 

5 

55.6377 

26  5} 

5 

121.0876 

39  0 

6 

15.9043 

14  H 

6 

56.7451 

26  81 

6 

122.7187 

39  3i 

7 

16.4986 

14  4^ 

7 

57.8628 

26  1H 

7 

124.3598 

39  fl 

8 

17.1041 

14  7£ 

8 

58.992 

27  2| 

8 

126.0127 

39  9* 

9 

17.7205 

14  11 

9 

60.1321 

27  5| 

9 

127.6765 

40   1 

10 

18.3476 

15  2i 

10 

61.2826 

27  9 

10 

129.3504 

40  ?| 

11 

18.9858 

11 

62.4445 

28   i 

11 

131.036 

40  6| 

54 


MENSURATION.— CIRCLES. 


Areas  and  Circumferences  of  Circles  (Feet  and  Inches) . 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Ft. 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

13  0 

132.7326 

40  10 

18  0 

254.4696 

56  C* 

23  0 

415.4766 

72  3 

1 

134.4391 

41  If 

1 

256.8303 

56  9£ 

1 

418.4915 

72  6i 

2 

136.1574 

41  4f 

2 

259.2033 

57   1 

2 

421.5192 

72  9f 

3 

137.8867 

41  7* 

3 

261.5872 

57  4 

3 

424.5577 

73   4- 

4 

139.626 

41  lOf 

4 

263.9807 

57  71 

4 

427.6055 

73  3f 

5 

141.3771 

42  If 

5 

266.3861 

57  10i 

5 

430.6658 

73  6i 

6 

143.1391 

42  41 

6 

268.8031 

58  1$ 

6 

433.7371 

73  91 

7 

144.9111 

42  8 

7 

271.2293 

58  44- 

7 

436.8175 

74  1 

8 

146.6949 

42  Hi 

8 

273.6678 

58  7f 

8 

439.9106 

74  41 

9 

148.4896 

43  2i 

0 

276.1171 

58  10i 

9 

443.0146 

74  7i 

10 

150.2943 

43  5fr 

10 

278.5761 

58  2 

10 

446.1278 

74  lOf 

11 

152.1109 

43  8f 

11 

281.0472 

59  5i 

11 

449.2536 

75  If 

14  0 

153.9384 

43  iif 

19  0 

283.5294 

59  8i 

24  0 

452.3904 

75  4i 

1 

155.7758 

44  21 

1 

286.021 

59  Hi 

1 

455.5362 

75  71 

2 

157.625 

44  6 

2 

288.5249 

60  2$ 

2 

458.6948 

75  11 

o 

159.4852 

44  9i 

3 

291.0397 

60  5£ 

3 

461.8642 

76  2i 

4 

161.3553 

45   i 

4 

293.5641 

60  8i 

4 

465.0428 

76  5i 

5 

163.2373 

45  34 

5 

296.1107 

60  111 

5 

468.2341 

76  8i 

6 

165.1303 

45  6| 

6 

298.6483 

60  3i 

6 

471.4363 

76  iif 

7 

167.0331 

45  9i 

7 

301.2054 

61  6i 

7 

474.6476 

77  2i 

8 

168.9479 

46   1 

8 

303.7747 

61  9* 

8 

477.8716 

77  51 

9 

170.S735 

46  4 

9 

306.355 

61   i 

9 

481.1065 

77  9 

10 

172.8091 

46  71 

10 

308.9448 

61  3f 

10 

484.3506 

78   i 

11 

174.7565 

46  Hi 

11 

311.5469 

62  6i 

11 

487.6073 

78  3i 

15  0 

176.715 

47  H 

20  0 

314.16 

62  91 

25  0 

490.875 

78  64- 

1 

178.6832 

47  4f 

1 

316.7821 

62  li 

1 

494.1516 

78  9i 

2 

180.6634 

47  7i 

9 

319.4173 

63  4i 

2 

497.4411 

79   i 

3 

182.6545 

47  101 

3 

322.063 

63  73 

3 

500.7415 

79  31 

4 

184.6555 

48  24- 

4 

324.7182 

63  1H 

4 

504.051 

79  7i 

5 

180.6684 

48  51 

5 

327.3S58 

63  If 

5 

507.3732 

79  Hi 

6 

188.6923 

48  8i 

6 

330.0643 

64  4| 

6 

510.7063 

80  1i 

7 

190.726 

48  111 

7 

332.7522 

64  71 

7 

514.0484 

80  4f 

8 

192.7716 

49  2f 

8 

335.4525 

64  11 

8 

517.4034 

80  7f 

9 

194.8282 

49  5i 

9 

338.1637 

65  2i 

9 

520.7692 

80  10f 

10 

196.8946 

49  81 

10 

340.8844 

65  5f 

10 

524.1441 

81  H 

11 

198.973 

50  0 

11 

343.6174 

65  8i 

11 

527.5318 

81  5 

16  0 

201.0624 

50  31 

21  0 

346.3614 

65  llf 

26  0 

530.9304 

81  81 

1 

203.1615 

50  6i 

1 

349.1147 

66  2i 

1 

534.3379 

81  Hi 

2 

205.2726 

50  9| 

2 

351.8804 

66  51 

2 

537.7583 

82  2f 

3 

207.3946 

51   £ 

3 

354.6571 

66  9 

3 

541.1896 

82  5} 

4 

209.5264 

51  3| 

4 

357.4432 

66   i 

4 

544.6299 

82  8-| 

5 

211.6703 

51  6J- 

5 

360.2417 

67  3f 

5 

548.083 

82  in 

6 

213.8251 

51  10 

6 

363.0511 

67  6* 

6 

551.5471 

83  3 

7 

215.9896 

52  11 

7 

365.8698 

67  9f 

7 

555.0201 

83  61 

8 

218.1662 

52  4i 

8 

368.7011 

68   i 

8 

558.5059 

83  9i 

9 

220.3537 

52  7| 

9 

371.5432 

68  3| 

9 

562.0027 

84   f 

10 

222.551 

52  10* 

10 

374.3947 

68  7 

10 

565.5084 

84  3i 

11 

224.7608 

53  If 

11 

377.2587 

68  10i 

11 

569.027 

84  6| 

17  0 

226.9806 

53  41 

22  0 

380.1336 

69  If 

27  0 

572.5566 

84  91 

1 

229.2105 

53  8 

1 

383.0177 

69  44 

1 

576.0949 

85  1 

2 

231.4525 

53  111 

2 

385.9144 

69  7f 

2 

579.6463 

85  4i 

3 

233.7055 

54  2i 

3 

388.822 

69  10f 

3 

583.2085 

85  81 

4 

235.9682 

54  5f 

4 

391.7389 

70  11 

4 

586.7796 

85  llf 

5 

238.243 

54  8* 

5 

394.6683 

70  5 

5 

590.3637 

86  H 

6 

240.5287 

54  llf 

6 

397.6087 

70  8i 

6 

593.9587 

86  4f 

7 

242.8241 

55  2-1 

7 

400.5583 

70  Hi 

7 

597.5625 

86  71 

8 

245.1316 

55  6 

8 

403.5204 

71  2^ 

8 

601.1793 

86  11 

9 

247.45 

55  91 

9 

406.4935 

71  5f 

o 

604.807 

87  21 

10 

249.7781. 

56   i 

10 

409.4759 

71  8i 

10 

608.4436 

87  5i 

11 

252.1184 

56  3* 

11 

412.4707 

71  111 

11 

612.0931 

87  8i 

MENSURATION.— CIRCLES.  55 

Areas  and  Circumferences  of  Circles  (Feet  and  Inches). 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Ft. 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

28  0 

615.7530 

87  iii 

33  0 

855.301 

103  8 

38  0 

1134.118 

119  4i 

1 

619.4228 

88  2£ 

1 

859.624 

103  iii 

1 

1139.095 

119  7f 

2 

623.105 

88  5f 

2 

863.961 

104  2i 

2 

1144.087 

119  101 

3 

626.7982 

88  9 

3 

868.309 

104  5f 

3 

1149.089 

120  2 

4 

630.5002 

89   i 

4 

872.665 

104  8f 

4 

1154.110 

1?0  5i 

5 

634.2152 

89  3i 

g 

877.035 

104  111 

5 

1159.124 

120  8  f 

6 

637.9411 

89  Of 

6 

881.415 

105  21 

6 

1164.159 

120  11J 

7 

641.6758 

89  9* 

7 

885.804 

105  6 

7 

1169.202 

121  2i 

8 

645.4235 

90 

8 

890.206 

105  9i 

8 

1174.259 

121  5| 

9 

649.1821 

90  31 

9 

394.619 

106   i 

9 

1179.327 

121  8f 

10 

652.9495 

90  6f 

10 

899.041 

106  3  1 

10 

1184.403 

121  ll| 

11 

656.73 

90  Hi 

11 

903.476 

106  6| 

11 

1189.493 

122  3i 

29  0 

660.5214 

91  H 

31  0 

907.922 

106  91 

39  0 

1194.593 

122  6i 

1 

664.3214 

91  41 

1 

912.377 

107   1 

1 

1199.719 

122  9£ 

2 

668.1346 

91  7i 

2 

916.844 

107  4 

9 

1204.824 

123   i 

3 

671.95S7 

91  lOf 

3 

921.323 

107  7i 

3 

1209.95S 

123  3| 

4 

675.7915 

92  If 

4 

925.810 

107  10i 

4 

1215.099 

123  61 

5 

679.6375 

92  41 

5 

930.311 

108  If 

5 

1220.254 

123  91 

6 

633.4943 

92  8i 

6 

934.822 

108  4£ 

6 

1225.420 

124  li 

7 

687.3598 

92  Hi 

7 

939.342 

108  7| 

7 

1230.594 

124  4i 

8 

691.2385 

93  21 

8 

943.875 

108  101 

8 

1235.782 

124  7| 

9 

695  1028 

93  5* 

9 

948.419 

109  2 

9 

1240.981 

124  10^ 

10 

699.0263 

93  8f 

10 

952.972 

109  5i 

10 

1246.188 

125  l| 

11 

702.9377 

93  Hi 

11 

957.538 

109  8i 

11 

1251.408 

125  41 

30  0 

706.86 

94  21 

35  0 

962.115 

109  11| 

40  0 

1256.64 

125  71 

1 

710.791 

94  6 

1 

906.770 

110  2f 

1 

1261.879 

125  11 

2 

714.735 

94  9i 

2 

971.299 

110  51 

2 

1267.133 

126  2i 

3 

718.69 

95   1 

3 

975.908 

110  81 

3 

1272.397 

126  51 

4 

722.654 

95  3i 

4 

980.526 

111  0 

4 

1277.669 

126  8i 

5 

726.631 

95  6| 

5 

985.158 

111  3i 

5 

1282.955 

126  llf 

p. 

730.618 

95  9f 

6 

989.803 

111  6i 

6 

1288.252 

127  21 

7 

734.615 

96   1 

7 

994.451 

111  9f 

7 

1293.557 

127  51 

8 

738.624 

96  4 

8 

999.115 

112   i 

8 

1298.876 

217  9 

9 

742.645 

96  7i 

9 

1003.79 

112  31 

9 

1304.206 

128   * 

10 

746.674 

96  101 

10 

1008.473 

112  61 

10 

1309.543 

12S  3| 

11 

750.716 

97  li 

11 

1013.170 

112  10 

11 

1314.895 

128  6i 

31  0 

754.769 

97  4f 

36  0 

1017.878 

113  li 

41  0 

1320.257 

128  9f 

1 

758.831 

97  71 

1 

1022.594 

113  4i 

1 

1325.628 

129   4 

9 

762.906 

97  101 

2 

1027.324 

113  71 

2 

1331.012 

129  31 

3 

766.992 

98  2 

3 

1032.064 

113  10| 

3 

1336.407 

129  7 

4 

771.0S6 

98  5i 

4 

1036.813 

114  If 

4 

1341.810 

129  10i 

5 

775.191 

98  8| 

5 

1041.570 

1  14  41 

5 

1347.227 

130  11 

p, 

779.313 

98  1U 

6 

1046.349 

114  8 

(\ 

1352.655 

130  4i 

7 

783.440 

99  2g 

7 

1051.130 

114  iii 

7 

1358.091 

ISO  7f 

8 

787.581 

99  5| 

8 

1055.926 

115  2i 

8 

1363.541 

130  101 

9 

791.732 

99  81 

9 

1060.731 

115  si- 

9 

1369.001 

131  11 

10 

795.892 

100  0 

10 

1065.546 

ns  9* 

10 

1374.47 

131  5 

11 

800.065 

100  3i 

11 

1070.374 

115  11| 

11 

1379.952 

131  8i 

32  0 

804.25 

100  6f 

37  0 

1075.2120 

116  21 

42  0 

1385.446 

131  llf 

1 

808.442 

100  9i 

1 

1080.059 

116  6 

1 

1390.247 

132  2J 

2 

812.648 

101   | 

2 

1084.920 

116  9i 

9 

1396.462 

132  5| 

3 

$16.865 

101  3| 

3 

1089.791 

117   i 

3 

1401.988 

132  81 

4 

821.090 

101  61 

4 

1094.671 

117  34- 

4 

1407.522 

132  HI 

5 

825.329 

101  10 

5 

1099.564 

117  6i 

5 

1413.07 

133  3 

6 

829.579 

102  li 

6 

1104.409 

117  9f 

6 

1418.629 

133  6i 

7 

833.837 

102  4| 

7 

1109.381 

118   1 

7 

1424.195 

133  9i 

S 

838.108 

102  7£ 

8 

1114.307 

118  4 

g 

1429.776 

134   J 

9 

842.391 

102  10$ 

9 

1119.244 

118  7i 

g 

1435.367 

134  3f 

10 

846.681 

103  11 

10 

1124.189 

118  10£ 

10 

1440.967 

134  61 

11 

850.985 

103  41 

11 

1129.118 

119  11 

11 

1446.580 

134  91 

56 


MENSURATION.— Cl&CULAR  ARCS. 


Areas  and  Circumferences  of  Circles  (Feet  and  Inches). 


Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Dia. 

Area. 

Circum. 

Ft. 

Feet. 

Ft.  In. 

Ft. 

Feet. 

Ft.  In. 

F*. 

Feet. 

Ft.  In. 

43  0 

1452.205 

135  1 

46  0 

1661.906 

144  6i 

49  0 

1885.745 

153  111 

1 

1457,830 

135  4i 

1 

1667.931 

144  91 

1 

1892.172 

154  2£ 

2 

1463.483 

135  71 

2 

1673.97 

145   £ 

2 

1898.504 

154  51 

3 

1469.14 

135  10* 

3 

1680.02 

145  31 

3 

1905.037 

154  8| 

4 

1474.804 

136  1$ 

4 

1686.077 

145  G| 

4 

1911.497 

154  11$ 

5 

1480.483 

136  4|- 

5 

1692.148 

145  9£ 

5 

1917.961 

155  2$ 

6 

1486.173 

136  7£ 

6 

1698.231 

146  li 

6 

1924.426 

155  6 

7 

1491.870 

136  11 

7 

1704.321 

146  4£ 

7 

1930.919 

155  91 

8 

1497.532 

137  2i 

8 

1710.425 

146  71 

8 

1937.316 

156   * 

9 

1503.305 

137  51 

9 

1716.541 

146  10| 

9 

1943.914 

156  3* 

10 

1509.035 

137  8f 

10 

1722.663 

147  1* 

10 

1950.439 

156  6f 

11 

1514.779 

137  llf- 

11 

1728.801 

147  4| 

11 

1956.969 

156  9f 

44  0 

1520.534 

138  24 

47  0 

1734.947 

147  7| 

50  0 

1963.5 

157   $ 

1 

1526.297 

138  51 

1 

1741.104 

147  11 

2 

1532.074 

138  9 

2 

1747.274 

148  2* 

3 

1537.862 

139   * 

3 

1753.455 

148  51 

4 

1543.658 

139  31 

4 

1759.643 

148  8f 

5 

1549.478 

139  6f 

5 

1765.845 

148  111 

6 

1555.288 

139  9f 

G 

1772.059 

149  21 

7 

1561.116 

140   f 

7 

1778.28 

149  5| 

8 

1566.959 

140  3$ 

8 

1784.515 

149  8^ 

9 

1572.812 

140  7* 

9 

1790.761 

150   i 

10 

1.578.673 

141  10i 

10 

1797.015 

150  31 

11 

15S4.549 

141  11 

11 

1803.283 

150  6$ 

45  0 

1590.435 

141  4f 

48  0 

1809.562 

150  9^ 

1 

1596.329 

141  7* 

1 

1815.848 

151   | 

2 

1602.237 

141  10f 

2 

1822.149 

151  3-2- 

3 

1608.155 

142  H 

3 

1828.460 

151  6* 

4 

1614.082 

142  5 

4 

1834.779 

151  10i 

5 

1620.023 

142  8fc 

5 

1841.173 

152  11 

6 

1625.974 

142  11| 

6 

1847.457 

152  4f 

7 

1631.933 

143  2f 

7 

1853.809 

152  7* 

s 

1637.907 

143  5* 

8 

1860.175 

152  10* 

9 

1643.S91 

143  8f 

9 

1866.552 

153  If 

10 

1649.S83 

143  Hi 

10 

1872.937 

153  4-J 

11 

1555.889 

144  3 

11 

1879.335 

153  8^ 

Circular  Arcs. 

To  /m«f  the  length  of  a  circular  arc  when  its  chord  and  height,  or 
versed  sine  is  given;  BY  THE  FOLLOWING  TABLE. 

RULE. — Divide  the  height  by  the  chord;  find  in  the  column  of 
heights  the  number  equal  to  this  quotient.  Take  out  the  corre- 
sponding number  from  the  column  of  lengths.  Multiply  this 
number  by  the  given  chord. 

EXAMPLE. — The  chord  of  an  arc  is  80  and  its  versed  sine  is  30, 
what  is  the  length  of  the  arc? 

Ans.  30^-80=0.375.  The  length  of  an  arc  for  a  height  of 
0.375  we  find  from  table  to  be  1.34063.  80 X  1.34063=  107.2504 
=  length  of  arc. 


MENSURATION.— CIRCULAR  ARCS. 


57 


TABLE  OF  CIRCULAR  ARCS. 


Hts. 

lengths 

Hts. 

Lengths 

Hts. 

Lengths 

Hts. 

Lengths 

Hts. 

Lengths 

.001 

1.00001 

.062 

1.01021 

.123 

1.03987 

.184 

1.08797 

.245 

1.15308 

.00? 

1.00001 

.063 

1.01054 

.124 

1.04051 

.185 

1.0S890 

.246 

1.15428 

.003 

1.00002 

.064 

1.01088 

.125 

1.04116 

.186 

1.08984 

.247 

1.15549 

.004 

1.00004 

.065 

1.01123 

.126 

1.04181 

.187 

1.09079 

.248 

1.15670 

.005 

1.00007 

.066 

1.01158 

.127 

1.04247 

.188 

1.09174 

.249 

1.15791 

.006 

1.00010 

.067 

1.01193 

.128 

1.04313 

.189 

1  .09269 

.250 

1.15912 

.007 

1.00013 

.068 

1.01228 

.129 

1.04380 

.190 

1.09365 

.251 

1.16034 

.008 

1.00017 

.069 

1.01264 

.130 

1  .04447 

.191 

1.09461 

.252 

1.16156 

.009 

1.00022 

.070 

1.01301 

.131 

1.04515 

.192 

1.09557 

.253 

1.16279 

.010 

1.00027 

.071 

1.01338 

.132 

1.04584 

.193 

1.09654 

.254 

1.16402 

.011 

1.00032 

.072 

1.01376 

.133 

1.04652 

.194 

1.09752 

.255 

1.16526 

.012 

1.0003S 

.073 

1.01414 

.134 

1.04722 

.195 

1.09850 

.256 

1.16650 

.013 

1.00045 

.074 

1.01453 

.135 

1.04792 

.196 

1.09949 

.257 

1.16774 

.014 

1.00053 

.075 

1.01493 

.136 

1.04862 

.197 

1.10048 

.258 

1.16899 

.015 

1.00061 

.076 

1.01533 

.137 

1.04932 

.198 

1.10147 

.259 

1.17024 

.016 

1.00069 

.077 

1.01573 

.138 

1.05003 

.199 

1.10247 

.260 

1.17150 

.017 

1.00078 

.078 

1.01614 

.139 

1.05075 

.200 

1.10347 

.261 

1.17276 

.018 

1.00087 

.079 

1.01656 

.140 

1.05147 

.201 

1.10447 

.262 

1.17403 

.019 

1.00097 

.080 

1.0169S 

.141 

1.05220 

.202 

.10548 

.263 

1.17530 

.020 

1.00107 

.081 

1.01741 

.142 

1.05293 

.203 

.10650 

.264 

1.17657 

.021 

1.00117 

.082 

1.01784 

.143 

1.05367 

.204 

.10752 

.205 

1.17784 

.022 

1.00128 

.083 

1.01828 

.144 

1  .05441 

.205 

.10855 

.266 

1.17912 

.023 

1.00140 

.084 

1.01872 

.145 

1.05516 

.206 

.10958 

.267 

1.18040 

.024 

1.00153 

.085 

1.01916 

.146 

1.05591 

.207 

.11062 

.268 

1.18169 

.025 

1.00167 

.086 

1.01961 

.147 

1.05667 

.208 

.11165 

.269 

1.18299 

.026 

1.00182 

.087 

1.02006 

.148 

.05743 

.209 

.11269 

.270 

1.18429 

.027 

1.00196 

.088 

1.02052 

.149 

.05819 

.210 

.11374 

.271 

1.18559 

.028 

1.00210 

.089 

1.02098 

.150 

.05896 

.211 

.11479 

.272 

1.18689 

.029 

]  .00225 

.090 

1.02145 

.151 

.05973 

.212 

.11584 

.273 

1.18820 

.030 

1.00240 

.091 

1.02192 

.152 

.06051 

.213 

.11690 

.274 

1.18951 

.031 

1.00256 

.092 

1.02240 

.153 

.06130 

.214 

.11796 

.275 

1.19082 

.032 

1.00272 

.093 

1.02289 

.154 

.06209 

.215 

.11904 

.976 

1.19214 

.033 

1.00289 

.094 

1.02339 

.155 

.06288 

.216 

.12011 

.277 

1.19346 

.034 

1.00307 

.095 

1.02389 

.156 

.06368 

.217 

.12118 

.278 

1.19479 

.035 

1.00327 

.096 

1.02440 

.157 

.06449 

.218 

.12225 

.279 

1.19612 

.036 

1.00345 

.097 

1.02491 

.158 

.06530 

.219 

.12334 

.280 

1.19746 

.037 

1.00364 

.098 

1.02542 

.159 

.06611 

.220 

.12444 

.281 

1.19880 

.038 

1.00384 

.099 

1.02593 

.160 

.06693 

.221 

.12554 

.282 

1.20014 

.039 

1.00405 

.100 

1.02645 

.161 

.06775 

.222 

.12664 

.283 

1.20149 

.040 

1.0042G 

.101 

1.02698 

.162 

.06858 

.223 

.12774 

.284 

1.20284 

.041 

1.00447 

.102 

1.02752 

.163 

.06941 

.224 

.12885 

.285 

1.20419 

.042 

1.00469 

.103 

1.02806 

.164 

.07025 

.225 

.12997 

.286 

1.20555 

.043 

1.00492 

.104 

1.02860 

.165 

.07109 

.226 

.13108 

.287 

1.20691 

.044 

1.00515 

.105 

1.02914 

.166 

1.07194 

.227 

.13219 

.288 

1.20827 

.045 

1.00539 

.106 

1.02970 

.167 

1.07279 

.228 

.13331 

.289 

1.20964 

.046 

1  .00563 

.107 

1.03026 

.168 

1.07365 

.229 

.13444 

.290 

1.21102 

.047 

1.00587 

.108 

1.03082 

.169 

1.07451 

.230 

.13557 

.291 

1.21239 

.048 

1.00612 

.109 

1.03139 

.170 

1.07537 

.231 

.13671 

.292 

1.21377 

.049 

1.0063S 

.110 

1.03196 

.171 

1.07624 

.232 

.13785 

.293 

1.21515 

.050 

1.00665 

.111 

1.03254 

.172 

1.07711 

.233 

.13900 

.294 

1.21654 

.051 

1.00692 

.112 

1.03312 

.173 

1.07799 

.234 

.14015 

.295 

1.21794 

.052 

1.00720 

.113 

1.03371 

.174 

1.07888 

.235 

.14131 

.296 

1.21933 

.053 

1.00748 

.114 

1.03430 

.175 

1.07977 

.236 

.1  4247 

.297 

1.22073 

.054 

1.00776 

.115 

1.03490 

.176 

1.08066 

.237 

.14363 

.298 

1.22213 

.055 

1.00805 

.116 

1.03551 

.177 

1.08156 

.238 

.14480 

.299 

1.22354 

.056 

1.00834 

.117 

1.03611 

.178 

1.08246 

.239 

.14597 

.300 

1.22495 

.057 

1.00864 

.118 

1.03672 

.179 

1.08337 

.240 

.14714 

.301 

1.22636 

.058 

1.00895 

.119 

1.03734 

.180 

1.08428 

.241 

.14832 

.302 

1.22778 

.059 

1.00926 

.120 

1.03797 

.181 

1.08519 

.242 

.14951 

.303 

1.22920 

.ono 

1.00957 

.121 

1.03860 

.182 

1.08611 

.243 

.15070 

.304 

1  .23063 

.061 

1.00989 

.122 

1.03923 

.183 

1.08704 

.244 

1.15189 

.305 

1.23206 

' 
HE 

58 


MENSURATION.— CIRCULAR  ARCS. 


Table  of  Circular  Arcs  (concluded) . 


Hts. 

Lengths 

Hts. 

Lengths 

Hts. 

Lengths 

Hts. 

Lengths 

Hts. 

Lengths 

.306 

1.23349 

.345 

1.29209 

.384 

1.35575 

.423 

1.42402 

.462 

1.49651 

.307 

1.23492 

.346 

1.29366 

.385 

1.35744 

.424 

1.42583 

.463 

1.49842 

.308 

1.23636 

.347 

1.29523 

.386 

1.35914 

.425 

1.42764 

.464 

1.50033 

.309 

1.23781 

.348 

1.29681 

.387 

1.36084 

.426 

1.42945 

.465 

1.50224 

.310 

1.23926 

.349 

1.29839 

.388 

1.36254 

.427 

1.43127 

.466 

1.50416 

.311 

1.24070 

.350 

1.29997 

.389 

1.36425 

.428 

1.43309 

.467 

1.50608 

.312 

1.24216 

.351 

1.30156 

.390 

1.36596 

.429 

1.43491 

.468 

1  .50800 

.313 

1.24361 

.352 

1.30315 

.391 

1.36767 

.430 

1.43673 

.469 

1.50992 

.314 

1.24507 

.353 

1.30474 

.392 

1.36939 

.431 

1.43856 

.470 

1.51185 

.315 

1.24654 

.254 

1.30634 

.393 

1.37111 

.432 

1  .44039 

.471 

1.51378 

.316 

1.24801 

.355 

1.30794 

.394 

1  .37283 

.433 

1.44222 

.472 

1.51571 

.317 

1.24948 

.356 

1.30954 

.395 

1.37455 

.434 

1.44405 

.473 

1.51764 

.318 

1.25095 

.357 

1.31115 

.396 

1.37623 

.435 

1.44589 

.474 

1.51958 

.319 

1.25243 

.358 

1.31276 

.397 

.37801 

.436 

1.44773 

.475 

1.52152 

.320 

1.25391 

.359 

1.31437 

.398 

1.37974 

.487 

1.44957 

.476 

1.52346 

.321 

1.25540 

.360 

1.31599 

.399 

.38148 

.438 

1.45142 

.477 

1.52541 

.322 

1.25689 

.301 

1.31761 

.400 

.38322 

.439 

1.45327 

.478 

1.52736 

.323 

1.25838 

.362 

1.31923 

.401 

.38496 

.440 

1.15512 

.479 

1.52931 

.324 

1.25988 

.363 

l.?2086 

.402 

.38671 

.441 

1.45697 

.480 

1.53126 

.325 

1.26138 

.364 

1.32249 

.403 

1.38846 

.442 

1.45883 

.481 

1.53322 

.326 

1.26288 

.365 

1.32413 

.404 

1.39021 

.443 

1.40069 

.482 

.53518 

.327 

1.26437 

.366 

1.32577 

.405 

1.39196 

.444 

1.46255 

.483 

.53714 

.328 

1.26588 

.367 

1.32741 

.406 

1.39372 

.445 

1.46141 

.484 

.53910 

.329 

1.26740 

.368 

1.32905 

.407 

1.39548 

.446 

1.46628 

.435 

.54106 

.330 

1.26892 

.369 

1.33069 

.408 

1.39724 

.447 

1.46815 

.486 

.54302 

.331 

1  .27044 

.370 

1.33234 

.409 

1.39900 

.448 

1.47002 

.487 

.54499 

.332 

1.27196 

.371 

1.33399 

.410 

1.40077 

.449 

1.47189 

.488 

.54696 

.333 

1.27349 

.372 

1.  33564 

.411 

1.40254 

.450 

1.47377 

.489 

.54893 

.334 

1.27502 

.373 

J  .33730 

.412 

1.40432 

.451 

1.47565 

.490 

.55091 

.335 

1.27656 

.374 

1.33S96 

.413 

1.40310 

.452 

1.47753 

.491 

.55289 

.336 

1.27810 

.375 

1.34063 

.414 

1.40788 

.453 

1.47942 

.492 

.55487 

.337 

1.27964 

.376 

1.34229 

.415 

1.40966 

.454 

1.48131 

.493 

.55685 

.338 

1.28118 

.377 

1.34396 

.416 

1.41145 

.455 

1.48320 

.494 

.55884 

.339 

1.28273 

.378 

1.34563 

.417 

1.41324 

.456 

1.48509 

.495 

.56083 

.340 

1.28428 

.379 

1.34731 

.418 

1.41503 

.457 

1.48699 

.496 

56282 

.341 

1.28583 

.3  SO 

1.34599 

.419 

1.41632 

.458 

1.48889 

.497 

.56481 

.342 

l.?8739 

.381 

1.350(58 

.420 

1.41861 

.459 

1.49079 

.498 

.56681 

.343 

1  .28895 

.382 

1.35237 

.421 

1.42041 

.460 

1  .49269 

.499 

.56831 

.344 

1.29052 

.333 

1.35406 

.422 

1.42221 

.461 

1.49460 

.500 

.570SO 

Table  of  Lengths  of  Circular  Arcs  whose  Radius 

is  1. 

RULE. — Knowing  the  measure  of  the  circle  and  the  measure  of 
the  arc  in  degrees,  minutes,  and  seconds ;  take  from  the  table  the 
lengths  opposite  the  number  of  degrees,  minutes,  and  seconds  in 
the  arc,  and  multiply  their  sum  by  the  radius  of  the  circle. 

EXAMPLE. — What  is  the  length  of  an  arc  subtending  an  angle 
of  13°  27'  8",  with  a  radius  of  8  feet. 


Ans.  Length  for  13°  = 

27'  = 

8// 
= 

13°  27'  8"= 


0.2268928 
0 . 0078540 
0 . 0000388 
0.2347856 

8 


Length  of  arc  =   1 . 8782848  feet. 


MENSURATION.— CIRCULAR  ARCS. 


59 


Lengths  of  Circular  Arcs;   Radius=l. 


Sec. 

Length. 

Min. 

Length. 

Deg. 

Length. 

Deg. 

Length. 

1 

0  .  0000048 

1 

0.0002909 

1 

0.0174533 

61 

1.0646508 

2 

0.0000097 

2 

0.0005818 

2 

0.0349066 

62 

1.0821041 

3 

0.0000115 

3 

0.0008727 

3 

0.0523599 

62 

1.0995574 

4 

0.0000194 

4 

0.0011636 

4 

0.069S132 

64 

1.1170107 

5 

0.0000242 

5 

0.0014544 

5 

0.0872665 

65 

1  .  1344640 

6 

0.0000291 

6 

0.0017453 

6 

0.1047198 

66 

1.1519173 

7 

0.0000339 

7 

0.0020362 

7 

0.1221730 

67 

1.1693706 

8 

0.0000388 

8 

0.0023271 

8 

0.1396263 

68 

1  .  1868239 

9 

0.0000436 

9 

0.0026180 

9 

0.1570796 

69 

1.2042772 

10 

0.0000485 

10 

0.0029089 

10 

0.1745329 

70 

1.2217305 

11 

0  .  0000533 

11 

0.0031998 

11 

0.1919862 

71 

1.2391838 

12 

0.0000582 

12 

0.0034907 

12 

0.2094395 

72 

1.2566371 

13 

0.0000630 

13 

0.0037815 

13 

0.2268928 

73 

1.2740904 

14 

0.0000079 

14 

0.0040724 

14 

0.2443461 

74 

1.2915436 

15 

0.0000727 

15 

0.0043633 

15 

0.2617994 

75 

1  .  3089969 

16 

0.0000776 

16 

0.0046542 

16 

0.2792527 

76 

1  .  3264502 

17 

0.0000824 

17 

0.0049451 

17 

0.2967060 

77 

1  .  3439035 

18 

0.0000873 

IS 

0.0052360 

18 

0.3141593 

78 

1.3613568 

19 

0.0000921 

19 

0.0055269 

19 

0.3316126 

79 

1.3788101 

20 

0.0000970 

20 

0.0058178 

20 

0.3490659 

80 

1  .  3962634 

21 

0.000101S 

21 

0.0061087 

21 

0.3665191 

81 

1.4137167 

22 

0.0001067 

22 

0.0063995 

22 

0.3839724 

82 

1.4311700 

23 

0.0001115 

23 

0  .  0066904 

23 

0.4014257 

83 

1.4486233 

24 

0.0001164 

24 

0.0069813 

24 

0.4188790 

84 

1.4660768 

25 

0.0001212 

25 

0.0072722 

25 

0.4363323 

85 

1.4835299 

20 

0.0001261 

26 

0.0075631 

26 

0.4537856 

86 

1.5009832 

27 

0.0001309 

27 

0  .  0078540 

27 

0.4712389 

87 

1.5184364 

28 

0.0001357 

28 

0.0081449 

28 

0.4886922 

88 

1.5358897 

29 

0.0001406 

29 

0.0084358 

29 

0.5061455 

.  89 

1  .  5533430 

30 

0.0001454 

30 

0.0087266 

30 

0.5235988 

90 

1.5707963 

31 

0.0001503 

31 

0.0090175 

31 

0  5410521 

91 

1.5882496 

32 

0.0001551 

32 

0.0093084 

32 

0.5585054 

92 

1  .  6057029 

33 

0.0001600 

33 

0.0095993 

33 

0.5759587 

93 

1.6231562 

34 

0.0001648 

34 

0.0098902 

34 

0.5934119 

94 

1  .  6406095 

35 

0.0001697 

35 

0.0101811 

35 

0.6108652 

95 

.  6580628 

36 

0.0001745 

36 

0.0104720 

36 

0.6283185 

96 

.6755161 

37 

0.0001794 

37 

0.0107629 

37 

0.6457718 

97 

.  6929694 

38 

0.0001842 

38 

0.0110538 

38 

0.6632251 

98 

.7104227 

39 

0.0001891 

39 

0.0113446 

39 

0.6806784 

99 

.  7278760 

40 

0.0001939 

40 

0.0116355 

40 

0.6981317 

100 

.7453293 

41 

0.0001988 

41 

0.0119264 

41 

0.7155850 

101 

.  7627825 

42 

0  .  0002036 

42 

0.0122173 

42 

0.7330383 

102 

.  7802358 

43 

0  .  0002085 

43 

0.0125082 

43 

0.7504916 

103 

.7976891 

44 

0.0002133 

44 

0.0127991 

44 

0.7679449 

104 

.8151424 

45 

0.0002132 

45 

0.0130900 

45 

0.7853982 

105 

8325957 

46 

0  .  0002230 

46 

0.0133809 

46 

0.8028515 

106 

.8500490 

47 

0  .  0002279 

47 

0.0136717 

17 

0.8203047 

107 

.8675023 

48 

0.0002327 

48 

0.0139626 

48 

0.8377580 

108 

.8849556 

49 

0  .  0002376 

49 

0.0142535 

49 

0.8552113 

109 

.9024089 

50 

0.0002124 

50 

0.0145444 

50 

0.8726646 

110 

.9198622 

51 

0.000?473 

51 

0.0148353 

51 

0.8901179 

111 

.9373155 

52 

0.0002521 

52 

0.01512-32 

52 

0.9075712 

112 

.9547688 

53 

0.0002570 

53 

0.0154171 

53 

0.9250245 

113 

.9722221 

54 

0.0002618 

54 

0.0157080 

54 

0.9424778 

114 

.9890753 

55 

0.0002666 

55 

0.0159989 

55 

0.9599311 

115 

2.0071286 

56 

0.0002715 

56 

0.0162897 

56 

0.9773844 

116 

2.0215819 

57 

0  .  0002763 

57 

0.0165806 

57 

0.9948377 

117 

2  .  0-120352 

58 

0.0002812 

58 

0.0168715 

58 

1.0122910 

118 

2.0591885 

59 

0  .  0002860 

59 

0.0171624 

59 

1  .  0297443 

119 

2.0769418 

60 

0.0002909 

60 

0.0174533 

60 

1.0471976 

120 

2.0943951 

60    MENSURATION.—  LENGTHS  OF  CHORDS. 

To  compute  the  chord  of  an  arc  when  the  chord  of  half  the  arc  and 
the  versed  sine  are  given.  (The  versed 
sine  is  the  perpendicular  bo,  Fig.  31.) 
RULE.  —  From  the  square  of  the  chord  of 
half  the  arc  subtract  the  square  of  the  versed 
sine,  and  take  twice  the  square  root  of  the 
remainder. 

EXAMPLE.  —  The  chord  of  half  the  arc  is  60,  and  the  versed 
sine  36,  what  is  the  length  of  the  chord  of  the  arc? 

Ans.  602-362=2304,  and  V/2304  =  48, 
and  48X2  =  96,  the  chord. 

To  compute  the  chord  of  an  arc  when  the  diameter  and  versed  sine 
are  given. 

Multiply  the  versed  sine  by  2,  and  subtract  the  product  from 
the  diameter;  then  subtract  the  square  of  the  remainder  from 
the  square  of  the  diameter,  and  take  the  square  root  of  that  re- 
mainder. 

EXAMPLE.  —  The  diameter  of  a  circle  is  100,  and  the  versed 
sine  of  an  arc  36,  what  is  the  chord  of  the  arc? 

Ans.  36X2=72.     100-72=28.     1002-282  =  9216. 
V9216  =  96,  the  chord  of  the  arc. 

To  compute  the  chord  of  half  an  arc  when  the  chord  of  the  arc  and 
the  versed  sine  are  given. 

RULE.  —  Take  the  square  root  of  the  sum  of  the  squares  of  the 
versed  sine  and  of  half  the  chord  of  the  arc. 

EXAMPLE.  —  The  chord  of  an  arc  is  96,  and  the  versed  sine  36, 
what  is  the  chord  of  half  the  arc?  _ 

Ans. 


To  compute  the  chord  of  half  an  arc  when  the  diameter  and  versed 
sine  are  given. 

RULE  —  Multiply  the  diameter  by  the  versed   sine,  and  take 
the  square  root  of  their  product. 
To  compute  a  diameter. 

RULE  1.  —  Divide  the  square  of  the  chord  of  half  the  arc  by 
the  versed  sine. 

RULE  2.  —  Add  the  square  of  half  the  chord  of  the  arc  to  the 
square  of  the  versed  sine,  and  divide  this  sum  by  the  versed  sine* 


MENSURATION.— ARCS  AND  VERSED  SINES.     61 

EXAMPLE. — What  is  the  radius  of  an  arc  whose  chord  is  96,  and 
whose  versed  sine  is  36? 

Ans.  482  +  36'=3600.     3600^36=100,  the  diameter, 
and  radius  =50. 

To  compute  the  versed  sine. 

RULE. — Divide  the  square  of  the  chord  of  half  the  arc  by  the 
diameter. 

To  compute  the  versed  sine  when  the  chord  of  the  arc  and  the  diame- 
ter are  given. 

RULE. — From  the  square  of  the  diameter  subtract  the  square 
of  the  chord,  and  extract  the  square  root  of  the  remainder;  sub- 
tract this  root  from  the  diameter,  and  halve  the  remainder. 

To  compute  the  length  of  an  arc  of  a  circle  when  the  number  of 
"degrees  and  the  radius  are  given. 

RULE  1. — Multiply  the  number  of  degrees  in  the  arc  by  3.1416 
multiplied  by  the  radius,  and  divide  by  180.  The  result  will  be 
the  length  of  the  arc  in  the  same  unit  as  the  radius. 

RULE  2. — Multiply  the  radius  of  the  circle  by  0.01745,  and  the 
product  by  the  degrees  in  the  arc. 

EXAMPLE. — The  number  of  degrees  in  an  arc  is  60,  and  the 
radius  is  10  inches,  what  is  the  length  of  the  arc  in  inches? 

Ans.  10X3.1416X60=1884.96-^-180=10.47    inches; 

or,  10X0.01745X60=10.47  inches. 

To  compute  the  length  of  the  arc  of  a  circle  when  the  length  is 
given  in  degrees,  minutes,  and  seconds. 

RULE  1. — Multiply  the  number  of  degrees  by  0.01745329,  and 
the  product  by  the  radius. 

RULE  2. — Multiply  the  number  of  minutes  by  0.00029,  and 
that  product  by  the  radius. 

RULE  3. — Multiply  the  number  of  seconds  by  0.0000048  times 
the  radius.  Add  together  these  three  results  for  the  length  of 
the  arc. 

See  also  table,  p.  59. 

EXAMPLE. — What  is  the  length  of  an  arc  of  60°  10'  5",  the 
radius  being  4  feet? 

Ans.  I.  60°XO. 01745329X4=4. 188789   feet. 

2.  10' X  0.00029        X  4  =  0.01 16       feet. 

3.  5" X 0.0000048   X 4  =  0.000096   feet. 


4.200485   feet. 


62     MENSURATION.— CIRCULAR  SEGMENTS,  ETC. 

To  compute  the  area  of  a  sector  of  a  circle  when  the  degrees  of  the 

arc  and  the  radius  are  given  (Fig.  32).* 
RULE. — Multiply  the  number  of  degrees  in 
the  arc  by  the  area  of  the  whole  circle,  and  di- 
vide by  360. 

EXAMPLE. — What  is  the  area  of  a  sector  of 
a  circle  whose  radius  is  5,  and  the  length  of  the 
arc  is  60°? 
Ans.  Area  of  circle  =  10X10X0.7854  =  78.54. 

78.5X60 

Then  area  of  sector  =  —  — — — =  13 . 09. 
ooO 

//  the  length  of  the  arc  is  given  in  degrees  and  minutes,  reduce  it 
to  minutes,  and  multiply  by  the  area  of  the  whole  circle,  and  di- 
vide by  21600. 
To  compute  the  area  of  a  sector  of  a  circle  when  the  length  of  the 

arc  and  radius  are  given. 

RULE. — Multiply  the  length  of  the  arc  by  half  the  length  of  the 
radius,  and  the  product  is  the  area. 
To  compute  the  area  of  a  segment  of  a  circle  when  the  chord  and 

versed  sine  of  the  arc  and  the  radius  or  diameter  of  the  circle 

are  given. 

NOTE. — The  versed  sine  is  the  distance  cd  (Fig.  32). 

RULE  1  (when  the  segment  is  less  than  a  semicircle). — Ascer- 
tain the  area  of  the  sector  having  the  same  arc  as  the  segment, 
then  ascertain  the  area  of  a  triangle  formed  by  the  chord  of  the 
segment  and  the  radii  of  the  sector,  and  take  the  difference  of 
these  areas. 

RULE  2  (when  the  segment  is  greater  than  a  semircicle). — As- 
certain by  the  preceding  rule  the  area  of  the  lesser  portion  of  the 
circle,  subtract  it  from  the  area  of  the  whole  circle,  and  the  re- 
mainder will  give  the  area. 
To  compute  the  convex  surface  of  a  sphere. 

RULE. — Multiply  the  diameter  by  the  circumference,  and  the 
product  will  give  the  surface. 

EXAMPLE. — What  is  the  convex  surface  of  a  sphere  of  10  inches 
diameter? 

Ans.  Circumference  of  sphere  =10X3. 1416  =  31 .416  inches] 
10X31. 416  =  314 . 16  sq.  in.,  the  surface  of  sphere. 

*  The  degrees  of  the  arc  are  the  same  as  of  the  angle  aob. 


MENSURATION.— SPHERES  AND   SPHEROIDS.     63 


Fig.  33 


To  compute  the  surface  of  a  segment  of  a  sphere. 

RULE.—  Multiply  the  height  (be,  Fig.  33) 
by  the  circumference  of  the  sphere,  and  add 
the  product  to  the  area  of  the  base. 

To  find  the  area  of  the  base,  we  have  the 
diameter  of  the  sphere  and  the  length  of  the 
versed  sine  of  the  arc  abd,  and  we  can  find 
the  length  of  the  chord  ad  by  the  rule  on 
p.  60.  Having,  then,  the  length  of  the 
chord  ad  for  the  diameter  of  the  base,  we 
can  easily  find  the  area. 

EXAMPLE.  —  The  height,  be,  of.  a  segment  abd,  is  36  inches,  and 
the  diameter  of  the  sphere  is  100  inches.  What  is  the  convex  sur- 
face, and  what  the  whole  surface? 

Ans.  100  X  3  .  1416  =  314  .  16  inches,  the  circumference  of  sphere. 
36X314  .  16=  11309  .  76,  the  convex  surface. 
The  length  of  ad=  100-36x2=28. 
VlOO'-282  =  96,  the  chord  ad. 
962XO.  7854=2738.  2464,  the  area  of  base. 
11309  .  76  -i-  7238  .  2464=  18548.0064,  F!r-_l4 

the  total  area. 
To  compute  the  surface  of  a  spherical 

zone. 

RULE.—  Multiply  the  height  (cd,  Fig.  34)  a 
by  the  circumference  of  the  sphere  for  the 
convex  surface,  and  add  to  it  the  area  of 
the  two  ends  for  the  whole  area. 

Spheroids,  or  Ellipsoids. 

DEFINITION.  —  Spheroids,  or  ellipsoids,  are  figures  generated  by 
the  revolution  of  a  semi-ellipse  about  one  of  its  diameters. 

When  the  revolution  is  about  the  long  diameter,  they  are  pro- 
late; and  when  it  is  about  the  short  diameter,  they  are  oblate. 

A  prolate  spheroid  is  cigar-shaped,  an  oblate  spheroid  is  like 
a  watch. 
To  compute  the  surface  of  a  spheroid. 

Let  a=  J  long  axis;  let  b  =  J  short  axis; 


let 


then  surface  of  oblate  spheroid 


I 


a2  —  b2  . 


64        MENSURATION.— CONES  AND  PYRAMIDS. 

Surface  of  prolate  spheroid 


e 

In  the  first  formula,  natural  logarithms  must  be  used.  The 
natural  logarithm  may  be  obtained  by  multiplying  the  common 
logarithm  by  2.302. 

sin~le  may  be  found,  by  finding  the  angle  whose  natural  sine 
is  equal  to  e  and  dividing  the  angle  so  obtained  by  57.3. 

[Although  the  above  formula?  are  complicated,  no  simpler  rules 
can  be  given  that  are  at  all  reliable.] 
To  compute  the  surface  of  a  cylinder. 

RULE. — Multiply  the  length  by  the  circumference  for  the  con- 
vex surface,  and  add  to  the  product  the  area 
of  the  two  ends  for  the  whole  surface. 
To  compute  the  sectional  area  of  a  circular 

ring  (Fig.  35). 

RULE. — Find  the  area  of  both  circles,  and 
subtract  the  area  of  the  smaller  from  the  area 
of  the  larger;  the  remainder  will  be  the  area 
Fig. 35  of  the  ring. 

To  compute  the  surface  of  a  cone. 

RULE. — Multiply  the  perimeter  or  circumference  of  the  base  by 
one-half  the  slant  height,  or  side  of  the  cone,  for  the  convex  area. 
Add  to  this  the  area  of  the  base,  for  the  whole  area. 

EXAMPLE. — The  diameter  of  the  base  of  a  cone  is  3  inches,  and 
the  slant  height  15  inches,  what  is  the  area  of  the  cone? 

Ans.  3X3.1416=  9. 4248=  circumference  of  base. 

9 . 4248  X  7J  =  70 . 686  square  inches,the  convex  surface. 
3X3X0.7854=   7. 068  square  inches,  the  area  of  base. 
Area  of  cone=77.754  square  inches. 

To  compute  the  area  of  the  surface  of  the  frus- 
tum of  a  cone. 

RULE. — Multiply  the  sum  of  the  perimeters 
of  the  two  ends  by  the  slant  height  of  the  frus- 
tum, and  divide  by  2,  for  the  convex  surface. 
Add  the  area  of  the  top  and  bottom  surfaces. 
To  compute  the  surface  of  a  pyramid. 

RULE. — Multiply  the  perimeter  of  the  base 
y  one-half  the  slant  height,  and  add  to  the 
product  the  area  of  the  base. 
To   compute   the  surface  of  the  frustum  of  a 
F'9-  36  pyramid. 


MENSURATION.— PRISMS. 


65 


Fig. 37 


RULE. — Multiply  the  sum  of  the  perimeters  of  the  two  ends  by 
the  slant  height  of  the  frustum,  halve  the  product,  and  add  to  the 
result  the  area  of  the  two  ends. 

MENSURATION  OP  SOLIDS. 
To  compute  the  volume  of  a  prism. 

RULE. — Multiply  the  area  of  the  base  by  the  height. 

This  rule  applies  to  any  prism  of  any  shape  on  the  base,  as  long 
as  the  top  and  bottom  surfaces  are  parallel. 
To  compute  the  volume  of  a  prismoid. 

DEFINITION. — A    prismoid    is  a  1) 

a  solid  having  parallel  ends  or 
bases  dissimilar  in  shape  with 
quadrilateral  sides. 

RULE. — To  the  sum  of  the 
areas  of  the  two  ends  add  four 
times  the  area  of  the  middle 
section  parallel  to  them,  andm 
multiply  this  sum  by  one-sixth 
of  the  perpendicular  height. 

EXAMPLE. — What  is  the  vol- 
ume of  a  quadrangular  prismoid,  as  in  Fig.  37,  in  which  a&=6", 
cd=4",  ac= 7^=10",  ce=8",  e/=8",  and  ih=6"  ? 

Ans.  Area  of  top  =— —  xlO=50. 

8+6' 


2 


Area  of  bottom 


Area  of  middle  section = 

z 

[50  +  70+  (4X60)]Xf  =480  cubic  inches. 

NOTE — The  length  of  the  end  of  the  middle  section,  as  mn  in  Fig.  37  = 
ed  +  ef 


To  find  the  volume  of  a  prism 
truncated  obliquely. 

RULE. — Multiply  the  area  of 
the  base  by  the  average  height  a 
of  the  edges. 

EXAMPLE.  — What  is  the 
volume  of  a  truncated  prism, 
as  in  Fig.  38,  where  e/=6 
inches,  fh=10  inches,  ea=10, 
ci=l2,  dh=S,  and  /6=8? 


Ficj.38 


66  MENSURATION.— POLYHEDRONS. 

Ans.    Area  of  base  =  6X10     =60  square  inches. 

10  I  12  I  S  I  R 
Average  height  of  edges = • —  =  9J  inches. 

60X9J  =  970  cubic  inches. 

To  compute  the  volume  of  a  wedge  when  the  ends  are  parallel  and 

equal. 

RULE. — Multiply  the  area  of  one 
end  by  the  length  of  the  wedge. 
To  compute  the  volume  of  a  wedge 

when  the  ends  are  not  parallel. 
RULE. — Add  together  the  lengths 
of  the  three  edges,  ab,  cd,  and  ef; 
multiply  their  sum  by  the  perpen- 
dicular height  of  the  wedge,  and 
then  by  the  breadth  of  the  back, 
and  divide  the  product  by  6. 


Regular  Polyhedrons. 

DEFINITION. — A  regular  body  is  a  solid  contained  within  a  cer- 
tain number  of  similar  and  equal  plane  faces,  all  of  which  are 
equal  regular  polygons. 

The  whole  number  of  regular  bodies  which  can  possibly  be 
found  is  five.  They  are: — 

1.  The  tetrahedron,  or  pyramid. 

2.  The  hexahedron,  or  cube,  which  has  six  square  faces. 

3.  The  octahedron,  which  has  eight  triangular  faces. 

4.  The  dodecahedron,  which  has  twelve  pentagonal  faces. 

5.  The  icosahedron,  which  has  twenty  triangular  faces. 

To  compute  the  volume  of  a  regular  polyhedron. 

RULE  1  (when  the  radius  of  the  circumscribing  sphere  is  given) . — 
Multiply  the  cube  of  the  radius  of  the  sphere  by  the  multiplier 
opposite  to  the  body  in  column  2  of  the  following  table. 

RULE  2  (when  the  radius  of  the  inscribed  sphere  is  given). — 
Multiply  the  cube  of  the  radius  of  the  inscribed  sphere  by  the  mul- 
tiplier opposite  to  the  body  in  column  3  of  the  following  table. 

RULE  3  (when  the  surface  is  given). — Cube  the  surface  given, 
extract  the  square  root,  and  multiply  the  root  by  the  multiplier 
opposite  to  the  body  in  column  4  of  the  following  table. 


MENSURATION.— CONES,  PYRAMIDS,  ETC.         67 


1 

2 

3 

4 

Figure. 

Volume  by 

Volume  by 

No.  of 

radius  of 

radius  of 

Volume  by 

sides. 

circumscribing 

inscribed 

surface. 

sphere. 

circle. 

Tef  riih.ed.ron 

4 

0.5132 

13.85641 

0.0517 

Hexahedron      .       

G 

1  .  5390 

8  .  0000 

0  .  06804 

Octahedron  

8 

1  .  33333 

6  .  9282 

0.07311 

Dodecahedron  

12 

2.78517 

5.55029 

0.08169 

Icosahedron  

20 

2.53G15 

5.05406 

0  .  085;> 

To  compute  the  volume  of  a  cylinder. 

RULE. — Multiply  the  area  of  the  base  by  the  height. 
To  compute  the  volume  of  a  cone. 

RULE. — Multiply  the  area  of  the  base  by  the  perpendicular 
height,  and  take  one- third  of  the  product. 
To  compute  the  volume  of   the  frustum  of  a 
cone. 

RULE. — Add  together  the  squares  of  the 
diameters  of  the  two  ends  and  the  prod- 
uct of  the  two  diameters;  multiply  this 
sum  by  0.7854,  and  this  product  by  the 
height,  and  then  divide  this  last  product 
by  3. 

EXAMPLE  — What  is  the  volume  of  a 
fruslum  of  a  cone  9  inches  high,  5  inches 
diameter  at  the  base,  and  3  inches  at  the  top  ? 

Ans.  52  +  32=34.      3X5-15.      15+34=49,    the    sum  of  the 
squares  and  product  of  the  diameters.  49X0.7854=  38.4846. 


Fig.  40 


38,4846X9 


=  115.4538  cubic  inches. 


To  commute  the  volume  of  a  pyramid. 

RULE. — Multiply  the  area  of  the  base  by  the  perpendicular 
height,  and  take  one-third  of  the  product. 
To  compute  the  volume  of  the  frustum  of  a  pyramid. 

RULE. — Find  the  height  that  the  pyramid  would  be  if  the  top 
were  put  on,  and  then  compute  the  volume  of  the  completed  pyra- 
mid and  the  volume  of  the  part  added ;  subtract  the  latter  from 
the  former,  and  the  remainder  will  be  the  volume  of  the  frustum. 
To  compute  the  volume  of  a  sphere. 

RULE. — Multiply  the  cube  of  the  diameter  by  0.5236. 


68  MENSURATION.— SPHEROIDS,  PARABOLOIDS,  ETC. 


To  compute  the  volume  of  a  segment  of  a  sphere. 

RULE  1. — To  three  times  the  square  of  the  radius  of  its  base 
add  the  square  of  its  height;  multiply  this  sum  by  the  height,  and 
the  product  by  0.5236. 

RULE  2. — From  three  times  the  diameter  of  the  sphere  sub- 
tract twice  the  height  of  the  segment;  multiply  this  remainder 
by  the  square  of  the  height,  and  the  product  by  0.5236. 

EXAMPLE. — The  segment  of  a  sphere  has  a  radius,  ac  (Fig.  41), 
of  7  inches  for  its  base,  and  a  height,  cb,  of  4  inches :  what  is  its 
volume? 

Ans.  (by  Rule  1).  3X72=147,  and  147  +  42=163,  three  times 
the  square  of  the  radius  of  the  base  plus  the  square  of  the  height. 
163X4X0.5236  =  341.3872  cubic  inches  vol- 


SECOND  SOLUTION. — By  the  rule  for  find- 
ing the  diameter  of  a  circle  when  a  chord 
and  its  versed  sine  are  given,  we  find  that 
the  diameter  of  the  sphere  in  this  case  is  10.25 
inches;  then,  by  Rule  2,  (3 X  16.25)  —  (2X4) 
=  40.75,  and  40.75  X  42X  0.5236  =  341.3872 
cubic  inches,  the  volume  of  the  segment. 


Fig  41. 


To  compute  the  volume  of  a  spherical  zone. 

DEFINITION. — The  part  of  a  sphere  in- 
cluded between  two  parallel  planes  (Fig. 
42). 

I b      RULE. — To  the  sum  of  the  squares  of 
the  radii  of  the  two  ends  add  one-third 
of  the  square  of  the  height  of  the  zone; 
multiply  this  sum  by  the  height,  and  that 
Fig.  42  product  by  1.5708. 

To  compute  the  volume  of  a  prolate  spheroid  (see  page  63). 

RULE. — Multiply  the  square  of  the  short  axis 
by  the  long  axis,  and  this  product  by  0.5236. 
To  compute  the  volume  of  an  oblate  spheroid. 

RULE. — Multiply  the  square  of  the  long  axis 
by  the  short  axis,  and  this  product  by  0.5236. 
To  compute  the  volume  of  a  paraboloid  of  revo- 

lution  (Fig.  43). 
RULE. — Multiply  the  area  of  the  base  by  half  the  altitude. 


MENSURATION— EXCAVATIONS. 


69 


To  compute  the  volume  of  a  hyperboloid  of  revolution  (Fig.  44). 

RULE. — To  the  square  of  the  radius  of  the 
base  add  the  square  of  the  middle  diameter; 
multiply  this  sum  by  the  height,  and  the  prod- 
uct by  0.5236. 

To  compute  the  volume  of  any  figure  of  revo- 
lution. F»9-44 
RULE. — Multiply  the  area  of  the  generating  surface  by  the  cir- 
cumference described  by  its  centre  of  gravity. 
To  compute  the  volume  of  an  excavation,  where  the  ground  is  irreg- 
ular, and  the  bottom  of  the  excavation  is  level  (Fig.  45). 
RULE. — Divide  the  surface  of  the  ground  to  be  excavated  into 
equal  squares  of  about  10  feet  on  a  side,  and  ascertain  by  means 
of  a  level  the  height  of  each  corner,  a,  a,  a,  b,  b,  b,  etc.,  above  the 
level  to  which  the  ground  is  to  be  excavated.     Then  add  together 
the  heights  of  all  the  corners  that  only  come  into  one  square. 
Next  take  twice  the  sum  of  the  heights  of  all  the  corners  that  come 

in  two  squares,  as  6,  b,  b ; 

n.  n  ci 

next    three     times    the 

sum  of  the  heights  of  all 
the  corners  that  come  in 
three  squares,  as  c,  c,  c; 
and  then  four  times  the 
sum  of  the  heights  of 
all  the  corners  that'  be- 
long to  four  squares,  as 
d,  d,  d,  etc.  Add  to- 
gether all  these  quan- 
tities, and  multiply  their  sum  by  one-fourth  the  area  of  one  of 
the  squares.  The  result  will  be  the  volume  of  the  excavation. 

EXAMPLE. — Let  the  plan  of  the  excavation  for  a  cellar  be  as  in 
the  figure,  and  the  heights  of  each  corner  above  the  proposed 
bottom  of  the  cellar  be  as  given  by  the  numbers  in  the  figure, 
then  the  volume  of  the  cellar  would  be  as  follows,  the  area  of  each 
square  being  10X10=100  square  feet: — 

Volume  =  i  of  100  (a's  +  2  6's  +  3  c's  +  4  d's). 
rhea's  in  this  case      =    4  +  6  +  3  +  2  +  1+7  +  4=27 
<>Xthe  sum  of  the  fc's=2X  (3  +  6  +  1  +4 +  3 +  4)  =  42 

3  X  the  sum  of  the  c's  =  3  X  (1  +  3  +  4)  =  24 

4  X  the  sum  of  the  d's= 4  X  (2  +  3  +  6  +  2)  =52 


c 

6 

3              4 
| 

c          b 

3 

1 

d 

2 

d 

3 

d 

<i             4 
1              « 

1 
2 

3 

i 

i         i 

0 

a 

*            b            b           b 
Fig.45 

145 


70 


GEOMETRICAL   PROBLEMS. 


Volume=  25 X  145=3625  cubic  feet,  the  quantity  of  earth  to  be 
excavated. 


GEOMETRICAL  PROBLEMS. 

PROBLEM  1. — To  bisect,  or  divide  into  equal  parts,  a  given  line, 
ab  (Fig.  46). 

From  a  and  b,  with  any  radius  greater 
than  half  of  ab,  describe  arcs  intersecting 
j  in  c  and  d.     The  line  cd,  connecting  these 

.intersections,  will  bisect  ab,  and  be  perpen- 


Fig.46 


>, 


£  dicular  to  it. 

PROBLEM  2.  —  To  draw  a  perpendicular 
to  a  given  straight  line  jrom  a  point  with- 
out  it. 

IST  METHOD  (Fig.  47).  —  From  the  point  a  describe  an  arc  with 
sufficient  radius  that  it  will  cut  the  line  be 
'c  in  two  places,  as  e  and  /.  From  e  and  / 
describe  two  arcs,  with  the  same  radium, 
intersecting  in  g;  then  a  line  drawn  from 
a  to  g  will  be  perpendicular  to  the  line  be. 

2o  METHOD  (Fig. 
48)  .  —  From  any  two 
points,  d  and  c,  at  some 
distance  apart  in  the 
given  line,  and  with 

radii  da  and  ca  respectively,  describe  arcs  cut- 
ting at  a  and  e.     Draw  ae,  and  it  will  be  the  - 
perpendicular  required.     This  method  is  use- 
ful where  the  given  point  is  opposite  the  end 
of  the  line,  or  nearly  so. 

PROBLEM  3.  —  To  draw  a  perpendicular  to 
a  straight  line  from  a  given  point,  a,  in  that 


Fig.48 


line. 


a 
Fig.49 


IST  METHOD  (Fig.  49).  —  With  any 
radius,  from  the  given  point  a  in  the 
line,  describe  arcs  cutting  the  line  in 
the  points  b  and  c.  Then  with  b  and 
c  as  centres,  and  with  any  radius 
greater  than  ab  or  ac,  describe  arcs 
cutting  each  other  at  d.  The  line  da 
will  be  the  perpendicular  desired. 


GEOMETRICAL   PROBLEMS. 


71 


Fig,SO 


Fig. 51 


2o  METHOD  (Fig.  50,  when  the  given  point  is  at  the  end  of 
the  line). — From  any  point,  6,  outside  of  the 
line,  and  with  a  radius  ba,  describe  a  semi- 
circle passing  through  a,  and  cutting  the 
given  line  at  d\  Through  b  and  d  draw  a 
straight  line  intersecting  the  semicircle  at  e. 
The  line  ea  will  then  be  perpendicular  to  the 
line  ac  at  tne  point  a. 

3o  METHOD  (Fig.  51)  OR  THE  3,  4,  AND  5 
METHOD. — From  the  point  a  on  the  given 
line  measure  off  4  inches,  or  4  feet,  or  4  of  any  other  unit,  and 
with  the  same  unit  of  measure  describe  an 
arc,  with  a  as  a  centre  and  3  units  as  a 
radius.  Then  from  b  describe  an  arc,  with 
a  radius  of  5  units,  cutting  the  first  arc  in  c. 
Then  ca  will  be  the  perpendicular.  This 
method  is  particularly  useful  in  laying 
out  a  right  angle  on  the  ground,  or  framing 
a  house  where  the  foot  is  used  as  the  unit,  and  the  lines  laid 
off  by  straight  edges. 

In  laying  out  a  right  angle  on  the  ground,  the  proportions  of  the 
triangle  may  be  30,  40,  and  50,  or  any  other  multiple  of  3,  4,  and 
5;  and  it  can  best  be  laid  out  with  the  tape.  Thus,  first  meas- 
ure off,  say  40  feet  from  a  on  the  given  line,  then  let  one  person 
hold  the  end  of  the  tape  at  b,  another  hold  the  tape  at  the  80-foot 
mark  at  a,  and  a  third  person  take  hold  of  the  tape  at  the  50-foot 
mark,  with  his  thumb  and  finger,  and  pull  the  tape  taut.  The 
50-foot  mark  will  then  be  at  the  point  c  in  the  line  of  the  per- 
pendicular. 

PROBLEM  4. — To  draw  a  straight  line  parallel  to  a  given  line 
at  a  given  distance  apart  (Fig.  52). 

c  d 


Fig.52  b 

From  any  two  points  near  the  ends  of  the  given  line  describe 
two  arcs  about  opposite  the  line.  Draw  the  line  cd  tangent  to 
these  arcs,  and  it  will  be  parallel  to  ab. 


72 


GEOMETRICAL   PROBLEMS. 


PROBLEM  5. — To  construct  an  angle  equal  to  a  given  angle. 

With  the  point  A,  at  the  apex  of  the  given 
angle,  as  a  centre,  and  any  radius,  describe  the 
arc  BC.  Then  with  the  point  a,  at  the  vertex 
of  the  new  angle,  as  a  centre,  and  with  the  same 
radius  as  before,  describe  an  arc  like  BC.  Then 
with  BC  as  a  radius,  and  b  as  a  centre,  describe 
an  arc  cutting  the  other  at  c.  Then  will  cab  be 
equal  to  the  given  angle  CA  B. 

PROBLEM  6. — From  a  point  on  a  given  line 
to  draw  a  line  making  an  angle  of  60°  with  the 
given  line  (Fig.  54). 

Take  any  distance,  as  ab,  as  a  radius,  and,  with  a  as  a  centre, 
describe  the  arc  be.  Then  with  b  as  a  centre,  and  the  same  radius, 
describe  an  arc  cutting  the  first  one  at  c.  Draw  from  a  a  line 
through  c,  and  it  will  make  with  ab  an  angle  of  60°. 

c 


Fig.54          &  Fig.55        I    * 

PROBLEM  7. — From  a  given  point,  A,  on  a  given  line,  AE,  to 
draw  a  line  making  an  angle  of  45°  with  the  given  line  (Fig.  55). 

Measure  off  from  A,  on  AE,  any  distance,  Ab,  and  at  b  draw  a 
line  perpendicular  to  AE.  Measure  off  on  this  perpendicular  be 
equal  to  A  b,  and  draw  a  line  from  A  through  c,  and  it  will  make 
an  angle  with  AE  of  45°. 

PROBLEM  8. — From  any  point,  A,  on  a  given  line,  to  draw  a  line 
which  shall  make  any  desired  angle  with  the  given  line  (Fig.  56). 

To  perform  this  problem  we  must  have  a 
table  of  chords  at  hand  (such  as  is  found 
on  pp.  88-96),  which  we  use  as  follows. 
Find  in  the  table  the  length  of  chord  to  a 
radius  1,  for  the  given  angle.  Then  take 
~Eany  radius,  as  large  as  convenient,  de- 
scribe an  arc  of  a  circle  be  with  A  as  a  cen- 


Fig.56 


tre.  Multiply  the  chord  of  the  angle,  found  in  the  table,  by  the 
length  of  the  radius  A  b,  and  with  the  product  as  a  new  radius,  and 
b  as  a  centre,  describe  a  short  arc  cutting  be  in  d.  Draw  a  line 
from  A  through  d,  and  it  will  make  the  desirecj  angle  with  f)E. 


GEOMETRICAL   PROBLEMS. 


EXAMPLE. — Draw  a  line  from  A  on  DE,  making  an  angle  of 
44°  40'  with  DE. 

SOLUTION. — We  find  that  the  largest  convenient  radius  for  our 
arc  is  8  inches :  so  with  A  as  a  centre,  and  8  inches  as  a  radius,  we 
describe  the  -arc  be.  Then,  looking  in  the  table  of  chords,  we  find 
the  chord  for  an  angle  or  arc  of  44°  40'  to  a  radius  1  is  0.76.  Mul- 
tiplying this  by  8  inches,  we  have,  for  the  length  of  our  new  ra- 
dius, 6.08  inches,  and  with  this  as  radius,  and  6  as  a  centre,  we 
describe  an  arc  cutting  be  in  d.  Ad  will  then  be  the  line  desired. 

PROBLEM  8a. — To  lay  off  a  given  angle  approximately  by  means 
of  an  ordinary  two-foot  rule.  Lay  one  le*g  of  the  rule  on  the  paper 
or  board  with  its  inner  edge  coinciding  with  the  given  line.  Open 
the  rule  until  the  distance  between  the  inner  edges  at  the  ends 
corresponds  with  that  given  for  the  angle  in  the  following  table ; 
then  draw  a  line  by  marking  along  the  inner  edge  of  the  other  leg, 
and  it  will  give  the  desired  angle  within  a  very  close  approxima- 
tion. 

TABLES  OF  ANGLES  CORRESPONDING  TO  OPENINGS 
OF  A  TWO-FOOT  RULE  (TRAUTWTNE). 


In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

1A 

1  12 

11  22 

4H 

21  37 

32   3 

m 

42  46 

1  48 

2V6 

11  58 

22  13 

6% 

32  40 

43  24 

X 

2  24 

12  34 

% 

22  50 

33  17 

9 

44   3 

3  00 

H 

13  10 

23  27 

7 

33  54 

44  42 

% 

3  36 

13  46 

5 

24   3 

34  33 

1A 

45  21 

4  11 

3 

14  22 

24  39 

M 

35  10 

45  59 

1 

4  47 

14  58 

1A 

25  16 

35  47 

K 

46  38 

5  23 

y* 

15  34 

25  53 

Y2 

36  25 

47  17 

H 

5  58 

16  10 

1A 

26  30 

37   3 

K 

47  56 

6  34 

Yz 

16  46 

27   7 

H 

37  41 

48  35 

te 

7  10 

17  22 

H 

27  44 

38  19 

10 

49  15 

7  46 

% 

17  59 

28  21 

8 

38  57 

49  54 

H 

8  22 

18  35 

3 

28  58 

39  35 

& 

50  34 

8  58 

4 

19  12 

29  35 

w 

40  13 

51  13 

2 

9  34 

19  48 

y* 

30  11 

40  51 

y? 

51  53 

10  10 

H 

20  24 

30  49 

K 

41  29 

52  33 

H 

10  46 

21  00 

y* 

31  26 

42   7 

PROBLEM  9. — To  bisect  a  given 
angle,  as  BAG  (Fig.  57). 

With  A  as^  centre,  and  any  radius, 
describe  an  arc,  as  cb.  With  c  and  b  as 
centres,  and  any  radius  greater  than 
one-half  of  cb,  describe  two  arcs  inter- 
secting in  d.  Draw  from  A  a  line 


^ 


Fig.  57 


through  d,  and  it  will  bisect  the  angle  BA  C. 

PROBLEM  10.  —  To  bisect  the  angle  contained  between  two  lines, 


74 


GEOMETRICAL  PROBLEMS. 


as  A B  and  CD,  when  the  vertex  of  the  angle  is  not  on  the  drawing 
(Fig.  58). 


Fig.58 


Fig.59 


Draw  fe  parallel  to  A  B,  and  cd  parallel  to  CD,  so  that  the  two 
lines  will  intersect  each  other,  as  at  i.  Bisect  the  angle  eid,  as  in 
the  preceding  problem,  and  draw  a  line  through  i  and  o  which  will 
bisect  the  angle  between  the  two  given  lines. 

PROBLEM  11. — Through  two  given  points, 
B  and  C,  to  describe  an  arc  of  a  circle  with 
a  given  radius  (Fig.  59). 

With  B  and  C  as  centres,  and  a  radius  N 
equal  to  the  given  radius,  describe  two  arcs 
intersecting  at  A .    With  A  as  a  centre,  and 
the  same  radius,  describe  the  arc  be,  which 
will  be  found  to  pass  through  the  given  points,  B  and  C. 

PROBLEM  12. — To  find  the  centre  of  a  given  circle  (Fig.  60). 

Draw  any  chord  in  the  circle,  as  ab,  and  bisect  this  chord  by 
the  perpendicular  cd.     This  line  will  pass  through  the  centre 
of  the  circle,  and  ef  will  be  a  diameter  of  the  circle.     Bisect  ef,  and 
the  centre  o  will  be  the  centre  of  the  circle. 
Fig.60 
e 

Fig.6l 

B 


y& 


PROBLEM    13. — To   draw   a  circular  arc   through   three  given 
points,  as  A,  B,  and  C  (Fig.  61). 


GEOMETRICAL  PROBLEMS. 


75 


Draw  a  line  from  A  to  B  and  from  B  to  C.  Bisect  AB  and  BC 
by  the  lines  aa  and  cc,  and  prolong  these  lines  until  they  intersect 
at  o,  which  will  be  the  centre  for  the  arc  sought.  With  o  as  a 
centre,  and  A  o  as  a  radius,  describe  the  arc  A  BC. 

PROBLEM  14. — To  describe  a  circular  arc  passing  through  three 
given  points,  when  the  centre  is  not  available,  by  means  of  a  tri- 
angle (Fig.  62). 

Let  A,  B,  and  C 
be  the  given  points. 
Insert  two  stiff  pins 
or  nails  at  A  and  C. 
Place  two  strips  of 
wood,  SSt  as  shown  - 
in  the  figure;  one 
against  A ,  the  other 
against  C,  and  in- 
clined so  that  their 
intersection  shall 
come  at  the  third 
point,  B.  Fasten  the  strips  together  at  their  intersection,  and 
nail  a  third  strip,  T,  to  their  other  ends,  so  as  to  make  a  firm 
triangle.  Place  the  pencil-point  at  B,  and,  keeping  the  edges  of 
the  triangle  against  A  and  B,  move  the  triangle  to  the  left  and 
right,  and  the  pencil  will  describe  the  arc  sought. 

When  the  points  A  and  C  are  at  the  same  distance  from  B,  if  a 
strip  of  wood  be  nailed  to  the  triangle,  so  that  its  edge  de  shall  be 
at  right  angles  to  a  line  joining  A  and  C  as  the  triangle  is  moved 
one  way  or  the  other,  the  edge  de  will  always  point  to  the  centre 
of  the  circle.  This  principle  is  used  in  the  perspective  lineard. 

PROBLEM  15. — To  find  a  circular  arc  which  shall  be  tangent  to 
a  given  point,  A,  on  a  straight  line,  and 
pass  through  a  given  point,  C,  outside  the  ~ 
line  (Fig.  63). 

Draw  from  A  a  line  perpendicular  to 
the  given  line.  Connect  A  and  C  by  a 
straight  line,  and  bisect  it  by  the  perpen- 
dicular ac.  The  point  where  tHese  two 
perpendiculars  intersect  will  be  the  cen- 
tre of  the  circle. 

PROBLEM  16. — To  connect  two  parallel  lines  by  a  reversed  curve 
composed  of  two  circular  arcs  of  equal  radius,  and  tangent  to  the 
lines  at  given  points,  as  A  and  B  (Fig.  64). 


76 


GEOMETRICAL   PROBLEMS, 


Join  A  and  B,  and  divide  the  line  into  two  equal  parts  at  C. 
Bisect  CA  and  CB  by 
perpendiculars.  At  A 
and  B  erect  perpen- 
diculars to  the  given 
lines,  and  the  intersec- 
tions a  and  b  will  be 
the  centres  of  the  arcs 
composing  the  re-  ^ 

quired  curve. 

PROBLEM  17. — On  a  given  line,  as  AB.  to  construct  a  corn- 
pound  curve  of  three  arcs  of  circles,  the  radii  of  the  two  side  ones 
being  equal  and  of  a 
given  length,  and  their 
centres  in  the  given 
line,'  the  central  arc 
to  pass  through  a 
given  point,  C,  on  the 
perpendicular  bisect- 
ing the  given  line,  and 
tangent  to  the  other 
two  arcs  (Fig.  65). 

Draw  the  perpen- 
dicular CD.     Lav  off 


'ig.65 


A  a,  Bb,  and  Cc,  each  equal  to  the  given  radius  of  the  side  arcs; 
join  ac;  bisect  ac  by  a  perpendicular.  The  intersection  of  this 
line  with  the  perpendicular  CD  will  be  the  required  centre  of  the 
central  arc.  Through  a  and  b  draw  the  lines  De  and  Def ;  from 
a  and  b,  with  the  given  radius,  equal  to  Aa,  Bb,  describe  the  arcs 
Ae'  and  Be;  from  D  as  a  centre,  and  CD  as  a  radius,  describe  the 
arc  eCe'  which  completes  the  curve  required. 

PROBLEM  18. — To  construct  a  triangle  upon  a  given  straight 
line  or  base,  the  length  of  the  two  sides  being  given  (Fig.  66). 


p 
Fig.GGa 

First  (an  equilateral  triangle,  Fig.  66a). — With  the  extremities 


GEOMETRICAL  PROBLEMS. 


77 


A  and  B  of  the  given  line  as  centres,  and  AB  as  a  radius,  describe 
arcs  cutting  each  other  at  C.  Join  AC  and  BC. 

Second  (when  the  sides  are  unequal,  Fig.  666). — Let  AD  be  the 
given  base,  and  the  other  two  sides  be  equal  to  C  and  B.  With 
D  as  a  centre,  and  a  radius  equal  to  C,  describe  an  indefinite  arc. 
With  A  as  a  centre,  and  B  as  a  radius,  describe  an  arc  cutting  the 
first  at  E.  Join  E  with  A  and  D,  and  it  will  give  the  required 
triangle. 

PROBLEM  19. — To  describe  a  circle  about  a  triangle  (Fig.  67). 

Bisect  two  of  the  sides,  as  AC  and  CB,  of  the  triangle,  and  at 
their  centres  erect  perpendicular  lines,  as  ae  and  be,  intersecting 
at  e.  With  e  as  a  centre,  and  eC  as  a  radius,  describe  a  circle,  and 
it  will  be  found  to  pass  through  A  and  B. 

C 


Fig.67 


PROBLEM  20. — To  inscribe  a  circle  in  a  triangle  (Fig.  68). 
Bisect  two  of  the  angles,  A  and  B,  of  the  triangle  by  lines  cut- 
ting each  other  at  o.     With  o  as  a  centre,  and  oe  as  a  radius, 
describe  a  circle,  which  will  be  found  to  just  touch  the  other  two 
sides. 

PROBLEM  21. — To  inscribe  a  square  in  a  circle,  and  to  describe 
a  circle  about  a  square  (Fig.  69). 

To  inscribe  the  square.  Draw  two  diameters,  AB  and  CD,  at 
right  angles  to  each  other.  Join  the  points  A}  D,  B}  C,  and  we 
'have  the  inscribed  square. 

To  describe  the  circle.  Draw  the  diagonals  as  before,  intersect- 
ing at  Ej  and,  with  E  as  a  centre  and  AE  as  a  radius,  describe  the 
(circle. 

PROBLEM  22. — To  inscribe  a  circle  in  a  square,  and  to  describe 
la  square  about  a  circle  (Fig.  70). 

To  inscribe  the  circle.  Draw  the  diagonals  AB  and  CD,  inter- 
secting at  E.  Draw  the  perpendicular  EG  to  one  of  the  sides. 
Then  with  E  as  a  centre,  and  EG  as  a  radius,  describe  a  circle, 
which  will  be  found  to  touch  all  four  sides  of  the  square. 


78 


GEOMETRICAL   PROBLEMS. 


To  describe  the  square.     Draw  two  diameters,  AB  and  CD,  at 
right  angles  to  each  other,  and  prolonged  beyond  the  circumfer- 


u  F 

Fig.  70 

ence.  Draw  the  diameter  GF,  bisecting  the  angle  CEA  or  BED. 
Draw  lines  through  G  and  F  perpendicular  to  OF,  and  terminat- 
ing in  the  diagonals.  Draw  AD  and  CB  to  complete  the  square. 

PROBLEM  23. — To  inscribe  a  penta- 
gon in  a  circle  (Fig.  71). 

Draw  two  diameters,  AB  and  CD,  at 
right  angles  to  each  other.  Bisect  AO 
at  E.  With  E  as  a  centre,  and  EC  as  a 
radius,  cut  OB  at  F.  With  C  as  a  centre 
and  C7*7  as  a  radius,  cut  the  circle  at  G 
and  H.  With  these  points  as  centres, 
and  the  same  radius,  cut  the  circle  at  / 
and  /.  Join  I,  J,  H,  G,  and  C,  and  we 
then  have  inscribed  in  the  circle  a  regular  pentagon. 

PROBLEM  24. — To  inscribe  a  regular  Hexagon  in  a  circle  (Fig.  72). 


Fig.72 

SOLUTION. — Lay  off  on  the  circumference  the  radius  of  the 
circle  six  times,  and  connect  the  points. 


GEOMETRICAL  PROBLEMS. 


79 


PROBLEM  25. — To  construct  a  regular  hexagon  upon  a  given 
straight  line,  AB  (Fig.  73). 

From  A  and  B,  with  a  radius  equal  to  AB,  describe  arcs  cut- 
ting at  0.  With  0  as  a  centre,  and  a  radius  equal  to  ABt  de- 
scribe a  circle,  and  from  A  and  B  lay  off  the  length  A  B  on  the 
circumference  of  the  circle,  and  join  the  points  thus  obtained. 
The  result  will  be  a  regular  hexagon. 

PROBLEM  26. — To  construct  a  regular  octagon  upon  a  given 
straight  line,  AB  (Fig.  74). 

Produce  the  line  AB  both  ways,  and  draw  the  perpendiculars 
A  a  and  Bb,  of  indefinite  length.  Bisect  the  external  angles  at  A 
and  B,  and  make  the  length  of  the  lines  equal  to  AB.  From  PI 
and  C  draw  lines  parallel  to  A  a,  and  equal  in  length  to  AB]  and 


Fig.  74  F.g.75 

from  the  centres  G  and  D  describe  arcs,  with  a  radius  AB,  cut- 
ting the  perpendiculars  Aa  and  Bb  in  F  and  E.  Join  GF,  FE, 
and  ED. 

PROBLEM  27. — To  mafye  a  regular  octagon  from  a  square  (Fig.  75). 
A 


Fig.77 


Draw  the  diagonals  AD  and  EC,  and  from  the  corners  A,  B, 
C,  and  D,  with  a  radius  equal  to  AO,  describe  arcs  cutting  the 


80 


GEOMETRICAL  PROBLEMS. 


sides  of  the  square  in  a,  b,  c,  d,  e,  /,  h,  and  i.     Join  these  points 
to  complete  the  octagon. 

PROBLEM  28. — To  inscribe  a  regular  octagon  in  a  circle  (Fig.  76). 

Draw  two  diameters,  AB  and  CD,  at  right  angles  to  each  other. 
Bisect  the  angles  AOD  and  AOC  by  the  diameters  EF  and  GH. 
Join  A,  E,  D,  H,  B,  etc.,  for  the  inscribed  figure. 

PROBLEM  29. — To  inscribe  a  circle  within  a  regular  polygon. 

First  (when  the  polygon  has  an  even  number  of  sides,  as  in  Fig. 
77). — Bisect  two  opposite  sides  at  A  and  B,  and  draw  AB,  and 
bisect  it  at  C  by  a  diagonal,  DE,  drawn  between  two  opposite 
angles.  With  the  radius  CA  describe  the  circle  as  required. 

Second  (when  the  number  of  sides  is  odd,  as  in  Fig.  78). — Bisect 
two  of  the  sides  at  A  and  J5,  and  draw 
lines,  AE  and  BD,  to  the  opposite  an- 
gles, intersecting  at  C.     With  C  as  a  cen- 
tre, and  CA   as  a  radius,  describe  thep 
circle  as  required. 

PROBLEM  30. — To  describe  a  circle 
without  a  regular  polygon. 

When  the  number  of  sides  is  even, 
draw  two  diagonals  from  opposite  an- 
gles, as  ED  and  GH  (Fig.  77),  inter- 
secting at  (7;  and  from  (7,  with  CD  as  a 
radius,  describe  the  circle  required. 

WThen  the  number  of  sides  is  odd,  find  the  centre,  C,  as  in  last 
problem ;  and  with  C  as  a  centre,  and  CD  (Fig.  78)  as  a  radius, 
describe  the  circle  required. 


GEOMETRICAL   PROBLEMS. 


81 


PROBLEMS  ON  THE  ELLIPSE,  THE  PARABOLA, 
THE  HYPERBOLA,  AND  THE   CYCLOID. 

The  Ellipse. 

PROBLEM  31. — To  describe  an  ellipse,  the  length  and  breadth,  or 
the  two  axes,  being  given. 

IST  METHOD  (Fig.  79,  the  two  axes,  A B  and  CD,  being  giv- 
en).—On  AB 
and  CD  as  di- 
ameters, and 
from  the  same 
centre,  0,  de- 
scribe the  cir- 
cles AGBH  and 
CLDK.  Take 
any  convenient 
number  of 
points  on  the 
circumference 
of  the  outer  cir- 
cle, as  6,  &',  6", 
etc.,  and  from 
them  draw  lines 
to  the  centre,  0, 
Fig. 79  cutting  the  in- 

ner circle  at  the  points  a,  a',  a",  etc.,  respectively.  From  the  points 
6,  b',  etc.,  draw  lines  parallel  to  the  shorter  axis;  and  from  the 
points  a,  a',  etc.,  draw 
lines  parallel  to  the 
longer  axis,  and  inter- 
secting the  first  set  of 
lines  at  c,  cf,  c",  etc. 
These  last  points  will  be 
points  in  the  ellipse, 
and,  by  obtaining  a  suf- 
ficient number  of  them, 
the  ellipse  can  easily  be 
drawn. 

2D  METHOD  (Fig.  80). 
—Take  the  straight 
edge  of  a  stiff  piece  of  paper,  cardboard,  or  wood,  and  from  some 
point  as  a,  mark  off  ab  equal  to  half  the  shorter  diameter,  and  ac 
equal  to  half  the  longer  diameter.  Place  the  straight  edge  so 


82 


GEOMETRICAL   PROBLEMS. 


that  the  point  b  shall  be  on  the  longer  diameter,  and  the  point  c 
on  the  shorter :  then  will  the  point  a  be  over  a  point  in  the 
ellipse.  Make  on  the  paper  a  dot  at  a,  and  move  the  slip  around, 
always  keeping  the  points  b  and  c  over  the  major  and  minor  axes. 
In  this  way  any  number  of  points  in  the  ellipse  may  be  ob- 
tained, which  may  be  connected  by  a  curve  drawn  freehand. 

3o  METHOD  (Fig.  81,  given  the  two  axes  AB  and  CD). — From 
the  point  D  as  a  centre, 
and  a  radius  A  0,  equal 
to  one-half  of  A  B,  de- 
scribe an  arc  cutting 
AB  at  F  and  F' '. 
These  two  points  are 
called  the  foci  of  the  A 
ellipse.  [One  property 
of  the  ellipse  is,  that  the 
sum  of  the  distances  of 
any  two  points  on  the 
circumference  from  the 
foci  is  the  same.  Thus  Fig. 81 

F'D  +  DF  =  F'E  +  EF  or  F'G  +  GF.]  Fix  a  couple  of  pins  into 
the  axis  AB  at  F  and  F',  and  loop  a  thread  or  cord  upon  them 
equal  in  length,  when  fastened  to  the  pins,  to  AB,  so  as,  when 
stretched  as  per  dotted  line  FDF',  just  to  reach  the  extremity  D 
of  the  short  axis.  Place  a  pencil-point  inside  the  chord,  as  at 
E,  and  move  the  pencil  along,  always  keeping  the  cord  stretched 
tight.  In  this  way  the  pencil  will  trace  the  outline  of  the  ellipse. 
PROBLEM  32. — To  draw  a  tangent  to  an  ellipse  at  a  given  point 

on  the  curve  (Fig. 
82). 

Let  it  be  re- 
quired to  draw 
a  tangent  at  the 
point  E  on  the 
ellipse  shown  in 
Fig.  82.  First 
find  the  foci  F 
and  F',  as  in 
the  third  method 
for  describing  an 
ellipse,  then  from 
E  draw  lines  EF  and  EF'.  Prolong  EF'  .to  a,  so  that  Ea  shall 


GEOMETRICAL   PROBLEMS. 


83 


equal  EF.  Bisect  the  angle  aEF  as  at  b,  and  through  b  draw  a 
line  touching  the  curve  at  E.  This  line  will  be  the  tangent  re- 
quired. If  it  were  desired  to  draw  a  line  normal  to  the  curve  at 
Ej  as,  for  instance,  the  joint  of  an  elliptical  arch,  bisect  the  angle 
FEF',  and  draw  the  bisecting  line  through  E,  and  it  will  be  the 
normal  to  the  curve,  and  the  proper  line  for  the  joint  of  an 
elliptical  arch  at  that  point. 

PROBLEM  33. — To  draw  a  tangent  to  an  ellipse  from  a  given 
point  without  the  curve  (Fig.  83). 


'  Fig.83 


From  the  point  T  as  a  centre,  and  a  radius  equal  to  the  distance 
to  the  nearer  focus  F,  describe  a  circle.  From  F'  as  a  centre,  and 
a  radius  equal  to  the  length  of  the  longer  axis,  describe  arcs  cut- 
ting the  circle  just  described  at  a  and  b.  Draw  lines  from  F'  to 
a  and  6,  cutting  the  circumference  of  the  ellipse  at  E  and  G. 
Draw  lines  from  T  through  E  and  G,  and  they  will  be  the  tan- 
gents required. 

PROBLEM  34. — To  describe  an  ellipse  approximately,  by  means 
of  circular  arcs. 

First  (with  arcs  of  two  radii,  Fig.  84). — Take  half  the  difference 
of  the  two  axes  A  B  and  CD,  and  set  it  off  from  the  centre  O  to  a 
and  c  on  OA  and  OC;  draw  ac,  and  set  off  half  ac  to  d\  draw  di 
parallel  to  ac;  set  off  Oe  equal  to  Od;  join  ei,  and  draw  em  and 
dm  parallels  to  di  and  ie.  On  m  as  a  centre,  with  a  radius  mC, 
describe  an  arc  through  C,  terminating  in  1  and  2 ;  and  with  i  as 
a  centre,  and  D  as  a  radius,  describe  an  arc  through  D,  termin- 
ating in  points  3  and  4.  On  d  and  e  as  centres  describe  arcs 


84 


GEOMETRICAL   PROBLEMS. 


through  A  and  B,  connecting  the  points  1  and  4,  2  and  3.     The 
four  arcs  thus  described  form  approximately  an  ellipse.     This 
method  does  not  apply  satisfactorily  when  the  conjugate  axis  is 
less  than  two-thirds  of  the  transverse  axis. 
Fig.84 
C 


XX            / 

\u/ 

/ 

\ 

a 

°             /\ 

Another  method  of  approximating  an  ellipse  by  means  of  arcs 
of  two  radii,  is  shown  in  Fig.  84a,  the  axis  AB,  and  the  semi- 


Fig.  84a. 

minor  axis  OC  being  given.  Draw  the  rectangle  AabB,  and 
the  diagonal  CB.  Lay  off  Cc  equal  to  the  difference  between 
OB  and  OC.  Bisect  cB  at  M,  and  erect  the  perpendicular  YD, 
intersecting  CO  produced  at  Y  and  OB,  at  x.  Make  Ox'=0x. 
Then  will  x}  xr ,  and  Y  be  the  three  centres  required,  the  curves 
becoming  tangent  at  D.  This  method  gives  a  slightly  fuller 
curve  at  the  haunches  than  the  preceding  one. 


GEOMETRICAL   PROBLEMS. 


85 


Second  (with  arcs  of  three  radii,  Fig.  85). — On  the  transverse 

axis  AB  draw  the  rectangle  AGEB,  equal  in  height  to  OC,  half 

N 


the  conjugate  axis.  Draw  GD  perpendicular  to  AC.  Set  off  OK 
equal  to  OC,  and  on  A K  as  a  diameter  describe  the  semicircle 
ANK.  Draw  a  radius  parallel  to  OC,  intersecting  the  semicircle 
at  N,  and  the  line  GE  at  P.  Extend  OC  toL  and  to  D.  Set  off 
OM  equal  to  PN,  and  on  D  as  a  centre,  with  a  radius  DM,  de- 
scribe an  arc.  From  A  and  B  as  centres,  with  a  radius  OL,  inter- 
sect this  arc  at  a  and  b.  The  points  H,  a,  D,  6,  //' ,  are  the  cen- 
tres of  the  arcs  required.  Produce  the  lines  aH,  Da,  Db,  bH', 
and  the  spaces  enclosed  determine  the  lengths  of  each  arc.  This 
process  works  well  for  nearly  all  ellipses.  It  is  employed  in 
striking  out  vaults,  stone  arches,  and  bridges. 

NOTE. — Tn  this  example  the  point  H'  happens  to  coincide  with  the  point 
K,  but  this  need  not  necessarily  be  the  case. 

The  Parabola. 

PROBLEM  35. — To  construct  a  parabola  when  the  vertex  A,  the 
axis  AB,  and  a  point,  M,  of  the  curve,  are  given  (Fig.  86). 

Construct  the  rectangle  A  ]}MC.  Divide  MC  into  any  number 
of  equal  parts,  four  for  instance.  Divide  A  C  in  like  manner. 
Connect  Al,  A2,  and  A3.  Through  1',  2',  3',  draw  parallels  to 


86 


GEOMETRICAL  PROBLEMS. 


the  axis.     The  intersections  I,  II,  and  III,  of  these  lines,  are 
points  in  the  required  curve. 

PROBLEM  36. — To  draw  a  tangent  to  a  given  point,  II,  of  the 
parabola  (Fig.  86). 

cr 


d 
Fig.86 

From  the  given  point  II  let  fall  a  perpendicular  on  the  axis 
at  b.  Extend  the  axis  to  the  left  of  A.  Make  Aa  equal  to  Ab. 
Draw  all,  and  it  is  the  tangent  required. 

The  lines  perpendicular  to  the  tangent  are  called  normals.  To 
find  the  normal  to  any  point  I,  having  the  tangent  to  any  other 
point,  II.  Draw  the  normal  lie.  From  I  let  fall  a  perpendicular 
Id,  on  the  axis  AB.  Lay  off  de  equal  to  be.  Connect  le,  an  we 
have  the  normal  required.  The  tangent  may  be  drawn  at  I  by 
laying  off  a  perpendicular  to  the  normal  le  at  I. 
The  Hyperbola, 

The  hyperbola  possesses  the  characteristic  that  if,  from  any 
point,  P,  two  straight  lines  be  drawn  to  two  fixed  points,  F  and 
F',  the  foci,  their  differ- 
ence  shall  always  be  the 
same. 

PROBLEM  37. — To  de- 
scribe an  hyperbola 
through  a  given  vertex, 
a,  with  the  given  differ- 
ence  ab,  and  one  of  the 
foci,  F  (Fig.  87). 

Draw  the  axis  of  the 
hyperbola  AB,  with  the 
given  distance  ab  and 
the  focus  F  marked  on 
it.  From  b  lay  off  bFl 
equal  to  aF  for  the 
other  focus.  Take  any  point,  as  1  on  AB,  and  wrth  al  as 


GEOMETRICAL   PROBLEMS. 


87 


a  radius,  and  F  as  a  centre,  describe  two  short  arcs  above  and 
below  the  axis.  With  bl  as  a  radius,  and  F'  as  a  centre,  describe 
arcs  cutting  those  just  described  at  P  and  P' .  Take  several 
points,  as  2,  3,  and  4,  and  obtain  the  corresponding  points  P2, 
P3,  and  P^  in  the  same  way.  Join 
these  points  with  a  curved  line,  and 
it  will  be  an  hyperbola. 

To  draw  a  tangent  to  any  point  of 
an  hyperbola,  draw  lines  from  the 
given  point  to  each  of  the  foci,  and 
bisect  the  angle  thus  formed.  The 
bisecting  line  will  be  the  tangent  re- 
quired. 

The  Cycloid. 

The  cycloid  is  the  curve  described 
by  a  point  in  the  circumference  of  a 
circle  rolling  in  a  straight  line. 

PROBLEM  38. — To  describe  a  cy- 
cloid (Fig.  88). 

Draw  the  straight  line  AB  as  the 
base.  Describe  the  generating  circle 
tangent  to  this  line  at  the  centre,  and 
through  the  centre  of  the  circle,  C, 
draw  the  line  EE  parallel  to  the  base. 
Let  fall  a  perpendicular  from  C  upon 
the  base.  Divide  the  semi-circumfer- 
ence into  any  number  of  equal  parts, 
for  instance,  six.  Lay  off  on  AB  and 
CE  distances  Cl',  VI1 ',  etc.,  equal  to 
the  divisions  of  the  circumference. 
Draw  the  chords  Dl,  D2,  etc.  From 
the  points  1',  2',  3',  on  the  line  CE, 
with  radii  equal  to  the  generating 
circle,  describe  arcs.  From  the 
points  1',  2',  3',  4',  5',  on  the  line  BA,  and  with  radii  equal 
respectively  to  the  chords  Dl,  D2,  D3,  D4,  D5,  describe  arcs 
cutting  the  preceding,  and  the  intersections  will  be  points  of 
the  curve  required. 


88 


GEOMETRICAL  PROBLEMS. 


TABLE  OF  CHORDS;  Radius -1.0000. 


M. 

0° 

1° 

2° 

.3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

M. 

0' 

.0000 

.0175 

.0349 

.0524 

.0698 

.0872 

.1047 

.1221 

.1395 

.1509 

.1743 

0' 

1 

.0003 

.0177 

.0352 

.0526 

.0701 

.0875 

.1050 

.1224 

.1398 

.1572 

.1746 

1 

2 

.0006 

.0180 

.0355 

.0529 

.0704 

.0878 

.1053 

.1227 

.1401 

.1575 

.1749 

2 

3 

.0009 

.0183 

.0358 

.0532 

.0707 

.0881 

.1055 

.1230 

.1404 

.1578 

.1752 

3 

4 

.0012 

.0186 

.0361 

.0535 

.0710 

.0884 

.1058 

.1233 

.1407 

.1581 

.1755 

4 

5 

.0015 

.0189 

.0364 

.0538 

.0713 

.0837 

.1061 

.1235 

.1410 

.1584 

.1758 

5 

6 

.0017 

.0192 

.0366 

.0541 

.0715 

.0890 

.1064 

.1238 

.1413 

.1587 

.1761 

6 

7 

0020 

0195 

.0369 

.0544 

0718 

.0893 

.1067 

.1241 

.1415 

.1589 

1763 

7 

8 

.0023 

.0198 

.0372 

.0547 

.0721 

.0896 

.1070 

.1244 

.1418 

.1592 

.1766 

8 

9 

.0026 

.0201 

.0375 

.0550 

.0724 

.0399 

.1073 

.1247 

.1421 

.1595 

.1769 

9 

10 

.0029 

.0204 

.0378 

.0553 

.0727 

.0901 

.1076 

.1250 

.1424 

.1598 

.1772 

10 

11 

.0032 

.0207 

.0381 

.0558 

.0730 

.0904 

.1079 

.1253 

.1427 

.1601 

.1775 

11 

12 

.0035 

.0209 

.0384 

.0558 

.0733 

.0907 

.1082 

.1256 

.1430 

.1604 

.1778 

12 

13 

.0038 

.0212 

.0387 

.0561 

.0736 

.0910 

.1084 

.1259 

.1433 

.1607 

1781 

13 

14 

.0041 

.0215 

.0390 

.0564 

.0739 

.0913 

.1087 

.1262 

.1436 

.1610 

.1784 

14 

15 

.0044 

.0218 

.0393 

.0567 

.0742 

.0916 

.1090 

.1265 

.1439 

.1613 

.1787 

15 

16 

.0047 

.0221 

.0396 

.0570 

.0745 

.0919 

.1093 

.1267 

.1442 

.1616 

1789 

16 

17 

.0049 

.0221 

.0398 

.0573 

.0747 

.0922 

.1096 

.1270 

.1444 

.1618 

.1792 

17 

18 

.0052 

.0227 

.0401 

.0576 

.0750 

.0925 

.1099 

.1273 

.1447 

.1621 

.1795 

18 

19 

.0055 

.0230 

.0404 

.0579 

.0753 

.0928 

.1102 

.1?76 

.1450 

.1624 

.1798 

19 

20 

.0058 

.0233 

.0407 

.0582 

.0756 

.0931 

.1105 

.1279 

.1453 

.1027 

.1801 

20 

21 

.0061 

.0236 

.0410 

.0585 

.0759 

.0933 

.1108 

.1282 

.1456 

.1630 

.1804 

21 

22 

.0064 

.0239 

.0413 

.0588 

.0762 

.0936 

.1111 

.1285 

.1459 

.1633 

.1807 

22 

23 

.0067 

.0241 

.0416 

.0590 

.0765 

.0939 

.1114 

.1288 

.1462 

.1636 

.1810 

23 

24 

.0070 

.0244 

.0419 

.0593 

.0768 

.0942 

.1116 

.1291 

.1465 

.1639 

.1813 

24 

25 

.0073 

.0247 

.0422 

.0596 

.0771 

.0945 

.1119 

.1294 

.1468 

.1642 

.1816 

25 

28 

.0076 

.0250 

.0425 

.0599 

.0774 

.0948 

.1122 

.1296 

.1471 

.1645 

.1818 

26 

27 

.0079 

.0253 

.0428 

.0602 

.0776 

.0951 

.1125 

.1299 

.1473 

.1647 

.1821 

27 

2h 

.0031 

.0255 

.0430 

.0605 

.0779 

.0954 

.1128 

.1302 

.1476 

.1650 

.1824 

28 

29 

.0084 

.0259 

.0433 

.0608 

.0782 

.0957 

.1131 

.1305 

.1479 

.1653 

.1827 

29 

30 

.0087 

.0262 

.0436 

.0611 

.0785 

.0960 

.1134 

.1308 

.1482 

.1656 

.1830 

30 

31 

.0090 

.0265 

.0439 

.0614 

.0788 

.0962 

.1137 

.1311 

.1485 

.1659 

1833 

31 

32 

.0093 

.0268 

.0442 

.0617 

.0791 

.0965 

.1140 

.1314 

.1488 

.1662 

.1836 

32 

33 

.0096 

.0271 

.0445 

.0619 

.0794 

.0968 

.1143 

.1317 

.1491 

.1665 

.1839 

33 

34 

.0099 

.0273 

.0448 

.0622 

.0797 

.0971 

.1145 

.1320 

.1494 

.1668 

.1842 

34 

35 

.0102 

.0276 

.0151 

.0625 

.0800 

.0974 

.1148 

.1323 

.1497 

.1671 

.1845 

35 

36 

.0105 

.0279 

.0454 

.0628 

.0803 

.0977 

.1151 

.1325 

.1500 

.1674 

.1847 

36 

37 

.0108 

.0282 

.0457 

.0631 

.0806 

.0980 

.1154 

.1328 

.1502 

.1676 

.1850 

37 

38 

.0111 

.0285 

.0460 

.0834 

.0808 

.0983 

.1157 

.1331 

.1505 

.1679 

.1853 

38 

39 

.0113 

.0288 

.0462 

.0637 

.0311 

.0986 

.1160 

.1334 

.1508 

.1682 

.1856 

39 

40 

.0116 

.0291 

.0465 

.0640 

.0814 

.0989 

.1163 

.1337 

.1511 

.1685 

.1859 

40 

41 

.0119 

.0294 

.0468 

.0643 

.0817 

.0992 

.1166 

.1340 

.1514 

.1688 

.1862 

41 

42 

.0122 

.0297 

.0471 

.0646 

.0320 

.0994 

.1169 

.1343 

.1517 

.1691 

.1865 

42 

43 

.0125 

.0300 

.0474 

.0649 

.0823 

.0997 

.1172 

.1346 

.1520 

.1694 

.1868 

43 

41 

.0128 

.0303 

.0477 

.0651 

.0826 

.1000 

.1175 

.1349 

.1523 

.1697 

.1871 

44 

45 

.0131 

.0305 

.0480 

.OU54 

.0329 

.1003 

.1177 

.1352 

.1526 

.1700 

1873 

45 

46 

.0134 

.0308 

.0483 

.0857 

.0832 

.1006 

.1180 

.1355 

.1529 

.1703 

.1876 

46 

47 

.0137 

.0311 

.0486 

.0660 

.0335 

.1009 

.1183 

.1357 

.1531 

.1705 

1879 

47 

48 

.0140 

.0314 

.0489 

.0683 

.0838 

.1012 

.1186 

.1360 

.1534 

.1708 

.1382 

48 

49 

.0143 

.0317 

.0492 

.0666 

.0840 

.1015 

.1189 

.1363 

.1537 

.1711 

1885 

49 

50 

.0145 

.0320 

.0494 

.0669 

.0843 

.1018 

.1192 

.1366 

.1540 

.1714 

.188? 

50 

51 

.0148 

.0323 

.0-197 

.0672 

.0846 

.1021 

.1195 

.1369 

.1543 

.1717 

.1891 

51 

52 

.0151 

.0326 

.0500 

.0675 

.0849 

.1023 

.1198 

.1372 

.1546 

.1720 

1894 

52 

53 

.0154 

.0329 

.0503 

.0678 

.0352 

.1026 

.1201 

.1375 

.1549 

.1723 

.1897 

53 

5t 

.0157 

.0332 

.0506 

.0681 

.0855 

.1029 

.1204 

.1378 

.1552 

.1726 

1900 

54 

OT 

.0160 

.0335 

.0509 

.0683 

.0858 

.1032 

.1206 

.1381 

.1555 

.1729 

.1902 

55 

53 

.0103 

.0337 

.0512 

.0686 

.0361 

.1035 

.1209 

.1384 

.1558 

.1732 

.1905 

56 

57 

.0166 

.0340 

.0515 

.0689 

.0864 

.1038 

.1212 

.1386 

.1560 

.1734 

.1908 

57 

53 

.0169 

.0343 

.0518 

.0092 

.0867 

.1041 

.1215 

.1389 

.1563 

.1737 

.1911 

53 

59 

.0172 

.0346 

.0521 

.0095 

.0369 

.1044 

.1218 

.1392 

.1566 

.1740 

.1914 

59 

60 

.0175 

.0349 

.0524 

.0698 

.087:2 

.1047 

.1221 

.1395 

.1509 

.1743 

.1917 

60 

GEOMETRICAL  PROBLEMS. 
Table  of  Chords;  Radius  =1.0000  (continued). 


M, 

11° 

13° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

M. 

0 

.1917 

.2091 

.2264 

.2437 

.2611 

.2783 

.2950 

.3129 

.3301 

.3473 

.3645 

0' 

1 

.1920 

.2093 

.2207 

.2440 

.2013 

.2786 

.2959 

.3132 

.3304 

.3476 

.3648 

1 

2 

.1923 

.2096 

.2270 

.2443 

.2616 

.2789 

.2902 

.3134 

.3307 

.3479 

.3650 

2 

3 

.1926 

.2099 

.2273 

.2446 

.2619 

.2792 

.2905 

.3137 

.3310 

.3482 

.3653 

3 

4 

.1928 

.2102 

.2276 

.2449 

.2622 

.2795 

.2968 

.3140 

.3312 

.3484 

.3056 

4 

5 

.1931 

.2105 

.22^9 

.2452 

.2625 

.2758 

.2971 

.3143 

.3315 

.3487 

.3059 

5 

6 

.1934 

.2108 

.2281 

.2455 

.2628 

.2801 

.2973 

.3146 

.3318 

.3490 

.3602 

6 

7 

.1937 

.2111 

.2284 

.2458 

.2631 

.2804 

.2976 

.3149 

.3321 

.3493 

.3665 

7 

8 

.1940 

.2114 

.2287 

.2460 

.2634 

.2807 

.2979 

.3152 

.3324 

.3496 

.3668 

8 

9 

.1943 

.2117 

.2290 

.2463 

.2636 

.2809 

.2982 

.3155 

.3327 

.3499 

.3670 

9 

10 

.1946 

.2119 

.2293 

.2466 

.2639 

.2812 

.2985 

.3157 

.3330 

.3502 

.3673 

10 

11 

.1949 

.2122 

.2296 

.2169 

.2642 

.2815 

.2988 

.3160 

.3333 

.3504 

.3670 

11 

12 

.1952 

.2125 

.2299 

.2472 

.2645 

.2818 

.2991 

.3163 

.3335 

.3507 

.3079 

12 

13 

.1955 

.2128 

.2302 

.2475 

.2648 

.2821 

.2994 

.3166 

.3338 

.3510 

.3082 

13 

14 

.1957 

.2131 

.2305 

.2478 

.2651 

.2824 

.2996 

.3169 

.3341 

.3513 

.3685 

14 

15 

.1900 

.2134 

.2307 

.2481 

.2654 

.2827 

.2999 

.3172 

.3344 

.3516 

.3688 

15 

10 

.1963 

.2137 

.2310 

.2484 

.2657 

.2^30 

.3002 

.3175 

.3347 

.3519 

.3690 

16 

17 

.1966 

.2140 

.2313 

.2486 

.2060 

.2832 

.3005 

.3178 

.3350 

.3522 

.3693 

17 

18 

.1969 

.2143 

.2316 

.2489 

.2662 

.2835 

.3008 

.3180 

.3353 

.3525 

.3696 

18 

19 

.1972 

.2146 

.2319 

.2492 

.2665 

.2838 

.3011 

.3183 

.3355 

.?527 

.3699 

19 

20 

.1975 

.2148 

.2322 

.2495 

.2668 

.2841 

.3014 

.3186 

.3358 

.3530 

.3702 

20 

21 

.1978 

.2151 

.2325 

.2498 

.2671 

.2844 

.3017 

.3189 

.3361 

.3533 

.3705 

21 

22 

.1981 

.2154 

.2328 

.2501 

.2674 

.2847 

.3019 

.3192 

.3364 

.3536 

.3708 

22 

23 

.1983 

.2157 

.2331 

.2504 

.2677 

.2850 

.3022 

.3195 

.3367 

.3539 

.3710 

23 

24 

.1986 

.2160 

.2333 

.2507 

.2680 

.2853 

.3025 

.3198 

.3370 

.3542 

.3713 

24 

25 

.1989 

.2163 

.2336 

.2510 

.2683 

.2855 

.3028 

.3200 

.3373 

.3545 

.3716 

25 

26 

.1992 

.2166 

.2339 

.2512 

.2685 

.2858 

.3031 

.3203 

.3376 

.3547 

.3719 

26 

27 

.1995 

.2169 

.2342 

.2515 

.2688 

.2861 

.3034 

.3206 

.3378 

.3550 

.3722 

27 

28 

.1998 

.2172 

.2345 

.2518 

.2691 

.2864 

.3037 

.3209 

.3381 

.3553 

.3725 

28 

29 

.2001 

.2174 

.2348 

.2521 

.2694 

.2*67 

.3040 

.3212 

.3384 

.3556 

.3728 

29 

30 

.2004 

.2177 

.2351 

.2524 

.2697 

.2870 

.3042 

.3215 

.3387 

.3559 

.3730 

30 

31 

.2007 

.2180 

.2354 

.2527 

.2700 

.2873 

.3045 

.3218 

.3390 

.3562 

.3733 

31 

32 

.2010 

.2183 

.2357 

.2530 

.2703 

.2876 

.3048 

.3221 

.3393  .3565 

.3736 

32 

33 

.2012 

.2186 

.2359 

.2533 

.2706 

.2878 

.3051 

.3223 

.3396  1  .3567 

.3739 

33 

34 

.2015 

.2189 

.2362 

.2530 

.2709 

.2881 

.3054 

.3226 

.3398 

.3570 

.3742 

34 

35 

.2018 

.2192 

.2365 

.2538 

.2711 

.2884 

.3057 

.3229 

.3401 

.3573 

.3745 

35 

30 

.2021 

.2195 

.2368 

.2541 

.2714 

.2887 

.3060 

.3232 

.3404 

.3576 

.3748 

36 

37 

.2024 

.2198 

.2371 

.2544 

.2717 

.2890 

.3063 

.3235 

.3407 

.3579 

.3750 

37 

38 

.2027 

.2200 

.2374 

.2547 

.2720 

.2893 

.3065 

.3238 

.3410 

.3582 

.3753 

38 

39 

.2030 

2203 

.2377 

.2550 

.2723 

.2896 

.3068 

.3241 

.3413 

.3585 

.3756 

39 

40 

.2033 

.2206 

.2380 

.2553 

.2726 

.2899 

.3071 

.3244 

.3416 

.3587 

.3759 

40 

41 

.2036 

.2209 

.2383 

.2550 

.2729 

.2902 

.3074 

.3246 

.3419 

.3590 

.3762 

41 

42 

.2038 

.2212 

.2385 

.2559 

.2732 

.2904 

.3077 

.3249 

.3421 

.3593 

.3765 

42 

43 

.2041 

.2215 

.2388 

.2501 

.2734 

.2907 

.3080 

.3252 

.3424 

.3596 

.3768 

43 

44 

.2044 

.2218 

.2391 

.2504 

.2737 

.2910 

.3083 

.3255 

.3427 

.3599 

.3770 

44 

45 

.2047 

.2221 

.2394 

.2567 

.2740 

.2913 

.3086 

.3258 

.3430 

.3002 

.3773 

45 

46 

.2050 

.2224 

.2397 

.2570 

.2743 

.2910 

.3088 

.3261 

.3433 

.3605 

.3776 

46 

47 

.2053 

.2226 

.2400 

.2573 

.2746 

.2919 

.3091 

,3264 

.3436 

.3608 

.3779 

47 

48 

.2056 

.2229 

.2403 

.2576 

.2749 

.2922 

.3094 

.3267 

.3439 

.3610 

.3782 

48 

49 

.2059 

.2232 

.2406 

.2579 

.2752 

.2925 

.3097 

.3269 

.3441 

.3613 

.3785 

49 

50 

.2062 

.2235 

.2409 

.2582 

.2755 

.2927 

.3100 

.3272 

.3444 

.3616 

.3788 

50 

51 

.2065 

.2238 

.2411 

.2585 

.2758 

.2930 

.3103 

.3275 

.3447 

.3619 

.3790 

51 

52 

.2067 

.2241 

.2414 

.2587 

.2700 

.2933 

.3106 

.3278 

.3450 

.3622 

.3793 

52 

53 

.2070 

.2244 

.2417 

.2590 

.2763 

.2930 

.3109 

.3281 

.3453 

.3625 

.3796 

53 

54 

.2073 

.2247 

.2420 

.2593 

.2766 

.2939 

.3111 

.3284 

.3456 

.3628 

.3799 

54 

55 

.2076 

.2250 

.2423 

.2596 

.2769 

.2942 

.3114 

.3287 

.3459 

.3630 

.3802 

55 

56 

.2079 

.2253 

.2426 

.2599 

.2772 

.2945 

.3117 

.3289 

.3462 

.3633 

.3805 

50 

57 

.2082 

.2255 

.2429 

.2602 

.2775 

.2948 

.3120 

.3292 

.3464 

.3636 

.3808 

57 

58 

.2085 

.2258 

.2432 

.2605 

.2778 

.2950 

.3123 

.3295 

.3467 

.3639 

.3310 

58 

59 

.2083 

.2201 

.2434 

.2608 

.2781 

.2953 

.3126 

.3298 

.3470 

.3642 

.3813 

59 

60 

.2091 

.2264 

.2437 

.2611 

.2783 

.2956 

.3129 

.3301 

.3473 

.3645 

.3816 

60 

90 


GEOMETRICAL  PROBLEMS. 


Table  of  Chords;   Radius=  1.0000  (continued) 


M. 

22° 

33° 

34° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

M. 

0' 

•3816 

3987 

.4158 

.4329 

.4499 

.4609 

.4838 

.5008 

.5176 

.5345 

.5513 

0' 

1 

9 

.3319 
3822 

.3990 
3993 

.4161 
.4164 

.4332 
.4334 

.4502 
.4505 

.4672 
.4675 

.4841 
.4844 

.5010 
.5013 

.5179 

.5182 

.5348 
.5350 

.5516 
.5518 

1 

2 

3 
4 
5 

6 

7 
8 
0 

.3825 
.3328 
.3830 
.3833 
.3336 
.3839 
3842 

.3996 
.3899 
.4002 
.4004 
.4007 
.4010 
4013 

.4167 
.4170 
.4172 
.4175 

.4178 
.4181 
.4184 

.4337 
.4340 
.4343 
.4346 
.4349 
.4352 
.4354 

.4508 
.4510 
.4513 
.4516 
.4519 
.4522 
.4525 

.4677 
.4680 
.4683 
.4686 
.4689 
.4692 
.4694 

.4847 
.4850 
.4853 
.4855 
.4858 
.4361 
.4864 

.5016 
.5019 
.5022 
.5024 
.5027 
.5030 
.5033 

.5185 
.5188 
.5190 
.5193 
.5196 
.5199 
.5202 

.5353 
.5356 
.5359 
.5362 
.5364 
.5367 
.5370 

.5521 
.5524 
.5527 
.5530 
.5532 
.5535 
.5538 

3 
4 
5 

6 

7 
8 

q 

10 

11 
12 

.3845 

.3848 
3850 

.4016 

.4019 
4022 

.4187 

.4190 

4192 

.4357 

.4360 
.4363 

.4527 

.4530 
.4533 

.4697 

.4700 
.4703 

.4867 

.4869 

.4872 

.5036 

.5039 
.5041 

.5204 

.5207 
.5210 

.5373 

.5376 
.5378 

.5541 

.5543 
.5546 

10 

11 

1?, 

13 
14 
15 
16 

17 

.3853 

.3856 
.3850 
.3862 

3865 

.4024 
.4027 
.4030 
.4033 
.4036 

.4195 
.4198 
.4201 
.4204 
.4207 

.1366 
.4369 
.4371 
.4374 

.4377 

.4536 
.4539 
.4542 
.4544 
.4547 

.4706 
.4708 
.4711 
.4714 
.4717 

.4875 
.4878 
.4881 
.4884 
.4886 

.5044 
.5047 
.5050 
.5053 
.5055 

.5213 
.5216 
.5219 
.5221 
.5224 

.5381 
.5384 
.5387 
.5390 
.5392 

.5549 
.5552 
.5555 
.5557 
.5560 

13 
14 
15 
16 
17 

18 
19 
20 

21 
22 
23 
24 

25 
26 

97 

.3868 
.3870 
.3873 

.3876 
.3879 
.3882 
.3885 
.3888 
.3890 
3893 

.4039 
.4042 
.4044 

.4047 
.4050 
.4053 
.4056 
.4059 
.4061 
4064 

.4209 
.4212 
.4215 

.4218 
.4221 
.4224 
.4226 
.4229 
.4232 
4235 

.4380 
.4383 
.4386 

.4388 
.4391 
.4394 
.4397 
.4400 
.4403 
.4405 

.4550 
.4553 
.4556 

.4559 
.4561 
.4564 
.4567 
.4570 
.4573 
.4576 

.4720 
.4723 
.4725 

.4728 
.4731 
.4734 
.4737 
.4740 
.4742 
.4745 

.4889 
.4892 
.4895 

.4898 
.4901 
.4903 
.4906 
.4909 
.4912 
.4915 

.5058 
.5061 
.5064 

.5067 
.5070 
.5072 
.5075 
.5078 
.5081 
.5084 

.5227 
.5230 
.5233 

.5235 
.5238 
.5241 
.5244 
.5247 
.5249 
.5252 

.5395 
.5398 
.5401 

.5404 
.5406 
.5409 
.5412 
.5415 
.5418 
.5420 

.5563 
.5566 
.5569 

.5571 
.5574 
.5577 
.5580 

.5583 
.5585 

.5588 

18 
19 
20 

21 
22 
23 
24 
25 
26 
27 

28 

9Q 

.3396 
3899 

.4067 
.4070 

.4238 
4241 

.4408 
4411 

.4578 
.4581 

.4748 
.4751 

.4917 
4920 

.5080 
.5089 

.5255 

.5258 

.5423 

.5426 

.5591 
.5594 

28 
29 

30 
31 

.3902 
.3905 

.4073 
.4076 

.4244 
.4246 

.4414 
.4417 

.4584 

.4587 

.4754 
.4757 

.4923 
.4926 

.5092 
.5095 

.5261 
.5263 

.5429 
.5432 

.5597 
.5599 

30 
31 

32 
33 
34 
35 

36 
37 

.3908 
.3910 
.3913 
.3916 
.3919 
.3922 

.4079 
.4081 
.4034 
.4087 
.4090 
.4093 

.4249 
.4252 
.4255 
.4258 
.4261 
4263 

.4420 
.4422 
.4425 
.4428 
.4431 
.4434 

.4590 
.4593 
.4595 
.4598 
.4601 
.4604 

.4759 
.4762 
.4765 
.4768 
.4771 
4773 

.4929 
.4932 
.4934 
.4937 
.4940 
.4943 

.5093 
.5100 
.5103 
.5106 
.5109 
5112 

.5266 
.5269 
.5272 
.5275 
.5277 
.5280 

.5434 
.5437 
.5440 
.5443 
.5446 
.5448 

.5602 
.5605 
.5608 
.5611 
.5613 
.5616 

32 
33 
34 
35 
36 
37 

38 
9,Q 

.3925 
.3927 

.4096 
.4098 

.4266 
4269 

.4437 
4439 

.4607 
4609 

.4776 
4779 

.4946 
4948 

.5115 
5117 

.5283 

.52,86 

.5451 
.5454 

.5619 
.5622 

38 
39 

40 

41 
42 
43 
44 
45 

.3930 

.3933 
.3936 
.3939 
.3942 
.3945 

.4101 

.4104 
.4107 
.4110 
.4113 
.4116 

.4272 

.4275 

.4278 
.4280 
.4283 
.4286 

.4442 

.4445 
.4448 
.4451 
.4454 
.4456 

.4612 

.4615 
.4613 
.4621 
.4624 
.4626 

.4782 

.4785 
.4788 
.4790 
.4793 
4796 

.4951 

.4954 
.4957 
.4960 
.4963 
.4965 

.5120 

.5123 
.5126 
.5129 
.5131 
.5134 

.5289 

.5291 
.5294 
.5297 
.5300 
5303 

.5457 

.5460 
.5462 
.5465 
.5468 
5471 

.5625 

.5627 
.5630 
.5633 
.5636 
5638 

40 

41 

42 
43 
44 
45 

46 
47 
48 
49 
50 

51 
52 
53 

54 
55 
56 
57 

58 
59 
60 

.3947 
.3950 
.3953 
.3955 
.3959 

.3962 
.3965 
.3967 
.3970 
.3973 
.3976 
.3979 
.3982 
.3985 
.3987 

.4118 
.4121 
.4124 
.4127 
.4130 

.4133 
.4135 
.4138 
.4141 
.4144 
.4147 
.4150 
.4153 
.4155 
.4158 

.4289 
.4292 
.4295 
.4298 
.4300 

.4303 
.4306 
.4309 
.4312 
.4315 
.4317 
.4320 
.4323 
.4326 
.4329 

.4459 
.4462 
.4465 
.4468 
.4471 

.4474 

.4476 
.4479 
.4182 
.4435 
.4488 
.4491 
.449? 
.4496 
.4499 

.4629 
.4632 
.4635 
.4638 
.4641 

.4643 
.4646 
.4649 
.4652 
.4655 
.4658 
.4660 
.4663 
.4666 
.4669 

.4799 
.4802 
.4805 
.4807 
.4810 

.4813 

.4816 
.4819 
.4822 
.4824 
.4827 
.4830 
.4833 
.4836 
.4838 

.4968 
.4971 
.4974 
.4977 
.4979 

.4982 
.4985 
.4988 
.4991 
.4994 
.4996 
.4999 
.5002 
.5005 
.5003 

.5137 
.5140 
.5143 
.5145 
.5148 

.5151 
.5154 
.5157 
.5160 
.5162 
.5165 
.5168 
.5171 
.5174 
.5176 

.5306 
.5308 
.5311 
.5314 
.5317 

.5320 
.5322 
.5325 
.5328 
.5331 
.5334 
.5336 
.5339 
.5342 
.5345 

.5474 
.5476 
.5479 

.5482 
.5485 

.5488 
.5490 
.5493 
.5490 
.5499 
.5502 
.5504 
.5507 
.5510 
.5513 

.5641 
.5644 
.5647 
.5650 
.5652 

.5655 
.5658 
.5661 
.5664 
.5666 
.5669 
.5672 
.5675 
.5678 
.5680 

46 
«*7 
48 
49 
50 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

GEOMETRICAL  PROBLEMS. 


Table  of  Chords;;  Radius  =1.0000  (continued). 


M. 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

43° 

43° 

M. 

0' 

.5680 

.5847 

.6014 

.6180 

.6346 

.6511 

.6676 

.6840 

.7004 

.7167 

.7330 

0' 

1 

.5683 

.5850 

.6017 

.6183 

.6349 

.6514 

.6679 

.6843 

.7007 

.7170 

.7333 

1 

2 

.5686 

.5853 

.6020 

.6186 

.6352 

.6517 

.6682 

.6846 

.7010 

.7173 

.7335 

2 

3 

.5689 

.5856 

.6022 

.6189 

.6354 

.6520 

.6684 

.6849 

.7012 

.7176 

.7338 

3 

4 

.5691 

.5859 

.6025 

.6191 

.6357 

.6522 

.6687 

.6851 

.7015 

.7178 

.7341 

4 

5 

.5694 

.5861 

.6028 

.6194 

.6360 

.6525 

.6690 

.6854 

.7018 

.7181 

.7344 

5 

6 

.5697 

.5864 

.6031 

.6197 

.6363 

.6528 

.6693 

.6857 

.7020 

.7184 

.7346 

6 

7 

.5700 

.5867 

.6034 

.6200 

.6365 

.6531 

.6695 

.6860 

.7023 

.7186 

.7349 

7 

8 

.5703 

.5870 

.6036 

.6202 

.6368 

.6533 

.6698 

.6862 

.7026 

.7189 

.7352 

8 

9 

.5705 

.5872 

.6039 

.6205 

.6371 

.6536 

.6701 

.6865 

.7029 

.7192 

.7354 

9 

10 

.5708 

.5875 

.6042 

.6208 

.6374 

.6539 

.6704 

.6868 

.7031 

.7195 

.7357 

10 

11 

.5711 

.5878 

.6045 

.6211 

.6376 

.6542 

.6706 

.6870 

.7034 

.7197 

.7360 

11 

12 

.5714 

.58S1 

.6047 

.6214 

.6379 

.C544 

.6709 

.6873 

.7037 

.7200 

.7362 

12 

13 

.5717 

.5884 

.6050 

.6216 

.6382 

.6547 

.6712 

.6876 

.7040 

.7203 

.7365 

13 

14 

.5719 

.5886 

.6053 

.6219 

.6385 

.6550 

.6715 

.6879 

.7042 

.7205 

.7368 

14 

15 

.5722 

.5889 

.6056 

.6222 

.6387 

.6553 

.6717 

.6881 

.7045 

.7208 

.7371 

15 

10 

.5725 

.5892 

.6058 

.6225 

.6390 

.6555 

.6720 

.6884 

.7048 

.7211 

.7373 

16 

17 

.5728 

.5895 

.6061 

.6227 

.6393 

.6558 

.6723 

.6887 

.7050 

.7214 

.7376 

17 

IS 

.5730 

.5897 

.6064 

.6230 

.6396 

.6561 

.6725 

.6890 

.7053 

.7216 

.7379 

18 

19 

.5733 

.5900 

.6067 

.6233 

.6398 

.6564 

.6728 

.6892 

.7056 

.7219 

.7381 

19 

20 

.5736 

.5903 

.6070 

.6236 

.6401 

.6566 

.6731 

.6895 

.7059 

.7222 

.7384 

20 

21 

.5739 

.5906 

.6072 

.6238 

.6404 

.6569 

.6734 

.6898 

.7061 

.7224 

.7387 

21 

22 

.5742 

.5909 

.6075 

.6241 

.6407 

.6572 

.6736 

.6901 

.7064 

.7227 

.7390 

22 

23 

.5744 

.5911 

.6078 

.6244 

.6410 

.6575 

.6739 

.6903 

.7067 

.7230 

.7392 

23 

24 

.5747 

.5914 

.6081 

.6247 

.6412 

.6577 

.6742 

.6906 

.7069 

.7232 

.7395 

24 

25 

.5750 

.5917 

.0083 

.6249 

.6415 

.6580 

.6745 

.6909 

.7072 

.7235 

.7398 

25 

26 

.5753 

.5920 

.(>OS6 

.6252 

.6418 

.6583 

.6747 

.6911 

.7075 

.7238 

.7400 

26 

27 

.5756 

.5922 

.6089 

.6255 

.6421 

.6586 

.6750 

.6914 

.7078 

.7241 

.7403 

27 

2S 

.5758 

.5925 

.6092 

.6258 

.6423 

.6588 

.6753 

.6917 

.7080 

.7243 

.7400 

28 

29 

.5761 

.5928 

.6095 

.6260 

.6426 

.6591 

.6756 

.6920 

.7083 

.7246 

.7408 

29 

30 

.5764 

.5931 

.6097 

.6263 

.6429 

.6594 

.6758 

.6922 

.70% 

.7249 

.7411 

30 

31 

.5767 

.5934 

.6100 

.6266 

.6432 

.6597 

.6761 

.6925 

.7089 

.7251 

.7414 

31 

32 

.5769 

.5936 

.6103 

.6269 

.6434 

.6599 

.6764 

.6928 

.7091 

.7254 

.7417 

32 

33 

.5772 

.5939 

.6106 

.6272 

.6437 

.6602 

.6767 

.6931 

.7094 

.7257 

.7419 

33 

34 

.5775 

.5942 

.6108 

.6274 

.0440 

.6605 

.6709 

.6933 

.7097 

.7260 

.7422 

34 

35 

.5778 

.5945 

.6111 

.6277 

.6443 

.6608 

.6772 

.6936 

.7099 

.7262 

.7425 

35 

36 

.5781 

.5947 

.6114 

.6280 

.6445 

.6610 

.6775 

.6939 

.7102 

.7265 

.7427 

36 

37 

.5783 

.5950 

.6117 

.6283 

.6448 

.6613 

.6777 

.6941 

.7105 

.7268 

.7430 

37 

38 

.5786 

.5953 

.6119 

.6285 

.6451 

.6616 

.6780 

.6944 

.7108 

.7270 

.7433 

38 

39 

.5789 

.5956 

.6122 

.6288 

.6454 

.6619 

.6783 

.6947 

.7110 

.7273 

.7435 

39 

40 

.5792 

.5959 

.6125 

.6291 

.6456 

.6621 

.6786 

.6950 

.7113 

.7276 

.7438 

40 

41 

.5795 

.5961 

.6128 

.6294 

.6459 

.6624 

.6788 

.6952 

.7116 

.7279 

.7441 

41 

42 

.5797 

.5964 

.6130 

.6296 

.6462 

.6627 

.6791 

.6955 

.7118 

.7281 

.7443 

42 

43 

.5800 

.5967 

.6133 

.6299 

.6465 

.6630 

.6794 

.6958 

.7121 

.7284 

.7446 

43 

44 

.5803 

.5970 

.6136 

.6302 

.6467 

.6632 

.6797 

.6961 

.7124 

.7287 

.7449 

44 

45 

.5806 

.5972 

.6139 

.6205 

.6470 

.6635 

.6799 

.6963 

.7127 

.7289 

.7452 

45 

46 

.5808 

.5975 

.6142 

.6307 

.6473 

.6638 

.6802 

.6966 

.7129 

.7292 

.7454 

46 

47 

.5811 

.5978 

.6144 

.6310 

.6476 

.6640 

.6S05 

.6969 

.7132 

.7295 

.7457 

47 

48 

.5814 

.5981 

.6147 

.6313 

.6478 

.6643 

.6808 

.6971 

.7135 

.7298 

.7460 

48 

49 

.5817 

.5984 

.6150 

.6316 

.6481 

.6646 

.6810 

.6974 

.7137 

.7300 

.7462 

49 

50 

.5820 

.5986 

.6153 

.6318 

.6484 

.6649 

.6813 

.6977 

.7140 

.7303 

.7405 

50 

51 

.5822 

.5989 

.6155 

.6321 

'.6487 

.6651 

.6816 

.6980 

.7143 

.7306 

.7468 

51 

52 

.5825 

.5992 

.6158 

.6324 

.6489 

.6654 

.6819 

.6982 

.7146 

.7308 

.7471 

52 

53 

.5828 

.5995 

.6161 

.6327 

.6492 

.6657 

.6821 

.6985 

.7148 

.7311 

.7473 

53 

54 

.5331 

.5997 

.6164 

.6330 

.6495 

.6660 

.6824 

.6988 

.7152 

.7314 

.7476 

51 

55 

.5834 

.6000 

.6166 

.6332 

.6498 

.6662 

.6827 

.6991 

.7154 

.7316 

.7479 

55 

56 

.5836 

.6003 

.6169 

.6335 

.6500 

.6665 

.6829 

.6993 

.7156 

.7319 

.7481 

56 

57 

.5839 

.6006 

.6172 

.6338 

.6503 

.6668 

.6832 

.6996 

.7159 

.7322 

.7484 

57 

5S 

.5842 

.6009 

.6175 

.6341 

.6506 

.6671 

.6835 

.6909 

.7162 

.7325 

.7487 

58 

59 

.5845 

.6011 

.6178 

.6343 

.6509 

.6673 

.6838 

.7001 

.7165 

.7327 

.7489 

59 

60 

.5847 

.6014 

.6180 

.6346 

.6511 

.6676 

.6840 

.7004 

.7167 

,7330 

.7492 

60 

92 


GEOMETRICAL  PROBLEMS. 


Table  of  Chords;  Radius  =1.0000  (continued). 


M. 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

53C 

53° 

54° 

M. 

0' 

.7492 

.7654 

.7815 

.7975 

.8135 

.8294 

.8452 

.8610 

.8767 

.8924 

.9080 

0 

1 

.7495 

.7656 

.7817 

.7978 

.8137 

.8297 

.8455 

.8613 

.8770 

.8927 

.9082 

1 

2 

.7498 

.7659 

.7820 

.7980 

.8140 

.8299 

.8458 

.8615 

.8773 

.8929 

.9085 

2 

3 

.7500 

.7662 

.7823 

.7983 

.8143 

.8302 

.8460 

.8618 

.8775 

.8932 

.9088 

3 

4 

.7503 

.7664 

.7825 

.7986 

.8145 

.8304 

.8463 

.8621 

.8778 

.8934 

.9090 

4 

5 

.7506 

.7667 

.7828 

.7988 

.8148 

.8307 

.8466 

.8623 

.8780 

.8937 

.9093 

5 

6 

.7508 

.7670 

.7831 

.7991 

.8151 

.8310 

.8468 

.8626 

.8783 

.8940 

.9095 

6 

7 

.7511 

.7672 

.7833 

.7994 

.8153 

.8312 

.8471 

.8629 

.8786 

.8942 

.9098 

7 

8 

.7514 

.7675 

.7836 

.7996 

.8156 

.8315 

.8473 

.8631 

.8788 

.8945 

.9101 

8 

9 

.7516 

.7678 

.7839 

.7999 

.8159 

.8318 

.8476 

.8634 

.8791 

.8947 

.9103 

9 

10 

.7519 

.7681 

.7841 

.8002 

.8161 

.8320 

.8479 

.8636 

.8794 

.8950 

.9106 

10 

11 

.7522 

.7683 

.7844 

.8004 

.8104 

.8323 

.8481 

.8639 

.8796 

.8953 

.9108 

11 

12 

.7524 

.7686 

.7847 

.8007 

.8167 

.8326 

.8484 

.8642 

.8799 

.8955 

.9111 

12 

13 

.7527 

.7689 

.7849 

.8010 

.8169 

.8328 

.8487 

.8644 

.8801 

.8958 

.9113 

13 

14 

.7530 

.7691 

.7852 

.8012 

.8172 

.8331 

.8489 

.8647 

.8804 

.8960 

.9116 

14 

15 

.7533 

.7694 

.7855 

.8015 

.8175 

.8334 

.8492 

.8650 

.8807 

.8963 

.9119 

15 

16 

.7535 

.7697 

.7857 

.8018 

.8177 

.8336 

.8495 

.8652 

.8809 

.8966 

.9121 

16 

17 

.7538 

.7699 

.7860 

.8020 

.8180 

.8339 

.8497 

.8655 

.8812 

.8968 

.9124 

17 

18 

.7541 

.7702 

.7863 

.8023 

.8183 

.8341 

.8500 

.8657 

.8814 

.8971 

.9126 

18 

19 

.7543 

.7705 

.7865 

.8026 

.8185 

.8344 

.8502 

.8660 

.8817 

.8973 

.9129 

19 

20 

.7546 

.7707 

.7868 

.8028 

.8188 

.8347 

.8505 

.8663 

.8820 

.8976 

.9132 

20 

21 

.7549 

.7710 

.7871 

.8031 

.8190 

.8349 

.8508 

.8665 

.8822 

.8979 

.9134 

21 

22 

.7551 

.7713 

.7873 

.8034 

.8193 

.8352 

.8510 

.8668 

.8825 

.8981 

.9137 

22 

23 

.7554 

.7715 

.7876 

.8036 

.8196 

.8355 

.8513 

.8671 

.8828 

.8984 

.9139 

23 

24 

.7557 

.7718 

.7879 

.8039 

.8198 

.8357 

.8516 

.8673 

.8830 

.8986 

.9142 

24 

25 

.7560 

.7721 

.7882 

.8042 

.8201 

.8360 

.8518 

.8676 

.8833 

.8989 

.9145 

25 

26 

.7562 

.7723 

.7884 

.8044 

.8204 

.8363 

.8521 

.8678 

.8835 

.8992 

.9147 

26 

27 

.7565 

.7726 

.7887 

.8047 

.8206 

.8365 

.8523 

.8681 

.8838 

.8994 

.9150 

27 

28 

.7568 

.7729 

.7890 

.8050 

.8209 

.8368 

.8526 

.8684 

.8841 

.8997 

9152 

28 

29 

.7570 

.7731 

.7892 

.8052 

.8212 

.8371 

.8529 

.8686 

.8843 

.8999 

.9155 

29 

30 

.7573 

.7734 

.7895 

.8055 

.8214 

.8373 

.8531 

.8689 

.8846 

.9002 

.9157 

30 

31 

.7576 

.7737 

.7898 

.8058 

.8217 

.8376 

.8534 

.8692 

.8848 

.9005 

.9160 

31 

32 

.7578 

.7740 

.7900 

.80GO 

.8220 

.8378 

.8537 

.8694 

.8851 

.9007 

.9163 

32 

33 

.7581 

.7742 

.7903 

.8063 

.8222 

.8381 

.8539 

.8697 

.8854 

.9010 

.9165 

33 

34 

.7584 

.7745 

.7906 

.8066 

.8225 

.8384 

.8542 

.8699 

.8856 

.9012 

.9168 

34 

35 

.7586 

.7748 

.7908 

.8068 

.8228 

.8386 

.8545 

.8702 

.8859 

.9015 

.9170 

35 

36 

.7589 

.7750 

.7911 

.8071 

.8230 

.8389 

.8547 

.8705 

.8861 

.9018 

.9173 

36 

37 

.7592 

.7753 

.7914 

.8074 

.8233 

.8392 

.8550 

.8707 

.8864 

.9020 

.9176 

37 

38 

.7595 

.7756 

.7916 

.8076 

.8236 

.8394 

.8552 

.8710 

.8867 

.9023 

.9178 

38 

39 

.7597 

.7758 

.7919 

.8079 

.8238 

.8397 

.8555 

.8712 

.8869 

.9025 

.9181 

39 

40 

.7600 

.7761 

.7922 

.8082 

.8241 

.8400 

.8558 

.8715 

.8872 

.9028 

.9183 

40 

41 

.7603 

.7764 

.7924 

.8084 

.8244 

.8402 

.8560 

.8718 

.8874 

.9031 

.9186 

41 

42 

.7605 

.7766 

.7927 

.8087 

.8246 

.8405 

.8563 

.8720 

.8877 

.9033 

.9188 

42 

43 

.7608 

.7769 

.7930 

.8090 

.8249 

.8408 

.8566 

.8723 

.8880 

.9036 

.9191 

43 

44 

.7611 

.7772 

.7932 

.8092 

.8251 

.8410 

.8568 

.8726 

.8882 

.9038 

.9194 

44 

45 

.7613 

.7774 

.7935 

.8095 

.8254 

.8413 

.8571 

.8728 

.8885 

.9041 

.9196 

45 

46 

.7616 

.7777 

.7938 

.8098 

.8257 

.8415 

.8573 

.8731 

.8887 

.9044 

.9199 

46 

47 

.7619 

.7780 

.7940 

.8100 

.8259 

.8418 

.8576 

.8734 

.8890 

.9046 

.9201 

47 

48 

.7621 

.7782 

.7943 

.8103 

.8262 

.8421 

.8579 

.8736 

.8893 

.9049 

.9204 

48 

49 

.7624 

.7785 

.7946 

.8105 

.8265 

.8423 

.8581 

.8739 

.8895 

.9051 

.9207 

49 

50 

.7627 

.7788 

.7948 

.8108 

.8267 

.8426 

.8584 

.8741 

.8898 

.9054 

.9209 

50 

51 

.7629 

.7791 

.7951 

.8111 

.8270 

.8429 

.8587 

.8744 

.8900 

.9056 

.9212 

51 

52 

.7632 

.7793 

.7954 

.8113 

.8273 

.8431 

.8589 

.8747 

.8903 

.9059 

.9214 

52 

53 

.7635 

.7796 

.7956 

.8116 

.8275 

.8434 

.8592 

.8749 

.8906 

.9062 

.9217 

53 

54 

.7638 

.7799 

.7959 

.8119 

.8278 

.8437 

.8594 

.8752 

.8908 

.9064 

.9219 

54 

55 

.7640 

.7801 

.7962 

.8121 

.8281 

.8439 

.8597 

.8754 

.8911 

.9067 

.9222 

.55 

56 

.7643 

.7804 

.7964 

.8124 

.8283 

.8442 

.8600 

.8757 

.8914 

.9069 

.9225 

56 

57 

.7646 

.7807 

.7967 

.8127 

.8286 

.8444 

.8602 

.8760 

.8916 

.9072 

.9227 

57 

58 

.7648 

.7809 

.7970 

.8129 

.8289 

.8447 

.8605 

.8762 

.8919 

.9075 

.9230 

58 

59 

.7651 

.7812 

.7972 

.8132 

.8291 

.8450 

.8608 

.8765 

.8921 

.9077 

.9232 

59 

60 

.7654 

.7815 

.7975 

.8135 

.8294 

.8452 

.8610 

.8767 

.8924 

.9080 

.9235 

60 

GEOMETRICAL  PROBLEMS. 


Table  of  Chords;  Radius=  1.0000  (continued). 


M. 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

63° 

63° 

64° 

M. 

0' 

.9235 

.9389 

.9543 

.9696 

.9848 

1.0000 

1.0151 

1.0301 

1.0450 

1.0598 

0' 

1 

.9238 

.9392 

.9546 

.9699 

.9851 

1.0003 

1.0153 

1.0303 

1.0452 

1.0601 

1 

2 

.9240 

.9395 

.9548 

.9701 

.9854 

1.0005 

1.0156 

1.0306 

1.0455 

1.0603 

2 

3 

.9243 

.9397 

.9551 

.9704 

.9856 

1.0008 

1.0158 

1.0308 

1.0457 

1.0606 

3 

4 

.9245 

.9400 

.9553 

.9706 

.9859 

1.0010 

1.0161 

1.0311 

1.0460 

1.0608 

4 

5 

.9248 

.9402 

.9556 

.9709 

.9861 

1.0013 

1.0163 

1.0313 

1.0462 

1.0611 

5 

6 

.9250 

.9405 

.9559 

.9711 

.9864 

1.0015 

1.0166 

1.0316 

1.0465 

1.0613 

6 

7 

.9253 

.9407 

.9561 

.9714 

.9866 

1.0018 

1.0168 

1.0318 

1.0467 

1.0616 

7 

8 

.9256 

.9110 

.9564 

.9717 

.9869 

1.0020 

1.0171 

1.0321 

1.0470 

1.0618 

8 

9 

.9258 

.9413 

.9566 

.9719 

.9871 

1.0023 

1.0173 

1.0323 

1.0472 

1.0621 

9 

10 

.9261 

.9415 

.9569 

.9722 

.9874 

1.0025 

1.0176 

1.0326 

1.0475 

1.0623 

10 

11 

.9263 

.9418 

.9571 

.9724 

.9876 

1.0028 

1.0178 

1.0328 

.0477 

1.0626 

11 

12 

.9266 

.9420 

.9574 

.9727 

.9879 

1.0030 

1.0181 

1.0331 

.0480 

1.0628 

12 

13 

.9268 

.9423 

.9576 

.9729 

.9881 

1.0033 

1.0183 

1.0333 

.0482 

1.0630 

13 

14 

.9271 

.9425 

.9579 

.9732 

.9884 

1.0035 

1.0186 

1  .0336 

.0485 

1.0633 

14 

15 

.9274 

.9428 

.9581 

.9734 

.9886 

1.0038 

1.0188 

1.0338 

.0487 

1.0635 

15 

16 

.9276 

.9430 

.9584 

.9737 

.9889 

1.0040 

1.0191 

1.0341 

.0490 

1.0638 

16 

17 

.9279 

.9433 

.9587 

.9739 

.9891 

1.0043 

1.0193 

1.0343 

.0492 

1.0640 

17 

18 

.9281 

.9436 

.9589 

.9742 

.9894 

1.0045 

1.0196 

1.0346 

.0495 

1.0643 

18 

19 

.9284 

.9438 

.9592 

.9744 

.9897 

1.0048 

1.0198 

1  .0348 

.0497 

1.0645 

19 

20 

.9287 

.9441 

.9594 

.9747 

.9899 

1.0050 

1.0201 

1.0351 

.0500 

1.0648 

20 

21 

.9289 

.9443 

.9597 

.9750 

.9902 

1.0053 

1.0203 

1.0353 

.0502 

1.0650 

21 

22 

.9292 

.9446 

.9599 

.9752 

.9904 

1.0055 

1.0206 

1.0356 

.0504 

1.0653 

22 

23 

.9294 

.9448 

.9602 

.9755 

.9907 

1.0058 

1.0208 

1.0358 

.0507 

1.0655 

23 

24 

.9297 

.9451 

.9604 

.9757 

.9909 

1.0060 

1.0211 

1.0361 

.0509 

1.0658 

24 

25 

.9299 

.9454 

,9607 

.9760 

.9912 

1.0063 

1.0213 

1.0363 

1.0512 

1.0660 

25 

26 

.9302 

-.9456 

.9610 

.9762 

.9914 

1.0065 

1.0216 

1.0366 

1.0514 

1.0662 

26 

27 

.9305 

.9459 

.9612 

.9765 

.9917 

1.006S 

1.0218 

1.0368 

1.0517 

1.0665 

27 

28 

.9307 

.9461 

.9615 

.9767 

.9919 

1.0070 

1.0221 

1.0370 

1.0519 

1.0667 

28 

29 

.9310 

.9464 

.9617 

.9770 

.9922 

1.0073 

1.0223 

1.0373 

1.0522 

1.0670 

29 

30 

.9312 

.9466 

.9620 

.9772 

.9924 

1.0075 

1.0226 

1.0375 

1.0524 

1.0672 

30 

31 

.9315 

.9469 

.9622 

.9775 

.9927 

1.0078 

1.0228 

1.0378 

1.0527 

1.0675 

31 

32 

.9317 

.9472 

.9625 

.9778 

.9929 

1.0080 

1.0231 

1.0380 

1.0529 

1.0677 

32 

33 

.9320 

.9474 

.9627 

.9780 

.9932 

1.0083 

1.0233 

1.0383 

1.0532 

1.0680 

33 

34 

.9323 

.9477 

.9630 

.9783 

.9934 

1.0086 

1.0236 

1.0385 

1.0534 

1.0682 

34 

35 

.9325 

.9479 

.9633 

.9785 

.9937 

1.0088 

1.0238 

1.0388 

1.0537 

1.0685 

35 

36 

.9328 

.9482 

.9635 

.9788 

.9939 

1.0091 

.0241 

1.0390 

1.0539 

1.0687 

36 

37 

.9330 

9484 

9638 

9790 

.9942 

1.0093 

.0243 

1.0393 

1  0542 

1  0690 

37 

38 

.9333 

.9487 

.9640 

.9793 

.9945 

1.0096 

.0246 

1.0395 

1.0544 

.0692 

38 

39 

.9335 

.9489 

.9643 

.9795 

.9947 

1.0098 

.0248 

1.0398 

1.0547 

.0694 

39 

40 

.9338 

.9492 

.9645 

.9798 

,9950 

1.0101 

.0251 

1.0400 

1.0549 

1.0697 

40 

41 

.9341 

.9495 

.9648 

.9800 

.9952 

1.0103 

1.0253 

1.0403 

1.0551 

.0699 

41 

42 

.9343 

.9497 

.9650 

.9803 

.9955 

1.0106 

1.0256 

1.0405 

1.0554 

.0702 

42 

43 

.9346 

.9500 

.9653 

.9805 

.9957 

1.0108 

1.0258 

1.0408 

1.0556 

.0704 

43 

44 

.9348 

.9502 

.9655 

.9808 

.9960 

1.0111 

1.0261 

1.0410 

1.0559 

.0707 

44 

45 

.9351 

.9505 

.9658 

.9810 

.9962 

1.0113 

1.0263 

1.0413 

1.0561 

.0709 

45 

46 

.9353 

.9507 

.9661 

.9813 

.9965 

1.0116 

1.0266 

1.0415 

1.0564 

.0712 

46 

47 

.9356 

.9510 

.9663 

.9816 

.9967 

1.0118 

1.0268 

1.0418 

1.0566 

.0714 

47 

48 

.9359 

.9512 

.9666 

.9818 

.9970 

1.0121 

1.0271 

1.0420 

1.0509 

.0717 

48 

49 

.9361 

.9515 

.9668 

.9821 

.9972 

1.0123 

1.0273 

1.0423 

1.0571 

.0719 

49 

50 

.9364 

.9518 

.9671 

.9823 

.9975 

1.0126 

1.0276 

1.0425 

1.0574 

.0721 

50 

51 

.9366 

.9520 

.9673 

.9826 

.9977 

1.0128 

.0278 

1.0428 

1.0576 

.0724 

51 

52 

.9369 

.9523 

.9676 

.9828 

.9980 

1.0131 

.0281 

1.0430 

1.0579 

.0726 

52 

53 

.9371 

.9525 

.9678 

.9831 

.9982 

1.0133 

.0283 

1.0433 

1.0581 

.0729 

53 

54 

.9374 

.9528 

.9681 

.9833 

.9985 

1.0136 

.0286 

1.0435 

1.0584 

.0731 

54 

55 

.9377 

.9530 

.9683 

.9836 

.9987 

1.0138 

.0288 

1.0438 

1.0586 

.0734 

55 

56 

.9379 

.9533 

.9686 

.9838 

.9990 

1.0141 

1.0291 

1.0440 

1.0589 

.0736 

56 

57 

.9382 

.9536 

.9689 

.9841 

.9992 

1.0143 

1.0293 

1.0443 

1.0591 

.0739 

57 

58 

.9384 

.9538 

.9691 

.9843 

.9995 

1.0146 

1.0296 

1.0445 

1.0593 

.0741 

58 

59 

.9387 

.9541 

.9694 

.9846 

.9998 

1.0148 

1.0298 

1.0447 

1.0596 

.0744 

59 

60 

.9389 

.9543 

.9696 

.9848 

1.0000 

1.0151 

1.0301 

1.0450 

1.0598 

.0746 

60 

94 


GEOMETRICAL  PROBLEMS. 


Table  of  Chords;  Radius  =1.0000  (continued). 


M 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

M. 

~~0 

1.0746 

1.0893 

1.1039 

1.1184 

1.1328 

1.1472 

1.1614 

1.175f 

1.1896 

0' 

] 

1.0748 

1.0S95 

1.1041 

1.1186 

1.1331 

1.1474 

1.1616 

1.1758 

1.1899 

• 

1.0751 

1.0898 

1.1044 

1.1189 

1.1333 

1.1476 

1.1C19 

1.1760 

1.1901 

2 

1.0753 

1.0900 

1.1016 

1.1191 

1.1335 

1.1479 

1.1621 

1.1703 

1.1903 

1 

1.0756 

1.0903 

1.1048 

1.1194 

1.1338 

1.1481 

1.1624 

1.1765 

1.1906 

t 

1.0758 

1.0905 

1.1051 

1.1196 

1.1340 

1.1483 

1.1626 

1.170" 

1.1908 

5 

1.0761 

1.0907 

1.1053 

1.1198 

1.1342 

1.1486 

1.16281  1.1770 

1.1910 

( 

1.0763 

1.0910 

1.1056 

1.1201 

1.1345 

1.1488 

1.1631 

1.1772 

1.1913 

' 

8 

1.0766 

1.0912 

1.1058 

1.1203 

1.1347 

1.1491 

1.1633 

1.1  77f 

1.1915 

g 

c 

1.0768 

1.0915 

1.1061 

1.1206 

1.1350 

1.1493 

1.1635 

1.1777 

1.1917 

( 

10 

1.0771 

1.0917 

1.1063 

1.1208 

1.1352 

1.1495 

1.1638 

1.1779 

1.1920 

10 

11 

1.0773 

1.0920 

1.1005 

1.1210 

1.1354 

1.1498 

1.1640 

1.1782 

1.1922 

11 

12 

1.0775 

1.0322 

1.1068 

1.1213 

1.1357 

1.1500 

1.1642 

1.1784 

1.1924 

12 

13 

1.0778 

1.0924 

1.1070 

1.1215 

1.1359 

1.1502 

1.1645 

1.1786 

1.1927 

13 

14 

1.0780 

1.0927 

1.1073 

1.1218 

1.1362 

1.1505 

1.1647 

1.1789 

1.1929 

14 

15 

1.0783 

1.0929 

1.1075 

1.1220 

1.1364 

1.1507 

1.1650 

1.1791 

1.1931 

15 

16 

1.0785 

1.0932 

1.1078 

1.1222 

1.1366 

1.1510 

1.1652 

1J793 

1.1934 

10 

17 

1.0788 

1.0934 

1.10SO 

1.1225 

1.1369 

1.1512 

1.1654 

1.1796 

1.1930 

17 

IS 

1.0790 

1.0937 

1.1082 

1.1227 

1.1371 

1J514 

1.1657 

1.1798 

1.1938 

18 

19 

1.0793 

1.0939 

1.1085 

1.1230 

1.1374 

1.1517 

1.1659 

1.1800 

1.1941 

19 

20 

1.0795 

1.0942 

1.1087 

1.1232 

1.1376 

1.1519 

1.1661 

1.1803 

1.1943 

20 

21 

1.0797 

1.0944 

1.1090 

1.1234 

1.1378 

1.1522 

1.1664 

1.1805 

1.1946 

?1 

22 

1.0800 

1.0946 

1.1092 

1.1237 

1.1381 

1.1524 

1.1666 

1.1807 

1.1948 

22 

23 

1.0802 

1.0949 

1.1094 

1.1239 

1.1383 

1.1526 

1.1668 

1.1810 

1.1950 

23 

24 

1.0805 

1.0951 

1.1097 

1.1242 

1.1386 

1.1529 

1.1671 

1.1812 

1.1952 

2- 

25 

1.0807 

1.0954 

1.1099 

1.1244 

1.1388 

1.1531 

1.1673 

1.1814 

1.1955 

25 

23 

1.0810 

1.0956 

1.1102 

1.1246 

1.1390 

1.1533 

1.1676 

1.1817 

1.1957 

26 

27 

1.0812 

1.0959 

1.1104 

1.1249 

1.1393 

1.1536 

1.1678 

1.1819 

1.1959 

27 

23 

1.0815 

1.0961 

1.1107 

1.1251 

1.1395 

1.1538 

1.1680 

1.1821 

1.1962 

28 

29 

1.0817 

1.0963 

1.1109 

1.1254 

1.1398 

1.1541 

1.1683 

1.1824 

1.1954 

29 

30 

1.0820 

1.0966 

1.1111 

1.1256 

1.1400 

1.1543 

1.1685 

1.1826 

1.1966 

30 

31 

1.0822 

1.0968 

1.1114 

1.1258 

1.1402 

1.1545 

1.1687 

1.1829 

1.1009 

31 

32 

1.0824 

1.0971 

1.1116 

1.1261 

1.1405 

1.1548 

1,1690 

1.1831 

1.1971 

32 

33 

1.0827 

1.0973 

1.1119 

1.1263 

1.1407 

1.1550 

1.1692 

1.1833 

1.1973 

33 

34 

1.0829 

1.0976 

1.1121 

1.1266 

1.1409 

1.1552 

1.1694 

1.1836 

1.1976 

34 

35 

1.0832 

1.0978 

1.1123 

1.1268 

1.1412 

1.1555 

1.1697 

1.1838 

1.1978 

35 

36 

1.0834 

1.0980 

1.1126 

1.1271 

1.1414 

1.1557 

1.1699 

1.1840 

1.1980 

30 

37 

1.0837 

1.0983 

1.1128 

1.1273 

1.1417 

1.1560 

1.1702 

1.1843 

1.1983 

37 

3S 

1.0839 

1.0985 

1.1131 

1.1275 

1.1419 

1.1502 

1.1704 

1.1845 

1.1985 

38 

39 

1.0841 

1.0988 

1.1133 

1.1278 

1.1421 

1.1564 

1.1706 

1.1847 

1.1987 

39 

40 

1.0844 

1.0990 

1.1136 

1.1280 

1.1424 

1.1567 

1.1709 

1.1850 

1.1990 

40 

41 

1.0846 

1.0993 

1.1138 

1.1283 

1.1426 

1.1569 

1.1711 

1.1852 

1.1992 

41 

42 

1.0849 

1.0995 

1.1140 

1.1285 

1.1429 

1.1571 

1.1713 

1.1854 

1.1994 

42 

43 

1.0851 

1.0997 

1.1143 

1.1287 

1.1431 

1.1574 

1.1716 

1.1857 

1.1997 

43 

41 

1.0854 

1.1000 

1.1145 

1.1290 

1.1433 

1.1576 

1.1718 

1.1859 

1.1999 

44 

45 

1.0856 

1.1002 

1.1148 

1.1292 

1.1436 

1.1579 

1.1720 

1.1861 

1.2001 

45 

46 

1.0859 

1.1005 

1.1150 

1.1295 

1.1438 

1.1581 

1.1723 

1.1864 

1.2004 

40 

47 

1.0861 

1.1007 

1.1152 

1.1297 

1.1441 

1.1583 

1.1725 

1.1866 

1.2006 

47 

48 

1.0863 

1.1010 

1.1155 

1.1299 

1.1443 

1.1586 

1.1727 

1.1868 

1.2008 

48 

49 

1.0806 

1.1012 

1.1157 

1.1302 

1.1445 

1.1588 

1.1730 

1.1871 

1.2011 

49 

50 

1.0868 

1.1014 

1.1160 

1.1304 

1.1448 

1.1590 

1.1732 

1.1873 

1.2013 

50 

51 

1.0871 

1.1017 

1.1162 

1.1307 

1.1450 

1.1593 

1.1735 

1.1875 

1.2015 

51 

52 

1.0873 

1.1019 

1.1165 

1.1309 

1.1452 

1.1595 

1.1737 

1.1878 

1.2018 

52 

53 

1.0876 

1.1022 

1.1167 

1.1311 

1.1455 

1.1598 

1.1739 

1.1880 

1.2020 

53 

54 

1.0878 

1.1024 

1.1169 

1.1314 

1.1457 

1.1600 

1.1742 

1.1882 

1.2022 

54 

55 

1.0881 

1.1027 

1.1172 

1.1316 

1.1460 

1.1602 

1.1744 

1.1885 

1.2025 

55 

56 

1.0S83 

1.1029 

1.1174 

1.1319 

1.1462 

1.1605 

1.1746 

1.1887 

1.2027 

56 

57 

1.0885 

1.1031 

1.1177 

1.1321 

1.1464 

1.1607 

1.1749 

1.1889 

1.2029 

57 

58 

1.0888 

1.1034 

1.1179 

1.1323 

1.1467 

1.1609 

1.1751 

1.1892 

1.2032 

58 

59 

1.0890 

1.1036 

1.1181 

1.1326 

1.1469 

1.1612 

1.1753 

1.1894 

1.2034 

59 

60 

1.0893 

1.1039 

1.1184 

1.1328 

1.1472 

1.1614 

1.1756 

1.1896 

.2036 

60 

GEOMETRICAL  PROBLEMS. 
Table  of  Chords;   Radius  =1.0000  (continued). 


M. 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

83° 

M. 

0 

1.2036 

1.2175 

1.2313 

1.2450 

1.2586 

1.2722 

1.2856 

1.2989 

1.3121 

0' 

1 

1.2039 

1.2178 

1.2316 

1.2453 

1.2589 

1.2724 

1.2858 

1.2991 

1.3123 

1 

2 

1.2041 

1.2180 

1.2318 

1.2455 

1.2591 

1.2726 

1.2860 

1.2993 

1.3126 

2 

3 

1.2043 

1.2182 

1.2320 

1.2457 

1.2593 

1.2728 

1.2862 

1.2996 

1.3128 

3 

4 

1.2046 

1.2184 

1.2322 

1.2459 

1.2595 

1.2731 

1.2865 

1.2998 

1.3130 

4 

5 

1.2048 

1.2  187 

1.2325 

1.2462 

1.2598 

1.2733 

1.2867 

1.3000 

1.3132 

5 

6 

1.2050 

1.2189 

1.2327 

1.2464 

1.2600 

1.2735 

1.2869 

1.3002 

1.3134 

6 

7 

1.2053 

1.2191 

1.2329 

1.2406 

1.2602 

1  .2737 

1.2871 

1.3004 

1.3137 

7 

8 

1.2055 

1.2194 

1.2332 

1.2468 

1.2604 

1.2740 

1.2874 

1.3007 

1.3139 

8 

9 

1.2057 

1.2196 

1.2334 

1.2471 

1.2607 

1.2742 

1.2876 

1.3009 

1.3141 

9 

10 

1.2060 

1.2198 

1.2336 

1.2473 

1.2609 

1.2744 

1.287S 

1.3011 

1.3143 

10 

11 

1.2062 

1.2201 

1.2338 

1.2475 

1.2611 

1.2746 

1.2880 

1.3013 

1.3145 

11 

12 

1.2064 

1.2203 

1.2341 

1.2478 

1.2614 

1.2748 

1.2882 

1.3015 

1.3147 

12 

13 

1.2066 

1.2205 

1.2343 

1.2480 

1.2616 

1.2751 

1.2885 

1.3018 

1.3150 

13 

14 

1.2069 

1.2208 

1.2345 

1.2482 

1.2618 

1.2753 

1.2887 

1.3020 

1.3152 

14 

15 

1.2071 

1.2210 

1.2348 

1.2484 

1.2620 

1.2755 

1.2889 

1.3022 

1.3154 

15 

16 

1.2073 

1.2212 

1.2350 

1.2487 

1.2623 

1.2757 

1.2891 

1.3024 

1.3156 

16 

17 

1.2076 

1.2214 

1.2352 

1.2489 

1.2625 

1.2760 

1.2894 

1.3027 

1.3158 

17 

18 

1.207S 

1.2217 

1.2354 

1.2491 

1.2627 

1.2762 

1.2896 

1.3029 

1.3161 

18 

19 

1.2080 

1.2219 

1.2357 

1.2493 

1.2629 

1.2764 

1.2898 

1.3031 

1.3163 

19 

20 

1.2083 

1.2221 

1.2359 

1.2496 

1.2632 

1.2766 

1.2900 

1.3033 

1.3165 

20 

21 

1.2085 

1.2224 

1.2361 

1.2498 

1.2634 

1.2769 

1.2903 

1.3035 

1.3167 

21 

22 

1.2087 

1.2226 

1.2364 

1.2500 

1.2636 

1.2771 

1.2905 

1.3038 

1.3169 

22 

23 

1.2090 

1.2228 

1.2366 

1.2503 

1.2638 

1.2773 

1.2907 

1.3040 

1.3172 

23 

24 

1.2092 

1.2231 

1.2368 

1.2505 

1.2641 

1.2775 

1.2909 

1.3042 

1.3174 

24 

25 

1.2094 

1.2233 

1.2370 

1.2507 

1.2643 

1.2778 

1.2911 

1.3044 

1.3176 

25 

26 

1.2097 

1.2235 

1.2373 

1.2509 

1.2645 

1.2780 

1.2914 

1.3046 

1.3178 

26 

27 

1.2099 

1.2237 

1.2375 

1.2512 

1.2648 

1.2782 

1.2916 

1.3049 

1.3180 

27 

28 

1.2101 

1.2240 

1.2377 

1.2514 

1.2650 

1.2784 

1.2918 

1.3051 

1.3183 

28 

29 

1.2104 

1.2242 

1.2380 

1.251.6 

1.2652 

1.2787 

1.2920 

1.3053 

1.3185 

29 

30 

1.2106 

1.2244 

1.2382 

1.2518 

1.2654 

1.2789 

1.2922 

1.3055 

1.3187 

30 

31 

1.2108 

1.2247 

1.2384 

1.2521 

1.2656 

1.2791 

1.2925 

1.3057 

1.3189 

31 

32 

1.2111 

1.2249 

1.2386 

1.2523 

1.2659 

1.2793 

1.2927 

1.3060 

1.3191 

32 

33 

1.2113 

1.2251 

1.2389 

1.2525 

1.2661 

1.2795 

1.2929 

1.3062 

1.3193 

33 

34 

1.2115 

1.2254 

1.2391 

1.2528 

1.2663 

1.2798 

1.2931 

1.3064 

1.3196 

34 

35 

1.2117 

1.2256 

1.2393 

1.2530 

1.2665 

1.2800 

1.2934 

1.3066 

1.3198 

35 

36 

1.2120 

1.2258 

1.2396 

1.2532 

1.2668 

1.2802 

1.2936 

1.3068 

1.3200 

36 

37 

1.2122 

1.2260 

1.2398 

1.2534 

1.2670 

1.2804 

1.2938 

1.3071 

1.3202 

37 

38 

1.2124 

1.2263 

1.2400 

1.2537 

1.2672 

1.2807 

1.2940 

1.3073 

1.3204 

38 

39 

1.2127 

1.2265 

1.2402 

1.2539 

1.2674 

1.2809 

1.2942 

1.3075 

1.3207 

39 

40 

1.2129 

1.2267 

1.2405 

1.2541 

1.2677 

1.2811 

1.2945 

1.3077 

1.3209 

40 

41 

1.2131 

1.2270 

1.2407 

1.2543 

1.2679 

1.2813 

1.2947 

1.3079 

1.3211 

41 

42 

1.2134 

1.2272 

1.2409 

1.2546 

1.2681 

1.2816 

1.2949 

1.3082 

1.3213 

42 

43 

1.2136 

1.2274 

1.2412 

1.2548 

1.2683 

1.2818 

1.2951 

1.3084 

1.3215 

43 

44 

1.2138 

1.2277 

1.2414 

1.2550 

1.2686 

1.2820 

1.2954 

1.3086 

1.3218 

44 

45 

1.2141 

1.2279 

1.2416 

1.2552 

1.2688 

1.2822 

1.2956 

1.3088 

1.3220 

45 

46 

1.2143 

1.2281 

1.2418 

1.2555 

1.2690 

1.2825 

1.2958 

1.3090 

1.3222 

46 

47 

1.2145 

1.2283 

1.2421 

1.2557 

1.2692 

1.2827 

1.2960 

1.3093 

1.3224 

47 

48 

1.2148 

1.2286 

1.2423 

1.2559 

1.2695 

1.2829 

1.2962 

1.3095 

1.3226 

48 

49 

1.2150 

1.2288 

1.2425 

1.2562 

1.2697 

1.2831 

1.2965 

1.3097 

1.3228 

49 

50 

1.2152 

1.2290 

1.2428 

1.2564 

1.2699 

1.2833 

1.2967 

1.3099 

1.3231 

50 

51 

1.2154 

1.2293 

1.2430 

1.2566 

1.2701 

1.2836 

1.2969 

1.3101 

1.3233 

51 

52 

1.2157 

1.2295 

1.2432 

1.2568 

1.2704 

1.2838 

1.2971 

1.3104 

1.3235 

52 

53 

1.2159 

1.2297 

1.2434 

1.2571 

1.2706 

1.2840 

1.2973 

1.3106 

1.3237 

53 

54 

1.2161 

1.2299 

1.2437 

1.2573 

1.2708 

1.2842 

1.2976 

1.3108 

1.3239 

54 

55 

1.2164 

1.2302 

1.2439 

1.2575 

1.2710 

1.2845 

1.2978 

1.3110 

1.3242 

55 

56 

1.2166 

1.2304 

1.2441 

1.2577 

1.2713 

1.2847 

1.2980 

1.3112 

1.3244 

56 

57 

1.2168 

1.2306 

1.2443 

1.2580 

1.2715 

1.2849 

1.2982 

1.3115 

1.3246 

57 

58 

1.2171 

1.2309 

1.2446 

1.2582 

1.2717 

1.2851 

1.2985 

1.3117 

1.3248 

58 

59 

1.2173 

1.2311 

1.2448 

1.2584 

1.2719 

1.2854 

1.2987 

1.3119 

1.3250 

59 

60 

1.2175 

1.2313 

1.2450 

1.2586 

1.2722 

1.2856 

1.2989 

1.3121 

1.3252 

60 

96 


GEOMETRICAL  PROBLEMS. 


Table  of  Chords;   Radius  =  1.0000  (concluded). 


M. 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

M. 

0' 

1.3252 

1.3383 

1.3512 

1.3640 

1.3767 

1.3893 

1.4018 

0' 

1 

1.3255 

1.3385 

1.3514 

1.3642 

1.3769 

1.3895 

1.4020 

1 

2 

1.3257 

1.3387 

1.3516 

1.3644 

1.3771 

1.3897 

1.4022 

2 

3 

1.3259 

1.33S9 

1.3518 

1.3646 

1.3773 

1.3899 

1.4024 

3 

4 

1.3261 

1.3391 

1.3520 

1.3648 

1.3776 

1.3902 

1.4026 

4 

5 

1.3263 

1.3393 

1.3523 

1.3651 

1.3778 

1.3904 

1.4029 

5 

6 

1.3265 

1.3396 

1.3525 

1.3653 

1.3780 

1.3906 

1.4031 

6 

7 

1.3268 

1.3398 

1.3527 

1.3655 

1.3782 

1.3908 

1.4033 

7 

8 

1.3270 

1.3400 

1.3529 

1.3657 

1.3784 

1.3910 

1.4035 

8 

9 

1.3272 

1.3402 

1.3531 

1.3659 

1.3786 

1.3912 

1.4037 

9 

10 

1.3274 

1.3404 

1.3533 

1.3661 

1.3788 

1.3914 

1.4039 

10 

11 

1.3276 

1.3406 

1.3535 

1.3663 

1.3790 

1.3916 

1.4041 

11 

12 

1.3279 

1.3409 

1.3538 

1.3665 

1.3792 

1.3918 

1.4043 

12 

13 

1.3281 

1.3411 

1.3540 

1.3668 

1.3794 

1.3920 

1.4045 

13 

14 

1.3283 

1.3413 

1.3542 

1.3670 

1.3797 

1.3922 

1.4047 

14 

15 

1.3285 

1.3415 

1.3544 

1.3672 

1.3799 

1.3925 

1.4049 

15 

16 

1.3287 

1.3417 

1.3546 

1.3674 

1.3801 

1.3927 

1.4051 

16 

17 

1.3289 

1.3419 

1.3548 

1.3676 

1.3803 

1.3929 

1.4053 

17 

18 

1.3292 

1.3421 

1.3550 

1.3678 

1.3805 

1.3931 

1.4055 

18 

19 

1.3294 

1.3424 

1.3552 

1.3680 

1.3807 

1.3933 

1.4058 

19 

20 

1.3296 

1.3426 

1.3555 

1.36S2 

1.3809 

1.3935 

1.4060 

20 

21 

1.3298 

1.3428 

1.3557 

1.3685 

1.3811 

1.3937 

1.4062 

21 

22 

1.3300 

1.3430 

1.3559 

1.3687 

1.3813 

1.3939 

1.4064 

22 

23 

1.3302 

1.3432 

1.3561 

1.3689 

1.3816 

1.3941 

1.4066 

23 

24 

1.3305 

1.3434 

1.3563 

1.3691 

1.3818 

1.3943 

1.4068 

24 

25 

1.3307 

1.3437 

1.3565 

1.3693 

1.3820 

1.3945 

1.4070 

25 

26 

1.3309 

1.3439 

1.3567 

1.3695 

1.3822 

1.3947 

1.4072 

20 

27 

1.3311 

1.3441 

1.3570 

1.3697 

1.3824 

1.3950 

1.4074 

27 

28 

1.3313 

1.3443 

1.3572 

1.3699 

1.3826 

1.3952 

1.4076 

28 

29 

1.3315 

1.3445 

1.3574 

1.3702 

1.3828 

1.3954 

1.4078 

29 

30 

1.3318 

1.3447 

1.3576 

1.3704 

1.3830 

1.3956 

1.4080 

30 

31 

1.3320 

1.3449 

1.3578 

1.3706 

1.3832 

1.3958 

1.4082 

31 

32 

1.3322 

1.3452 

1.3580 

1.3708 

1.3834 

1.3960 

1.4084 

32 

33 

1.3324 

1.3454 

1.3582 

1.3710 

1.3837 

1.3962 

1.40S6 

33 

34 

1.3326 

1.3456 

1.3585 

1.3712 

1.3839 

1.3964 

1.4089 

34 

35 

1.3328 

1.3458 

1.3587 

1.3714 

1.3841 

1.3966 

1.4091 

35 

36 

1.3331 

1.3460 

1.3589 

1.3716 

1.3843 

1.3968 

1.4093 

36 

37 

1.3333 

1.3462 

1.3591 

1.3718 

1.3845 

1.3970 

1.4095 

37 

38 

1.3335 

1.3465 

1.3593 

1.3721 

1.3847 

1.3972 

1.4097 

38 

39 

1.3337 

1.3467 

1.3595 

1.3723 

1.3849 

1.3975 

1.4099 

39 

40 

1.3339 

1.3469 

1.3597 

1.3725 

1.3851 

1.3977 

1.4101 

40 

41 

1.3341 

1.3471 

1.3599 

1.3727 

1.3853 

1.3979 

1.4103 

41 

42 

1.3344 

1.3473 

1.3602 

1.3729 

1.3855 

1.3981 

1.4105 

42 

43 

1.3346 

1.3475 

1.3604 

1.3731 

1.3858 

1.3983 

1.4107 

43 

44 

1.3348 

1.3477 

1.3606 

1.3733 

1.3860 

1.39S5 

1.4109 

14 

45 

1.3350 

1.3480 

1.360S 

1.3735 

1.3862 

1.3987 

1.4111 

45 

46 

1.3352 

1.3482 

1.3610 

1.3738 

1.3S64 

1.3989 

1.4113 

46 

47 

1.3354 

1.3484 

1.3612 

1.3740 

1.3866 

1.3991 

1.4115 

47 

48 

1.3357 

1.3486 

1.3614 

1.3742 

1.3868 

1.3993 

1.4117 

48 

49 

1  3359 

1.3488 

1.3617 

1.3744 

1.3870 

1.3995 

1.4119 

49 

50 

L3361 

1.3490 

1.3619 

1.3746 

1.3872 

1.3997 

1.4122 

50 

51 

1.3363 

1.3492 

1.3621 

1.3748 

1.3874 

1.3999 

1.4124 

51 

52 

1.3365 

1.3495 

1.3623 

1.3750 

1.3876 

1.4002 

1.4126 

52 

53 

1.3367 

1.3497 

1.3625 

1.3752 

1.3879 

1.4004 

1.4128 

53 

54 

1.3370 

1.3499 

1.3627 

1.3754 

1.3881 

1.4006 

1.4130 

54 

55 

1.3372 

1.3501 

1.3629 

1.3757 

1.3883 

1.4008 

1.4132 

55 

56 

1.3374 

1.3503 

1.3631 

1.3759 

1.3885 

1.4010 

1.4134 

56 

57 

1.3376 

1.3505 

1.3634 

1.3761 

1.3887 

1.4012 

1.4136 

57 

58 

1.3378 

1.3508 

1.3636 

1.3763 

1.3889 

1.4014 

1.4  138 

58 

59 

1.3380 

1.3510 

1.3638 

1  .3765 

1.3891 

1.4016 

1.4140 

59 

60 

1.3383 

1.3512 

1.3640 

1.3767 

1.3893 

1.4018 

1.4142 

60 

HIP  AND   JACK   RAFTERS. 


97 


Lengths  and  Bevels  of  Hip   and  Jack  Rafters. 

The  lines  ab  and  be  in  Fig.  89  represent  the  walls  at  the  angle 
of  a  building;  be  is  the  seat  of  the  hip-rafter,  and  gf  of  a  jack- 
rafter.  Draw  eh  at  right  angles  to  be,  and  make  it  equal  to  the 
rise  of  the  roof;  join  b  and  h,  and  hb  will  be  the  length  of  the  hip- 
rafter.  Through  e  draw  di  at  right  angles  to  be.  Upon  b,  with 
the  radius  bh,  describe  the  arc  hi,  cutting  di  in  i.  Join  b  and  i, 


m  yd  c 

Fig.  89. 

and  extend  gf  to  meet  bi  in  /;  then  gj  will  be  the  length  of  the 
jack-rafter.  The  length  of  each  jack-rafter  is  found  in  the  same 
manner, — by  extending  its  seat  to  cut  the  line  bi.  From  /  draw 
fk  at  right  angles  to  fg,  also  fl  at  right  angles  to  be.  Make  fk 
equal  to  fl  by  the  arc  Ik,  or  make  gk  equal  to  gj  by  the  arc  jk; 
then  the  angle  at  j  will  be  the  top  bevel  of  the  jack-rafters,  and 
the  one  at  k  the  down  berel. 

Backing  of  the  hip-rafter.  At  any  convenient  place  in  be  (Fig. 
89),  as  o}  draw  mn  at  right  angles  to  be.  From  o  describe  a  circle, 
tangent  to  bh,  cutting  be  in  s.  Join  m  and  s  and  n  and  .s ;  then 
these  lines  will  form  at  s  the  proper  angle  for  bevelling  the  top  of 
the  hip-rafter. 


98  TRIGONOMETRY. 


TRIGONOMETRY. 

IT  is  not  the  purpose  of  the  author  to  teach  the  use  of  trigonom- 
etry, or  what  it  is;  but,  for  the  benefit  of  those  readers  who  have 
already  acquired  a  knowledge  of  this  science,  the  following  con- 
venient formulas,  and  tables  of  natural  sines  and  tangents,  have 
been  inserted.  To  those  who  know  how  to  apply  these  trigono- 
metric functions,  they  will  often  be  found  of  great  convenience 
and  utility. 

These  tables  are  taken  from  Searle's  "  Field  Engineering,"  John 
Wiley  &  Sons,  publishers,  by  permission. 


TRIGONOMETRIC  FORMULAS. 


99 


TRIGONOMETRIC  FUNCTIONS. 

Let  A  (Fig.  107)  =  angle  7?AC  =  arc  BF,  and  let  the  radius  AF  =  AB  = 
AH=1. 
We  then  have 

sin  A          =  BC                                 H                      K                         G 

cos  A         =AC 
tan  A         =DF 
cot  A         =//(? 

L          ^<if^ 

sec  A          =AD 
cosec  A      =  AC? 
versin  A    =CF  =  BE 
covers  A    =BK  =  HL 
exsec  A     =  BD 
coexsec  A  =  BG 
chord  A     =BF 
chord  2  A  =57  =2  SC 

In  the  right-angled  triangle  ABC 
Let  AB  =  c,  AC  =  b,  and  BC  =  a. 
We  then  have: 

1  .  sin  A           =•=     —     =  cos  B 

2.  cos  A          —     —     =  sinB 
c 

3.  tan  A          —      a     —cot  B 

IxT\ 

J^a\ 
±^b   '       F 

A               c    F 

/ 

A 

FIG.  107. 
(Fig.  107) 

11.  a  =  c  sin  A  =  b  tan  A 
12.  b=c  cos  A  =acot  A 
1-    c        n                b 

b 

4.  cot  A          =    —     =  tan  B 
a 

5.  sec  A          =    —    =  cosec  B 
b 

6    cosec  A      —           —  sec  B 

sin  A         cos  A 
14.  a  =  c  cosB=--6  cot  B 

15.  6  =  csin  B  =  a  tan  5 
IR    /-          a               b 

a 
7.  vers  A        *=  -  =  covers  B 
c  —  b 

cos  B         sin  /> 

17.  a  =  V(c  +  6)(c-6) 

8.  exsec  A      =  —  -  —  =  coexsec  B 
b 

18.  6=>/(c  +  a)(c-a) 

19.  c=Va2+62 
20.  C  =  90°  =  A+5 

a6 
i-  — 

c 

a 
21.  are* 

100  TRIGONOMETRIC  FORMULAS. 


SOLUTION  OF  OBLIQUE  TRIANGLES. 

B 


FIG.  108. 


22 


A,  B,  a 


A,a,b 


C,a,b 


a,  b,  c 


A,  B,  C,  a 


B,C,c 


c 

area 
A 


FORMULAE. 


-A 
sin  A 


a      .  sin  (7. 
~&in  A 


tan  y2(A-B)^  —      tan  ^(.4  +/?) 


c  =  (a+b) 


Let  s=--V£(a 


be 


a?  sin  g.sin  C 
2  sin  A 


TRIGONOMETRIC   FORMULAS. 


101 


34.  sin  A     = 

35.  sin  A     = 

36.  sin  A     = 

37.  cos  A     = 

38.  cos  A     - 

39.  cos  A     = 

40.  tan  A    = 

41.  tan  A    = 

42.  tan  A 

43.  cot  A 

44.  cot  A 

45.  cot  A 

46.  vers  A 

47.  vers  A 

48.  exsec  A 


1 


cosec  A 
2  sin  ^ 


GENERAL  FORMULAE. 
=  V/l  —  cos2A=  tan  A  cos  A 
4  cos  HA  —  vers  A  cot 


rs  2A  = 


-  cos  2  A  ) 


—  -T=Vl-sin2A=cot  A  sin  A 
sec  A 


I  -  vers  A  =  2  cos2  J^A  —  1  =  1  —  2  sin 
cos2  HjA  —  sin2  HA  = 


cos  2A 


1  ?m  A      ./ — 5-: — 

7  = =  V  sec?A  —  1 

cot  A       cos  A 


cos2A  cos  A  1  +  cos  2A 

1  —  cos  2 A      vers  2 A 


sin  2A  si: 

1          cos  A 


. 
-  =  exsec  A  co 


tan  A      sin  A 

sin  2 A     '        sin  2A         l-feos2A 


1  —  cos  2A      vers  2  A          sin  2A 
tan  ^A 


exsec  A 

=  1  -  cos  A  =  sin  A  tan  ^A  =  2  sin2  J^ A 
=  exsec  A  cos  A 
=  sec  A  —  1  —  tan  A  tan  } 


vers  A 


cos  A 


1  --cos  A 


49.  sin  HA 

50.  sin  2A   =  2  sin  A  cos  A 


51.  cosfcM 

52.  cos  2  A 


1  +cos  A 


2  cos2A  -  1  =  cos2A  -  sin2A  =  1-2  sin2A 


102  TRIGONOMETRIC  FORMULAS. 


==~~ shrA~=cosecA-cotA 


i^vers  A       2  +  V2(l  +  cos  A) 
58.  vers  2A  =  2  sinM 

1—  cos  A 


. 

(1  +  cos 

2  tan2  A 
"•"""^-l-taa^ 

61.  sin(A  ±  J5)  =  sin  A  .  cos  /?  ±  sin  B  .  cos  A 

62.  cos  (A  ±  .B)  =  cos  A  .  cos  B  T  sin  A  .  sin  B 

63.  sin  A4-smB  =  2sin^(A+5)cos^(A-B) 

64.  sin  A  -sin  5  =  2  cos  ^(A  +5)  sin  H(A-B) 

65.  cos  A  +  cos  B  =  2  cos  J4(A  +  5)  cos  J^(  A  -  B) 

66.  cos  5  -  cos  A  -  2  sin  ^(A  +  J5)  sin  J^(A  -  B) 

67.  sin2A  -  sin2£  ==  cos2^  -  cos2A  =-  sin  (  A  +  B)  sin  (A  —  B} 

68.  cos2A  -  siii2B  =  cos(  A  +  B)  cos  (A  —  B) 

„      sin  (A  +  B) 
—  -- 


69. 


70. 


NATURAL  SINES  AND  COSINES. 


103 


0° 

1° 

2° 

3° 

4° 

i 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

.00000 

One. 

.01745 

.99985 

.03490 

.99939 

.05234 

.99863 

.06976 

.99756 

60 

1 

.00029 

One. 

.01774 

.99984 

.03519 

.99938 

.05263 

.99861 

.07005 

.99754 

59 

2 

.00058 

One. 

.01803 

.99984 

.03548 

.99937 

.05292 

.99860 

.07034 

.99752 

58 

3 

.00087 

One. 

.01832 

.99983 

.03577 

.99936 

.05321 

.9985S 

.07063 

.99750 

57 

4 

.00116 

One. 

.01862 

.99983 

.03608 

.99935 

.05350 

.99857 

.07092 

.99748 

56 

5 

.00145 

One. 

.01891 

.99982 

.03635 

.99934 

.05379 

.99855 

.07121 

.99746 

55 

6 

.00175 

One. 

.01920 

.99982 

.03664 

.99933 

.05408 

.99854 

.07150 

.99744 

54 

7 

.00204 

One. 

.01949 

.99981 

.0369.' 

.99932 

.05437 

.99852 

.07179 

.99742 

53 

8 

.00233 

One. 

.01978 

.99980 

.03723 

.99931 

.05466 

.99851 

.07208 

.99740 

52 

9 

.00262 

One. 

.02007 

.99980 

.03752 

.99930 

.05495 

.99849 

.07237 

.99738 

51 

10 

.00291 

One. 

.0203P 

.99979 

.03781 

.99929 

.05524 

.99847 

.07266 

.99736 

50 

11 

.00320 

.99999 

.02065 

.99979 

.03810 

.99927 

.05553 

.99846 

.07295 

.99734 

49 

12 

.00349 

.99999 

.02094 

.99978 

.03839 

.99926 

.05582 

.99844 

.07324 

.99731 

48 

13 

.00378 

.99999 

.02123 

.99977 

.03868 

.99925 

.05611 

.99842 

.07353 

.99729 

47 

14 

.00407 

.99999 

.02152 

.99977 

.03897 

.99924 

.05640 

.99841 

.07382 

.99727 

46 

15 

.00436 

.99999 

.02181 

.99976 

.03926 

.99923 

.05669 

.99839 

.07411 

.99725 

45 

16 

.00465 

.99999 

.02211 

.99976 

.03955 

.99922 

.05698 

.99838 

.07440 

.99723 

44 

17 

.00495 

.99999 

.02240 

.99975 

.03984 

.99921 

.05727 

.99836 

.07469 

.99721 

43 

18 

.00524 

.99999 

.02269 

.99974 

.04013 

.99919 

.05756 

.99834 

.07498 

.99719 

42 

19 

.00553 

.99998 

.02298 

.99974 

.04042 

.99918 

.05785 

.99833 

.07527 

.99716 

41 

20 

.00582 

.99998 

.02327 

.99973 

.04071 

.99917 

.05814 

.99831 

.07556 

.99714 

40 

21 

.00611 

.99998 

.02356 

.99972 

.04100 

.99916 

.05844 

.99829 

.07585 

.99712 

39 

22 

.00640 

.99998 

.02385 

.99972 

.04129 

.99915 

.05873 

.99827 

.07614 

.99710 

38 

23 

.00669 

.99998 

.02414 

.99971 

.04159 

.99913 

.05902 

.99826 

.07643 

.99708 

37 

24 

.00698 

.99998 

.02443 

.99970 

.04188 

.99912 

.05931 

.99824 

.07672 

.99705 

36 

25 

.00727 

.99997 

.02472 

.99969 

.04217 

.99911 

.05960 

.99822 

.07701 

.99703 

35 

26 

.00756 

.99997 

.02501 

.99969 

.04241 

.99910 

.05989 

.99821 

.07730 

.99701 

34 

27 

.00785 

.9999? 

.02530 

.99968 

.04275 

.99909 

.06018 

.99819 

.07759 

.99699 

33 

28 

.00814 

.99997 

.02560 

.99967 

.0430- 

.99907 

.06047 

.99817 

.07788 

.99696 

32 

29 

.00844 

.99996 

.02589 

.99966 

.04333 

.99906 

.06076 

.99815 

.07817 

.99694 

31 

3C 

.00873 

.99996 

.02618 

.99966 

.04362 

.99905 

.06105 

.99813 

.07846 

.99692 

30 

31 

.00902 

.99996 

.02647 

.99965 

.04391 

.99904 

.06134 

.99812 

.07875 

.99689 

29 

32 

.00931 

.99996 

.02676 

.99964 

.04420 

.99902 

.06163 

.99810 

.07904 

.99687 

28 

33 

.00960 

.99995 

.02705 

.99963 

.04449 

.99901 

.06192 

.99808 

.07933 

.99685 

27 

34 

.00989 

.99995 

.02734 

.99963 

.04478 

.99900 

.06221 

.99806 

.07962 

.99683 

26 

35 

.01018 

.99995 

.02763 

.99962 

.04507 

.99898 

.06250 

.99804 

.07991 

.99680 

25 

36 

.01047 

.99995 

.02792 

.99961 

.04536 

.99897 

.06279 

.99803 

.08020 

.99678 

24 

37 

.01076 

.99994 

.02821 

.99960 

.04565 

.99896 

.06308 

.99801 

.08049 

.99676 

23 

38 

.01105 

.99994 

.02850 

.99959 

.04594 

.99894 

.06337 

.99799 

.08078 

.99673 

22 

39 

.01134 

.99994 

.02879 

.99959 

.04623 

.99893 

.06366 

.99797 

.08107 

.99671 

21 

40 

.01164 

.99993 

.02908 

.99958 

.04653 

.99892 

.06395 

.99795 

.08136 

.99668 

20 

41 

.01193 

.99993 

.02938 

.99957 

.04682 

.99890 

.06424 

,99793 

.08165 

.99666 

19 

42 

.01222 

.09993 

.02967 

.99956 

.04711 

.99889 

.06453 

.99792 

.08194 

.99664 

18 

43 

.01251 

.99992 

.02996 

.99955 

.04740 

.99888 

.06482 

.99790 

.08223 

.99661 

17 

44 

.01280 

.99992 

.03025 

.99954 

.04769 

.99886 

.06511 

.99788 

.08252 

.99659 

16 

45 

01309 

.99991 

.03054 

99953 

.04798 

.99885 

.06540 

.99786 

.08281 

.99657 

15 

46 

01338 

.99991 

.03083 

99952 

.04827 

.99883 

.06569 

.99784 

.08310 

.99654 

14 

47 

01367 

.99991 

.03112 

99952 

.04856 

.99882 

.06598 

.99782 

.08339 

.99652 

13 

48 

01396 

.99990 

.03141 

99951 

.04885 

.99881 

.0^)627 

.99780 

.08368 

.99649 

12 

49 

01425 

.99990 

.03170 

99950 

.04914 

.99879 

.06656 

.99778 

.08397 

.99647 

11 

50 

01454 

.99989 

.03199 

99949 

.04943 

.99878 

.06685 

.99776 

.08426 

.99644 

10 

51 

01483 

.99989 

.03228 

99948 

.04972 

.99876 

.06714 

.99774 

.08455 

.99642 

9 

52 

01513 

.99989 

.03257 

09947 

.05001 

.99875 

.06743 

.99772 

.08484 

.99639 

8 

53 

01542 

.99988 

.03286 

99946 

.05030 

.99873 

.06773 

.99770 

.08513 

.99637 

7 

54 

01571 

.99988 

.03316 

99945 

.05059 

.99872 

.06802 

.99768 

.08542 

.99635 

6 

55 

01600 

.99987 

.03345 

99944 

.05088 

.99870 

.06831 

.99766 

.08571 

.99632 

5 

56 

01629 

.99987 

.03374 

99943 

.05117 

.99869 

.06860 

.99764 

.08600 

.99630 

4 

57 

01658 

99986 

.03403 

99942 

.05146 

99867 

.06889 

.99762 

.08629 

.99627 

3 

58 

01687 

99980 

.03432 

99941 

.05175 

99866 

.06918 

.99760 

.0865? 

.99625 

2 

59 

01716 

99985 

.03461 

99940 

.05205 

99864 

.06947 

.99758 

.08687 

.99622 

1 

60 

~"~ 

01745 

99985 

.03490 

99939 

.05234 

99863 

.06976 

.99756 

.08716 

.99619 

0 

Co  sin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

, 

89° 

88° 

87° 

86° 

85° 

104 


NATURAL  SINES  AND  COSINES. 


5° 

6° 

7° 

8° 

9° 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

,0871f 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

60 

1 

.08745 

.99617 

.10482 

.99449 

.12216 

.99251 

.1394f 

.99023 

.15672 

.98764 

59 

2 

.08774 

.99614 

.10511 

.9944? 

.12245 

.99248 

.13975 

.99019 

.15701 

.98700 

58 

3 

.0880? 

.99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755 

57 

4 

.08831 

.99609 

.10569 

.99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

5 

.08860 

.99607 

.10597 

.99437 

.12331 

.99237 

.14061 

.99006 

.15787 

.9874( 

55 

6 

.08889 

.99604 

.1062C 

.99434 

.12360 

.99233 

.14090 

.99002 

.15810 

.98741 

54 

7 

.08918 

.99602 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

8 

.08947 

.99599 

.10684 

.9942S 

.12418 

.99220 

.14148 

.98994 

.15873 

.98732 

52 

9 

.0897( 

.99596 

.10713 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

.09005 

.99594 

.10742 

.99421 

.12470 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

.99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

.99588 

.10800 

.99415 

.12533 

.99211 

.14263 

.98978 

.15988 

.98714 

48 

13 

.09092 

.99586 

.10829 

.99412 

.12562 

.99208 

.14292 

.98973 

.16017 

.98709 

47 

14 

.09121 

.99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.98969 

.16046 

.98704 

46 

15 

.09150 

.99580 

.10887 

.99408 

.12620 

.99200 

.14349 

.98965 

.16074 

.98700 

45 

16 

.09179 

.99578 

.10916 

.99402 

.12649 

.99197 

.14378 

.98961 

.16103 

.98695 

44 

17 

.09208 

.99575 

.10945 

.99399 

.12678 

.99193 

.14407 

.98957 

.16132 

.98690 

43 

18 

.09237 

.99572 

.10973 

.99396 

.12706 

.99189 

.14436 

.98953 

.16160 

.98686 

42 

19 

.09266 

.99570 

.11002 

.99393 

.12735 

.99180 

.14464 

.98948 

.16189 

.98681 

41 

20 

.09295 

.99567 

.11031 

.99390 

.12764 

.99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

.09353 

.99562 

.11089 

.99383 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667 

38 

23 

09382 

.99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

24 

09411 

99556 

.11147 

.99377 

.12880 

.99167 

.14608 

.98927 

.16333 

.98657 

36 

25 

09440 

99553 

.11176 

.99374 

.12908 

.99163 

.14637 

.98923 

.16361 

.98652 

35 

26 

09469 

99551 

.11205 

99370 

.12937 

.99160 

.14666 

.98919 

.16390 

.98648 

34 

27 

09498 

99548 

.11234 

99367 

.12966 

.99156 

.14695 

.98914 

.16419 

.98643 

33 

28 

09527 

99545 

.11263 

99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

09556 

99542 

.11291 

99360 

.13024 

.99148 

.14752 

.98906 

.16476 

.98633 

31 

30 

09585 

99540 

.11320 

99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

09614 

99537 

.11349 

99354 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

09642 

99534 

.11378 

99351 

.13110 

99137 

.14838 

98893 

.16562 

.98619 

28 

33 

09671 

99531 

11407 

99347 

.13139 

99133 

.14867 

.98889 

.16591 

.98614 

27 

34 

09700 

99528 

1H36 

.99344 

.13168 

99129 

.14896 

.98884 

.16620 

.98609 

26 

35 

09729 

99526 

11465 

99341 

.13197 

99125 

.14925 

98880 

.16648 

.98604 

25 

36 

09758 

99523 

11494 

99337 

.13226 

99122 

.14954 

98876 

.16677 

.98600 

24 

37 

09787 

99520 

11523 

99334 

.13254 

99118 

.14982 

98871 

.16706 

98595 

23 

38 

09816 

99517 

11552 

99331 

.13283 

99114 

.15011 

98867 

.16734 

98590 

22 

39 

09845 

99514 

11580 

99327 

.13312 

99110 

.15040 

98863 

.16763 

98585 

21 

40 

09874 

99511 

11609 

99324 

.13341 

99106 

.15069 

98858 

.16792 

98580 

20 

41 

09903 

99508 

11638 

99320 

.13370 

99102 

.15097 

98854 

.16820 

98575 

19 

42 

09932 

99506 

11667 

99317 

.13399 

99098 

.15126 

98849 

.16849 

98570 

18 

43 

09961 

99503 

11696 

99314 

.13427 

99094 

.15155 

98845 

.16878 

98565 

17 

44 

09990 

99500 

11725 

99310 

.13456 

99091 

.15184 

98841 

.16906 

98561 

16 

45 

10019 

99497 

11754 

99307 

.13485 

99087 

.15212 

98836 

.16935 

98556 

15 

46 

10048 

99494 

11783 

99303 

.13514 

99083 

.15241 

98832 

.16964 

98551 

14 

47 

10077 

99491 

11812 

99300 

.13543 

99079 

.15270 

98827 

.16992 

98546 

13 

48 

10106 

99488 

11840 

99297 

.13572 

99075 

.15299 

98823 

.17021 

98541 

12 

49 

10135 

99485 

11869 

99293 

.13600 

99071 

.15327 

98818 

.17050 

98536 

11 

50 

10164 

99482 

11898 

99290 

.13629 

99067 

.15356 

98814 

.17078 

98531 

10 

51 

10192 

99479 

11927 

99286 

.13658 

99063 

.15385 

98809 

.17107 

98526 

9 

52 

10221 

99476 

11956 

99283 

.13687 

9905P 

.15414 

98805 

.17136 

98521 

8 

53 

10250 

99473 

11985 

99279 

.13716 

99055 

.15442 

98800 

.17164 

98516 

7 

54 

10279 

99470 

12014 

99276 

.13744 

99051 

.15471 

98796 

.17193 

98511 

6 

55 

10308 

99467 

12043 

99272 

.13773 

99047 

.15500 

98791 

.17222 

98506 

5 

56 

10337 

99464 

12071 

99269 

.13802 

99043 

.15529 

98787 

.17250 

98501 

4 

57 

10366 

99461 

12100 

90265 

.13831 

99039 

.15557 

98782 

.17279 

98496 

3 

58 

.10395 

99458 

12129 

99262 

.13860 

99035 

.15586 

98778 

.17308 

98491 

2 

59 

.10424 

99455 

12158 

99258 

.13889 

99031 

.15615 

98773 

.17336 

98486 

1 

60 

.10453 

99452 

12187 

99255 

.13917 

99027 

.15643 

98769 

.17365 

98481 

0 

t 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

t 

84° 

83° 

82° 

81° 

80° 

NATURAL  SINES  AND  COSINES. 


105 


10° 

11° 

13° 

13° 

14° 

Sine 

Oosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

17365 

.98481 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

60 

1 

17393 

.98476 

.19109 

.98157 

.20820 

.97809 

.22523 

.97430 

.24220 

.97023 

59 

2 

17422 

.98471 

.19138 

.98152 

.20848 

.97803 

.22552 

.97424 

.24249 

.97015 

58 

3 

17451 

.98466 

.19167 

.98146 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008 

57 

4 

17479 

.98461 

.19195 

.98140 

.20905 

.97791 

.22608 

.97411 

.24305 

.97001 

56 

5 

17508 

.98455 

.19224 

.98135 

.20933 

.97784 

.22637 

.97404 

.24333 

.96994 

55 

6 

17537 

.98450 

.19252 

.98129 

.20962 

.97778 

.22665 

.97398 

.24362 

.96987 

54 

7 

17565 

.98445 

.19281 

.98124 

.20990 

.97772 

.22693 

.97391 

.24390 

.96980 

53 

8 

17594 

.98440 

.19309 

.98118 

.21019 

.97766 

.22722 

.97384 

.24418 

.96973 

52 

9 

17623 

.98435 

.19338 

.98112 

.21047 

.97760 

.22750 

.97378 

.24446 

.96966 

51 

10 

17651 

.>>8430 

.19366 

.98107 

.21076 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

17680 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807 

.97365 

.24503 

.96952 

49 

12 

17708 

.98420 

.19423 

.98096 

21132 

.97742 

.22835 

.97358 

.24531 

.96945 

48 

13 

17737 

.98414 

.19452 

.98090 

.21161 

.97735 

.22863 

.97351 

.24559 

.96937 

47 

14 

17766 

98409 

.19481 

.98084 

.21189 

.97729 

.22892 

.97345 

.24587 

.96930 

46 

15 

17794 

98404 

.19509 

.98079 

.21218 

.97723 

.22920 

.97338 

.24615 

.96923 

45 

16 

17823 

98399 

.19538 

.98073 

.21246 

.97717 

.22948 

.97331 

.24644 

.96916 

44 

17 

17852 

.98394 

.19566 

.98067 

21275 

.97711 

.22977 

.97325 

.24672 

.96909 

43 

18 

17880 

98389 

.19595 

.98061 

21303 

.97705 

.23005 

.97318 

.24700 

.96902 

42 

19 

17909 

.98383 

.19623 

.98056 

21331 

.97698 

.23033 

.97311 

.24728 

.96894 

41 

20 

17937 

.98378 

.19652 

.98050 

.21360 

.97692 

.23062 

.97304 

.24756 

.96887 

40 

21 

17966 

98373 

.19680 

.98044 

.21388 

.97686 

.23090 

.97298 

.24784 

.96880 

39 

22 

17995 

.98368 

.19709 

.98039 

.21417 

.97680 

.23118 

.97291 

.24813 

.96873 

38 

23 

18023 

.98362 

.19737 

.98033 

.21445 

.97673 

.23146 

.97284 

.24841 

.96866 

37 

24 

18052 

.98357 

.19766 

.98027 

.21474 

.97667 

.23175 

.97278 

.24869 

.96858 

36 

25 

18081 

.98352 

.19794 

.98021 

.21502 

.97661 

.23203 

.97271 

.24897 

.96851 

35 

26 

18109 

.98347 

.19823 

.98016 

.21530 

.97655 

.23231 

.97264 

.24925 

.96844 

34 

27 

18138 

.98341 

,19851 

.98010 

.21559 

.97648 

.23260 

.97257 

.24954 

.96837 

33 

28 

18166 

.98336 

.19880 

,98004 

.21587 

.97642 

.23288 

.97251 

.24982 

.96829 

32 

29 

18195 

.98331 

'.1990S 

.97998 

.21616 

.97636 

.23316 

.97244 

.25010 

.96822 

31 

30 

18224 

.98325 

.19937 

.97992 

.21644 

.97630 

.23345 

.97237 

.25038 

.96815 

30 

31 

18252 

.98320 

.19965 

.97987 

.21672 

.97623 

.23373 

.97230 

.25066 

.96807 

29 

32 

18281 

.98315 

.19994 

.97981 

.21701 

.97617 

.23401 

.97223 

.25094 

.96800 

28 

33 

18309 

.98310 

.20022 

.97975 

.21729 

.97611 

.23429 

.97217 

.25122 

.96793 

27 

34 

18338 

.98304 

.20051 

.97969 

.21758 

.97604 

.23458 

.97210 

.25151 

.96786 

26 

35 

18367 

.98299 

.20079 

.97963 

.21786 

.97598 

.23486 

.97203 

.25179 

.96778 

25 

36 

18395 

.98294 

.20108 

.97958 

.21814 

.97592 

.23514 

.97196 

.25207 

.96771 

24 

37 

18424 

.98288 

.20136 

.97952 

.21843 

.97585 

.23542 

.97189 

.25235 

.96764 

23 

38 

.18452 

.98283 

.20165 

.97946 

.21871 

.97579 

.23571 

.97182 

.25263 

.96756 

22 

39 

.18481 

.98277 

.20193 

.97940 

.21899 

.97573 

.23599 

.97176 

.25291 

.96749 

21 

40 

.18509 

.98272 

.20222 

.97934 

.21928 

.97566 

.23627 

.97169 

.25320 

.96742 

20 

41 

.18538 

.98267 

.20250 

.97928 

.21956 

.97560 

.23656 

.97162 

.25348 

.96734 

19 

42 

.18567 

.98261 

.20279 

.97922 

.21985 

.97553 

.23684 

.97155 

.25376 

.96727 

18 

43 

.18595 

.98256 

.20307 

.97916 

.22013 

.97547 

.23712 

.97148 

.25404 

.96719 

17 

44 

.18624 

.98250 

.20336 

.97910 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

16 

45 

.18652 

.98245 

.20364 

.97905 

.22070 

.97534 

.23769 

.97134 

.25460 

.96705 

15 

46 

.18681 

.98240 

.20393 

.97899 

.22098 

.97528 

.23797 

.97127 

.25488 

.96697 

14 

47 

.18710 

.98234 

.20421 

.97893 

.22126 

.97521 

.23825 

.97120 

.25516 

.96690 

13 

48 

.18738 

.98229 

.20450 

.97887 

.22155 

.97515 

.23853 

.97113 

.25545 

.96682 

12 

49 

.18767 

.98223 

.20478 

.97881 

.22183 

.97508 

.23882 

.97106 

.25573 

.96675 

11 

50 

.18795 

.98218 

.20507 

.97875 

.22212 

.97502 

.23910 

.97100 

.25601 

.96667 

10 

51 

.18824 

.98212 

.20535 

.97869 

.22240 

.97496 

.23938 

.97093 

.25629 

.96660 

9 

52 

.18852 

.98207 

.20563 

.97863 

.22268 

.97489 

.23966 

.97086 

.25657 

.96653 

8 

53 

.18881 

.98201 

.20592 

.97857 

.22297 

.97483 

.23995 

.97079 

.25685 

.96645 

7 

54 

.18910 

.98196 

.20620 

.97851 

.22325 

.97476 

.24023 

.97072 

.25713 

.96638 

6 

55 

.18938 

.98190 

.20649 

.97845 

.22353 

.97470 

.24051 

.97065 

.25741 

.96630 

5 

56 

.18967 

.98185 

.20677 

.97839 

.22382 

.97463 

.24079 

.97058 

.25769 

.96623 

4 

57 

.18995 

.98179 

.20706 

.97833 

.22410 

.97457 

.24108 

.97051 

.25798 

.96615 

3 

58 

.19024 

.98174 

.20734 

.97827 

.22438 

.97450 

.24136 

.97044 

.25826 

.96608 

2 

59 

.19052 

.98168 

.20763 

.97821 

.22467 

.97444 

.24164 

.97037 

.25854 

.96600 

1 

60 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

.25882 

.96593 

0 

/ 

Co  sin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

/ 

79° 

78° 

77° 

76° 

75° 

106 


NATURAL  SINES  AND  COSINES. 


p 

15* 

1 

Sine" 

6°  

Cosin 

17° 

18° 

19° 

/ 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

25882 

96593 

.27564 

.96126 

.29237 

95630 

.30902 

.95106 

.32557 

.94552 

60 

1 

25910 

96585 

.27592 

96118 

.29265 

95622 

.30929 

95097 

.32584 

.94542 

59 

2 

25938 

96578 

.27620 

96110 

.29293 

95613 

.30957 

.95088 

.32612 

.94533 

58 

3 

25966 

96570 

.27648 

96102 

.29321 

95605 

.30985 

95079 

.32639 

.94523 

57 

4 

25994 

96562 

.27676 

95094 

.29348 

95596 

.31012 

95070 

.32667 

.94514 

56 

5 

26022 

96555 

.27704 

96086 

.29376 

95588 

.31040 

95061 

.32694 

.94504 

55 

6 

26050 

96547 

.27731 

96078 

.29404 

95579 

.31068 

95052 

.32722 

.94495 

54 

7 

26079 

96540 

.27759 

96070 

.29432 

95571 

.31095 

95043 

.32749 

.94485 

53 

8 

26107 

96532 

.27787 

96062 

.29460 

95562 

.31123 

95033 

.32777 

.94476 

52 

9 

26135 

96524 

.27815 

96054 

.29487 

95554 

.31151 

95024 

.32804 

.94466 

51 

10 

26163 

96517 

.27843 

96046 

.29515 

95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

26191 

96509 

.27871 

96037 

.29543 

95536 

.31206 

95006 

.32859 

.94447 

49 

12 

26219 

96502 

.27899 

96029 

.29571 

95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

26247 

96494 

.27927 

90021 

.29599 

95519 

.31261 

94988 

.32914 

.94428 

47 

14 

26275 

96486 

.27955 

96013 

.29626 

95511 

.31289 

94979 

.32942 

.94418 

46 

15 

26303 

96479 

.27983 

96005 

.29654 

95502 

.31316 

94970 

.32909 

.94409 

45 

16 

26331 

96471 

.28011 

95997 

.29682 

95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

26359 

96463 

.28039 

95989 

.29710 

95485 

.31372 

94952 

.33024 

.94390 

43 

18 

26387 

96456 

.28067 

95981 

.29737 

95476 

.31399 

94943 

.33051 

.94380 

42 

19 

26415 

96448 

.28095 

95972 

.29765 

95467 

.31427 

94933 

.33079 

.94370 

41 

20 

26443 

96440 

.28123 

95964 

.29793 

95459 

.31454 

.94924 

.33106 

.94361 

40 

21 

26471 

96433 

.28150 

95956 

.29821 

95450 

.31482 

94915 

.33134 

.94351 

39 

22 

26500 

96425 

.28178 

95948 

.29849 

95441 

.31510 

94906 

.33161 

.94342 

38 

23 

26528 

96417 

.28206 

95940 

.29876 

95433 

.31537 

94897 

.33189 

.94332 

37 

24 

26556 

96410 

.28234 

95931 

.29904 

95424 

.31565 

94888 

.33216 

.94322 

36 

25 

26584 

96402 

.28262 

95923 

.29932 

95415 

.31593 

94.878 

.33244 

.94313 

35 

26 

26612 

96394 

.28290 

95915 

.29960 

95407 

.31620 

94869 

.33271 

.94303 

34 

37 

26640 

96386 

.28318 

95907 

.29987 

95398 

.31648 

94860 

.33298 

.94293 

33 

28 

26668 

96379 

.28346 

95898 

.30015 

95389 

.31675 

94851 

.33326 

.94284 

32 

29 

26696 

96371 

.28374 

95890 

.30043 

95380 

.31703 

94842 

.33353 

.94274 

31 

30 

26724 

.96363 

.28402 

95882 

.30071 

95372 

.31730 

94832 

.33381 

.94264 

30 

31 

26752 

.96355 

.28429 

95874 

.30098 

95363 

.31758 

94823 

.33408 

.94254 

29 

32 

26780 

.96347 

.28457 

958G5 

.30126 

95354 

.31786 

94814 

.33436 

.94245 

28 

33 

26808 

.96340 

.28485 

95857 

.30154 

95345 

.31813 

94805 

.33463 

.94235 

27 

34 

26836 

.96332 

.28513 

95849 

.30182 

95337 

.31841 

94795 

.33490 

.94225 

26 

35 

26864 

.96324 

.28511 

95841 

.30209 

95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28569 

95832 

.30237 

95319 

.31896 

94777 

.33545 

.94206 

24 

37 

26920 

.96308 

.28597 

95824 

.30265 

95310 

.31923 

94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

95301 

.31951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.96293 

.28652 

.95807 

.30320 

95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.2870* 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30403 

.95266 

.32061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

.32089 

.94712 

.23737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.30486 

.95240 

.32144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.95749 

.30514 

.95231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222 

.32199 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.95204 

.32254 

.94656 

.33901 

.94078 

11 

50 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.32282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.33983 

.94049 

8 

53 

.27368 

.96182 

.29042 

.95690 

.30708 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96174 

.29070 

.95681 

.30736 

.95159 

.32392 

.94609 

.34038 

.94029 

6 

55 

.27424 

.96166 

.29098 

.95673 

.30763 

.95150 

.32419 

.94599 

.34065 

.94019 

5 

56 

.27452 

.96158 

.29126 

.95664 

.30791 

.95142 

.32447 

.94590 

.34093 

.94009 

4 

57 

.27480 

.96150 

.29154 

.95656 

.30819 

.95133 

.32474 

.94580 

.34120 

.93999 

3 

58 

.27508 

.96142 

.29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59 

.27536 

.96134 

.29209 

.95839 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

60 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

/ 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

» 

74° 

1    73° 

72° 

71° 

70° 

NATURAL  SINES  AND  COSINES. 


107 


20° 

21° 

22° 

23° 

21° 

Sine 

Cosin 

Sine 

Cosin 

Sine 

?osin 

Sine 

Josin 

Sine 

Josin 

0 

34202 

93969 

35837 

93358 

37461 

92718 

39073 

92050 

40074 

91355 

60 

1 

34229 

93959 

35884 

93348 

37488 

92707 

39100 

92039 

40700 

91343 

59 

2 

34257 

93949 

35891 

93337 

37515 

92697 

39127 

92028 

40727 

91331 

58 

3 

34284 

93939 

35918 

93327 

37542 

92686 

39153 

92016 

40753 

91319 

57 

4 

34311 

93929 

35945 

93316 

37509 

92675 

391SO 

92005 

.40780 

91307 

56 

5 

34339 

93919 

35973 

93306 

37595 

92604 

39207 

91994 

.40806 

91295 

55 

6 

34366 

93909 

36000 

93295 

37622 

92053 

39234 

91982 

.40833 

91283 

54 

7 

34393 

93899 

36027 

93285 

37649 

92642 

39260 

91971 

.40860 

91272 

53 

8 

34421 

93889 

36054 

93274 

37676 

92631 

39287 

91959 

.40886 

91260 

52 

9 

34448 

93879 

36081 

93264 

37703 

92620 

39314 

91948 

.40913 

91248 

51 

10 

34475 

93869 

36108 

93253 

37730 

92609 

39341 

91936 

.40939 

91236 

50 

11 

34503 

93859 

36135 

93243 

37757 

92598 

39367 

.91925 

.40966 

91224 

49 

12 

34530 

93849 

36162 

93232 

37784 

92587 

39394 

.91914 

.40992 

91212 

48 

13 

34557 

93839 

36190 

93222 

37811 

92576 

.39421 

.91902 

.41019 

91200 

47 

14 

34584 

93829 

36217 

93211 

37838 

92565 

.39448 

.91891 

.41045 

91188 

46 

15 

34612 

93819 

36244 

93201 

37865 

92554 

.39474 

.91879 

.41072 

91176 

45 

16 

34639 

93809 

36271 

93190 

37892 

92543 

.39501 

.91868 

.41098 

91164 

44 

17 

34666 

93799 

30298 

93180 

37919 

92532 

.39528 

.91856 

.41125 

91152 

43 

18 

34694 

93789 

30325 

93169 

37946 

92521 

.39555 

.91845 

.41151 

91140 

42 

19 

34721 

93779 

36352 

93159 

.37973 

92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

34748 

93769 

36379 

93148 

.37999 

92499 

.39608 

.91822 

.41204 

.91116 

40 

21 

34775 

93759 

36406 

93137 

.38026 

92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

34803 

9374S 

36434 

93127 

.38053 

92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

34830 

9373S 

36461 

93116 

.38080 

92466 

.39688 

.91787 

.41284 

.91080 

37 

24 

34S57 

93728 

36488 

93106 

.38107 

92455 

.39715 

.91775 

.41310 

.91068 

30 

25 

34884 

93718 

36515 

93095 

.38134 

92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

34912 

93708 

36542 

93084 

.38161 

92432 

.39768 

.91752 

.41363 

.91044 

34 

27 

34939 

93698 

30569 

93074 

.38188 

92421 

.39795 

.91741 

.41390 

.91032 

33 

28 

34966 

93688 

36596 

93063 

.38215 

92410 

.39822 

.91729 

.41416 

.91020 

32 

29 

34993 

93677 

.36623 

93052 

.28241 

.92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

35021 

93667 

.36650 

93042 

.38268 

92388 

.39875 

.91706 

.41469 

.90996 

30 

31 

35048 

93657 

.36677 

93031 

.38295 

.92377 

.39902 

.91694 

.41496 

.90984 

29 

o2 

35075 

93647 

.36704 

93020 

.38322 

.92366 

.39928 

.91683 

.41522 

.90972 

28 

33 

35102 

93637 

.36731 

93010 

.38349 

.92355 

.39955 

.91671 

.41549 

.90960 

27 

31 

35130 

93626 

.36758 

92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

35157 

93616 

.36785 

92988 

.38403 

9^332 

.40008 

.91648 

.41602 

.90936 

25 

36 

35184 

93606 

.36812 

92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

35211 

93590, 

.36839 

92967 

.38456 

92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

35239 

93585 

.36867 

92956 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

35266 

93575 

.36894 

92945 

.38510 

.92287 

.40115 

.91601 

.41707 

.90887 

21 

40 

.35293 

93565 

.36921 

92935 

.38537 

.92276 

.40141 

.91590 

.41734 

.90875 

20 

41 

.35320 

93555 

.36948 

92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.9086? 

19 

40 

.35347 

33544 

.36975 

92913 

.38591 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

13 

.35375 

93534 

.37002 

92902 

.38617 

.92243 

.40221 

.91555 

.41813 

.90839 

17 

44 

.35402 

93524 

.37029 

92892 

.38644 

.92231 

.40248 

.91543 

.41*40 

.9082f 

16 

45 

.35429 

93514 

.37056 

92881 

.38671 

.92220 

.40275 

.91531 

.41866 

.90814 

15 

46 

.35456 

93503 

.37083 

92870 

.38698 

.92209 

.40301 

.91519 

.41892 

.90802 

14 

17 

.35484 

.93493 

.37110 

.92859 

.38725 

.92198 

.40328 

.91508 

.41919 

.90790 

13 

48 

.35511 

.93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945 

.90778 

12 

49 

.35538 

.93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972 

.90760 

11 

50 

.35565 

.93462 

.37191 

.92827 

.38805 

.92164 

.4040^ 

.91472 

.41998 

.90753 

10 

51 

.35592 

.93452 

.37218 

.92816 

.38832 

.92152 

.40434 

.91461 

.42024 

.90741 

9 

52 

.35619 

.93441 

.37245 

.92805 

.38859 

.92141 

.40461 

.91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886 

.92130 

.40488 

.91437 

.42077 

.90717 

7 

54 

.3567- 

.93420 

.37299 

.92784 

.38912 

.92119 

.40514 

.91425 

.42104 

.90704 

6 

55 

.3570 

.93410 

.37326 

.92773 

.38939 

.92107 

.40541 

.9141 

.42130 

.90692 

5 

50 

.35728 

.93400 

.37353 

.92762 

.38966 

.92096 

.40567 

.91402 

.42150 

.90680 

4 

57 

.3575 

.93389 

.37380 

.92751 

.38993 

.92085 

.40594 

.91390 

.42183 

.90668 

3 

58 

.3578 

.93379 

.37407 

.92740 

.39020 

.92073 

.40621 

.91378 

.42209 

.90055 

2 

59 

.3581 

.93368 

.37434 

.92729 

.3904( 

.9206? 

.40647 

.9136f 

.42235 

.90643 

1 

60 

.3583 

.93358 

.3746 

.92718 

.39073 

.92050 

.40674 

.91350 

.42262 

.90631 

0 

, 

Cosin 

Sine 

Cosin 

Sine 

Cofiin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

, 

69° 

68° 

67° 

fi(f>° 

65° 

108 


NATURAL  SINES  AND   COSINES. 


25° 

26° 

27° 

28° 

29° 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

.12262 

.9063 

.4383 

.8987 

.4539$ 

.89101 

.4694 

.8829 

.4848 

.8746S 

60 

1 

.4228,^ 

.9061 

.4386 

.8986 

.4542,' 

.89087 

.4697 

.8828 

.4850 

.874  4J- 

59 

J 

.42315 

.9060 

.4388 

.8985 

.45451 

.89074 

.4699 

.8826 

.4853 

.8743^ 

58 

£ 

.42341 

.9059 

.4391 

.8984 

.4547; 

.89061 

.4702 

.8825 

.4855 

.8742C 

57 

4 

.42367 

.9058 

.4394 

.8982 

.4550? 

.89048 

.4705 

.8824 

.4858 

.8740( 

56 

K 

.12394 

.9056 

.4396 

.89816 

.4552S 

.89035 

.4707 

.8822 

.48608 

.87391 

55 

6 

.42420 

.9055 

.4399 

.89803 

.45554 

.89021 

.4710 

.8821 

.48634 

.87377 

54 

7 

.42446 

.9054 

.44020 

.89790 

.4558(1 

.89008 

.4712 

.8819 

.48659 

.87363 

53 

8 

.42473 

.9053 

.41040 

.89777 

.4560( 

.88995 

.47153 

.8818 

!.  48684 

.87349 

52 

9 

.42499 

.90520 

.44072 

.89764 

.45632 

.88981 

.47178 

.8817 

,.48710 

.87335 

51 

10 

.42525 

.9050 

.44098 

.89752 

.45658 

.88968 

.47204 

.8815 

.48735 

.8732 

50 

11 

.42552 

.90495 

.44124 

.39739 

.45684 

.88955 

.47229 

.88144 

.48761 

.87306 

49 

12 

.42578 

.9048, 

.4415 

.89726 

.45710 

.88942 

.17255 

.88130 

.48786 

.87292 

48 

13 

.42604 

.90470 

.44177 

.89713 

.45736 

.88928 

.47281 

.88117 

.48811 

.87278 

47 

14 

.42631 

.90458 

.41203 

.89700 

.45762 

.88915 

.47306 

.88103 

.48837 

.87264 

40 

15 

.42657 

.90446 

.44229 

.89687 

.457S7 

.88902 

.47332 

.88089 

.48862 

87250 

45 

16 

.42683 

.90133 

.44255 

.89674 

.15813 

.88888 

.47358 

.88075 

.48888 

87235 

44 

17 

.42709 

.9042 

.44281 

.89662 

.45839 

.88875 

.47383 

.88062 

.48913 

87221 

43 

18 

.42736 

.90408 

.44307 

.89649 

.45865 

.88862 

.47409 

88048 

.48938 

87207 

42 

19 

.42762 

.90396 

.44333 

.89636 

.45891 

.88848 

.47434 

88034 

.48964 

87193 

41 

20 

.42788 

.90383 

.44359 

.89623 

.45917 

.88835 

.47460 

88020 

.48989 

87178 

40 

21 

.42815 

.90371 

.44385 

.89610 

.45942 

.88822 

.47486 

88006 

.49014 

87164 

39 

22 

.42841 

.90358 

.44411 

.89597 

.45908 

.88808 

.47511 

87993 

.49040 

87150 

38 

23 

.42867 

.90346 

.44437 

.89584 

.45994 

.88795 

.47537 

87979 

.49065 

87136 

37 

24 

.42894 

90334 

.44464 

89571 

.46020 

.88782 

.47562 

87965 

.49090 

87121 

36 

25 

.42920 

90321 

.44490 

89558 

.46046 

.88768 

.47588 

87951 

.49116 

87107 

35 

26 

42946 

90309 

.44516 

89545 

.46072 

.88755 

.47614 

87937 

.49141 

87093 

34 

27 

42972 

90296 

.44542 

89532 

.46097 

.88741 

.47639 

87923 

.49166 

87079 

33 

28 

42999 

90284 

.44568 

89519 

.46123 

.88728 

.47665 

87909 

.49192 

87064 

32 

29 

13025 

.90271 

.44594 

89506 

.46149 

88715 

.47690 

87896 

.49217 

87050 

31 

30 

43051 

.90259 

.44620 

89493 

.46175 

88701 

.47716 

87882 

.4924? 

87036 

30 

31 

43077 

.90246 

.44646 

89480 

.46201 

88688 

.47741 

87868 

.49268 

87021 

29 

32 

43104 

.90233 

.44072 

89467 

46226 

88674 

.47767 

87854 

.49293 

87007 

28 

33 

43130 

.90221 

.44698 

89451 

46252 

.88661 

.47793 

87840 

.49318 

86993 

27 

34 

43156 

.90208 

.44724 

89441 

46278 

.88647 

.47818 

87826 

.49344 

86978 

26 

35 

13182 

.90196 

.44750 

89428 

46304 

.88634 

.47844 

87812 

.49369 

86964 

25 

36 

43209 

.90183 

.44776 

89415 

46330 

.88620 

.47869 

87798 

.49394 

86949 

24 

37 

43235 

.90171 

.44802 

89402 

46355 

.88607 

.47895 

87784 

.49419 

86935 

23 

38 

43261 

.90158 

.44828 

89389 

46381 

.88593 

.47920 

87770 

.49445 

86921 

22 

39 

432S7 

.90146 

.44854 

89376 

46407 

.88580 

.47946 

S7756 

.49470 

86906 

21 

40 

43313 

.90133 

.44880 

89363 

46433 

.88566 

.47971 

87743 

.49495 

86892 

20 

41 

43310 

.90120 

.44906 

89350 

46458 

.88553 

.47997 

87729 

.49521 

86878 

19 

42 

43366 

.90108 

.44932 

89337 

46484 

.88539 

.48022 

87715 

.49546 

86863 

18 

43 

43392 

.90095 

.44958 

89324 

46510 

.88526 

.48048 

87701 

.49571 

86849 

17 

44 

43418 

.90082 

.44984 

89311 

16536 

.88512 

.48073 

87687 

.49596 

86834 

16 

45 

43445 

.90070 

.45010 

89298 

46561 

.88499 

.48099 

87673 

.49622 

86820 

15 

46 

43471 

.90057 

.45036 

89285 

46587 

.88485 

.48124 

S7659 

.49647 

86805 

14 

47 

43497 

.90045 

.45062 

89272 

46613 

.88472 

.48150 

87645 

.49672 

86791 

13 

48 

43523 

90032 

.45088 

89259 

46639 

.88458 

.48175 

87631 

.49697 

86777 

12 

49 

43549 

.90019 

.15114 

89245 

46664 

.88445 

48201 

87617 

.49723 

86762 

11 

50 

43575 

.90007 

.45140 

89232 

46690 

.88431 

48226 

87603 

.49748 

86748 

10 

51 

43602 

.89994 

.45166 

89219 

46716 

.88417 

48252 

S7589 

.49773 

86733 

9 

52 

13628 

.89981 

.45192 

89206 

46742 

.88404 

48277 

87575 

.49798 

86719 

8 

53 

43654 

89968 

.45218 

89193 

46767 

.88390 

48303 

87561 

.49824 

86704 

7 

54 

43680 

89956 

45243 

89180 

46793 

.88377 

48328 

87546 

.49849 

86690 

6 

55 

43706 

89943 

45269 

89167 

46819 

.88363 

48354 

87532 

.49874 

86675 

5 

56 

43733 

89930 

45295 

89153 

46844 

.88349 

48379 

87518 

.49899 

86661 

4 

57 

43759 

89918 

45321 

89140 

46870 

.88336 

48405 

87504 

.49924 

86646 

3 

58 

43785 

89905 

45347 

8<U27 

46896 

.88322 

48430 

87490 

.49950 

86632 

2 

59 

43811 

89892 

45373 

89114 

46921 

.88308 

4S456 

87476 

.49975 

86617 

1 

60 

43837 

89879 

45399 

89101 

46947 

.88295 

48481 

87462 

50000 

86603 

0 

, 

osin 

Sine 

Cosin 

Sine 

osin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

, 

64° 

63° 

62° 

61° 

60° 

NATURAL  SINES  AND  COSINES. 


109 


30° 

31° 

32° 

33° 

34° 

' 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

o 

.50000 

.80603 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

60 

1 

.50025 

.86588 

.51529 

.85702 

.53017 

.84789 

.54488 

.83851 

.55943 

.82S87 

59 

2 

.50050 

.86573 

.51554 

.85687 

.53041 

.84774 

.54513 

.83835 

.55968 

.82871 

58 

3 

.50076 

.86559 

.51579 

.85672 

.53066 

.84759 

.54537 

.83819 

.55992 

.82855 

57 

4 

.50101 

.86544 

.51604 

.85657 

.53091 

.84743 

.54561 

.83804 

.56016 

.82839 

56 

5 

.50126 

.86530 

.51628 

.85642 

.53115 

.84728 

.54586 

.83788 

.56040 

.82822 

55 

6 

.50151 

.86515 

.51653 

.85627 

.53140 

.84712 

.54610 

.83772 

.56064 

.82806 

54 

7 

.50176 

.86501 

.51678 

.85612 

.53164 

.84697 

.54635 

.83756 

.56088 

.82790 

53 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659 

.83740 

.56112 

.82773 

52 

9 

.50227 

.86471 

.51728 

.85582 

.53214 

.84666 

.54683 

.83724 

.56136 

.82757 

51 

10 

.50252 

.80457 

.51753 

.85567 

.53238 

.84650 

.54708 

.83708 

.56160 

;82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

,84635 

.54732 

.83692 

.56184 

'.82724 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83676 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51S28 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82692 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.54805 

.83645 

.56256 

.82675 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.54829 

.83629 

.56280 

.82659 

45 

16 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.54854 

.83613 

.56305 

.82643 

44 

17 

.50428 

.86354 

.51927 

.85461 

.53411 

.84542 

.54878 

.83597 

.56329 

.82626 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84526 

.54902 

.83581 

.56353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53460 

.81511 

.54P27 

.83565 

.56377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52026 

.85401 

.53509 

.84480 

.54975 

.83533 

.56425 

.82501 

39 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84464 

.51999 

.83517 

.56449 

.82544 

38 

23 

.50578 

.86266 

.52076 

.85370 

.53558 

.84448 

,55024 

.83501 

.56473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.84433 

.55048 

.83485 

.56497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83469 

.56521 

.82495 

35 

26 

.50654 

.86222 

.52151 

.85325 

.53632 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

27 

.50679 

.86207 

.52175 

.85310 

.53656 

.84386 

.55121 

.83437 

.56569 

.82462 

33 

28 

.50704 

.86192 

.02200 

.85294 

.53681 

.84370 

.55145 

.83421 

.56593 

.82446 

32 

29 

.50729 

.86178 

.52225 

.85279 

.53705 

.84355 

.55169 

.83405 

.56617 

.82429 

31 

30 

.50754 

.36163 

.52250 

.85264 

.53730 

.84339 

.55194 

.83389 

.56641 

.82413 

30 

31 

.50779 

.86148 

.52275 

.85249 

.53754 

.84324 

.55218 

.83373 

.56665 

.82396 

29 

32 

.50804 

.86133 

.52299 

.85234 

.53779 

.84308 

.55242 

.83356 

.56689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.55266 

.83340 

.56713 

.82363 

27 

34 

.50854 

.86104 

,52349 

.85203 

.53828 

.84277 

.55291 

.83324 

.56736 

.82347 

26 

35 

.50*79 

.86089 

.52374 

.85188 

.53853 

.84261 

.55315 

.83308 

.56760 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.55339 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83276 

.56808 

.82297 

23 

38 

.50954 

.86045 

.52448 

.85142 

.53926 

.84214 

.55388 

.83260 

.56832 

.82281 

22 

39 

.50979 

.86030 

.52473 

.85127 

.53951 

.84198 

.55412 

.83244 

.56856 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112 

.53975 

.84182 

.55436 

.83228 

.56880 

.82248 

20 

41 

.51029 

.86000 

.52522 

.85096 

.54000 

.84167 

.55460 

,83212 

.56904 

.82231 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

18 

43 

.51079 

.85970 

.52572 

.85066 

.54049 

.84135 

.55509 

.83179 

.56952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051 

.54073 

.84120 

.55533 

.83163 

.56976 

.82181 

16 

45 

.51129 

.85941 

.52621 

,85035 

.54097 

.84104 

.55557 

.83147i 

.57000 

.82165 

15 

46 

.51154 

.85926 

.52646 

.85020 

.54122 

.8408S 

.55581 

.83131' 

.57024 

.82148 

14 

47 

.51179 

.85911 

.52671 

.85005 

.54146 

.84072 

.55605 

.83115 

.57047 

,82132 

13 

48 

.51204 

,85896 

.52696 

.84989 

.54171 

.84057 

.55630 

.83098 

.57071 

.82115 

12 

49 

.51229 

.85881 

.52720 

.84974 

.54195 

.84041 

.55654 

.83082 

.57095 

.82098 

11 

50 

.51254 

.85866 

.52745 

.84959 

.54220 

.84025 

.55678 

.83066 

.57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.55702 

.83050 

.57143 

.82065 

9 

52 

.51304 

.85836 

.52794 

.84928 

.54269 

.83994 

.55726 

.83034 

.57167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293 

.83978 

.55750 

.83017 

.57191 

.82032 

7 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82015 

6 

55 

.51379 

.85792 

.52869 

.84882 

.54342 

.83940 

.55799 

.82985 

.57238 

.81999 

5 

56 

.51404 

,85777 

.52893 

.84866 

.54366 

.83920 

.55823 

.82969 

.57262 

.81982 

4 

57 

.51429 

.85762 

.52918 

.84851 

.54391 

.83915 

.55847 

.82953 

.57286 

.81965 

3 

58 

.51454 

.85747 

,52943 

.84836 

.54415 

.83899 

.55871 

.82936 

.57310 

.81949 

2 

59 

.51479 

.85732 

.52967 

.84*20 

.54440 

.83883 

.55895 

.82920 

.57334 

.81932 

1 

60 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

.57358 

.81915 

0 

, 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

, 

59° 

58° 

57°    1 

56° 

55° 

110 


NATURAL  SINES  AND  COSINES. 


3 

5° 

3 

6° 

3 

7° 

3 

8° 

|    3 

9° 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

57358 

81915 

58779 

80902 

.60182 

79864 

.61566 

.78801 

.62932 

.77715 

60 

1 

57381 

81899 

58802 

80885 

.60205 

79846 

.61589 

.78783 

.62955 

.77096 

59 

2 

57405 

81882 

58826 

80867 

.60228 

79829 

.61612 

.78765 

.62977 

.77678 

58 

3 

57429 

81805 

58849 

80850 

,60251 

79811 

.61635 

.78747 

.63000 

.77660 

57 

4 

57453 

81848 

58873 

80833 

.60274 

79793 

.61658 

.78729 

.63022 

.77641 

56 

5 

57477 

81832 

58896 

80816 

.60298 

79776 

.61681 

78711 

.63045 

.77023 

55 

6 

57501 

81815 

58920 

80799 

.60321 

79758 

.61704 

78694 

.63068 

.77005 

54 

7 

57524 

81798 

58943 

80782 

.60344 

79741 

.61726 

78676 

.63090 

.77586 

53 

8 

57548 

81782 

58967 

80765 

.60367 

79723 

.61749 

78658 

.63113 

.77568 

52 

9 

57572 

81765 

58990 

80748 

.60390 

79706 

.61772 

78640 

.63135 

77550 

51 

10 

57596 

81748 

59014 

80730 

.60414 

79688 

.61795 

78622 

.63158 

77531 

50 

11 

57619 

81731 

59037 

80713 

.60437 

79671 

.61818 

78604 

.63180 

77513 

40 

12 

57643 

81714 

59061 

80696 

.60460 

79653 

.61841 

78586 

.63203 

77494 

48 

13 

57667 

81698 

59084 

80679 

.60483 

79635 

.61864 

78568 

.63225 

77476 

47 

14 

57691 

81681 

59108 

80662 

.60506 

79618 

.61887 

78550 

.63248 

77458 

40 

15 

57715 

81664 

59131 

80644 

.60529 

79600 

61909 

78532 

.63271 

77439 

45 

16 

57738 

81  647 

59154 

80627 

.60553 

79583 

61932 

78514 

.63293 

77421 

44 

17 

57762 

.81631 

59178 

80610 

.60576 

79565 

G1955 

78496 

.63316 

77402 

43 

18 

57786 

.81614 

59201 

80593 

.60599 

79547 

61978 

78478 

.63338 

77384 

42 

19 

.57810 

.81597 

59225 

80576 

.60622 

79530 

62001 

78460 

.63361 

77360 

41 

20 

.57833 

.81580 

59248 

80558 

.60645 

79512 

.62024 

78442 

.63383 

77347 

40 

21 

.57857 

.81563 

59272 

80541 

.60668 

79494 

.62046 

78424 

.03406 

77329 

39 

22 

.57881 

.81546 

59295 

80524 

.60691 

79477 

.62069 

78405 

.63428 

77310 

38 

23 

.5790-1 

.81530 

59318 

80507 

.60714 

79459 

.62092 

78387 

.63451 

77292 

37 

24 

.57928 

.81513 

59342 

80489 

.60738 

79441 

.62115 

78369 

.63473 

77273 

36 

25 

.57952 

.81496 

59365 

80472 

.60761 

79424 

.62138 

78351 

.63496 

77255 

35 

26 

.57976 

.81479 

59389 

80455 

.60784 

79406 

.62160 

78333 

.63518 

77236 

34 

27 

.57999 

.81462 

59412 

80438 

.60807 

79388 

.62183 

78315 

.63540 

77218 

33 

28 

.58023 

.81445 

59436 

80420 

.60830 

79371 

.62206 

78297 

.63563 

77199 

32 

29 

.58047 

.81428 

59459 

80403 

.60853 

79353 

.62229 

78279 

.63585 

77181 

31 

30 

.58070 

.81412 

59482 

80386 

.60876 

79335 

.62251 

782G1 

.63608 

77162 

30 

31 

.58094 

.81395 

.59506 

80368 

.60899 

79318 

.62274 

78243 

.63630 

77144 

29 

32 

.58118 

.81378 

.59529 

80351 

.60922 

79300 

.62297 

78225 

.63653 

:7i25 

28 

33 

.58141 

.81361 

.59552 

80334 

.60945 

79282 

.62320 

78206 

'.63675 

77107 

27 

34 

.58165 

.81344 

.59576 

80316 

.60968 

79264 

.62342 

78188 

.63698 

.77088 

26 

35 

.58189 

.81327 

.59599 

80299 

.60991 

79247 

.62365 

78170 

.63720 

.77070 

25 

36 

.58212 

.82310 

.59622 

80282 

.61015 

79229 

.62388 

78152 

.63742 

.77051 

24 

37 

.58236 

.81293 

.59646 

80264 

.61038 

79211 

.62411 

78134 

.63765 

.77033 

23 

38 

.58260 

.81276 

.59669 

80247 

.61061 

79193 

.62433 

78116 

.03787 

.77014 

22 

39 

.58283 

.81259 

.59693 

80230 

.61084 

79176 

.62456 

.78098 

.63810 

.76996 

21 

10 

.58307 

.81242 

.59716 

80212 

.81107 

79158 

.62479 

.78079 

.63832 

.76977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.61130 

79140 

.62502 

.78061 

.63854 

.76959 

19 

4-2 

.58354 

.81208 

.59763 

.80178 

.61153 

79122 

.62524 

.78043 

.63877 

.70940 

18 

43 

.58378 

.81191 

.59786 

.80160 

.61176 

79105 

.62547 

.78025 

.63899 

.76921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.61199 

79087 

.62570 

.78007 

.63922 

.70903 

10 

45 

.58425 

.81157 

.59832 

.80125 

.61222 

.79069 

.62592 

.77988 

.63944 

.76884 

15 

46 

.58449 

.81140 

.59856 

.80108 

.61245 

.79051 

.62615 

.77970 

.63966 

.76866 

14 

47 

.58472 

.81123 

.59879 

.80091 

.61268 

.79033 

.62638 

.77952 

.63989 

.76847 

13 

48 

.58496 

.81106 

.59902 

.80073 

.61291 

.79016 

.62660 

.77934 

.64011 

.70828 

12 

49 

.58519 

.81089 

.59926 

.80056 

.61314 

.78998 

.62683 

.77916 

.64033 

.76810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879 

.64078 

.76772 

9 

52 

.58590 

.81038 

.59995 

.80003 

.61383 

.78944 

.62751 

.77861 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986 

.61406 

.78926 

.6?774 

.77843 

.64123 

.76735 

7 

54 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.53661 

.80987 

.60065 

.79951 

.61451 

.78891 

.62819 

.7780C 

.64167 

.76698 

5 

56 

.58684 

.80970 

.60089 

.79934 

.61474 

.78973 

.62842 

.77788 

.64190 

.76679 

4 

57 

.58708 

.80953 

.60112 

.79916 

.61497 

.78855 

.62^64 

.77769 

.64212 

.76601 

3 

58 

.58731 

.80936 

.6013" 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.7064? 

2 

59 

.58755 

.80919 

.60158 

.79881 

.61543 

.78819 

.62909 

.77733 

.64256 

.76023 

1 

60 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

.04279 

.76604 

0 

, 

Cosin 

Sine 

Cosin 

Sine 

[Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

~7~ 

I 

4° 

I 

3° 

1    5 

2° 

1    5 

I 

0° 

NATURAL  SINES  AND  COSINES. 


Ill 


40° 

41° 

42° 

43° 

44° 

Sine 

Cosin 

Sine 

^osin 

Sine 

Dosin 

Sine 

Cosin 

Sine 

Cosin 

0 

64279 

76604 

.65606 

75471 

66913 

74314 

68200 

.73135 

.69466 

.71934 

60 

1 

64301 

76586 

.65628 

75452 

66935 

74295 

68221 

.73116 

.69487 

.71914 

59 

2 

64323 

76567 

.65650 

75433 

66956 

74276 

.68242 

.73096 

.69508 

.71894 

58 

3 

64346 

76548 

.65672 

754H 

66978 

74256 

.68264 

.73076 

.69529 

.71873 

57 

4 

64368 

76530 

.65694 

75395 

66999 

74237 

.68285 

.73056 

.69549 

.71853 

50 

5 

64390 

76511 

.65716 

75375 

67021 

74217 

.68306 

.73036 

.69570 

.71833 

55 

6 

64412 

76492 

.65738 

75356 

67043 

74198 

.68327 

.73016 

.09591 

.71813 

54 

7 

64435 

76473 

.65759 

75337 

67064 

74178 

.68349 

.72996 

.69612 

.71792 

53 

8 

64457 

76455 

.65781 

75318 

67086 

74159 

.68370 

72976 

.69633 

.71772 

52 

9 

64479 

76436 

.65803 

75299 

.67107 

74139 

.68391 

.72957 

.09654 

.71752 

31 

10 

64501 

76417 

.65825 

75280 

.67129 

74120 

.68412 

.72937 

.69675 

.71732 

50 

11 

64524 

76398 

.65847 

75261 

.67151 

74100 

.68434 

.72917 

.69696 

.71711 

49 

12 

64546 

76380 

.65869 

75241 

.67172 

74080 

.68455 

.72897 

.69717 

.71691 

48 

13 

64568 

76361 

.65891 

75222 

.67194 

74061 

.68476 

.72877 

.69737 

.71671 

47 

14 

64590 

76342 

.65913 

75203 

.67215 

74041 

.68497 

.72857 

.69758 

.71650 

46 

15 

64612 

76323 

.65935 

75184 

.67237 

.74022 

.68518 

.72837 

.69779 

.71630 

45 

16 

64635 

76304 

.65956 

75165 

.67258 

.74002 

.68539 

.72817 

.69800 

.71610 

44 

17 

64657 

76286 

.65978 

75146 

.67280 

.73983 

.68561 

.72797 

.69821 

.71590 

43 

18 

64679 

76267 

.66000 

75126 

.67301 

.73963 

.68582 

.72777 

.69842 

.71569 

42 

19 

64701 

76248 

.66022 

75107 

.67323 

.73944 

.6860? 

.72757 

.69862 

.71549 

41 

20 

64723 

76229 

.66044 

75088 

.67344 

.73924 

.68624 

.72737 

.69883 

.71529 

40 

21 

64746 

76210 

.66066 

75069 

.67366 

.73904 

.68645 

.72717 

.69904 

.71508 

39 

22 

64768 

76192 

.66088 

75050 

.07387 

.73885 

.68666 

.72697 

.69925 

.71488 

38 

23 

64790 

76173 

.66109 

75030 

.67409 

.73865 

.68688 

.72677 

.69946 

.71468 

37 

24 

64812 

76154 

.06131 

75011 

.67430 

.73846 

.68709 

.72657 

.69966 

.71447 

36 

25 

64834 

76135 

.66153 

74992 

.67452 

.73826 

.68730 

.72637 

.09987 

.71427 

35 

20 

64856 

76116 

.66175 

74973 

.67473 

.73806 

.68751 

.72617 

.70008 

.71407 

34 

27 

64878 

76097 

.66197 

74953 

.67495 

.73787 

.68772 

.72597 

.70029 

.71386 

33 

28 

64901 

76078 

.66218 

74934 

.67516 

.73767 

.68793 

.72577 

.70049 

.71366 

32 

29 

64923 

76059 

.66240 

74915 

.67538 

.73747 

.68814 

.72557 

.70070 

.71345 

31 

30 

64945 

76041 

.66262 

74896 

.67559 

.73728 

.68835 

.72537 

.70091 

.71325 

30 

31 

64967 

76022 

.66284 

74876 

.67580 

.73708 

.68857 

.72517 

.70112 

.71305 

29 

32 

64989 

76003 

.66306 

74857 

.67602 

.73688 

.68878 

.72497 

.70132 

.71284 

28 

33 

65011 

75984 

.66327 

74838 

.67623 

.73669 

.68899 

.72477 

.70153 

.71264 

27 

34 

65033 

75965 

.66349 

74818 

.67645 

.73649 

.68920 

.72457 

.70174 

.71243 

26 

35 

65055 

75946 

.66371 

74799 

.67666 

.73629 

.68941 

.72437 

.70195 

.71223 

25 

38 

65077 

75927 

.66393 

74780 

.67688 

.73610 

.68962 

.72417 

.70215 

.71203 

24 

37 

65100 

75908 

.66414 

74760 

.67709 

.73590 

.68983 

.72397 

.70236 

.71182 

23 

38 

65122 

75889 

.66436 

74741 

.67730 

.73570 

.69004 

.72377 

.70257 

.71162 

22 

39 

65144 

75870 

.66458 

74722 

.67752 

.73551 

.69025 

.72357 

.70277 

.71141 

21 

40 

65166 

75851 

.66480 

.74703 

.67773 

73531 

.69046 

.72337 

.70298 

.71121 

20 

41 

65188 

75832 

.66501 

.74683 

.67795 

.73511 

.69067 

.72317 

.70319 

.71100 

19 

42 

65210 

75813 

.66523 

.74664 

.67816 

73491 

.69088 

.72297 

.70339 

.71080 

18 

43 

65232 

75794 

.66545 

.74644 

.67837 

73472 

.69109 

.72277 

.70360 

.71059 

17 

44 

65254 

75775 

.66566 

.74625 

.67859 

73452 

.69130 

.72257 

.70381 

.71039 

16 

45 

65276 

75756 

.66588 

.71606 

.67880 

73132 

.69151 

.72236 

.70401 

.71019 

15 

40 

65298 

75738 

.66610 

.74586 

.67901 

73413 

.69172 

.72216 

.70422 

.70998 

14 

47 

65320 

75719 

.66632 

.74567 

.67923 

.73393 

.69193 

.72196 

.70443 

.70978 

13 

48 

65342 

75700 

.66653 

.74548 

.67944 

.73373 

.69214 

.72176 

.70463 

.70957 

12 

49 

65364 

75680 

.66675 

.74528 

.67965 

.73353 

.69235 

.72156 

.70484 

.70937 

11 

50 

65386 

75661 

.66697 

.74509 

.67987 

.73333 

.69256 

.72136 

.70505 

.70916 

10 

51 

65408 

.75642 

.66718 

.74489 

.68008 

.73314 

.69277 

.72116 

.70525 

.70896 

9 

52 

65430 

.75623 

.66740 

.74470 

.68029 

.73294 

.69298 

.72095 

.70540 

.70875 

8 

53 

65452 

.75604 

.66762 

.74451 

.68051 

.73274 

.69319 

.72075 

.70567 

.70855 

7 

54 

.65474 

.75585 

.66783 

.74431 

.68072 

.73254 

.69340 

.72055 

.70587 

.70834 

0 

55 

.65490 

.75566 

.66805 

.74412 

.68093 

.73234 

.69361 

.72035 

.70608 

.70813 

5 

56 

.65518 

.75547 

.66827 

.7-1392 

.68115 

.73215 

.69382 

.72015 

.70628 

.70793 

4 

57 

.65540 

.75528 

.66848 

.74373 

.6813f 

.73195 

.69403 

.71995 

.70649 

.7H772 

3 

58 

.65562 

.75509 

.66870 

.74353 

.68157 

.73175 

.69424 

.71974 

.70670 

.70752 

2 

59 

.65584 

.75490 

.66891 

.74334 

.68179 

.73155 

.69445 

.71954 

.70690 

.70731 

1 

60 

.65603 

.75471 

.66913 

74314 

.68200 

.73135 

.69466 

.71934 

.70711 

.70711 

0 

, 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

t 

10° 

48° 

47° 

46° 

45° 

112   NATURAL  TANGENTS  AND  COTANGENTS. 


O° 

1° 

2° 

3° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infinite. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

58 

3 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.9372 

.05328 

18.7678 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

56 

5 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

55 

6 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

54 

7 

.00204 

401.106 

.01949 

51.3032 

.03696 

27.0566 

.05145 

18.3655 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2077 

52 

9 

.00262 

381.971 

.02007 

49.8157 

.03754 

26.6?67 

.05503 

18.1708 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05562 

17.9802 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

•17 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

45 

18 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.S978 

.05766 

17.3432 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24.7185 

.05795 

17.2558 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

35 

26 

.00756 

132.219 

.02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.01308 

23.2137 

.06058 

16.5075 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

30 

31 

.00902 

110.892 

.02648 

37.7686 

.04305 

22.7519 

.06145 

16.2722 

29 

32 

.00931 

107.425 

.02877 

37.3579 

.04424 

22.6020 

.06175 

1(3.1952 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.454J 

.06204 

16.1190 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.00262 

15.9687 

25 

36 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

22 

39 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

21 

40 

.01164 

85.9398 

.02910 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21.2049 

.06467 

15.4638 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

15 

46 

.01338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

11 

50 

.01455 

68.7501 

.03201 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

9 

52 

.01513 

66.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

7 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

6 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

5 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

4 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.1051 

.06905 

14.4823 

3 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.421? 

2 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

1 

60 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

0 

, 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

89° 

88° 

87° 

S6° 

NATURAL  TANGENTS  AND   COTANGENTS.      113 


4° 

5° 

ft0 

7° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.06993 

14.3007 

.08749 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

60 

1 

.07022 

14.2411 

.08778 

11.3919 

.10540 

9.48781 

.12308 

8.12481 

59 

2 

.07051 

14.1821 

.08807 

11.3540 

.10569 

9.46141 

.12338 

8.10536 

58 

3 

.07080 

14.1235 

.08837 

11.3163 

.10599 

9.43515 

.12367 

8.08600 

57 

4 

.07110 

14.0655 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06674 

56 

5 

.07139 

14.0079 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04750 

55 

6 

.07168 

13.9507 

.08925 

11.2048 

.10687 

9.35724 

.12456 

8.02848 

54 

7 

.07197 

13.8940 

.08954 

11.1681 

.10716 

9.33155 

.12485 

8.00948 

63 

8 

.07227 

13.8378 

.089  S3 

11.1316 

.10746 

9.30599 

.12515 

7.99058 

52 

9 

.07256 

13.7821 

.09013 

11.0954 

.10775 

9.28058 

.12544 

7.97176 

51 

10 

.07285 

13.7267 

.09042 

11.0594 

.10805 

9.25530 

.12574 

7.95302 

50 

11 

.07314 

13.6719 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

49 

12 

.07344 

13.6174 

.09101 

10.9882 

.10«63 

9.20518 

.12633 

7.91582 

48 

13 

.07373 

13.5634 

.09130 

10.9529 

.10893 

9.18028 

.12662 

7.89734 

47 

14 

.07402 

13.5098 

.09159 

10.9178 

.10922 

9.15554 

.12692 

7.87895 

46 

15 

.07431 

13.4566 

.09189 

10.8829 

.10952 

9.13093 

.12722 

7.86064 

45 

16 

.07461 

13.4039 

.09218 

10.8483 

.10981 

9.10646 

.12751 

7.84242 

44 

17 

.07490 

13.3515 

.09247 

10.8139 

.11011 

9.08211 

.12781 

7.82428 

43 

18 

.07519 

13.2996 

.09277 

10.7797 

.11040 

9.05789 

.12810 

7.S0622 

42 

19 

.07548 

13.2480 

.09306 

10.7457 

.11070 

9.03379 

.12840 

7.78825 

41 

20 

.07578 

13.1969 

.09335 

10.7119 

.11099 

9.00983 

.12869 

7.77035 

40 

21 

.07607 

13.1461 

.09365 

10.6783 

.11128 

8.98598 

.12899 

7.75254 

39 

22 

.07636 

13.0958 

.09394 

10.6450 

.11158 

8.96227 

.12929 

7.734SO 

38 

23 

.07665 

13.0458 

.09423 

10.6118 

.11187 

8.93867 

.12958 

7.71715 

37 

24 

.07695 

12.9962 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.69957 

36 

25 

.07724 

12.9469 

.09482 

10.5462' 

.11246 

8.89185 

.13017 

7.68208 

35 

26 

.07753 

12.8981 

.09511 

10.5136 

.11276 

8.86862 

.13047 

7.66466 

34 

27 

.07782 

12.8496 

.09541 

10.4813 

.11305 

8.84551 

.13076 

7.64732 

33 

28 

.07812 

12.8014 

.09570 

10.4491 

.11335 

8.82252 

.13106 

7.63005 

32 

29 

.07841 

12.7536 

.09600 

10.4172 

.11364 

8.79964 

.13136 

7.61287 

31 

30 

.07870 

12.7062 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

30 

31 

.07899 

12.6591 

.09658 

10.3538 

.11423 

8.75425 

.13195 

7.57872 

29 

32 

.07929 

12.6124 

.09688 

10.3224 

.11452 

8.73172 

.13224 

7.56176 

23 

33 

.07958 

12.5660 

.09717 

10.2913 

.114^2 

8.70931 

.13254 

7.54487 

27 

34 

.07987 

12.5199 

.09746 

10.2602 

.11511 

8.68701 

.13284 

7.52806 

26 

35 

.08017 

12.4742 

.09776 

10.2294 

.11541 

8.66482 

.13313 

7.51132 

25 

36 

.08046 

12.4288 

.09805 

10.1988 

.11570 

8.64275 

.13343 

7.49465 

24 

37 

.08075 

12.3838 

.09834 

10.1683 

.11600 

8.62078 

.13372 

7.47806 

23 

38 

.08104 

12.3390 

.09864 

10.1381 

.11629 

8.59893 

.13402 

7.46154 

22 

39 

.08134 

12.2946 

.09893 

10.1080 

.11659 

8.57718 

.13432 

7.44509 

21 

40 

.08163 

12.2505 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

20 

41 

.08192 

12.2067 

.09952 

10.0483 

.11718 

8.53402 

.13491 

7.41240 

19 

42 

.08221 

12.1632 

.09981 

10.0187 

.11747 

8.51259 

.13521 

7.39616 

18 

43 

.08251 

12.1201 

.10011 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

17 

44 

.08280 

12.0772 

.10040 

9.96007 

.11806 

8.47007 

.13580 

7.36389 

16 

45 

.08309 

12.0346 

.10069 

9.93101 

.11836 

8.44896 

.13609 

7.34786 

15 

46 

.08339 

11.9923 

.10099 

9.90211 

.11865 

8.42795 

.13639 

7.33190 

14 

47 

.08368 

11.9504 

.10128 

9.87338 

.11895 

8.40705 

.13669 

7.31600 

13 

48 

.08397 

11.9087 

10158 

9.84482 

.11924 

8.38625 

.13698 

7.30018 

12 

49 

.08427 

11.8673 

.10187 

9.81641 

.11954 

8.36555 

.13728 

7.28442 

11 

50 

.08456 

11.8262 

.10216 

9.78817 

.11983 

8.34496 

.13758 

7.26873 

10 

51 

.08485 

11.7853 

.10246 

9.76009 

.12013 

8.32446 

.13787 

7.25310 

9 

52 

.08514 

11.7448 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

8 

53 

.08544 

11.7045 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

7 

54 

.08573 

11.6645 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20661 

6 

55 

.08602 

11.6218 

.10363 

9.64935 

.12131 

8.24345. 

.13906 

7.19125 

5 

56 

.08632 

11.5853 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

4 

57 

.08661 

11.5461 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

3 

58 

.08690 

11.5072 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

2 

59 

.08720 

11.4685 

.10481 

9.54106 

.12249 

8.1039.8 

.14024 

7.13042 

1 

GO 

.08749 

11.4301 

.10510 

9.51436 

.12278 

:S.  14435 

.14054 

7.11537 

0 

, 

Dotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

, 

85° 

84° 

83° 

82° 

114     NATURAL  TANGENTS  AND  COTANGENTS. 


8° 

9° 

10° 

11° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.14054 

7.11537 

.15838 

6.31375 

.17633 

5.67128 

.19438 

5.14455 

60 

1 

.14084 

7.10038 

.15868 

6.30189 

.17663 

5.66165 

.19468 

5.13658 

59 

2 

.14113 

7.08546 

.15898 

6.29007 

.17693 

5.65205 

.19498 

5.12862 

58 

3 

.14143 

7.07059 

.15928 

6.27829 

.17723 

5.6424S 

.19529 

5.12069 

57 

4 

.14173 

7.05579 

.15958 

6.26655 

.17753 

5.63295 

.19559 

5.11279 

56 

5 

.14202 

7.04105 

.15988 

6.25486 

.17783 

5.62344 

.19589 

5.10490 

55 

6 

.14232 

7.02637 

.16017 

6.24321 

.17813 

5.61397 

.19619 

5.09704 

54 

7 

.14262 

7.01173 

.16047 

6.23160 

.17843 

5.60452 

.19649 

5.08921 

53 

8 

.14291 

6.9971S 

.10077 

6.22003 

.17873 

5.59511 

.19680 

5.08139 

52 

9 

.14321 

6.98268 

.16107 

6.20851 

.17903 

5.58573 

.19710 

5.07360 

51 

10 

.14351 

6.96823 

.16137 

6.19703 

.17933 

5.57638 

.19740 

5.065S4 

50 

11 

.14381 

6.95385 

.16167 

6.18559 

.17963 

5.56706 

.19770 

5.05809 

49 

12 

.14110 

6.93952 

.16196 

6.17419 

.17993 

5.55777 

.19801 

5.05037 

48 

13 

.14440 

6.92525 

.16226 

6.16283 

.18023 

5.54851 

.19831 

5.04267 

47 

14 

.14470 

6.91104 

.10256 

6.15151 

.18053 

5.53927 

.19861 

5.03499 

46 

15 

.14499 

6.89688 

.16286 

6.14023 

.18083 

5.53007 

.19891 

5.02734 

45 

16 

.14529 

6.88278 

.16316 

6.12899 

.18113 

5.52090 

.19921 

5.01971 

44 

17 

.14559 

6.86874 

.16346 

6.11779 

.18143 

5.51176 

.19952 

5.01210 

43 

18 

.14588 

6.85475 

.16376 

6.10664 

.18173 

5.50264 

.19982 

5.00451 

42 

19 

.14618 

6.84082 

.16405 

6.09552 

.18203 

5.49356 

.20012 

4.99695 

41 

20 

.14648 

6.82694 

.16435 

6.08444 

.18233 

5.48451 

.20042 

4.98940 

40 

21 

.14678 

6.81312 

.16465 

6.07340 

.18263 

5.47548 

.20073 

4.98188 

39 

22 

.14707 

6.79936 

.16495 

6.06240 

.18293 

5.46648 

.20103 

4.97438 

38 

23 

.14737 

6.78564 

.16525 

6.05143 

.18323 

5.45751 

.20133 

4.96690 

37 

24 

.14767 

6.77199 

.16555 

6.04051 

.18353 

5.44857 

.20164 

4.95945 

36 

25 

.14796 

6.75838 

.16585 

6.02962 

.18384 

5.43966 

.20194 

4.95201 

35 

26 

.14826 

6.74483 

.16615 

6.01878 

.18414 

5.43077 

.20224 

4.94460 

34 

27 

.14856 

6.73133 

.16645 

6.00797 

.18444 

5.42192 

.20254 

4.93721 

33 

28 

.14886 

6.71789 

.16674 

5.99720 

.18474 

5.41309 

.20285 

4.92984 

32 

29 

.14915 

6.70450 

.16704 

5.98646 

.18504 

5.40429 

.20315 

4.92249 

31 

30 

.14945 

6.69116 

.16734 

5.97576 

.18534 

5.39552 

.20345 

4.91516 

30 

31 

.14975 

6.67787 

.16764 

5.96510 

.18564 

5.38677 

.20376 

4.90785 

29 

32 

.15005 

6.66463 

.16794 

5.95448 

.18594 

5.37805 

.20406 

4.00056 

28 

33 

.15034 

6.65144 

.16824 

5.94390 

.18624 

5.36936 

.20436 

4.89330 

27 

34 

.15064 

6.63831 

.16854 

5.93335 

.18054 

5.30070 

.20466 

4.88605 

26 

35 

.15094 

6.62523 

.16884 

5.92283 

.18684 

5.35206 

.20497 

4.87882 

25 

36 

.15124 

6.61219 

.16914 

5.91236 

.18714 

5.34345 

.20527 

4.87162 

24 

37 

.15153 

6.59921 

.16944 

5.90191 

.18745 

5.33487 

.20557 

4.86444 

23 

38 

.15183 

6.58627 

.16974 

5.89151 

.18775 

5.32631 

.20588 

4.85727 

22 

39 

.15213 

6.57339 

.17004 

5.88114 

.18805 

5.31778 

.20618 

4.85013 

21 

10 

.15243 

6.56055 

.17033 

5.87080 

.18835 

5.30928 

.20648 

4.84300 

20 

41 

.15272 

6.54777 

.17063 

5.86051 

.18865 

5.30080 

.20679 

4.83590 

19 

42 

.15302 

6.53503 

.17093 

5.85024 

.18895 

5.29235 

.20709 

4.82882 

18 

43 

.15332 

6.52234 

.17123 

5.84001 

.18925 

5.28393 

.20739 

4.82175 

17 

44 

.15362 

6.50970 

.17153 

5.82982 

.18955 

5.27553 

.20770 

4.81471 

16 

45 

.15391 

6.49710 

.17183 

5.81966 

.18986 

5.26715 

.20800 

4.80769 

15 

46 

.15421 

6.48456 

.17213 

5.80953 

.19016 

5.25880 

.20830 

4.80068 

14 

47 

.15451 

6.47206 

.17243 

5.79944 

.19046 

5.25048 

.20861 

4.79370 

13 

48 

.15481 

6.45961 

.17273 

5.78938 

.19076 

5.24218 

.20891 

4.78673 

12 

49 

.15511 

6.44720 

.17303 

5.77936 

.19106 

5.23391 

.20921 

4.77978 

11 

50 

.15540 

6.43484 

.17333 

5.76937 

.19136 

5.22536 

.20952 

4.77286 

10 

SI 

.15570 

6.42253 

.17363 

5.75941 

.19166 

5.21744 

.20982 

4.76595 

9 

52 

.15600 

6.41026 

.17393 

5.74949 

.19197 

5.20925 

.21013 

4.75906 

Q 

53 

.15630 

6.39804 

.17423 

5.73960 

.19227 

5.20107 

.21043 

4.75219 

7 

54 

.15660 

6.38587 

.17453 

5.72974 

.19257 

5.19293 

.21073 

4.74534 

6 

55 

.15689 

6.37374 

.17483 

5.71992 

.19287 

5.18480 

.21104 

4.73851 

5 

56 

.15719 

6.36165 

.17513 

5.71013 

.19317 

5.17671 

.21134 

4.73170 

4 

57 

.15749 

6.34961 

.17543 

5.70037 

.19347 

5.16863 

.21164 

4.72490 

3 

58 

.15779 

6.33761 

.17573 

5.69064 

.19378 

5.16058 

.21195 

4.71813 

2 

59 

.15809 

6.32566 

.17603 

5.68094 

.19408 

5.15256 

.21225 

4.71137 

1 

60 

.15838 

6.31375 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4.70463 

0 

r 

Cotang 

Tang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

81° 

80° 

79° 

78° 

NATURAL  TANGENTS  AND  COTANGENTS.   115 


12° 

13° 

14° 

15° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

o 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

60 

] 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

.26826 

3.72771 

59 

2 

.21.316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

.26857 

3.72338 

58 

3 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

.26888 

3.71907 

57 

4 

.21377 

4.67786 

.23209 

4.30860 

.25056 

3.99099 

.26920 

3.71476 

56 

5 

.21408 

4.67121 

.23240 

4.30291 

.25087 

3.98607 

.26951 

3.71046 

55 

6 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

.26982 

3.70616 

54 

7 

.21469 

4.65797 

.23301 

4.20159 

.25149 

3.97627 

.27013 

3.70188 

53 

8 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

.27044 

3.69761 

52 

9 

.21529 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

.27076 

3.69335 

51 

10 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

.27107 

3.8S909 

50 

11 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

.27138 

3.68485 

49 

12 

.21621 

4.62518 

.23455 

4.26352 

.25304 

3.95196 

.27169 

3.68061 

48 

13 

.21651 

4.61888 

.23485 

4.25795 

.25335 

3.94713 

.27201 

3.67638 

47 

11 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

.27232 

3.67217 

46 

15 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

.27263 

3.66796 

45 

16 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

.27294 

3.66376 

44 

17 

.21773 

4.59283 

.2360S 

4.23580 

.25459 

3.92793 

.27326 

3.65957 

43 

18 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

.27357 

3.65538 

42 

19 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

.27388 

3.65121 

41 

20 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91364 

.27419 

3.64705 

40 

21 

.21895 

4.56726 

.23731 

4.213S7 

.25583 

3.90890 

.27451 

3.64289 

39 

22 

.21925 

4.56091 

.23762 

4.20842 

.25614 

3.90417 

.27482 

3.63874 

38 

23 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

.27513 

3.63461 

37 

24 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

.27545 

3.63048 

36 

25 

.22017 

4.54196 

.23854 

4.  19215 

.25707 

3.89004 

.27576 

3.62636 

35 

26 

.22047 

4.53568 

.23885 

4.1%75 

.25738 

3.88536 

.27607 

3.62224 

34 

27 

.22078 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

.27638 

3.61814 

33 

28 

.22108 

4.52316 

.23946 

4.1  7800 

.25800 

3.87601 

.27670 

3.61405 

32 

29 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

.27701 

3.60996 

31 

30 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

.27732 

3.60588 

30 

31 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

.27764 

3.60181 

29 

32 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

.27795 

3.59775 

28 

33 

.22261 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

.27826 

3.59370 

27 

34 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

.27858 

3.58966 

26 

35 

.22322 

4.47988 

|  .24162 

4.13877 

.26017 

3.84364 

.27889 

3,58562 

25 

36 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

.27921 

3.58160 

24 

37 

.22383 

4.46764 

.24223 

4.12825 

.26079 

3.83449 

">7952 

3.57758 

23 

38 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

J27983 

3.57357 

22 

39 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

.28015 

3.56957 

21 

40 

.22475 

4.44942 

.24316 

4.11256 

.26172 

3.82083 

.28046 

3.56557 

20 

41 

.22505 

4.44338 

.24347 

4.10736 

.26203 

3.81630 

.28077 

3.56159 

19 

42 

.22530 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

.28109 

3.55761 

18 

43 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

.28140 

3.55364 

17 

44 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80276 

.28172 

3.54968 

16 

45 

.22628 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

.28203 

3.54573 

15 

46 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

.28234 

3.54179 

14 

47 

.22689 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

.28266 

3.53785 

13 

18 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.78485 

.28297 

3.53393 

12 

49 

.22750 

4.39560 

.24593 

4.06616 

.26452 

3.78040 

.28329 

3.53001 

11 

50 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

.28360 

3.52609 

10 

51 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

.28391 

3.52219 

9 

52 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

.28423 

3.51829 

8 

53 

.22872 

4.37207 

.24717 

4.045S6 

.26577 

3.76268 

.28454 

3.51441 

54 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

.28486 

3.51053 

fi 

55 

.22934 

4.36040 

.24778 

4.03578 

.26639 

3.75388 

.28517 

3.50666 

5 

56 

.22964 

4.35459 

.24809 

4.03076 

.26670 

3.74950 

.28549 

3.50279 

4 

57 

22995 

4.34879 

.24840 

4.02574 

.26701 

3.74512 

.28580 

3.49894 

3 

58 

.23026 

4.34300 

.24871 

4.02074. 

.26733 

3.74075 

.28612 

3.49509 

2 

59 

.23056 

4.33723 

.24902 

4.01576 

.26764 

3.73640 

.28643 

3.49125 

1 

60 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

.28675 

3.48741 

0 

t 

Cotang 

Tang 

Cotang 

Tang 

Cotang  Tang 

Cotang 

Tang 

/ 

77° 

76° 

75° 

74° 

116   NATURAL  TANGENTS  AND  COTANGENTS. 


10° 

17° 

18° 

19° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

60 

1 

.28706 

3.48359 

.30605 

3.26745 

.32524 

3.07464 

.34465 

2.90147 

59 

2 

.28738 

3.47977 

.30637 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

58 

3 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

4 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2,89327 

56 

5 

.28832 

3.4^837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

55 

6 

.28864 

3.46458 

.30764 

3.25055 

.32685 

3.05950 

.34628 

2.88783 

54 

7 

.28805 

3.46080 

.30790 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

8 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.88240 

52 

9 

.28958 

3.45327 

.30860 

3.24049 

.32782 

3.05049 

.34726 

2.87970 

51 

10 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2.87700 

50 

11 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.29053 

3.44202 

.30955 

3  23048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2.86356 

45 

16 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3  02963 

.34954 

2.86089 

44 

17 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

18 

.29242 

3.41973 

.31117 

3.21063 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.29305 

3.41236 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.29337 

3.40869 

.31242 

3.20079 

.33169 

3.01489 

.35118 

2.84758 

39 

22 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

.29400 

3.40136 

.31306 

3.19426 

.33233 

3.00903 

.35183 

2.84229 

37 

24 

.29432 

3.39771 

.31338 

3.19100 

.33266 

3.00611 

.35216 

2.83965 

36 

25 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

28 

.29495 

3.39042 

.31402 

3.18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

33 

28 

.29558 

3.38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

32 

29 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

30 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98S68 

.35412 

2.82391 

30 

31 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.985SO 

.35445 

2.82130 

29 

32 

.29685 

3.36875 

.31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81610 

27 

34 

.29748 

3.36158 

.31658 

3.15877 

.33589 

2.97717 

.35543 

2.81350 

26 

35 

.29780 

3.35800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2.97144 

.35608 

2.80833 

24 

37 

.29813 

3.35087 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.29875 

3.34732 

.31786 

3.14605 

.33718 

2.96573 

.35674 

2.80316 

22 

39 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.79289 

18 

43 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

17 

44 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

16 

45 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

13 

48 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2.77507 

11 

50 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92910 

.36101 

2.77002 

9 

52 

.30319 

3.29829 

.32235 

3.10223 

.34173 

2.92632 

.36134 

2.76750 

8 

53 

.30351 

3.29483 

.32267 

3.09914 

.34205 

2.92354 

.36167 

2.76498 

7 

54 

.30382 

3.29139 

.32299 

3.09606 

.34238 

2.92076 

.36199 

2.76247 

6 

55 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.36232 

2.75996 

5 

56 

.30446 

3.28452 

.32363 

3.08991 

.34303 

2.91523 

.36265 

2.75746 

4 

57 

.30478 

3.28109 

.32396 

3.08685 

.34335 

2.91246 

.36298 

2.75496 

3 

58 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.36331 

2.75246 

1 

59 

.30541 

3.27426 

.32460 

3.08073 

.34400 

2.90696 

.36364 

2.74997 

0 

60 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

.36397 

2.74748 

2 

, 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tarig 

Cotang 

Tang 

/ 

73° 

72° 

71° 

70° 

NATURAL  TANGENTS  AND  COTANGENTS.   117 


20° 

21° 

23° 

23° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.36397 

2.74748 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

60 

1 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

59 

2 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

58 

3 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

57 

4 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

56 

5 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

55 

6 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

54 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

52 

9 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

.42757 

2.33881 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

49 

12 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

46 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.3275G 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

44 

17 

.36958 

2.70577 

.38955 

2,56707 

.40979 

2.44027 

.43032  2.32383 

43 

18 

.36991 

2.70335 

.38988 

2.56487 

.41013 

2.43825 

.43067  2.32197 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

39 

22 

.37123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

.43205 

2.31456 

38 

23 

.37157 

2.69131 

.39156 

2.553S9 

.41183 

2.42819 

.43239 

2.31271 

37 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

34 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

33 

28 

.37322 

2.67937 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41387 

2.41620 

.43447 

2.30167 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

29 

32 

.37455 

2.66989 

.39458 

2.53132 

.41490 

2.41025 

.43550 

2.29619 

28 

33 

.37488 

2.66752 

.39192 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

18 

43 

.37820 

2.64110 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2  27626 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41*99 

2.38668 

.43966 

2.27447 

16 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

15 

40 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

14 

47 

.37953 

2.63483 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.28909 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2,37891 

.44105 

2.26730 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.42070 

2.37697 

.44140 

2.26552 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44244 

2.26018 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

7 

54 

.38186 

2.61874 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

6 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

5 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

4 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.3615S 

,44418 

2.25132 

3 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

2 

59 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

1 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

0 

, 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

, 

69° 

68° 

67° 

66° 

118   NATURAL  TANGENTS  AND  COTANGENTS. 


24° 

25° 

26° 

37° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.44523 

2.24604 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

GO 

1 

.44558 

2.24428 

.46666 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

59 

2 

.44593 

2.2425'2 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

58 

3 

.44627 

2.24077 

.46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

57 

4 

.44062 

2.23902 

.46772 

2.13801 

.48917 

2.04426 

.51099 

1  .95698 

56 

5 

.44G97 

2.23727 

.46808 

2.13639 

.48953 

2.04276 

.51136 

1.95557 

55 

6 

.44732 

2.23553 

.46843 

2.13477 

.48989 

2.04125 

.51173 

1.95417 

54 

7 

.44767 

2.23378 

.46879 

2.13316 

.49026 

2.03975 

.51209 

1.95277 

53 

8 

.44802 

2.23204 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

52 

9 

.44837 

2.23030 

.46950 

2.12993 

.49098 

2.03675 

.51283 

1.94997 

51 

10 

.44872 

2.22857 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

50 

11 

.44907 

2.22683 

.47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

49 

12 

.44942 

2.22510 

.  47056 

2.12511 

.49206 

2.03227 

.51393 

1.94579 

48 

13 

.44977 

2.22337 

.47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

47 

14 

.45012 

2.22164 

.47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

46 

15 

.45047 

2.21992 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

45 

10 

.45082 

2.21819 

.47199 

2.11871 

.49351 

2.02631 

.51540 

1  .94023 

44 

17 

.45117 

2.21647 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

43 

18 

.45152 

2.21475 

.47270 

2.11552 

.49423 

2.02335 

.51614 

1.93746 

42 

19 

.45187 

2.21304 

.47305 

2.11392 

.48459 

2.02187 

.51651 

1.93608 

41 

20 

.45222 

2.21132 

.47341 

2.11233 

.49495 

2.02039 

51688 

1.93470 

40 

21 

.45257 

2.20961 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

39 

22 

.45292 

2.20790 

.47412 

2.10916 

.49568 

2.01743 

.51761 

1.93195 

38 

23 

.45327 

2.20619 

.47448 

2.10758 

.49604 

2.01596 

.51798 

1.93057 

37 

24 

.45362 

2.20449 

.47483 

2.10000 

.49640 

2.01449 

.51835 

1.92920 

36 

25 

.45397 

2.20278 

.47519 

2.10442 

.49677 

2.01302 

.51872 

1.92782 

35 

26 

.45432 

2.20108 

.47555 

2  10284 

.49713 

2.01155 

.51909 

1.92645 

34 

27 

.45467 

2.19938 

.47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

33 

28 

.45502 

2.1P769 

.47626 

2.099G9 

.49786 

2.00862 

.51983 

1.92371 

32 

29 

.45538 

2.19599 

.47662 

2.09S11 

.49822 

2.00715 

.52020 

1.92235 

31 

30 

.45573 

2.19430 

.47698 

2.09654 

.49858 

2.00569 

.52057 

1.92098 

30 

31 

.45608 

2.19261 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

29 

32 

.45643 

2.19092 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

28 

33 

.45678 

2.18923 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91690 

27 

34 

.45713 

2.18755 

.47840 

2.C9028 

.50004 

1.99986 

.52205 

1.91552 

26 

35 

.45748 

2.18587 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91414 

25 

36 

.45784 

2.18419 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91288 

24 

37 

.45819 

2.18251 

.47948 

2.08560 

.50113 

1  .99550 

.52316 

1.91142 

23 

38 

.45854 

2.18084 

.47984 

2.08405 

.50149 

1.99406 

.52353 

1.91017 

22 

39 

.45889 

2.17916 

.48019 

2.08250 

.50185 

1.99261 

.52390 

1.90876 

21 

40 

.45924 

2.17749 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

20 

41 

.45960 

2.17582 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

19 

42 

.45995 

2.17416 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

18 

43 

.46030 

2.17249 

.48163 

2.07630 

.50331 

1.98684 

.52538 

1  .90337 

17 

44 

.46065 

2.170S3 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

16 

45 

.46101 

2.16917 

.48234 

2.07321 

.50404 

1.98396 

.52613 

1.90069 

15 

46 

.46136 

2.16751 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

14 

47 

.46171 

2.165S5 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

13 

48 

.46206 

2.16420 

.48342 

2.06860 

.50514 

1.97966 

.52724 

1.89667 

12 

49 

.46242 

2.16255 

.48378 

2.06706 

.50550 

1.97823 

.52761 

1.89533 

11 

50 

.46277 

2.16090 

.48414 

2.06553 

.50587 

1.97681 

.52798 

1.89400 

10 

51 

.46312 

2.15925 

.48450 

2.06400 

.50623 

1.97538 

.52836 

1.89266 

9 

52 

.46348 

2.15760 

.48486 

2.06247 

.50660 

1.97395 

.52873 

1.89133 

8 

53 

.46383 

2.15596 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

7 

54 

.46418 

2,15132 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

6 

55 

.46454 

2.15268 

.48593 

2.05790 

.50769 

1.96969 

.52985 

1.88734 

5 

56 

.46489 

2.15104 

.48629 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

4 

57 

.46525 

2.14940 

.48665 

2.05485 

.50843 

1.96685 

.53059 

1.88469 

3 

58 

.46560 

2.14777 

.48701 

2.05333 

.50879 

1.96544 

.53096 

1.88337 

2 

59 

.46595 

2.14614 

.48737 

2.05182 

.50916 

1  .96402 

.53134 

1.88205 

1 

60 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

0 

i 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

~7~ 

65° 

64° 

63° 

63°     1 

NATURAL  TANGENTS  AND  COTANGENTS.   119 


2 

>8° 

2 

•9° 

jj 

0° 

3 

1° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.53171 

1.88073 

.55431 

1.80405 

.57735 

.73205 

.60086 

1.66428 

60 

1 

.53208 

1.87941 

.55469 

1.80281 

.57774 

.73089 

.60126 

1.66318 

59 

2 

.53246 

1.87809 

.55507 

1.80158 

.57-813 

.72973 

.60165 

1.66209 

58 

3 

.53283 

1.87677 

.55545 

1.80034 

.57851 

.72857 

.60205 

1.66099 

57 

4 

.53320 

1.87546 

.55583 

1.79911 

.57890 

.72741 

.60245 

1.65990 

56 

5 

.53358 

1.87415 

.55621 

1.79788 

.57929 

.72625 

.60284 

1.65881 

55 

6 

.53395 

1.87283 

.55659 

1  .79665 

.57968 

.72509 

.60324 

1.65772 

54 

7 

.53432 

1.87152 

.55697 

1.79542 

.58007 

.72393 

.60364 

1.65663 

53 

8 

.53470 

1.87021 

.55736 

1.79419 

.58016 

.72278 

.60403 

1.65554 

52 

9 

.53507 

1.86891 

.55774 

1.79296 

.58085 

.72163 

.60443 

1.65445 

51 

10 

.53545 

1.86760 

.55812 

1.79174 

.58124 

.72047 

.60483 

1.65337 

50 

11 

.53582 

1.86630 

.55850 

1.79051 

.58162 

.71932 

.60522 

1.65228 

49 

12 

.53620 

1.86499 

.55888 

1.78929 

.58201 

.71817 

.60562 

1.65120 

48 

13 

.53657 

1.86369 

.55926 

1.78807 

.58240 

.71702 

.60602 

1.65011 

47 

14 

.53694 

1.86239 

.55964 

1.78685 

.58279 

.71588 

.60642 

1.64903 

46 

15 

.53732 

1.86109 

.56003 

1.78563 

.58318 

.71473 

.60681 

1.64795 

45 

16 

.53769 

1.85979 

.56041 

1.78441 

.58357 

.71358 

.60721 

1.64687 

44 

17 

.53807 

1.85850 

.56079 

1.78319 

.58396 

.71244 

.60761 

1.64579 

43 

18 

.53844 

1.85720 

.56117 

1.78198 

.58435 

.71129 

.60801 

1.64471 

-42 

19 

.53882 

1.85591 

.56156 

1.78077 

.58474 

.71015 

.60841 

1.64363 

41 

20 

.53920 

1.85462 

.56194 

1.77955 

.58513 

.70901 

.60881 

1.64256 

40 

21 

.53957 

1.85333 

.56232 

1.77834 

.58552 

.70787 

.60921 

1.64148 

39 

22 

.53995 

1.85204 

.56270 

1.77713 

.58591 

.70673 

.60960 

1.64041 

38 

23 

.54032 

1.85075 

.56309 

1.77592 

.58631 

.70560 

.61000 

1.63934 

37 

24 

.54070 

1.84946 

.56347 

1.77471 

.58670 

.70446 

.61040 

1.63826 

36 

25 

.54107 

1.84818 

.56385 

1.77351 

.58709 

1.70332 

.61080 

1.63719 

35 

26 

.54145 

1.84689 

.56424 

1.77230 

.58748 

1.70219 

.61120 

1.63612 

34 

27 

.54183 

1.845G1 

.56462 

1.77110 

.58787 

1.70106 

.61160 

1.63505 

33 

28 

.54220 

1.84433 

.56501 

1.76990 

.58826 

1.69992 

.61200 

1.63398 

32 

29 

.54258 

1.84305 

.56539 

1.76869 

.58865 

1.69879 

.61240 

1.63292 

31 

30 

.54296 

1.84177 

.56577 

1.76749 

.58905 

1.69766 

.61280 

1.63185 

30 

31 

.54333 

1.84049 

.56616 

1.76629 

.58944 

1.69653 

.61320 

1.63079 

29 

32 

.54371 

1.83922 

.56654 

1.76510 

.58983 

1.69541 

.61360 

1.62972 

28 

33 

.54409 

1.83794 

.56693 

1.76390 

.59022 

1.69428 

.61400 

1.62866 

27 

34 

.54446 

1.83667 

.56731 

1.76271 

.59061 

1.69316 

.61440 

1.62760 

26 

35 

.54484 

1.83540 

.56769 

1.76151 

.59101 

1.69203 

.61480 

1.62654 

25 

36 

.54522 

1.83413 

.56808 

1.76032 

.59140 

1.69091 

.61520 

1.62548 

24 

37 

.54560 

1.83286 

.56846 

1.75913 

.59179 

1.68979 

.61561 

1.62442 

23 

38 

.54597 

1.83159 

.56885 

1.75794 

.59218 

1.68866 

.61601 

1.62336 

22 

39 

.54635 

1.83033 

.56923 

1.75675 

.59258 

1.68754 

.61641 

1.62230 

21 

40 

.54673 

1.82906 

.56962 

1.75556 

.59297 

1.68643 

.61681 

1.62125 

20 

41 

.54711 

1.82780 

.57000 

1.75437 

.59336 

1.68531 

.61721 

1.62019 

19 

42 

.54748 

1.82654 

.57039 

1.75319 

.59376 

1.68419 

.61761 

1.61914 

18 

43 

.54786 

1.82528 

.57078 

1.75200 

.59415 

1.68308 

.61801 

1.61808 

17 

44 

.54824 

1.82402 

.57116 

1.75082 

.59454 

1.68196 

.61842 

1.61703 

16 

45 

.54862 

1.82276 

.57155 

1.74964 

.59494 

1.68085 

.61882 

1.61598 

15 

46 

.54900 

1.82150 

.57193 

1.74846 

.59533 

1.67974 

.61922 

1.61493 

14 

47 

.54938 

1,82025 

.57232 

1.74728 

.59573 

1.67863 

.61962 

1.61388 

13 

48 

.54975 

1.81899 

.57271 

1.74610 

.59612 

1.67752 

.62003 

1.612^3 

12 

49 

.55013 

1.81774 

.57309 

1.74492 

.59651 

1.67641 

.62043 

1.61179 

11 

50 

.55051 

1.81649 

.57348 

1.74375 

.59691 

1.67530 

.62083 

1.61074 

10 

51 

.55089 

1.81524 

.57386 

1.74257 

.59730 

1.67419 

.62124 

1.60970 

9 

52 

.55127 

1.81399 

.57425 

1.74140 

.59770 

1  .67309 

.62164 

1.60865 

8 

53 

.55165 

1.81274 

.57464 

1.74022 

.59809 

1.67198 

.62204 

1.60761 

7 

54 

.55203 

1.81150 

.57503 

1.73905 

.59849 

1.67088 

.62245 

1.60657 

6 

55 

.55211 

1.81025 

.57541 

1.73788 

.59888 

1.66978 

.62285 

1.60553 

5 

56 

.55279 

1.80901 

.57580 

1.73671 

.59928 

1  .66867 

.62325 

1.60449 

4 

57 

.55317 

1.80777 

.57619 

1.73555 

.59907 

1.66757 

.62366 

1.60345 

3 

58 

.55355 

1.80653 

.57657 

1.73438 

.60007 

1.66647 

.62406 

1.60241 

2 

59 

55393 

1.80529 

.57696 

1.73321 

.60046 

1.66538 

.62446 

1.60137 

1 

60 

.55431 

1.80405 

.57735 

1.73205 

.60086 

1.66428 

.62187 

1.60033 

0 

, 

Cotang 

Tang 

Ootang 

Tang 

Cotang 

Tang 

Cotang 

Tanar 

/ 

€ 

1° 

€ 

0° 

5 

9° 

5 

8° 

120  NATURAL  TANGENTS  AND  COTANGENTS. 


33° 

33° 

34° 

35° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

' 

0 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

.70021 

1.42815 

60 

1 

.62527 

1.59930 

.64982 

1.53888 

.67493 

1.48163 

.7000  1 

1.42726 

59 

2 

.62568 

1.59826 

.65024 

1.53791 

.67536 

1.48070 

.70170 

1.42638 

58 

3 

.62608 

1.59723 

.65065 

1.53693 

.67578 

1.47977 

.70151 

1.42550 

57 

4 

.62649 

1.59620 

.65106 

1.53595 

.67620 

1.47885 

.70194 

1.42462 

56 

5 

.62689 

1.59517 

.65148 

1.53497 

.67663 

1.47792 

.70238 

1.42374 

55 

6 

.62730 

1.59414 

.65189 

1.53400 

.67705 

1.47699 

.70281 

1.42286 

54 

7 

.62770 

1.59311 

.65231 

1.53302 

.67748 

1.47607 

.70325 

1.42198 

53 

8 

.62811 

1.59208 

.65272 

1.53205 

.67790 

1.47514 

.70368 

1.42110 

52 

9 

.62852 

1.59105 

.65314 

1.53107 

.67832 

1.47422 

.70412 

1.42022 

51 

10 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.473SO 

.70455 

1.41934 

50 

11 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

.70499 

1.41847 

49 

12 

.62973 

1.58797 

.65438 

1.52816 

.67960 

1.47146 

.70542 

1.41759 

48 

13 

.63014 

1.58695 

.65480 

1.52719 

.68002 

1.47053 

.70586 

1.41672 

47 

14 

.63055 

1.58593 

.65521 

1.52622 

.68015 

1.4696? 

.70629 

1.41584 

46 

15 

.63095 

1.58490 

.65563 

1.52525 

.68088 

1.46870 

.70673 

1.41497 

45 

16 

.63136 

1.58388 

.65604 

1.52429 

.68130 

1.46778 

.70717 

1.41409 

44 

17 

.63177 

1.58286 

.65646 

1.52332 

.68173 

1.46686 

.70760 

1.41322 

43 

18 

.63217 

1.58184 

.65688 

1.52235 

.68215 

1.46595 

.70804 

1.41235 

42 

10 

.63258 

1.58083 

.65729 

1.52139 

.68258 

1.46503 

.70848 

1.41148 

41 

20 

.63299 

1.57981 

.65771 

1.52043 

.68301 

1.46411 

.70891 

1.41061 

40 

21 

.63340 

1.57879 

.65813 

1.51946 

.68343 

1.46320 

.70935 

1.40974 

39 

22 

.63380 

1.57778 

.65854 

1.51850 

.68386 

1.46229 

.70979 

1.40887 

38 

23 

.63421 

1.57676 

.65396 

1.51751 

.68429 

1.46137 

.71023 

1.40800 

37 

24 

.63462 

1.57575 

.65938 

1.51658 

.68471 

1.46046 

.71066 

1.40714 

86 

25 

.63503 

1.57474 

.65980 

1.51562 

.68514 

1.45955 

.71110 

1.40627 

35 

26 

.63544 

1.57372 

.66021 

1.51466 

.68557 

1.45864 

.71154 

1.40540 

34 

27 

.63584 

1.57271 

.66063 

1.51370 

.68600 

1.45773 

.71198 

1.40454 

33 

28 

.63625 

1.57170 

.66105 

1.51275 

.68642 

1.45682 

.71242 

1.40367 

29 

.63066 

1.57069 

.66147 

1.51179 

.68685 

1.45592 

.71285 

1.40281 

31 

30 

.63707 

1.56969 

.66189 

1.51084 

.68728 

1.15501 

.71329 

1.40195 

30 

31 

.63748 

1.56868 

.60230 

1.50988 

.68771 

1.45410 

.71373 

1.40109 

29 

32 

.63789 

1.56767 

.66272 

1.50893 

1  .68814 

1.45320 

.71417 

1.40022 

28 

33 

.63830 

1.56667 

.66314 

1.50797 

.68857 

1.45229 

.71461 

1.39936 

27 

34 

.63871 

1  .565% 

.66356 

1  .50702 

.68900 

1.45139 

.71505 

1.39850 

26 

35 

.63912 

1.56466 

.66398 

1.50607 

.68942 

1.45049 

.71549 

1.39764 

25 

36 

.63953 

1  .563*6 

.66440 

1.50512 

.68985 

1.44958 

.71593 

1.39679 

24 

37 

.63994 

1.56265 

.66482 

1.50417 

.69028 

1  .44808 

.71637 

1.39593 

23 

38 

.64035 

1.56165 

.66524 

1.50322 

.69071 

1.44778 

.71681 

1.39507 

22 

39 

.64076 

1.56065 

.66566 

1.50228 

.69114 

1.44688 

.71725 

1.39421 

21 

40 

.64117 

1.55966 

.66608 

1.50133 

.69157 

1.44598 

.71769 

1.39336 

20 

41 

.64158 

1.55866 

.66650 

1.5003S 

.69200 

1.44508 

.71813 

1.39250 

19 

42 

.64199 

1.55766 

.66692 

1.49944 

.69243 

1.44418 

.71857 

1.39165 

18 

43 

.64240 

1.55666 

.66734 

1.49849 

.69286 

1.44329 

.71901 

1.39079 

17 

44 

.64281 

1.55567 

.66776 

1.49755 

.69329 

1.44239 

.71946 

1.3S994 

16 

45 

.64322 

1.55467 

.66818 

1.49661 

.69372 

1.44149 

.71990 

1.3^909 

15 

46 

.  64363 

1.55368 

.66860 

1.49566 

.69416 

1.44060 

.72034 

1.38824 

14 

47 

.64404 

1.55269 

.66902 

1.49472 

.69459 

1.43970 

.72078 

1  .38738 

13 

48 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

.72122 

1.38653 

12 

49 

.64487 

1.55071 

.66986 

1.49284 

.69545 

1.43792 

.72167 

1.38568 

11 

50 

.64528 

1.54972 

.67028 

1.49190 

.69588 

1.43703 

.72211 

1.38484 

10 

51 

.64569 

1.54873 

.67071 

1.49097 

.69631 

1.43614 

.72255 

1.38399 

9 

V2 

.64610 

1.54774 

.67113 

1.49003 

.09675 

1.43525 

.72299 

1.38314 

8 

53 

.64652 

1.54675 

.67155 

1.48909 

.69718 

1.43436 

.72344 

1.38229 

7 

54 

.64693 

1.54576 

.67197 

1.48816 

.69761 

1.43347 

.72388 

1.38145 

6 

55 

.64734 

1.54478 

.67239 

1.48722 

.69804 

1  .43258 

.72432 

1.38060 

5 

56 

.64775 

1.54379 

.67282 

1.48629 

.69847 

1.43169 

.72477 

1.37976 

4 

57 

.64817 

1.54281 

.67324 

1.48536 

.69891 

1.43080 

.72521 

1.37891 

3 

58 

.64858 

1.54183 

.67366 

1.48442 

.69934 

1.42992 

.72565 

1  .37807 

2 

59 

.64899 

1.54085 

.67409 

1.48349 

.69977 

1.42903 

.72610 

1.37722 

1 

60 

.64941 

1.53986 

.67451 

1.48256 

.70021 

1.42815 

.72651 

1  .37638 

*\ 

f 

CY)tang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang; 

Tang 

•71 

57° 

56° 

55° 

54° 

NATURAL  TANGENTS  AND  COTANGENTS.      121 


36° 

37° 

38° 

39° 

' 

Tang 

Cctang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.72654 

1.37638 

.75355 

1.32704 

.78120 

1.27994 

.80978 

1.23490 

60 

1 

.72699 

1.37554 

.75401 

1.32624 

.78175 

1.27917 

,81027 

1.23416 

59 

2 

.72743 

1.37470 

.75447 

1  .32544 

.78222 

1.27841 

.81075 

1.23343 

58 

3 

.72788 

1.37386 

.75492 

1.32464 

.78269 

1.27764 

.81123 

1.23270 

57 

4 

.72832 

1  .37302 

.75538 

1.32384 

.78316 

1.27688 

.81171 

1.23196 

56 

5 

.72877 

1.37218 

.75584 

1.32304 

.78363 

1.27611 

.81220 

1.23123 

55 

6 

.72921 

1.37134 

.75F>29 

1.32224 

.78410 

1.27535 

.81268 

1.23050 

54 

7 

.72966 

1.37050 

.75675 

1.32144 

.78457 

1.27458 

.81316 

1.22977 

53 

8 

.73010 

1  .36967 

.75721 

1.32064 

.78504 

1.27382 

.81364 

1.22904 

52 

9 

.73055 

1.36883 

.75767 

1.31984 

.78551 

1.27306 

.81413 

1.22831 

51 

10 

.73100 

1.36800 

.75812 

1.31904 

.78598 

1.27230 

.81461 

1.22758 

50 

11 

.73144 

1.36716 

.75858 

1.31825 

.78645 

1.27153 

.81510 

1  .22685 

49 

12 

.73189 

1.36633 

.75904 

1.31745 

.78692 

1.27077 

.81558 

1.22612 

48 

13 

.73234 

1.36549 

.75950 

1.31666 

.78739 

1.27001 

.81606 

1.22539 

47 

14 

.73278 

1.36466 

.75996 

1.31586 

.7879-6 

1.26925 

.81655 

1  .22  1  67 

46 

15 

.73323 

1.36383 

.76042 

1.31507 

.78834 

1.26849 

.81703 

1.22394 

45 

16 

.73368 

1.36300 

.76088 

1.31427 

.78881 

1.26774 

.81752 

1.22321 

44 

17 

.73413 

1.36217 

.76134 

1.31348 

.78928 

1.26698 

.81800 

1.22249 

43 

18 

.73457 

1.36134 

.76180 

1.31269 

.78975 

1.26622 

.81849 

1.22176 

42 

19 

.73502 

1.36051 

.76226 

1.31190 

.79022 

1.26546 

.81898 

1.22104 

41 

20 

.73547 

1.35968 

.76272 

1.31110 

.79070 

1.26471 

.81946 

1.22031 

40 

21 

.73592 

1.35885 

.76318 

1.31031 

.79117 

1.26395 

.81995 

1.21959 

39 

22 

.73637 

1.35802 

.76364 

1.30952 

.79164 

1.26319 

.82044 

1.21886 

38 

23 

.73681 

1.35719 

.76410 

1.30873 

.79212 

1.26244 

.82092 

1.21814 

37 

2i 

.73726 

1.35637 

.76456 

1.30795 

.79259 

1.26169 

.82141 

1.21742 

36 

25 

.73771 

1.35554 

.76502 

1.30716 

.79306 

1.26093 

.82190 

1.21670 

35 

26 

.73816 

1.35472 

.76548 

1.30637 

.79354 

1.26018 

.82238 

1.21598 

34 

27 

.73861 

1.35389 

.76594 

1.30558 

.79401 

1.25943 

.82287 

1.21526 

33 

28 

.73906 

1.35307 

.76640 

1  .30480 

.79449 

1.25867 

.82336 

1.21454 

32 

29 

.73951 

1.35224 

.76686 

1.30401 

.79496 

1.25792 

.82385 

1.21382 

31 

30 

.73996 

1.35142 

.76733 

1.S0323 

.79544 

1.25717 

.82434 

1.21310 

30 

31 

.74041 

1.35060 

.76779 

1.30244 

.79591 

1.25642 

.82483 

1.21238 

29 

32 

.74086 

1.34978 

.76825 

1.30166 

.79639 

1.25567 

.82531 

1.21166 

28 

33 

.74131 

1.34896 

.76871 

1.30087 

.79686 

1.25492 

.82580 

1.21094 

27 

34 

.74176 

1.34814 

.76918 

1.30009 

.79724 

1.25417 

.82629 

1.21023 

26 

35 

.74221 

1.34732 

.76964 

1.29931 

.79781 

1.25343 

.82678 

1.20951 

25 

36 

.74267 

1.34G50 

.77010 

1.29853 

.79829 

1.25268 

.82727 

1.20879 

24 

37 

.74312 

i  .34568 

.77057 

1.29775 

.79877 

1.25193 

.82776 

1.20808 

23 

38 

.74357 

1.34487 

.77103 

1.29696 

.79924 

1.25118 

.82825 

1.20736 

22 

39 

.74402 

1.34405 

.77149 

1.29618 

.79972 

1.25044 

.82874 

1.20665 

21 

40 

.74447 

1.34323 

.77196 

1.29541 

.80020 

1.24969 

.82923 

1.20593 

20 

41 

.74492 

1.34242 

.77242 

1.29463 

.80067 

1.24895 

.82972 

1.20522 

19 

42 

.74538 

1.34160 

.77289 

1.29385 

.80115 

1.24820 

.83022 

1.20451 

18 

43 

.74583 

1.34079 

.77335 

1.29307 

.80163 

1.24746 

.83071 

1.20379 

17 

44 

.74628 

1.33998 

.77382 

1.29229 

.80211 

1.24672 

.83120 

1.20308 

16 

45 

.74674 

1.33916 

.77428 

1.29152 

.80258 

1.24597 

.83169 

1.20237 

15 

4fi 

.74719 

1.33835 

.77475 

1.29074 

.80306 

1.24523 

.83218 

1.20166 

14 

47 

.74764 

1.33754 

.77521 

1.28997 

.80354 

1.24449 

.83268 

1.20095 

13 

48 

.74810 

1.33673 

.77568 

1.28919 

.80402 

1.24375 

.83317 

1.20024 

•  ]2 

49 

.74855 

1  .33592 

.77615 

1.28842 

.80450 

1.24301 

.83366 

1.19953 

11 

50 

.74900 

1.33511 

.77661 

1.28764 

.80498 

1.24227 

.83415 

1.19882 

10 

51 

.74946 

1.33430 

.77708 

1.28687 

.80546 

1.24153 

.83465 

1.19811 

9 

52 

.74991 

1.33349 

.77754 

1.28610 

.80594 

1.24079 

.83514 

1.18740 

8 

53 

.75037 

1.33268 

.77801 

1.28533 

.80642 

1.24005 

.83564 

1.19669 

7 

54 

.75082 

1.33187 

.77848 

1.28456 

.80690 

1.23931 

.83613 

1.19599 

6 

55 

.75128 

1.33107 

.77895 

1.28379 

.80738 

1.23858 

.83662 

1.19528 

5 

56 

.75173 

l.°3026 

.77941 

1.28302 

.80786 

1.23784 

.83712 

1.19457 

4 

57 

.75219 

1.32946 

.77988 

1.28225 

.80834 

1.23710 

.83761 

1.19387 

3 

58 

.75204 

1.32865 

.7803* 

1.28148 

.80882 

1.23637 

.83811 

1.19316 

2 

59 

.75310 

1.32785 

.7808? 

1.28071 

.80930 

1  .23563 

.83860 

1.19246 

1 

60 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

.83910 

1.19175 

0 

, 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

53° 

53° 

51° 

50' 

122  NATURAL  TANGENTS  AND  COTANGENTS. 


40° 

41° 

*2° 

i 

13° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

1.19175 

.86929 

1.15037 

.90040 

1.110G1 

.93252 

1.07237 

60 

1 

.83960 

1.19105 

.86980 

1.14969 

.90093 

1.10996 

.93306 

1.07174 

59 

2 

.84009 

1.19035 

.87031 

1.14902 

.90146 

1.10931 

.93360 

1.07112 

58 

3 

.84059 

1.18964 

.87082 

1.14834 

.90199 

1.10867 

.93415 

1.07049 

57 

4 

.84108 

1.18894 

.87133 

1.14767 

.90251 

1.10802 

.93469 

1.06987 

50 

5 

.84158 

1.18824 

.87184 

1.14699 

.90304 

1.10737 

.93524 

1  .06925 

55 

0 

.84208 

1.18754 

.87236 

1.14632 

.90357 

1.10672 

.93578 

1  .06862 

54 

7 

.84258 

1.18684 

.87287 

1.14565 

.90410 

1.10607 

.93633 

1.06800 

53 

8 

.84307 

1.18614 

.87338 

1.14498 

.90463 

1.10543 

.93688 

1.06738 

52 

0 

.84357 

1.18544 

.87389 

1.14430 

.90516 

1.10478 

.93742 

1.06G76 

51 

is 

.84407 

1.18474 

.87441 

1.14363 

.90569 

1.10414 

.93797 

1.06613 

50 

11 

.84457 

1.18404 

.87492 

1.14296 

.90621 

1.10349 

.93852 

1.06551 

49 

12 

.84507 

1.18334 

.87543 

1.14229 

.90674 

1.10285 

.93906 

1.06489 

48 

13 

.84556 

1.18264 

.87595 

1.14162 

.90727 

1.10220 

.93961 

1.00427 

47 

14 

.84606 

1.18194 

.87646 

1.14095 

.90781 

1.10156 

.94016 

1  .06365 

46 

15 

.84656 

1.18125 

.87698 

1.14028 

.90834 

1.10091 

.94071 

1  .06303 

45 

16 

.84706 

1.18055 

.87749 

1.13961 

.90887 

1.10027 

.94125 

1.00241 

44 

17 

.84756 

1.17986 

.87801 

1.13894 

.90940 

1.09963 

.94180 

1.06179 

43 

18 

.84806 

1.17916 

.87852 

1.13828 

.90993 

1.09899 

.94235 

1.06117 

42 

19 

.84856 

1.17846 

.87904 

1.13761 

.91046 

1.09834 

.94290 

1.06056 

41 

20 

.84906 

1.17777 

.87955 

1.13694 

.91099 

1.09770 

.94345 

1.05994 

40 

21 

.84956 

1.17708 

.88007 

1.13627 

.91153 

1.09706 

.94400 

1  .05932 

39 

22 

.85006 

1.17638 

.88059 

1.13501 

.91206 

1.09642 

.94455 

1.05870 

38 

23 

.85057 

1.17569 

.88110 

1.13494 

.91259 

1.09578 

.94510 

1.05809 

37 

24 

.85107 

1.17500 

.88162 

1.13428 

.91313 

1.09514 

.94565 

1.05747 

36 

25 

.85157 

1.17430 

.88214 

1.13361 

.91366 

1.09450 

.94620 

1.05685 

35 

26 

.85207 

1.17361 

.88265 

1.13295 

.91419 

1.09386 

.94676 

1.05624 

34 

27 

.85257 

1.17292 

.88317 

1.13228 

.91473 

1.09322 

.94731 

1.05562 

33 

28 

.85308 

1.17223 

.88369 

1.13162 

.91526 

1.09258 

.94786 

1.05501 

32 

29 

.85358 

1.17154 

.88421 

1.13096 

.91580 

1.09195 

.94841 

1.05439 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.05317 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

28 

33 

.85559 

1.16878 

.88628 

1.12831 

.91794 

1.08940 

.95062 

1.05194 

27 

34 

.85609 

1.16809 

.88680 

1.12765 

.91847 

1.0S876 

.95118 

1.05133 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.91901 

1.08813 

.95173 

1.05072 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

24 

37 

.85761 

1.16603 

.88836 

1.12657 

.92008 

1.08686 

.95284 

1.04949 

23 

38 

.85811 

1.16535 

.88888 

1.12501 

.92062 

1.08922 

.95340 

1.04888 

22 

39 

.85862 

1.16468 

.88940 

1.12435 

.92116 

1.08559 

.95395 

1.04827 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08496 

.95451 

1.04766 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

19 

42 

.86014 

1.16261 

.89097 

1.12238 

.92277 

1.08369 

.95562 

1.04644 

18 

43 

.86064 

1.16192 

.89149 

1.12172 

.92331 

1.08306 

.95618 

1.04583 

17 

44 

.86115 

1.16124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

1.04522 

16 

45 

.86166 

1.16056 

.89253 

1.12041 

.92439 

1.08170 

.95729 

1.04461 

15 

46 

.86216 

1.15987 

.89306 

1.11975 

.92493 

1.08110 

.95785 

1.04401 

14 

47 

.86267 

1.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

1.04340 

13 

48 

.86318 

1.15851 

.89410 

1.11844 

.92601 

1.07990 

.95897 

1.04279 

12 

49 

.86368 

1.15783 

.89463 

1.11778 

.92655 

1.07927 

.95952 

1.04218 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

10 

51 

.86470 

1.15647 

.89567 

1.11648 

.92763 

1.07801 

.96064 

1.04097 

9 

52 

.86521 

1.15579 

.89620 

1.11582 

.92817 

1.07738 

.96120 

1.04036 

8 

53 

.86572 

1.15511 

.89672 

1.11517 

.92872 

1.07676 

.96176 

1.03976 

7 

54 

.86623 

1.15443 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

6 

55 

.80674 

1.15375 

.89777 

1.11387 

.92980 

1.07550 

.96288 

1.03855 

5 

56 

.86725 

1.15308 

.89830 

1.11321 

.93034 

1.07487 

.96344 

1.03794 

4 

57 

.86776 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

3 

58 

.86827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.96457 

1.03674 

2 

59 

.86878 

1.15104 

.89988 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

1 

60 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1  .03553 

0 

, 

Ootang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

t 

4 

9° 

4 

8° 

4 

7° 

4 

6° 

NATURAL   TANGENTS  AND  COTANGENTS.      123 


4 

4° 

4 

t4° 

4 

1° 

, 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.96509 

1.03553 

60 

20 

.97700 

1.02355 

40 

40 

.98843 

1.01170 

20 

1 

.96625 

1.03493 

59 

21 

.97756 

1.02295 

39 

41 

.98901 

1.01112 

19 

2 

.96681 

1.03433 

58 

22 

.97813 

1.02236 

38 

42 

.98958 

1.01053 

18 

3 

.96738 

1.03372 

57 

23 

.97870 

1.02176 

37 

43 

.99016 

1.00994 

17 

4 

.96794 

1.03312 

56 

24 

.97927 

1.02117 

36 

44 

.99073 

1.00935 

16 

5 

.96850 

1  .03252 

55 

25 

.97984 

1.02057 

35 

45 

.99131 

1.00876 

15 

6 

.96907 

1.03192 

54 

26 

.98041 

1.01998 

34 

46 

.99189 

1.00818 

14 

7 

.96963 

1.03132 

53 

27 

.98098 

1.01939 

33 

47 

.99247 

1.00759 

13 

8 

.97020 

1.03072 

52 

28 

.98155 

1.01879 

32 

48 

.99304 

1.00701 

12 

9 

.97076 

1.03012 

51 

29 

.98213 

1.01820 

31 

49 

.99362 

1  .00642 

11 

10 

.97133 

1.02952 

50 

30 

.98270 

1.01761 

30 

50 

.99420 

1.00583 

10 

11 

.97189 

1.02892 

49 

31 

.98327 

1.01702 

29 

51 

.99478 

.00525 

9 

12 

.97246 

1.02832 

48 

32 

.98384 

1.01642 

28 

52 

.99536 

.00467 

8 

13 

.97302 

1.02772 

47 

33 

.98441 

1.01583 

27 

53 

.99594 

.00408 

7 

14 

.97359 

1.02713 

46 

34 

.98499 

1.01524 

26 

54 

.99652 

.00350 

6 

15 

.97416 

1.02653 

45 

35 

.98556 

1.01465 

25 

55 

.99710 

1.00291 

5 

10 

.97472 

1.02593 

44 

36 

.98613 

1.01406 

24 

56 

.997f\S 

1.00233 

4 

17 

.97529 

1.02533 

43 

37 

.98671 

1.01347 

23 

57 

.99826 

.00175 

3 

IS 

.97586 

1.02474 

42 

38 

.98728 

1.01288 

22 

58 

.99884 

.00116 

2 

19 

.97643 

1.02414 

41 

39 

.98786 

1.01229 

21 

59 

.99942 

.00058 

1 

20 

.97700 

1.02355 

40 

40 

.98843 

1.01170 

20 

60 

1.00000 

.00000 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

4 

t5° 

4 

5° 

4, 

5° 

123a        NATURAL   SECANTS  AND  COSECANTS. 
NATURAL  SECANTS  AND  COSECANTS. 


Secants. 


0' 

10' 

20' 

30' 

40' 

50' 

60' 

1.00000 
1.00015 
1.00061 
1.00137 
1.00244 

1.00001 
1.00021 
1.00072 
1.00153 
1  .  00265 

1.00002 
1.00027 
1  .  00083 
1.00169 
1.00287 

1.00004 
1  .  00034 
.  00095 
.00187 
.00309 

1.00007 
1  .  00042 
1.00108 
1.00205 
1  .  00333 

1.00011 
1  .  00051 
1.00122 
1  .  00224 
1.00357 

1.00015 
1.00061 
1.00137 
1  .  00244 
1  .  00382 

1  .  00382 
1.00551 
1.00751 
1  .  00983 
1  .  01247 

1.00408 
1.00582 
1.00787 
1.01024 
1.01294 

1.00435 
1.00614 
1.00825 
1.01067 
1.01342 

.00463 
.  00647 
.00863 
.01111 
.01391 

1.00491 
1.00681 
1.00902 
1.01155 
1.01440 

1.00521 
1.00715 
1  .  00942 
1.01200 
1.01491 

1.00551 
1.00751 
1  .  00983 
1.  01247 
1.01545 

1.01543 

1.01872 
1  .  02234 
1.02630 
1.03061 

1.01595 
1.01930 
1.02298 
1  .  02700 
1.03137 

1.01649 
1.01989 
1.02362 
1.02770 
1.03213 

.01703 
.  02049 
.02428 
.02842 
.03290 

1.01758 
1.02110 
1.02494 
1.02914 
1.03368 

1.01815 
1.02171 
1.02562 
1.02987 
1  .  03447 

1.01872 
1.0223- 
1.02630 
1.0306 
1  .  0352$ 

1.03528 
1  .  04030 
1.04569 
1.05146 
1.05762 

1.03609 
1.04117 
1.04663 
1  .  05246 
1.05869 

1.03691 
1  .  04206 
1.04757 
1  .  05347 
1.05976 

1.03774 
1.04295 
1.04853 
1  .  05449 
1.06085 

1.03858 
1.04385 
1.04950 
1.05552 
1.06195 

1.03944 
1.04477 
1  .  05047 
1.05657 
1.06306 

1  .  04030 
1  .  0456) 
1.0514) 
1  .  0576J 
1.06415 

1.06418 
1.07115 
1.07853 
1.08636 
1  .  09464 

1.06531 
1.07235 
1.07981 
1.08771 
1.09606 

1.06645 
1.07356 
1.08109 
1.08907 
1.09750 

1.06761 
1.07479 
1.08239 
1  .  09044 
1.09895 

1  .  06878 
1.07602 
1.08370 
1.09183 
1  .  10041 

1  .  06995 
1.07727 
1  .  08503 
1.09323 
1.10189 

1.07115 
1.078S 
1.0863 
1.09461 
1.1033 

1  .  10338 
1.11260 
1.12233 
1.13257 
1  .  14335 

1  .  10488 
1.11419 
1  .  12400 
1.13433 
1.14521 

1  .  10640 
1.11579 
1  .  12568 
1.13610 
1  .  14707 

.10793 
.11740 
.  12738 
.13789 
.  14896 

1  .  10947 
1.11903 
1.12910 
1.13970 
1  .  15085 

.11103 
.12067 
.13083 
.14152 
.15277 

1.1120 
1  .  1223 
1.132^ 
1.1435 
1.1547) 

1  .  15470 
1  .  16663 
1.17918 
1.19236 
1.20622 

1  .  15665 
1  .  16868 
1.18133 
1  .  19463 
1  .  20859 

1.15861 
1  .  17075 
1  .  18350 
1.19691 
1.21099 

1  .  16059 
1.17283 
I  .  18569 
1.19920 
1.21341 

1.16259 
1  .  17493 
1  .  18790 
1.20152 
1.21584 

1.16460 
1  .  17704 
1.19012 
1.20386 
1.21830 

1.1666 
1  .  179B 
1  .  1923 
1  .  2062 
1.22077 

1.22077 
1  .  23607 
1.25214 
1.26902 
1.28676 

1.22327 
1.23869 
1.25489 
1.27191 
1.28980 

1.22579 
1.24134 
1.25767 
1.27483 
1.29287 

1.22833 
1  .  24400 
1  .  26047 

1.27778 
1.29597 

1.23089 
1.24669 
1.26330 
1.28075 
1.29909 

1.23347 
1  .  24940 
1.26615 
1.28374 
1  .  30223 

1.236(7 
1.252:4 
1.269(2 
1.286'6 
1  .  305d 

1  .  30541 
1.32501 
1  .  34563 
1  .  36733 
1.39016 

1  .  30861 
1  .  32838 
1.34917 
1.37105 
1  .  39409 

1.31183 
1.33177 
1  .  35274 
1  .  37481 
1  .  39804 

1.31509 
1.33519 
1  .  35634 

1  .  37860 
1  .  40203 

1.31837 
1  .  33864 
1  .  35997 
1  .  38242 
1.40606 

1.32168 
1.34212 
1  .  36363 
1  .  38628 
1.41012 

1  .  325(1 
1  .  345(3 
1.367:3 
1  .  390  6 
1.41411 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

Cosecants 

NATURAL  SECANTS  AND  COSECANTS. 


1286 


NATURAL    SECANTS    AND    COSECANTS— (Continued) . 


1 

h£ 

<U 

o 

0 

1 

2 
3 
4 

Cosecants. 

89 

88 
87 
86 

85 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

oo 
57.29869 
28.65371 
19.10732 
14.33559 

343.77516 
49.11406 
26.45051 
18.10262 
13.76312 

171.88831 
42.97571 
24.56212 
17.19843 
13.23472 

14.59301  85.94561 
38.20155  34.38232 
22.9255921.49368 
16.38041  15.63679 
12.74550^2.29125 

68.75736 
31.25758 
20  .  23028 

4.95788 
1.86837 

57.29869 
28.65371 
19.10732 
14.33559 
11.47371 

5 
6 

7 
8 
9 

11.47371 
9.56677 
8.20551 
7.18530 
6.39245 

11.10455 
9.30917 
8.01565 
7.03962 
6.27719 

10.75849 
9.06515 
7.83443 
6.89979 
6.16607 

10.43343 
8.83367 
7.66130 
6  .  76547 
6.05886 

10.12752 
8.61379 
7.49571 
6.63633 
5.95536 

9.83912 
8.40466 
7.33719 
6.51208 
5.85539 

9.56677 
8.20551 
7.18530 
6.39245 

5.75877 

84 
83 
82 
81 
80 

10 
11 

12 
13 
14 

5.75877 
5.24084 
4.80973 
4.44541 
4.13357 

5.66533 
5.16359 
4  .  74482 
4.39012 
4.08591 

5.57493 
5  .  08863 
4.68167 
4.33622 
4.03938 

5.48740 
5.01585 
4.62023 
4.28366 
3.99393 

5.40263 
4.94517 
4.56041 
4.23239 
3.94952 

5.32049 
4.87649 
4.50216 
4.18238 
3.90613 

5.24084 
4.80973 
4.44541 
4.13357 
3.86370 

79 

78 
77 
76 
75 

15 
16 
17 
18 
19 

3.86370 
3.62796 
3.42  30 
3.23607 
3.07155 

3.82223 
3.59154 
3  .  38808 
3.20737 
3.04584 

3.78166 
3.55587 
3.35649 
3.17920 
3.02057 

3.74198 
3.52094 
3.32551 
3.15155 
2.99574 

3.70315 
3.48671 
3.29512 
3.12440 
2.97135 

3.66515 
3.45317 
3.26531 
3.09774 
2.94737 

3.62796 
3  .  42030 
3  .  23607 
3.07155 
2.9238 

74 
73 
72 
71 
70 

20 
21 
22 
23 
24 

2.92380 
2.79043 
2.66947 
2.55930 
2.45859 

2  .  90063 
2  .  76945 
2.65040 
2.54190 
2.44264 

2.87785 
2.74881 
2.63162 
2.52474 
2.42692 

2.85545 
2.72850 
2.61313 
2.50784 
2.41142 

2.83342 
2.70851 
2.59491 
2.49119 
2.39614 

2.81175 
2.68884 
2.57698 

2.47477 
2.38107 

2.79043 
2.66947 
2.55930 
2.45859 
2.36620 

69 

68 
67 
66 
65 

25 
26 
27 
28 
29 

2.36620 
2.28117 
2  .  20269 
2  .  13005 
2.06267 

2.35154 
2.26766 
2.19019 
2.11847 
2.05191 

2  .  33708 
2.25432 
2.17786 
2.10704 
2.04128 

2.32282 
2.24116 
2.16568 
2.19574 
2.03077 

2.30875 
2.22817 
2.15366 
2.08458 
2.02039 

2.29487 
2.21535 
2.14178 
2.07356 
2.01014 

2.28117 
2.20269 
2.13005 
2.06267 
2.0  000 

64 
63 
62 
61 
60 

30 
31 
32 
33 
34 

2.00000 
1.94160 
1.88708 
1.83608 
1.78829 

1.98998 
1.93226 
1.87834 
1.82790 
1.78062 

1.98008 
1.92302 
1.86990 
1.81981 
1.77303 

1.97029 
1.91388 
1.86116 
1.81180 
1  .  76552 

1.96062 
1.90485 
1.85271 
1.80388 
1.75808 

1.95106 
1.89591 
1.84435 
1.79604 
1.75073 

1.94160 
1.88708 
1.83608 
1.78829 
1.74345 

59 
58 
57 
56 
55 

35 
36 
37 

38 
39 

1.74345 
1.70130 
1.66164 
1.62427 

1.58902 

1.73624 
1.69452 
1.65526 
1.61825 
1.58333 

1.72911 
1.68782 
1.64894 
1.61229 
1.57771 

1.72205 
1.68117 

1.64268 
1.60639 
1.57213 

1.71506 
1.67460 
1.63648 
1  .  60054 
1.56661 

1.70815 
1.66809 
1.63035 
1.59475 
1.56114 

1.70130 
1.66164 
1.62427 
1  .  58902 
1  .  55572 

54 
53 
52 
51 
50 

4( 
41 
42 
43 
44 

1.55572 
1.52425 
1  .  49448 
1.46628 
1  .  43956 

60' 

1.  55033 
1.51918 
1.48967 
1.46173 
1.43524 

1.54504 
1.51415 
1.48491 
1.45721 
1  .  43096 

1.53977 
1.50916 
1.48019 
I.  4527  4 
1.42672 

1  .  53455 
1.50422 
1.47551 
1.44831 
1.42251 

1.52938 
1.49933 
1.47087 
1.44391 
1.41835 

1  .  52425 
1  .  49448 
1.46628 
1.43956 
1.41421 

49 
48 
47 
46 
45 

50' 

40' 

30' 

20' 

10' 

0' 

Secants. 

PART  II. 

STRENGTH  OF  MATERIALS,  AND  STABILITY  OF 
STRUCTURES. 


INTRODUCTION.  127 


INTRODUCTION. 

In  the  following  chapters  the  author  has  endeavored  to  give 
the  necessary  rules,  formulas,  and  data  for  computing  the 
strength  and  stability  of  all  ordinary  forms  of  building  con- 
struction, whether  of  wood,  steel,  or  masonry,  and  in  fact  of 
all  but  the  more  intricate  problems  of  steel  construction,  with 
which  few  architects  care  to  cope,  and  which,  indeed,  are  more 
especially  within  the  province  of  the  trained  engineer. 

The  rules  and  formulas  have  been  reduced  to  their  simplest 
form  or  expression,  and,  in  general,  require  only  an  elementary 
knowledge  of  mathematics  to  understand  them.  Every  pains 
has  also  been  taken  to  show  the  application  of  the  formulas  and 
to  preserve  their  accuracy,  and  it  is  believed  that  they  repre- 
sent the  most  intelligent  practice  of  the  present  day. 

In  giving  constants  for  the  strength  of  materials,  the  author 
has  been  guided  by  the  practice  of  leading  structural  engineers, 
by  the  available  records  of  tests,  and  by  his  own  experience  of 
many  years  as  a  practising  and  consulting  architect.  The  vary- 
ing conditions  of  building  construction  have  also  been  taken 
into  account,  and  an  attempt  made  to  adapt  the  values  to  the 
practical  conditions  usually  governing  such  construction.  Every 
possible  precaution  has  been  taken  to  prevent  the  misapplica- 
tion of  rules  and  formulas  and  to  insure  absolute  safety  without 
undue  waste  of  materials. 

Much  thought  and  labor  has  been  given  to  the  preparation 
of  the  numerous  tables  contained  in  this  portion  of  the  book, 
both  to  insure  their  accuracy  and  to  arrange  them  in  the  most 
convenient  shape  for  instant  use  by  architects  and  builders. 
Nearly  all  of  these  tables  were  computed  by  the  author,  and  all 
have  been  carefully  verified,  and  it  is  believed  that  they  may 
be  used  with  perfect  confidence.  In  all  cases  they  give  the  same 
values  that  would  be  obtained  by  using  the  formulas,  while 
affording  a  great  saving  of  time  and  labor,  as  well  as  obviating 
any  chance  for  error  in  making  the  necessary  computations. 

Owing  to  the  nature  of  the  book,  and  the  large  number  of 
pages  required  to  compass  its  scope  as  a  book  of  reference, 
some  forms  of  construction,  such  as  foundations,  masonry  and 


128        EXPLANATION   OF  SIGNS   AND   TERMS 

fireproof  construction,  roof  trusses,  etc.,  have  necessarily  been 
treated  rather  briefly,  and  more  in  the  way  of  giving  necessary 
data  than  of  going  into  an  elaborate  description  or  discussion 
of  the  principles  involved.  Those  persons  who  wish  a  more 
complete  treatise  on  foundations  and  masonry  in  general,  the 
author  would  refer  to  Part  I.  of  his  work  on  Building  Construc- 
tion and  Superintendence,  which  supplements  the  rules  and  data 
herein  contained.  References  to  various  works  containing 
more  complete  information  on  some  subjects  are  also  made  in 
the  different  chapters. 


EXPLANATION   OP    SIGNS   AND    TERMS    USED 
IN  THE  FOLLOWING-  FORMULAS. 

Besides  the  usual  arithmetical  signs  and  characters  in  general 
use,  the  following  characters  and  abbreviations  will  frequently 
be  used : 

The  sign  V    means  square  root  of  number  behind. 
^/    means  cube  root  of  number  behind. 
()    means  that  all  the  numbers  between  are  to  be 
taken  as  one  quantity. 

means  decimal  parts;    2.5=2^,  or  .46=^%. 
'      denotes  feet. 
"      denotes  inches. 

The  letter  A  denotes  the  co-efficient  of  strength  for  beams  one 

inch  square,  and  one  foot  between  the  supports. 
C  denotes  resistance,  in  pounds,  of  a  block  of  any 

material  to  crushing,  per  square  inch  of  section. 
E  denotes  the  modulus  of  elasticity  of  any  material, 

in  pounds  per  square  inch. 
e  denotes  constant  for  stiffness  of  beams. 
F  denotes  resistance  of  any  material  to  shearing, 

per  square  inch. 

R  denotes  the  modulus  of  rupture  of  any  material. 
S  denotes  a  factor  of  safety. 
T  denotes  resistance  of  any  material  to  being  pulled 

apart,   in   pounds,    per  square   inch   of  cioss- 

section. 
X  between  letters  or  words,  denotes  multiplication. 


EXPLANATION  OF  SIGNS  AND   TERMS.        129 

[Note.  In  a  few  places  in  the  book  it  has  been  necessary  to 
give  a  different  meaning  to  one  or  more  of  the  above  letters  but 
in  all  such  cases  the  new  meaning  has  been  very  clearly 
indicated.] 

Breadth  is  used  to  denote  the  horizontal  thickness  of  a  beam 
or  the  least  side  of  a  rectangular  post  or  strut,  and  is  always 
measured  in  inches. 

Depth  denotes  the  vertical  height  of  a  beam  or  girder,  and  is 
always  to  be  taken  in  inches,  unless  expressly  stated  otherwise. 

Length  denotes  the  distance  between  supports  and  in  feet,  unless 
otherwise  specified.  * 

Abbreviations. — In  order  to  shorten  the  formulas,  it  has 
often  been  found  necessary  to  use  certain  abbreviations,  such  as 
bet.  for  between,  bot.  for  bottom,  dist.  for  distance,  diam.  for 
diameter,  hor.  for  horizontal,  sq.  for  square,  etc.,  which,  how- 
ever, can  in  no  case  lead  to  uncertainty  as  to  their  meaning. 

Where  the  word  "ton"  is  used  in  this  volume,  it  always  means 
2000  pounds. 


130  DEFINITIONS  OF  TERMS 


CHAPTER  I. 
DEFINITIONS  OF  TERMS  USED  IN  MECHANICS. 

THE  following  terms  frequently  occur  in  treating  of  mechani- 
cal construction,  and  it  is  essential  that  their  meaning  be  well 
understood. 

Mechanics  is  the  science  which  treats  of  the  action  of  forces. 

Applied  Mechanics  treats  of  the  laws  of  mechanics  which 
relate  to  works  of  human  art;  such  as  beams,  trusses,  arches,  etc. 

Rest  is  the  relation  between  two  points,  when  the  straight 
line  joining  them  does  not  change  in  length  or  direction. 

A  body  is  at  rest  relatively  to  a  point,  when  any  point  in  the 
body  is  at  rest  relatively  to  the  first-mentioned  point. 

Motion  is  the  relation  between  two  points,  when  the  straight 
line  joining  them  changes  in  length  or  direction,  or  in  both. 

A  body  moves  relatively  to  a  point,  when  any  point  in  the 
body  moves  relatively  to  the  point  first  mentioned. 

Force  is  that  which  changes,  or  tends  to  change,  the  state  of  a 
body  in  reference  to  rest  or  motion.  It  is  a  cause  regarding  the 
essential  nature  of  which  we  are  ignorant.  We  cannot  deal  with 
forces  properly,  but  only  with  the  laws  of  their  action. 

Equilibrium  is  that  condition  of  a  body  in  which  the  forces 
acting  upon  it  balance  or  neutralize  each  other. 

Statics  is  that  part  of  Applied  Mechanics  which  treats  of  the 
conditions  of  equilibrium,  and  is  divided  into: — 

a.  Statics  of  rigid  bodies. 

b.  Hydrostatics. 

In  building  we  have  to  deal  only  with  the  former. 

Structures  are  artificial  constructions  in  which  all  the  parts 
are  intended  to  be  in  equilibrium  and  at  rest,  as  in  the  case  of  a 
bridge  or  roof-truss. 

They  consist  of  two  or  more  solid  bodies,  called  pieces, 
which  are  connected  at  portions  of  their  surfaces  called  joints. 

There  are  three  conditions  of  equilibrium  in  a  structure,  viz. : — 

I.  The  forces  exerted  on  the  whole  structure  must  balance 
each  other.  These  forces  are: — 


USED  IN  MECHANICS.  131 

a.  The  weight  of  the  structure. 

b.  The  load  it  carries. 

c.  The  supporting  pressures,  or  resistance  of  the  foundations, 
called  external  forces. 

II.  The  forces  exerted  on  each  piece  must  balance  each  other. 
These  forces  are: — 

a.  The  weight  of  the  piece. 

6.  The  load  it  carries. 

c.  The  resistance  of  its  joints. 

III.  The  forces  exerted  on  each  of  the  parts  into  which  any 
piece  may  be  supposed  to  be  divided  must  balance  each  other. 

Stability  consists  in  the  fulfilment  of  conditions  I.  and  II., 
that  is,  the  ability  of  the  structure  to  resist  displacement  of  its 
parts. 

Strength  consists  in  the  fulfilment  of  condition  III.,  that  is, 
the  ability  of  a  piece  to  resist  breaking. 

Stiffness  consists  in  the  ability  of  a  piece  to  resist  bending. 

The  theory  of  structures  is  divided  into  two  parts;  viz.: — 

I.  That  which  treats  of  strength  and  stiffness,  dealing  only 
with  single  pieces,  and  generally  known  as  strength,  of  ma- 
terials. 

II.  That  which  treats  of  stability,  dealing  with  structures. 
Stress. — The  load  or  system  of  forces  acting  on  any  piece 

of  material  is  often  denoted  by  the  term  " stress/'  and  the  word 
will  be  so  used  in  the  following  pages. 

The  intensity  of  the  stress  per  square  inch  on  any  normal  sur- 
face of  a  solid  is  the  total  stress  divided  by  the  area  of  the  sec- 
tion in  square  inches.  Thus,  if  we  had  a  bar  ten  feet  long  and 
two  inches  square,  with  a  load  of  8000  pounds  pulling  in  the 
direction  of  its  length,  the  stress  on  any  normal  section  of  the 
rod  would  be  8000  pounds;  and  the  intensity  of  the  stress  per 
square  inch  would  be  8000  -f-  4,  or  2000  pounds. 

Strain. — When  a  solid  body  is  subjected  to  any  kind  of 
stress,  an  alteration  is  produced  in  the  volume  and  figure  of  the 
body,  and  this  alteration  is  called  the  "strain."  In  the  case 
of  the  bar  given  above,  the  strain  would  be  the  amount  that 
the  bar  would  stretch  under  its  load. 

The  Ultimate  Strength,  or  Breaking  !Load,of  abody 
is  the  load  required  to  produce  fracture  in  some  specified  way. 

The  Safe  Load  is  the  load  that  a  piece  can  support  without 
impairing  its  strength, 


132  DEFINITIONS  OF  TERMS 

Factors  of  Safety. — When  not  otherwise  specified,  a 
factor  of  safety  means  the  ratio  in  which  the  breaking  load  ex- 
ceeds the  safe  load.  In  designing  a  piece  of  material  to  sustain 
a  certain  load,  it  is  required  that  it  shall  be  perfectly  safe  under 
all  circumstances;  and  hence  it  is  necessary  to  make  an  allow- 
ance for  any  defects  in  the  material,  workmanship,  etc.  It  is 
obvious,  that,  for  materials  of  different  composition,  different 
factors  of  safety  will  be  required.  Thus,  steel  being  more  homo- 
geneous than  wood,  and  less  liable  to  defects,  it  does  not  require 
so  great  a  factor  of  safety.  And,  again,  different  kinds  of  strains 
require  different  factors  of  safety.  Thus,  a  long  wooden  column 
or  strut  requires  a  greater  factor  of  safety  than  a  wooden  beam. 
As  the  factors  thus  vary  for  different  kinds  of  strains  and  mate- 
rials, we  will  give  the  proper  factors  of  safety  for  the  different 
strains  when  considering  the  resistance  of  the  material  to  those 
strains. 

Unit  Stress  is  the  allowed  stress  per  unit  of  measurement, 
generally  the  square  inch,  and  corresponds  to  intensity. 

Distinction  between  Dead  and  Live  Load. — The 
term  "dead  load,"  as  used  in  mechanics,  means  a  load  that  is 
applied  by  imperceptible  degrees,  and  that  remains  steady; 
such  as  the  weight  of  the  structure  itself. 

A  "live  load"  is  one  that  is  applied  suddenly,  or  accompanied 
with  vibrations;  such  as  swift  trains  travelling  over  a  railway- 
bridge,  or  a  force  exerted  in  a  moving  machine. 

It  has  been  found  by  experience  that  the  effect  of  a  live  load 
on  a  beam  or  other  piece  of  material  is  twice  as  severe  as  that 
of  a  dead  load  of  the  same  weight:  hence  a  piece  of  material 
designed  to  carry  a  live  load  should  have  a  factor  of  safety 
twice  as  large  as  one  designed  to  carry  a  dead  load. 

The  load  produced  by  a  crowd  of  people  walking  on  a  floor  is 
usually  considered  to  produce  an  effect  which  is  a  mean  between 
that  of  a  dead  and  live  load,  and  a  factor  of  safety  is  adopted 
accordingly. 

In  municipal  ordinances  and  laws  relating  to  the  load  on 
floors,  the  load  to  be  supported  by  the  floor,  exclusive  of  its 
inherent  construction,  and  of  stationary  fixtures,  is  generally 
referred  to  as  the  "live  load,"  no  matter  of  what  it  may  consist; 
but  the  term  does  not  have  the  significance  given  to  it  by  en- 
gineers, and  as  defined  in  the  paragraph  above. 

The  Modulus  of  Rupture  is  a  constant  quantity  found 


USED  IN  MECHANICS.  133 

in  the  formulas  for  the  strength  of  beams,  and  is  eighteen  times 
the  value  of  the  constant  "A"    used  for  wooden  beams. 

In  recent  works  the  term  fibre  stress  is  more  frequently  used, 
and  represents  the  same  quantity. 

Modulus  of  Elasticity. — If  we  take  a  bar  of  any  elastic 
material,  one  inch  square,  and  of  any  length,  secured  at  one  end, 
and  to  the  other  apply  a  force  pulling  in  the  direction  of  its 
length,  we  shall  find  by  careful  measurement  that  the  bar  has 
been  stretched  or  elongated  by  the  action  of  the  force. 

Now,  if  we  divide  the  total  elongation  in  inches  by  the  original 
length  of  the  bar  in  inches,  we  shall  have  the  elongation  of  the 
bar  per  unit  of  length;  and,  if  we  divide  the  pulling  force  per 
square  inch  by  this  latter  quantity,  we  shall  have  what  is  known 
as  the  modulus  of  elasticity. 

Hence  we  may  define  the  modulus  of  elasticity  as  the  pulling 
or  compressing  force  per  unit  of  section  divided  by  the  elongation 
or  compression  per  unit  of  length. 

As  an  example  of  the  method  of  determining  the  modulus  of 
elasticity  of  any  material  we  will  take  the  following: — 

Suppose  we  have  a  bar  of  wrought  iron,  two  inches  square  and 
ten  feet  long,  securely  fastened  at  one  end,  and  to  the  other  end 
we  apply  a  pulling-force  of  40,000  pounds.  This  force  causes 
the  bar  to  stretch,  and  by  careful  measurement  we  find  the 
elongation  to  be  0.0414  of  an  inch.  Now,  as  the  bar  is  ten  feet,  • 
or  120  inches,  long,  if  we  divide  0.0414  by  120,  we  shall  have  th3 
elongation  of  the  bar  per  unit  of  length. 

Performing  this  operation,  we  have  as  the  result  0.00034  of 
an  inch.  As  the  bar  is  two  inches  square,  the  area  of  cross- 
section  is  four  square  inches,  and  hence  the  pulling-force  per 
square  inch  is  10,000  pounds.  Then,  dividing  10,000  by  0.00034, 
we  have  as  the  modulus  of  elasticity  of  the  bar  29,400,000 
pounds. 

This  is  the  method  generally  employed  to  determine  the 
modulus  of  elasticity  of  iron  ties;  but  it  can  also  be  obtained 
from  the  deflection  of  beams,  and  it  is  in  that  way  that  the 
values  of  the  modulus  for  most  woods  have  been  found. 

Another  definition  of  the  modulus  of  elasticity,  and  which  is 
a  natural  consequence  of  the  one  just  given,  is  the  number  of 
pounds  that  would  be  required  to  stretch  or  shorten  a  bar  one 
inch  square  by  an  amount  equal  to  its  length,  provided  that  the 
law  of  perfect  elasticity  would  hold  good  for  so  great  a  range. 


134  CLASSIFICATION   OF  STRAINS. 

The  modulus  of  elasticity  is  generally  denoted  by  E,  and  is  used 
in  the  determination  of  the  stiffness  of  beams. 

Moment.— If  we  take  any  solid  body,  and  pivot  it  at  any 
point,  and  apply  a  force  to  the  body,  acting  in  any  direction 
except  in  a  line  with  the  pivot,  we  shall  produce  rotation  of  the 
body,  provided  the  force  is  sufficiently  strong.  This  rotation  is 
produced  by  what  is  called  the  moment  of  the  force;  and  the 
moment  of  a  force  about  any  given  point  or  pivot  is  the  product 
of  the  force  into  the  perpendicular  distance  from  the  pivot  to 
the  line  of  action  of  the  force,  or,  in  common  phrase,  the  product 
of  the  force  into  the  arm  with  which  it  acts. 

The  Centre  of  Gravity  of  a  body  is  the  point  through 
which  the  resultant  of  the  weight  of  the  body  always  acts,  no 
matter  in  what  position  the  body  be.  If  a  body  be  suspended 
at  its  centre  of  gravity,  and  revolved  in  any  direction,  it  will 
always  be  in  equilibrium. 

(For  centre  of  gravity  of  surfaces,  lines,  and  solids,  see  Chap. 
V.) 

CLASSIFICATION  OP  STRAINS  WHICH  MAY  BE 
PRODUCED  IN  A  SOLID  BODY. 

The  different  strains  to  which  building  materials  may  be  ex- 
posed are:— 

I.  Tension,  as  in  the  case  of  a  weight  suspended  from  one 
end  of  a  rod,  rope,  tie-bar,  etc.,  the  other  end  being  fixed,  tend- 
ing to  stretch  or  lengthen  the  fibres. 

II.  Shearing-   Strain,  as  in  the  case  of  rivets,  treenails, 
pins  in  bridges,  etc.,  where  equal  forces  are  applied  on  opposite 
sides  in  such   a  manner  as  to  tend  to  force  one  part  over  the 
adjacent  one. 

III.  Compression,,  as  in  the  case  of  a  weight  resting  on 
top  of  a  column  or  post,  tending  to  compress  the  fibres. 

IV.  Transverse  or  Cross   Strain,  as  in  the  case  of  a 
load  on  a  beam,  tending  to  bend  it. 

V.  Torsion,    a    twisting    strain,    which    seldom    occurs    in 
building  construction,  though  quite  frequently  in  machinery. 

Combined  Strains. — The  parts  of  structures  are  often 
subjected  to  two  or  more  of  the  above  strains  at  the  same  time, 
as  in  the  case  of  "strut  beams"  and  "tie  beams,"  and  all  beams 
and  girders  are  subjected  to  a  shearing  strain^  as  well  as  to 
a.  transverse  strain. 


FOUNDATIONS  AND  SPREAD  FOOTINGS.       135 


CHAPTER  II. 
FOUNDATIONS  AND  SPREAD  FOOTINGS. 

THE  term  "foundation"  is  used  to  designate  all  that  portion 
of  any  structure  which  serves  only  as  a  basis  on  which  to  erect 
the  superstructure. 

This  term  is  sometimes  applied  to  that  portion  of  the  solid 
material  of  the  earth  upon  which  the  structure  rests,  and  also 
to  the  artificial  arrangements  which  may  be  made  to  support 
the  base. 

In  the  following  pages  these  will  be  designated  by  the  term 
"foundation-bed." 

Object  of  Foundations. — The  object  to  be  obtained 
in  the  constrviction  of  any  foundation  is  to  form  such  a  solid  base 
for  the  superstructure  that  no  movement  shall  take  place  after 
its  erection.  But  all  structures  built  of  coarse  masonry,  whether 
of  stone,  or  brick,  will  settle  to  a  certain  extent;  and,  with  a  few 
exceptions,  all  soils  will  become  compressed  under  the  weight 
of  almost  any  building. 

The  main  object  of  the  architect  or  engineer,  therefore,  is  not 
to  prevent  settlement  entirely,  but  to  insure  that  it  shall  be 
uniform;  so  that,  after  the  structure  is  finished,  it  will  have  no 
cracks  or  flaws,  however  irregularly  it  may  be  disposed  over 
the  area  of  its  site. 

Nature  and  Bearing  Power  of  Soils. — The  architect 
should  in  all  cases  endeavor  to  discover  the  nature  of  the  soil 
upon  which  the  building  is  to.be  built  before  commencing  the 
foundation  plans,  as  a  foundation  that  will  prove  satisfactory 
in  one  soil  or  locality  may  not  be  sufficient  for  another. 

For  most  buildings  a  sufficient  idea  of  the  soil  may  be  ob- 
tained from  an  inspection  of  adjoining  excavations,'  or  from 
inquiry  amongst  builders  who  have  erected  buildings  on  ad- 
joining lots. 

Many  soils,  however,  vary  greatly  within  a  comparatively 
small  area.  This  is  especially  true  of  soils  composed  of  strata 
of  different  materials,  as  sand  or  gravel  and  clay,  and  very  often 


136       FOUNDATIONS  AND  SPREAD  FOOTINGS. 

these  strata  have  a  decided  dip,  so  that  they  are  encountered 
at  different  levels  under  different  portions  of  the  building. 
For  these  reasons,  therefore,  the  character  and  bearing  power 
of  the  soil  under  all  large  or  heavy  buildings  should  be  deter- 
mined at  different  points  by  borings  or  excavations,  unless  the 
composition  of  the  soil  is  homogenous  and  fully  known. 

Testing  Soils. —  For  ordinary  buildings  borings  to  the 
depth  of  6  feet  below  the  bottom  of  the  trenches  will  be  suffi- 
cient to  determine  the  composition  of  the  soil.  These  should 
preferably  be  made  by  a  6-inch  auger,  but  a  4-inch  auger  may 
be  used  if  a  larger  one  cannot  be  had,  and  the  borings  examined 
for  every  foot  in  depth  and  memoranda  made  of  the  same. 
For  very  heavy  and  costly  buildings  the  bearing  power  of  the 
soil,  even  when  apparently  of  firm  earth,  is  often  determined 
by  testing.  Clay  soils,  especially,  vary  much  in  their  bearing 
capacity,  and  are  most  frequently  tested.  Good  sand  or  gravel 
will  seldom  need  to  be  tested. 

Tests  may  be  made  with  a  platform  resting  on  four  legs,  or 
by  a  large  pole  or  mast.  The  test  should  be  made  in  several 
places,  and  always  at  the  proposed  depth  of  the  footings. 

The  ground  under  the  Congressional  Library  at  Washington, 
D.C.,  was  tested  by  means  of  a  traveling  car  having  four  cast- 
iron  pedestals,  each  one  foot  square  at  the  base  and  set  4  feet 
apart  each  way.  In  testing  the  soil  under  the  State  Capitol  at 
Albany,  N.  Y.,  the  load  was  placed  on  a  mast  12  inches  square, 
held  vertically  by  guys,  with  a  cross-frame  to  hold  the  weights. 
The  bottom  of  the  mast  was  set  in  a  hole  3  feet  deep,  18  inches 
square  at  the  top,  and  14  at  the  bottom.*  A  permanent  bench 
mark  should  be  established  before  loading,  and  accurate  levels 
taken  by  means  of  an  engineer's  level  before  the  load  is  applied, 
and  frequent  levels  taken  as  the  load  is  gradually  increased 
until  a  sinkage  is  shown.  From  one-fifth  to  one-half  of  the  load 
required  to  produce  settlement  is  generally  adopted  for  the 
safe  load  according  to  circumstances. 

Values  for  the  Bearing  Power  of  Soils.  —  The 
following  values  for  the  bearing  power  of  soils,  given  by  Prof. 
Ira  O.  Baker,f  of  the  University  of  Illinois,  have  been  quite 
generally  accepted  by  engineers: 

*  For  more  complete  descriptions  of  these  tests  see  "Building  Construc- 
tion and  Superintendence,"  Part  I,  p.  20. 

t  See  "Treatise  on  Masonry  Construction,"  p.  194. 


FOUNDATIONS  AND  SPREAD  FOOTINGS.       137 
TABLE  I.— BEARING  POWER  OF  SOILS. 


Kind  of  material. 

Bearing  power  in  tons 
per  square  foot. 

Min. 

Max. 

Hock  —  the  hardest  —  in  thick  layers,  in  native  bed  . 
"Rock  equal  to  best  ashlar  masonry  

200 
25 
15 
5 
4 
2 
1 
8 
4 
2 
0.5 

30 
20 
10 
6 
4 
2 
10 
6 
4 
1 

Rock  equal  to  best  brick  masonry  

Rock  equal  to  poor  brick  masonry  

Clay  on  thick  beds,  always  dry.  ... 

Clay  on  thick  beds,  moderately  dry  

Clav,  soft  

Gravel  and  coarse  sand,  well  cemented  

Sand,  compact  and  well  cemented   . 

Sand,  clean,  dry  

Quicksand,  alluvial  soils,  etc  

When  deciding  upon  the  pressure  which  may  safely  be  put 
upon  the  soil  several  practical  considerations  should  be  taken 
into  account.  "For  example,  the  pressure  on  the  foundation 
of  a  tall  chimney  should  be  considerably  less  than  that  of  the 
low  massive  foundation  of  a  fire-proof  vault.  In  the  former  case 
a  slight  inequality  of  bearing  power,  and  consequent  unequal 
settling,  might  endanger  the  stability  of  the  structure;  while 
in  the  latter  no  serious  harm  would  result.  The  pressure  per 
unit  of  area  should  be  less  for  a  light  structure  subject  to  the 
passage  of  heavy  loads — as  for  example  a  railroad  viaduct — 
than  for  a  heavy  structure,  subject  only  to  a  quiescent  load, 
since  the  shock  and  jar  of  the  moving  load  are  far  more  serious 
than  the  heavier  quiescent  load."  * 

The  pressure  under  piers  supporting  a  tier  of  columns  should 
also  be  a  little  greater  than  under  a  masonry  wall,  so  that  the 
pier  may  settle  a  little  more  to  allow  for  the  compression  in 
the  joints  of  the  mason- work  of  the  wall.  Usually  an  increase 
of  pressure  of  about  10  per  cent,  may  be  allowed. 

The  following  example  of  the  known  weight  on  different  soils 
will  give  a  very  good  idea  of  what  has  been  done  in  actual  practice. 

Rock. — St.  Rollox  chimney,  poorest  kind  of  sandstone,  2 
tons  per  sq.  ft. 

Clay. — Chimney,  McCormick  Reaper  Works,  Chicago,  If 
tons  per  square  foot  on  dry,  hard  clay. 

Capitol  at  Albany,  N.  Y.,  rests  on  blue  clay  containing  from 
60  to  90  per  cent,  of  alumina,  the  remainder  being  fine  sand, 


*Ira  O.  Baker,  "  American  Architect,"  November  3,  1888. 


138       FOUNDATIONS  AND   SPREAD  FOOTINGS. 

and  containing  40  per  cent,  of  water  on  an  average.  The  safe 
load  was  taken  at  2  tons  per  square  foot. 

In  the  case  of  the  Congressional  Library  at  Washington,  which 
rests  on  "yellow  clay  mixed  with  sand,"  2J  tons  per  square  foot 
was  taken  for  the  safe  load.  "Experience  in  Central  Illinois 
shows  that  if  the  foundation  is  carried  down  below  the  action  of 
the  frost  the  clay  subsoil  will  bear  1J  to  2  tons  per  square  foot 
without  appreciable  settling."  * 

Sand  and  Gravel. — "In  an  experiment  in  France  clean 
river  sand  compacted  in  a  trench  supported  100  tons  per  square 
foot. 

"The  piers  of  the  Cincinnati  Suspension  Bridge  are  founded 
on  a  bed  of  coarse  gravel  12  feet  below  water;  the  maximum 
pressure  on  the  gravel  is  4  tons  per  square  foot. 

"The  piers  of  the  Brooklyn  Suspension  Bridge  are  founded  44 
feet  below  the  bed  of  the  river;  upon  a  layer  of  sand  2  feet  thick 
resting  upon  bed-rock;  the  maximum  pressure  is  about  5J  tons 
per  square  foot. 

"At  Chicago  sand  and  gravel  about  15  feet  below  the  surface 
are  successfully  loaded  with  2  to  2J  tons  per  square  foot. 

"At  Berlin  the  safe  load  for  sandy  soil  is  generally  taken  at  2 
to  2J  tons  per  square  foot. 

"The  Washington  Monument,  Washington,  D.  C.,  rests  upon 
a  bed  of  very  fine  sand  2  feet  thick.  The  ordinary  pressure  on 
certain  parts  of  the  foundation  being  not  far  from  11  tons  per 
square  foot,  which  the  wind  may  increase  to  nearly  14  tons  per 
square  foot."  * 

The  Home  Insurance  Building,  La  Salle  and  Adams  St., 
Chicago,  was  proportioned  for  a  bottom  pressure  of  2  tons  per 
square  foot.  Settled  2-£  inches. 

"Probably  none  of  the  high  buildings  on  spread  footings 
settled  less  than  6  inches.  The  amount  of  settlement  generally 
is  between  6  and  12  inches.  The  Auditorium  settled  more 
than  20  inches  under  the  tower."  f 

Bearing1  Power  of  Soils,  as  Fixed  by  Municipal 
Laws. —  Many  of  the  larger  cities  prescribe  the  maximum 
pressure  to  be  placed  on  the  ground  under  the  footings,  although 
as  a  rule  the  laws  are  somewhat  indefinite  as  regards  the 
nature  of  the  soil. 

*  Ira  O.  Baker,  "American  Architect,"  November  3,  1888. 
f  E.  C-  Shankland  in  "Inland  Architect,"  January,  1898. 


FOUNDATIONS  AND  SPREAD  FOOTINGS.       139 

The  building  code  of  Greater  New  York  specifies  the  follow- 
ing as  the  maximum  permissible  loads  for  different  soils : 

"Soft  clay,  one  ton  per  square  foot; 

"Ordinary  clay  and  sand  together,  in  layers,  wet  and  springy, 
two  tons  per  square  foot; 

"  Loam,  clay,  or  fine  sand,  firm  and  dry,  three  tons  per  square 
foot ; 

"Very  firm  coarse  sand,  stiff  gravel,  or  hard  clay,  four  tons 
per  square  foot,  or  as  otherwise  determined  by  the  Com- 
missioner of  Buildings  having  jurisdiction." 

The  requirements  of  the  Chicago  Building  Ordinance  is  as 
follows : 

"If  the  soil  is  a  layer  of  pure  clay  at  least  fifteen  feet  thick 
without  admixture  of  any  foreign  substance  excepting  gravel, 
it  shall  not  be  loaded  more  than  at  the  rate  of  3,500  pounds  per 
square  foot.  If  the  soil  is  a  layer  of  pure  clay  at  least  fifteen 
feet  thick  and  is  dry  and  thoroughly  compressed,  it  may  be 
loaded  not  to  exceed  4,500  pounds  per  square  foot. 

"If  the  soil  is  a  layer  of  dry  sand  fifteen  feet  or  more  in  thick- 
ness, and  without  admixture  of  clay,  loam,  or  other  foreign 
substance,  it  shall  not  be  loaded  more  than  at  the  rate  of  4,000 
pounds  per  square  fooD. 

"If  the  soil  is  a  mixture  of  clay  and  sand,  it  shall  not  be 
loaded  more  than  at  the  rate  of  3,000  pounds  per  square  foot." 

Proportioning-  tlie  Footings. — The  footings  under 
dwellings  and  light  buildings,  when  on  firm  soil,  are  usually 
proportioned  according  to  the  thickness  of  the  wall  above, 
rather  than  by  the  pressure  on  the  soil,  as  the  weight  of  such 
buildings,  when  not  more  than  three  stories  high,  will  seldom 
exceed  1}  tons  per  square  foot  when  distributed  by  the  footings. 
The  width  of  the  footings,  however,  even  in  light  buildings, 
should  be  proportioned  so  that  the  pressure  on  the  soil  will  be 
approximately  the  same  per  square  foot  under  all  parts  of  the 
building.  It  is  owing  largely  to  the  unequal  pressure  on  the 
soil,  as  where  wide  openings  occur,  or  where  one  wall  is  higher 
than  the  adjacent,  that  cracks  occur  in  brick  and  stone  walls. 

For  high  and  heavily  loaded  buildings,  the  area  of  the  foot- 
ings should  be  carefully  proportioned  both  to  the  load  and  to 
the  bearing  power  of  the  soil. 

In  computing  the  weight  to  be  supported  by  the  footings,  all 
of  the  dead  or  permanent  load,  such  as  the  weight  of  the  mate- 
rials entering  into  and  forming  a  part  of  the  building  should  be 


140       FOUNDATIONS  AND  SPREAD  FOOTINGS. 

taken,  and  to  this  should  be  added  only  so  much  of  the  live  or 
movable  load  that  the  floors  are  to  support  as  will  probably  be 
upon  the  floor  most  of  the  time,  as  to  secure  uniform  settlement, 
it  is  necessary  that  the  loads  for  which  the  footings  are  pro- 
portioned shall  be  as  near  the  actual  weight  of  the  building  as 
possible. 

For  warehouses,  stores,  etc.,  about  50  per  cent,  of  the  live  load 
for  which  the  floor  beams  are  proportioned  should  be  added  to 
the  dead  load  supported  on  the  footings. 

For  office-buildings,  hotels,  etc.,  the  weight  of  the  people  who 
may  occupy  them  should  be  neglected  altogether  in  propor- 
tioning the  footings,  and  only  about  15  Ibs.  per  square  foot  of 
floor  allowed  to  cover  the  weight  of  furniture,  books,  safes,  etc. 

For  theatres  and  similar  buildings  some  allowance  should 
probably  be  made  for  the  weight  of  the  people,  the  actual  amount 
depending  upon  the  arrangement  of  the  plan  and  the  character 
of  the  soil.  Almost  any  soil,  after  it  has  been  compacted  by 
the  dead  weight  of  the  building,  wilt  carry  a  shifting  load  of 
people  without  further  settlement,  while  if  the  footings  were 
computed  to  carry  the  full  live  loads  for  which  the  floor  beams 
were  designed,  it  would  be  found  when  the  building  was  finished 
that  the  actual  loads  on  the  footings  under  the  walls  would  be 
much  greater  than  under  the  columns,  and  if  the  ground  had 
settled  at  all  during  the  erection  of  the  building,  the  probabili- 
ties would  be  that  the  building  would  be  higher  in  the  centre 
than  at  the  walls.* 

Municipal  Requirements  as  to  Proportioning 
Footings  to  liive  Loads. —  The  Building  Code  of  Greater 
New  York  requires  that  footings  shall  be  proportioned  as  follows : 

"  The  load  exerting  pressure  under  the  footings  of  founda- 
tions in  buildings  more  than  three  stories  in  height  are  to  be 
computed  as  follows :  For  warehouses  and  factories  they  are  to 
be  the  full  dead  load  and  the  full  live  load  established  by  this 
code.  In  stores  and  buildings  for  light  manufacturing  pur- 
poses, they  are  to  be  full  dead  load  and  75  per  cent,  of  the  live 

*  It  is  the  judgment  of  the  best  engineers  that  the  areas  of  foundations 
on  compressible  soil  should  be  proportioned  to  the  dead  loads  only,  and 
not  to  theoretical  or  occasional  loads.  When  live  loads  have  been 
figured  on  both  the  interior  columns  and  on  the  columns  in  the  exterior 
walls,  the  exterior  columns  have  always  been  found  to  settle  more,  from 
the  fact  that  the  live  load  forms  a  larger  percentage  of  the  interior  column 
loads  than  of  the  wall  column  loads. — J.  K.  FREITAG. 


FOUNDATIONS  AND   SPREAD   FOOTINGS        141 

load  established  by  this  code.  The  same  applies  to  churches, 
schoolhouses,  and  places  of  public  assembly.  In  office-build- 
ings, hotels,  dwellings,  apartment  houses,  tenement  houses, 
lodging  houses,  and  stables,  they  are  to  be  the  full  dead  load 
and  60  per  cent,  of  the  live  load  established  by  this  code."  The 
footings  must  be  designed  to  distribute  the  loads  as  uniformly 
as  possible,  so  as  not  to  exceed  the  safe  bearing  capacity  of  the 
soil  as  established  in  this  code." 

The  Chicago  ordinance  merely  specifies  that  "Foundations 
shall  be  proportioned  to  the  actual  average  loads  they  will  have 
to  carry,  and  not  to  theoretical  and  occasional  loads." 

The  Boston  Building  Laws  make  no  specific  requirements  as 
to  how  the  loads  shall  be  computed. 

The  following  examples  illustrate  the  proper  method  of  pro- 
portioning the  area  of  footings: 

EXAMPLE  1. — To  proportion  the  footings  under  a  six-story 
warehouse,  with  solid  side  walls  of  brick,  and  iron  columns  and 
steel  girders,,  spaced  16  ft.  c.  to  c.  across  the  building,  and 
the  same  distance  longitudinally,  the  safe  bearing  capacity 
of  the  soil  being  assumed  at  3  tons  per  square  foot. 

Com  putation — Wa  Us . 
Cubic  feet  of  brickwork  in  one  lineal  foot  of  side 

wall,  from  footing  to  top  of  fire-wall  164;   at 

120  Ibs.  per  ft =  19,680  Ibs. 

Floor  area  supported  by  1  ft.  of  bearing  wall,  8  ft. 

in  each  story. 
Actual  weight  of  materials  in  1  sq.  ft.  of  floor, 

75  Ibs.     75X8  ft.X6  floors .  =   3,600  Ibs. 

Actual  weight  of  8  sq.  ft.  of  roof,  60X  8 =       480  Ibs. 

Probable  constant  load  on  first  three  floors,  50  Ibs. 

per  sq.  ft.,  50X8X3 =    1,200  Ibs. 

Probable  constant  load  on  4th,  5th,  and  6th  floors, 

40  Ibs.  per  sq.  ft.,  8X40X3 -      960  Ibs. 

Probable  constant  load  on  roof 

Total  load  on  1  lineal  foot  of  footing =25,920  Ibs. 

25,920  -f-  6,000  (3  tons)  =  4  ft.  4  ins.  width  of  footing. 

Under  Columns. 
Weight  of  one  tier  of  columns  from  footing  to  roof, 

including  fireproof  covering  and  plaster =  12,000  Ibs. 

Floor  area  in  each   story  supported   by   column 
16X16  feet  =256  sq.  ft. 


142       FOUNDATIONS  AND   SPREAD  FOOTINGS. 

Load  under  columns  from  preceding  page  12;000  Ibs. 
Actual  weight  of  256  sq.  ft.  of  floor  for  6  stories 

(256X75X6) =115,200  lb& 

Actual  weight  of  256  sq.  ft.  of  roof,  at  60  Ibs =  15,360  Ibs. 

Probable  constant  load  on  first  three  floors,  50  Ibs. 

X256X3 =  38,400  Ibs. 

Probable  constant  load  on  4th,  5th,  and  6th  floors, 

40lbs.X256X3 * =  30,720  Ibs, 

Probable  constant  load  on  roof 


Total  load  on  footings =211,680 Ibs. 

211,680^6,600    (3   tons  increased   10%)  =  32  sq.   ft.  =  area  of 
footing. 

The  front  and  rear  walls  would  probably  be  divided  into 
piers  by  large  openings  and  should  be  proportioned  in  the  same 
way  as  frhe  column  footings,  except  that  only  the  piers  support- 
ing ends  of  girders  would  be  figured  for  floor  loads. 

Only  warehouses  for  storage  of  heavy  merchandise  should 
be  figured  for  a  probable  constant  load  of  50  Ibs.  For  ordinary 
merchandise  30  Ibs.  would  be  more  nearly  correct.* 

For  an  office-building  or  hotel,  the  calculation  would  be  the 
same  for  the  dead  load,  but  the  probable  constant  load  would 
not  exceed  15  Ibs. 

EXAMPLE  2. — To  proportion  the  footings  under  the  tower, 
front  and  side  walls  of  a  church,  built  on  ground  capable  of 
sustaining  4  tons  to  the  square  foot. 

Data. — Tower  walls,  82  ft.  high  above  footings;  18  ft.  of 
wall  2  ft.  thick,  13  ft.  of  wall  20"  thick,  51  ft.  of  wall  16"  thick. 

Side  wall  adjacent  to  tower,  36  ft.  high,  14  ft.  of  wall  20" 
thick,  balance  of  wall  16"  thick. 

The  front  wall  is  divided  in  the  centre  by  a  wide  opening, 
leaving  piers  12  ft.  wide  at  each  side  one  pier  being  adjacent  to 
the  tower. 

Computation. — It  is  proposed  to  make  the  footings  under 
the  side  wall  3  ft.  wide  and  to  proportion  the  other  footings  to 
the  same  unit  pressure. 

Weight  of  masonry  in  one  lineal  foot  of  side  wall .  .  .     6,320  Ibs. 
Weight  of  floor  material  and  pews  supported  by  one 

lineal  foot  of  side  wall 200  Ibs. 

*  The  floor  beams,  of  course,  should  be  computed  for  the  full  possible  load. 


FOUNDATIONS  AND  SPREAD  FOOTINGS.      143 

Weight  of  roof  and  ceiling  supported  by  one  lineal 

foot  of  side  wall 200  Ibs. 

Weight  of  snow  on  roof,  and  people  on  floors  disregarded. 

Total  weight  on  one  lineal  foot  of  footing. .    6,720  Ibs. 
6, 720 -i- 3  ft.  (width  of  footing) =2, 240  Ibs.  per  sq.  ft.  on  trenches, 
which  should  be  used  as  a  basis  for  proportioning  all  other 
footings. 

Weight  of  masonry  in  one  lineal  foot  of  tower  wall. .  15,080  Ibs. 
Weight  of  floors  supported  by  one  lineal  foot  of  tower 

wall 296  Ibs. 

Weight  of  roof  supported  by  one  lineal  foot  of  tower 

wall '. 140  Ibs. 

Total  weight  of  one  lineal  foot  of  footing. . .  15,516  Ibs. 

15,516-=- 2,240=7  ft.  =  width  of  footing. 
Each  of  the  12-ft.  piers  of  front  wall  contains  and 

supports  masonry  weighing 149,040  Ibs. 

Weight  of  gallery  and  pews  supported  by  each  pier.      3,876  Ibs. 

Total  weight  on  12  ft.  of  footing 152,916  Ibs. 

or  12,743  Ibs.  per  lineal  ft. 

12,743-^-2,240  lbs.=5.1  ft.  width  of  footing. 

As  the  pressure  on  the  soil  in  this  case  is  so  slight,  the  width 
of  the  tower  footings  could  be  reduced  to  6  ft.  and  of  the  front- 
wall  footings  to  4'— 4"  without  causing  cracks  where  the  walls 
join,  but  the  theoretical  width  should  always  be  computed. 

Where  the  unit  pressure  approaches  closely  to  the  safe  bear- 
ing of  the  soil  no  reduction  should  be  made  from  the  computed 
widths. 

Centre  of  Pressure  Should  Coincide  with  Centre 
of  Base. — That  the  walls  and  piers  of  a  building  may  settle 
uniformly  and  without  producing  cracks  in  the  superstructure 
it  is  not  only  essential  that  the  area  of  the  footings  shall  be  in 
proportion  to  the  load  and  the  bearing  power  of  the  soil,  but 
also  that  the  centre  of  pressure  (a  vertical  line  through  the  centre 
of  gravity  of  the  wall  or  pier)  shall  pass  through  the  centre  of  the 


This  condition  is  of  the  first  importance,  for  if  the  centre  of 
pressure  does  not  coincide  with  the  centre  of  the  footing,  or 
base,  the  ground  will  yield  most  on  the  side  which  is  nearest 
to  the  centre  of  pressure,  and,  as  the  ground  yields,  the  base 
assumes  an  inclined  position,  often  tilting  the  lower  portion  of 


144       FOUNDATIONS  AND  SPREAD   FOOTINGS. 

the  wall  or  pier,  and  producing  unsightly  cracks  in  the  super- 
structure. 

Foundations  on  Rock. — To  prepare  a  rock  foundation 
for  being  built  upon,  all  that  is  generally  required  is  to  cut  away 
the  loose  and  decayed  portions  of  the  rock,  and  to  dress  the 
rock  to  a  plane  surface  as  nearly  perpendicular  to  the  direction 
of  the  pressure  as  is  practicable;  or,  if  the  rock  forms  an  in- 
clined plane,  to  cut  a  series  of  plane  surfaces,  like  those  of  steps? 
for  the  wall  to  rest  on.  If  there  are  any  fissures  in  the  rock 
they  should  be  filled  with  concrete.  Concrete  is  better  than 
masonry  for  this  purpose,  as,  when  once  set,  it  is  nearly  incom- 
pressible under  anything  short  of  a  crushing  force;  so  that 
it  forms  a  base  almost  as  solid  as  the  rock  itself,  while  the  com- 
pression of  the  mortar  joints  of  masonry  is  certain  to  cause  some 
irregular  settlement. 

If  it  is  unavoidably  necessary  that  some  parts  of  the  founda- 
tion shall  start  from  a  lower  level  than  others,  care  should  be 
taken  to  keep  the  mortar  joints  as  close  as  possible,  or  to  execute 
the  lower  portions  of  the  work  in  cement,  or  some  hard-setting 
mortar;  otherwise  the  foundations  will  settle  unequally  and 
thus  cause  much  injury  to  the  superstructure.  The  load  placed 
on  the  rock  should  at  no  time  exceed  one-eighth  of  that  neces- 
sary to  crush  it.  When  building  on  a  ledge  much  trouble  is 
often  caused  by  the  water  which  collects  on  top  of  the  stone, 
and  stands  or  runs  on  its  surface.  Some  method  of  draining 
the  water  is  absolutely  necessary  if  the  basement  is  to  be  kept 
dry. 

Foundations  on  Clay. — This  soil  is  found  in  every  con- 
dition, varying  from  slate  or  shale,  which  will  support  almost 
any  load,  to  a  soft,  damp  material,  which  will  squeeze  out  in 
every  direction  when  a  moderately  heavy  pressure  is  brought 
upon  it. 

Ordinary  clay  soils,  however,  when  they  can  be  kept  dry, 
will  carry  any  usual  load  without  trouble,  but  as  a  rule  clay 
soils  will  give  more  trouble  than  either  sand,  gravel,  or  stone. 

In  the  first  place,  the  top  of  the  footings  must  be  carried 
below  the  frost-line  to  prevent  heaving,  and  for  the  same  reason 
the  outside  face  of  the  wall  should  be  built  with  a  slight  batter, 
about  f "  to  the  foot,  and  perfectly  smooth.  The  frost-line  varies 
with  different  localities,  attaining  a  depth  of  six  feet  in  some  of 
the  very  Northern  States,  although  between  three  and  four  feet 
is  the  usual  depth  in  the  so-called  Northern  States.  The  effect 


FOUNDATIONS  AND   SPREAD  FOOTINGS.       145 

of  freezing  and  thawing  on  clay  soils  is  very  much  greater  than 
on  other  soils. 

The  surface  of  the  ground  around  the  building  should  be 
graded  so  that  the  rain-water  will  run  away  from  the  building, 
and  in  most  clays  subsoil  drains  are  necessary.  When  the 
clay  occurs  in  inclined  layers  great  care  must  be  exercised  to 
prevent  it  from  sliding,  and  when  building  on  a  side  hill  the 
utmost  precautions  must  be  taken  to  exclude  water  from 
the  soil,  for  if  the  clay  becomes  wet  the  pressure  of  the  walls 
may  cause  it  to  ooze  from  under  the  footings.  The  erection  of 
very  heavy  buildings  in  such  locations  must  be  considered 
hazardous,  even  when  every  precaution  is  taken. 

Should  it  be  necessary  to  carry  a  portion  of  the  foundations 
to  a  greater  depth  than  the  rest,  the  lower  portion  of  the  walls 
should  be  built  as  described  under  "  Foundations  on  Rock," 
and  care  must  be  taken  to  prevent  the  upper  part  of  the  bed 
from  slipping.  Wherever  possible  the  footings  should  be 
carried  all  around  the  building  at  the  same  level. 

If  the  clay  contains  coarse  sand  or  gravel  its  supporting 
power  is  increased,  and  it  is  less  liable  to  slide  or  ooze  away. 

Foundations  on  Sand  and  Gravel. — Gravel  gives 
less  trouble  than  any  other  material  as  a  foundation  bed.  It 
does  not  settle  under  any  ordinary  load,  and  will  safely  carry 
the  heaviest  of  buildings  if  the  footings  are  properly  propor- 
tioned. It  is  not  affected  by  water,  provided  it  is  confined 
laterally,  so  that  the  sand  and  fine  gravel  cannot  wash  out. 
This  soil  is  also  not  greatly  affected  by  frost. 

Sand  also  makes  an  excellent  foundation  bed  when  confined 
laterally,  and  is  practically  incompressible,  as  clean  river  sand 
compacted  in  a  trench  has  been  known  to  support  100  tons  to 
the  square  foot. 

As  long  as  the  sand  is  confined  on  all  sides,  and  the  footings 
are  all  on  the  same  level,  no  trouble  whatever  will  be  encountered, 
unless  it  be  in  the  caving  of  the  banks  in  making  the  excava- 
tions. Should  the  cellar  be  excavated  to  different  levels,  how- 
ever, sufficient  retaining  walls  must  be  erected  where  the  depth 
changes  to  prevent  the  sand  of  the  upper  level  from  being  forced 
out  from  under  the  footings,  and  precautions  should  be  taken 
in  such  a  case  to  keep  water  from  penetrating  under  the  upper 
footings. 

Foundations  on  Loam  and  Made  Land.  —  No 
foundation  should  start  on  loam  (soil  containing  vegetable 


146       FOUNDATIONS  AND   SPREAD  FOOTINGS. 

matter),  or  on  land  that  has  been  made  or  filled  in,  unless,  in- 
deed, the  filling  consist  of  clean  beach  sand,  which,  when  settled 
with  water,  may  be  considered  equal  to  the  natural  soil. 

Loam  should  always  be  penetrated  to  the  firm  soil  beneath, 
and  when  the  made  land  or  filling  overlies  a  firm  earth,  the 
footings  should  be  carried  to  the  natural  soil.  When  the  filled 
land  is  always  wet,  as  on  the  coast  or  the  borders  of  a  lake, 
piles  may  be  used,  extending  into  the  firm  earth,  and  the  tops 
cut  off  below  low- water  mark;  but  piles  should  never  be  used 
where  it  is  not  certain  that  they  will  be  always  wet. 

Foundations  for  Chimneys. — As  examples  of  the 
foundations  required  for  very  high  chimneys  we  quote  the 
following  from  a  treatise  on  foundations,  in  the  latter  part  of  a 
work  on  "Foundations  and  Foundation  Walls,"  by  George  T. 
Powell. 

Fig.  1  represents  the  base  of  a  chimney  erected  in  1859  for 
the  Chicago  Refining  Company,  151  feet  high,  and  12  feet  square 
at  the  foot.  The  base,  merely  two  courses  of  heavy  dimension 


Fig.  I. 


stone,  as  shown,  is  bedded  upon  the  surface-gravel  near  the 
mouth  of  the  river,  there  recently  deposited  by  the  lake.  The 
mortar  employed  in  the  joint  between  the  stone  is  roofing-gravel 
in  cement.  The  area  of  the  base  is  256  square  feet,  the  weight 
of  chimney,  inclusive  of  base,  625  tons,  giving  a  pressure  of 
2.44  tons  to  the  square  foot.  This  foundation  proved  to  be 
perfect. 

Fig.  2  represents  the  base  of  a  chimney  erected  in  1872  for  the 
McCormick  Reaper  Works,  Chicago,  which  is  160  feet  high,  14 
feet  square  at  the  foot,  with  a  round  flue  of  6  feet  8  inches 
diameter. 


PILE  FOUNDATIONS. 


147 


The  base  covers  625  square  feet;  the  weight  of  the  chimney 
and  base  is  approximately  1,100  tons;  the  pressure  upon  the 
ground,  (dry  hard  clay)  is  therefore  1.76  tons  to  the  square  foot. 
This  foundation  also  proved  to  be  perfect  in  every  respect. 


Pile  Foundations. — When  it  is  required  to  build  upon 
a  compressible  soil  that  is  constantly  saturated  with  water  and 
of  considerable  depth,  the  most  practicable  method  of  obtain- 
ing a  solid  and  enduring  foundation  for  buildings  of  moderate 
height  is  by  driving  piles. 

A  large  proportion  of  the  buildings  in  the  city  of  Boston,  Mass., 
and  several  of  the  tall  office-buildings  of  New  York  City  and 
Chicago,  rest  on  piles,  and  piles  are  extensively  used  for  sup- 
porting buildings,  grain  elevators,  etc.,  erected  along  the  water 
front  of  coast  and  lake  cities. 

The  durability  of  piles  in  ground  constantly  saturated  with 
water  is  beyond  question,  as  several  instances  exist  where  piles 
have  been  found  in  a  perfectly  sound  condition  after  the  lapse 
of  from  six  to  seventeen  centuries. 

Municipal  Requirements. — The  laws  of  Boston  re- 
quire that  piles  shall  be  capped  with  granite,  and  that  the 
spacing  shall  not  exceed  3  ft.  between  centres.  The  laws  of 
Chicago  require  that  piles  shall  be  driven  to  rock  or  hard  pan 
and  be  capped  with  an  oak  grillage;  they  also  specify  a  maxi- 
mum load  of  25  tons  per  pile  and  a  maximum  fibre  stress  of 
1,200  pounds  per  square  inch  for  the  oak  grillage. 

The  laws  of  New  York  specify  a  minimum  diameter  of  5  inches, 
a  maximum  spacing  of  3  feet  between  centres,  and  a  maximum 
safe  load  of  20  tons  per  pile. 


148  PILE  FOUNDATIONS. 

The  Piles  are  made  from  the  trunks  of  trees;  they  should 
be  as  straight  as  possible  and  not  less  than  5  ins.  in  diameter 
at  small  end  for  light  buildings,  or  8  ins.  for  heavy  buildings. 
The  woods  generally  used  for  piles  in  the  Northern  States  are 
the  spruce,  hemlock,  white  pine,  Norway  pine,  Georgia  pine, 
and  occasionally  oak,  hickory,  elm,  black  gum,  and  basswpod. 
In  the  Southern  States,  Georgia  or  pitch  pine,  c}^press  and  oak 
are  used.  There  does  not  appear  to  be  much  difference  in  the 
woods  as  to  durability  under  water,  but  the  tougher  and  stronger 
woods  are  to  be  preferred,  especially  where  the  piles  are  to  be 
driven  to  hard  pan  and  heavily  loaded. 

The  piles  should  be  prepared  for  driving  by  cutting  off  all 
limbs  close  to  the  trunk,  and  sawing  the  ends  square.  It  is 
probably  .better  to  remove  the  bark,  although  piles  are  more 
often  driven  with  the  bark  on,  and  it  is  doubtful  if  the  bark 
makes  much  difference  one  way  or  the  other. 

For  driving  in  soft  and  silty  soils,  experience  has  shown  that 
the  piles  drive  better  with  a  square  point.  When  the  pene- 
tration is  less  than  6  ins.  at  each  blow  the  top  of  the  pile  should 
be  protected  from  "brooming"  by  putting  on  an  iron  ring  about 
1  inch  less  in  diameter  than  the  head  of  the  pile,  and  from  2J 
to  3  inches  wide  by  f "  thick.  The  head  should  be  chamfered 
to  fit  the  ring.  When  driven  into  compact  soil,  such  as  sand, 
gravel  or  stiff  clay  the  point  of  the  pile  should  be  shod  with  iron 
or  steel.  The  method  shown  at  A,  Fig.  3,  answers  very  well 
for  all  but  very  hard  soils,  and  for  these  a  cast  conical  point  about 
5  inches  in  diameter,  secured  by  a  long  dowel,  with  a  ring  around 
the  end  of  the  pile,  as  shown  at  J5,  makes  the  best  shoe. 

Piles  that  are  to  be  driven  in  or  exposed  to  salt  water  should 
be  thoroughly  impregnated  with  creosote,  dead  oil  or  coal  tar, 
or  some  mineral  poison  to  protect  them  from  the  "teredo" 
or  ship  worm,  which  will  completely  honeycomb  an  ordinary 
pile  in  three  or  four  years. 

Driving. — The  piles  should  always  be  driven  to  an  even 
bearing,  which  is  determined  by  the  penetration  under  the  last 
four  or  five  blows  of  the  hammer. 

The  usual  method  of  driving  piles  for  the  support  of  buildings 
is  by  a  successsion  of  blows  given  with  a  block  of  cast  iron,  or 
steel,  called  the  "hammer,"  which  slides  up  and  down  between 
the  uprights  of  a  machine  called  a  "pile-driver."  The  ma- 
chine is  placed  over  the  pile,  so  that  the  hammer  descends  fairly 
on  its  head,  the  piles  always  being  driven  with  the  small  end 


PILE  FOUNDATIONS. 


149 


down.  The  hammer  is  generally  raised  by  steam  power,  and 
is  dropped  either  automatically  or  by  hand.  The  usual  weight 
of  the  hammers  used  for  driving  piles  for  building  foundations 
is  from  1,500  to  2,500  pounds,  and  the  fall  varies  from  5  to  20 
feet,  the  last  blows  being  given  with  a  short  fall.  Occasionally, 
hammers  weighing  up  to  4,000  pounds  and  over  are  used. 

Steam  hammers  are  to  a  considerable  extent  taking  the  place 
of  the  ordinary  drop-hammer  in  large  cities,  as  they  will  drive 
many  more  piles  in  a  day,  and  with  less  damage  to  the  piles. 
The  steam  hammer  delivers  short  quick  blows,  from  60  to  70 


A. 


Fig.  3. 

to  the  minute,  and  seems  to  jar  the  piles  down,  the  short  interval 
between  the  blows  not  giving  time  for  the  soil  to  settle  around 
the  pile.* 

In  driving  piles  care  should  be  taken  to  keep  them  plumb, 
and  when  the  penetration  becomes  small,  the  fall  should  be 


*  The  5,000  piles,  averaging  48  ft.  in  net  length,  under  the  new  Chicago 
Post  Office  were  driven  with  a  steam  hammer,  weighing  4,400  Ibs.  and  making 
60  blows  per  minute. 


150  PILE  FOUNDATIONS. 

reduced  to  about  5  feet,  the  blows  being  given  in  rapid  succes- 
sion. 

Whenever  a  pile  refuses  to  sink  under  several  blows,  before 
reaching  the  average  depth,  it  should  be  cut  off  and  another 
pile  driven  beside  it. 

When  several  piles  have  been  driven  to  a  depth  of  20  feet  or 
more  and  refuse  to  sink  more  than  $  inch  under  five  blows  of 
a  1,200-pound  hammer  falling  15  feet,  it  is  useless  to  try  them 
further,  as  the  additional  blows  only  result  in  brooming  and 
crushing  the  head  and  point  of  the  pile,  and  splitting  and  crush- 
ing the  intermediate  portions  to  an  unknown  extent. 

Spacing". — Piles  should  not  be  spaced  less  than  2  feet  on 
centres,  nor  more  than  3  feet,  unless  iron  or  wooden  grillage  is 
used. 

When  long  piles  are  driven  nearer  than  2  feet  from  centres 
there  is  danger  that  they  may  force  each  other  up  from  their 
solid  bed  on  the  bearing  stratum.  Driving  the  piles  close 
together  also  breaks  up  the  ground  and  diminishes  the  bearing 
power. 

When  three  rows  of  piles  are  used  the  most  satisfactory  spac- 
ing is  2  feet  6  inches  from  centres  across  the  trench  and  3  feet 
from  centres  longitudinally,  provided  this  number  of  piles  will 
carry  the  weight  of  the  building.  If  they  will  not,  then  the 
piles  must  be  spaced  closer  together  longitudinally,  or  another 
row  of  piles  driven,  but  in  no  case  should  the  piles  be  less  than 
2  feet  apart  from  centres,  unless  driven  by  means  of  a  water  jet. 

The  number  of  piles  under  the  different  portions  of  the  build- 
ing should  be  proportioned  to  the  weight  which  they  are  to 
support,  so  that  each  pile  will  receive  very  nearly  the  same  load. 

Capping-. — The  tops  of  the  piles  should  invariably  be  cut 
off  at  or  a  little  below  low  water-mark,  otherwise  they  will  soon 
commence  to  decay.  They  should  then  be  capped,  either  with 
large  stone  blocks,  concrete  or  timber  or  steel  grillage. 

Granite  Capping. — In  Boston  it  is  obligatory  to  cap  the  piles 
with  blocks  of  granite,  which  rest  directly  on  the  tops  of  the 
piles.  If  the  stone  does  not  fit  the  surface  of  the.  pile,  or  a  pile 
is  a  little  low,  it  is  wedged  up  with  oak  or  stone  wedges.  In 
capping  with  stone  a  section  of  the  foundation  should  be  laid 
out  on  the  drawings  showing  the  arrangement  of  the  capping 
stones. 

A  single  stone  may  rest  on  one,  two,  or  three  piles,  but  not  on 
four,  nor  on  three  piles  in  a  straight  line,  as  it  is  practically  impos- 


PILE  FOUNDATIONS. 


151 


r 


r 


sible  to  make  the  stone  bear  evenly.  Fig.  4  shows  the  best  arrange- 
ment of  the  capping  for  three  rows  of 
piles.  Under  dwellings  and  light  build- 
ings the  piles  are  often  driven  in  two 
rows,  staggered,  in  which  case  each 
stone  should  rest  on  three  piles.  After 
the  piles  are  capped,  large  footing- 
stones,  extending  in  one  piece  across 
the  wall,  should  be  laid  in  cement  mor- 
tar on  the  capping. 

Fig.  5  shows  a  partial  piling  plan, 
with  the  arrangement  of  the  cap 
stones,  of  the  Boston  Chamber  of 
Commerce.  It  may  seem  that  most 
of  the  stones  rest  on  three  piles,  and 
a  very  few  on  two  piles. 

Concrete    Capping. — In    New    York 
Fig.  4.  a   very    common   method   of   capping 

is  to  excavate  to  a  depth  of  1  foot  below  the  top  of  the  piles 
and  one  foot  outside  of  them,  and  fill  the  space  thus  excavated 
solid  with  Portland  cement  concrete,  deposited  in  layers  and 
well  rammed. 

After  the  concrete  is  brought  level  with  the  top  of  the  piles 
additional  layers  are  deposited  over  the  whole  width  of  the 
foundation  until  the  concrete  attains  a  depth  of  18  inches  above 
the  piles.  On  this  foundation  brick  or  stone  footings  are  laid 
as  on  solid  earth.  If  long  bars  of  twisted  steel,  about  J"  square 
are  imbedded  in  the  concrete  about  3  inches  above  the  tops  of 
the  piles,  this  makes,  in  the  opinion  of  the  author,  the  best 
form  of  capping,  the  twisted  bars  giving  great  transverse  strength 
to  the  concrete. 

Grillage. — Most  of  the  pile  foundations  of  Chicago  have 
heavy  timber  grillage  bolted  to  the  tops  of  the  piles,  and  on 
these  timbers  are  laid  the  stone  or  concrete  footings. 

The  timbers  for  the  grillage  should  be  at  least  10"XlO"  in 
cross-section,  and  should  have  sufficient  transverse  strength 
to  sustain  the  load  from  centre  to  centre  of  piles,  using  a  low 
fibre  stress.  They  should  be  laid  longitudinally  on  top  of  the 
piles  and  be  fastened  to  them  by  means  of  drift  bolts,  which  are 
plain  bars  of  iron,  either  round  or  square,  driven  into  a  hole 
about  20  per  cent,  smaller  than  the  iron.  One-inch  round  or 
square  bars  are  generally  used,  the  hole  being  bored  by  a  j-incb 


152       FOUNDATIONS  AND  SPREAD  FOOTINGS. 

auger  for  the  round  bolts  or  a  |-inch  auger  for  the  square  bolts. 
The  bolts  should  enter  the  pile  at  least  1  foot. 


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Fig.  5. 

If  heavy  stone  or  concrete  footings  are  used,  and  the  space 
between  the  piles  and  timbers  is  filled  with  concrete  level  with 


FOUNDATIONS  AND  SPREAD  FOOTINGS.       153 

the  top  of  the  timbers,  no  more  timbering  is  required;  but  if 
the  footings  are  to  be  made  of  small  stones,  and  no  concrete  is 
used,  a  solid  floor  of  cross  timbers,  at  least  6  inches  thick,  for 
heavy  buildings,  should  be  laid  on  top  of  the  longitudinal  cap- 
ping and  drift-bolted  to  them. 

Where  timber  grillage  is  used  it  should,  of  course,  be  kept 
entirely  below  the  lowest  recorded  water  line,  otherwise  it  will 
rot  and  allow  the  building  to  settle.  It  has  been  proved  con- 
clusively, however,  that  any  kind  of  sound  timber  will  last 
practically  forever  if  completely  immersed  in  water. 

The  advantages  of  timber  grillage  are  that  it  is  easily  laid  and 
effectually  holds  the  tops  of  the  piles  in  place.  It  also  tends  to 
distribute  the  pressure  evenly  over  the  piles,  as  the  transverse 
strength  of  the  timber  will  help  to  carry  the  load  over  a  single 
pile,  which  for  some  reason  may  not  have  the  same  bearing 
capacity  as  the  others.  Steel  beams,  imbedded  in  concrete,  are 
sometimes  used  to  distribute  the  weight  over  piles,  but  some 
other  form  of  construction  can  generally  be  employed  at  less 
expense  and  with  equally  good  results.  * 

For  Concrete  Piles,  see  page  177. 

Specifications  for  Pile  Foundations. — This  con- 
tractor is  to  furnish  and  drive  the  piles  indicated  on  sheet  No.  1 . 

The  piles  are  to  be  of  sound  spruce  (hemlock,  Georgia  pine) 
perfectly  straight  from  end  to  end,  trimmed  close,  and  cut  off 
square  to  the  axis  at  both  ends. 

They  must  be  not  less  than  six  (6)  inches  in  diameter,  at  the 
small  end,  ten  (10)  inches  at  the  large  end,  when  cut  off,  and  of 
sufficient  length  to  reach  solid  bottom,  the  necessary  length  of 
piles  to  be  determined  by  driving  test  piles  in  different  parts  of 
the  foundation. 

All  piles  to  be  driven  vertically,  in  the  exact  positions  shown 
by  the  plan,  until  they  do  not  move  more  than  five  (5)  inches  under 
the  last  five  blows  of  a  hammer  weighing  2,000  Ibs.  and  falling 
twenty  (20)  feet.  All  split  or  shattered  piles  are  to  be  removed  if 
possible  and  a  good  one  driven  in  place  of  each  imperfect  one. 
In  cases  where  such  piles  cannot  be  removed  an  additional  one 
must  be  driven  for  each  imperfect  one.  If  the  piles  show  a  ten- 
dency to  broom,  they  shall  be  bound  with  a  wrought-iron  ring, 
2J  ins.  wide,  and  J  in.  thick. 

*  For  description  of  the  pile  foundations  and  capping  of  the  Chicago 
Post  Office,  see  Freitag's  "Architectural  Engineering,"  pp.  350-352, 


1/54  PILE  FOUNDATIONS. 

All  piles,  when  driven  to  the  required  depth  shall  be  sawed  off 
square  and  horizontal  at  the  grade  indicated  on  the  drawings. 

Bearing  Power  of  Piles. — As  used  for  supporting  build- 
ings, piles  may  be  divided  into  two  classes:  A.  Those  which  are 
driven  to  rock  or  "hard  pan,"  i.e.,  firm  gravel  or  clay,  and  (B) 
those  which  do  not  reach  hard  pan. 

Piles  of  Class  A,  when  driven  through  a  soil  that  is  sufficiently 
firm  to  brace  the  pile  at  every  point,  may  be  computed  to  sustain 
a  load  equal  to  the  safe  resistance  to  crushing  on  the  least  cross 
section.  If  the  surrounding  soil  is  plastic  the  bearing  power  of 
the  pile  will  be  its  safe  load  computed  as  a  column,  having  a 
length  equal  to  the  length  of  "the  pile  when  capped. 

Test  piles  driven  on  the  site  of  the  Chicago  Public  Library 
through  27  ft.  of  soft,  plastic  clay,  23  ft.  of  tough  compact  clay, 
and  2  ft.  into  hard  pan  sustained  a  load  of  50.7  tons  per  pile  for 
two  weeks  without  apparent  settlement.  There  are  many,  in- 
stances where  piles  driven  to  the  depth  of  20  ft.  in  hard  clay  sus- 
tain from  20  to  40  tons,  and  a  few.  instances  up  to  80  tons  per  pile. 

Piles  of  Class  B  depend  for  their  bearing  power  upon  the 
friction,  cohesion,  and  buoyancy  of  the  soil  into  which  they  are 
driven.  The  safe  load  for  such  piles  is  usually  determined  by 
the  average  penetration  of  the  pile  under  the 'last  four  or  five 
blows  of  the  hammer.  Several  engineers  have  formulated  rules 
for  determining  the  safe  load  of  piles  of  this  class,  but  there  are 
so  many  elements  that  modify  the  penetration,  or  its  exact  de- 
termination, as  well  as  varying  conditions  in  driving,  and  in  the 
soil,  that  it  is  regarded  an  impossibility  to  formulate  any  rule 
that  can  be  considered  entirely  satisfactory  for  all  the  conditions 
under  which  such  piles  are  driven. 

The  formula  now  most  generally  used  by  engineers  was  de- 
rived by  Mr.  M.  A.  Wellington,  and  is  often  referred  to  as  the 
Engineering  News  formula. 

The  formula  is 

Safe  load  _  2.  w.  h. 
in  tons        S  +  1 ' 

in  which  w= weight  of  hammer  in  tons,  h=  height  of  fall  of  hammer 
in  feet,  S=  penetration  under  last  blow,  or  the  average  under  the 
last  five  blows.  When  loads  are  based  on  this  formula  the  piles 
should  be  driven  until  the  penetration  does  not  exceed  the  limit 
assumed,  or  if  this  is  found  to  be  impracticable,  new  calculations 
must  be  made  based  on  the  smallest  average  penetration  that 


PILE  FOUNDATIONS. 


can  be  obtained,  and  a  greater  number  of  piles  used.  In  locali- 
ties where  piling  is  commonly  used  for  obtaining  the  foundation, 
the  least  penetration  that  can  be  obtained  within  practical  limits 
of  length  of  pile  can  generally  be  ascertained  by  observation, 
or  by  consulting  an  experienced  pile-driver.  The  longer  the  pile 
the  less  will  be  the  final  set  or  penetration  as  a  rule.  Where 
there  is  no  experience  to  guide  one  it  will  be  necessary  to  drive 
a  few  piles  to  determine  the  length  of  pile  required,  or  the  least 
set  for  a  given  length  of  pile.  Some  piles  will  have  to  be  driven 
further  than  others  to  bring  to  an  equal  bearing.  When  the 
piles  are  to  be  loaded  to  more  than  50  per  cent,  of  the  assumed 
safe  load,  the  final  set  of  each  pile  should  be  carefully  meas- 
ured by  an  inspector,  the  broom  and  splinters  being  removed 
from  the  head  of  the  pile  for  the  last  blow. 

The  following  table,  computed  by  the  above  formula,  gives 
the  safe  loads  for  different  penetrations,  under  different  falls,  of 
a  hammer  weighing  one  ton.  For  a  hammer  of  different  weight 
multiply  the  safe  load  in  table  by  the  actual  weight  of  hammer, 
in  tons.  Thus  for  a  hammer  weighing  1,000  Ibs.  the  values  in  the 
table  should  be  multiplied  by  J  or  for  a  1,500  Ib.  hammer  by  J. 

TABLE  IL— SAFE  LOADS,  IN  TONS,  FOR  PILES. 

(Hammer  weighing  1  ton.) 


Penetra- 
tion of 
Pile  ,  in 
inches. 

Height  of  the  fall  of  the  hammer,  in  feet. 

3 

4.8 
4.0 
3.4 
3.0 

4 

6.4 
5.3 
4.6 
4.0 
3.6 
3.2 

5 

8.1 
6.7 
5.7 
5.0 
4.5 
4.0 
1  6 

6 

8 

10 

12 

19.4 
16.1 
13.8 
12.0 
10.7 
9.6 
8.8 

14 

22.5 

18.7 
16.1 
14.0 
12.5 
11.2 
10.2 

16 

18 

20 

25 

30 

0.25 
0.50 
0.75 
1.00 
1.25 
1.50 
1.75 
2,00 
2,50 
3.00 
3.50 
4.00 
5.00 
6.00 

9.7 

8.0 
6.9 
6.0 
5.4 

4.8 
4  4 

12.9 
10.7 
9.2 
8.0 
7.1 
6.4 
5.8 

16.1 
13.3 
11.5 
10.0 
8.9 
8.0 
7.3 

25.8 
21.3 
18.4 
16.0 
14  3 
12.8 
11.7 

29.1 
24.0 
20.7 
J8.0 
16.1 
14.4 
13.1 

32  3 

26!e 

23.0 
20.0 
17.9 
16.0 
14.6 

33.3 
28.8 
25.0 
22.3 
20.0 
18  2 

34.5 
30.0 
26.7 
24.0 
21  9 

3.3 

4.0 
3.4 
3.0 

5.3 
4.6 
4.0 
3.6 
3.2 

6.7 
5.7 
5.0 
4.4 
4.0 
3.3 

8.0 
6.9 
6.0 
5.3 
4.8 
4.0 
3.4 

9.3 

8.0 
7.0 
6.2 
5.6 
4.7 
4.0 

10.7 
9.1 
S.O 
7.1 
6.4 
5.3 
4.6 

12.0 
10.3 
9.0 
8.0 
7.2 
6.0 
5.1 

13.3 
11.4 
10.0 
8.9 
8.0 
6.7 
5.7 

16.7 
14.3 
12.5 
11.1 
10.0 
8.3 
7.1 

20.0 
17.1 
15.0 
13.3 
12.0 
10.0 
8.6 

Example  of  Pile  Foundations. — As  an  example  of  the 
method  of  determining  the  necessary  number  of  piles  to  support 
a  given  building,  we  will  determine  the  number  of  piles  required 
to  support  the  side  walls,  and  interior  piers  of  the  warehouse 


156  PILE  FOUNDATIONS. 

computed  in  Example  1.  The  method  of  computing  the  weights 
being  exactly  the  same  in  both  cases,  and  the  remarks  regarding 
the  weight  of  people  being  applicable  to  pile  foundations  as  well 
as  to  foundations  placed  directly  on  the  soil. 

Data. — From  observation  of  the  pile-driving  for  an  adjacent 
building  it  is  found  that  piles  driven  from  20  to  30  feet,  take  a 
set  of  1  inch  under  a  1,200-lb.  hammer  falling  20  feet,  and  that 
additional  blows  give  about  the  same  set. 

Computation. — From  the  above  table  we  find  that  the  safe  load 
for  a  fall  of  20  ft.  and  penetration  of  1  inch  is  20  tons.  Multi- 
plying by  the  weight  of  our  hammer  in  tons  (.6),  we  have  12  tons 
as  the  safe  load  per  pile. 

Referring  to  the  computations  on  page  139,  we  see  that  the  total 
load  on  one  lineal  foot  of  footing  is  25,920  Ibs.,  or  about  13  tons. 
As  we  must  have  at  least  two  rows  of  piles,  and  the  two  piles  will 
support  24  tons,  it  follows  that  the  spacing  of  the  piles  longitudi- 
nally should  be  24  -~  13=1  ft.  10  ins.  As  this  is  too  close,  we 
should  use  3  rows  of  piles,  spaced  2  ft.  apart,  and  the  longitudinal 
spacing  would  then  be  36 -v- 13=  2  ft.  9  ins.  The  width  of  the 
capping  would  be  about  five  feet. 

Under  the  Interior  Piers. — The  load  on  the  piles,  under  the  in- 
terior columns  (p.  140)  is  211,680  Ibs.,  or  105.8  tons.  This  di- 
vided by  12,  the  safe  load  for  one  pile,  gives  9  piles,  or  three  rows 
of  three  piles  each,  which  should  be  spaced  2'  6"  apart  each  way. 

Some  Instances  of  the  Actual  Lioad  on  Piles. — The 
following  instances  of  the  actual  loads  supported  by  piles,  under 
well-known  buildings,  and  of  loads  which  piles  have  borne  for  a 
short  time  without  settlement,  should  be  of  value  when  design- 
ing pile  foundations. 

Boston. — At  the  new  Southern  R.R.  Station  three  piles  were 
loaded  with  about  60  tons  of  pig  iron  (20  tons  per  pile),  with- 
out settlement.  The  allowed  load  was  10  tons  per  pile. 

Piles  12  ins.  in  diameter  at  the  butt,  6  ins.  at  the  point,  driven 
31  ft.  in  hard  blue  clay,  near  Haymarket  Square,  failed  to  show 
movement  under  30  tons.  Ultimate  load  believed  to  be  60 
tons.*  Other  piles  driven  17.9  ft.  sustained  a  load  of  31  tons. 
Average  penetration  under  last  ten  blows  of  a  1,710-lb.  hammer 
falling  from  9  to  12  feet  varied  from  0.4  to  0.95  ins.  per  blow  for 
fifteen  piles. 

Piles  25  ft.  long  under  the  Chamber  of  Commerce  building 

*  Horace  J.  Howe,  "American  Architect*"  June  11,  1898. 


PILE  FOUNDATIONS.  157 

penetrated  about  3  ins.  under  the  last  blow  of  a  2,000-lb.  ram 
»  falling  about  15  feet. 

Chicago. — New  Public  Library  building ; — piles  proportioned  to 
30  tons  each.  Tested  to  50. 7, tons  without  settlement. 

Schiller  Building; — estimated  load  55  tons  per  pile;  building 
settled  from  1J  to  2|  ins. 

Passenger  Station,  Northern  Pacific  Railroad,  Harrison  St.; 
piles  50  ft.  long  carry  25  tons  each  without  perceptible  settlement. 

The  Art  Institute  and  portions  of  the  Stock  Exchange  rest 
on  piles,  and  also  a  large  proportion  of  the  warehouses  and  other 
buildings  on  the  banks  of  the  river. 

New  York  City. — The  Ivins  (Park  Row)  Building  is  supported 
by  about  3,500  fourteen-inch  spruce  piles,  arranged  in  clusters 
of  fifty  or  sixty,  for  single  columns,  and  a  corresponding  number 
under  piers  supporting  two  or  more  columns. 

The  piles  were  driven  to  a  refusal  of  1  inch  under  a  20-foot  blow 
of  a  2,000-lb.  hammer.  Material,  fine  dense  sand  to  a  depth  of 
over  90  feet.  But  few  piles  could  be  driven  more  than  15  or  20 
feet.  Average  maximum  load  per  pile,  9  tons.* 

The  American  Tract  Society  Building  is  also  supported  by 
piles. 

Brooklyn,  N.  Y. — Piles  under  the  Government  Graving  Dock 
driven  32  ft.  on  the  average  in  fine  sand  mixed  with  fine  mica 
and  a  little  vegetable  loam  are  supposed  to  sustain  from  10  to 
15  tons  each. 

New  Orleans. — Piles  driven  from  25  to  40  ft.  in  a  soft  alluvial 
soil  carry  safely  from  15  to  25  tons  with  a  factor  of  safety  of  6  to 
8. — Patton. 

'  Cost  of  Driving  Piles. — The  cost  of  driving  piles  natu- 
rally varies  with  the  character  of  the  soil,  and  the  conditions 
under  which  they  are  driven. 

In  New  York  City  a  2,500-lb.  drop-hammer  drove  4  piles 
per  day  of  10  hours.  With  a  steam-hammer,  13  piles  per  day 
were  driven,  for  the  same  foundation.  Piles  were  70  ft.  long,  8 
ins.  in  diameter  at  the  point,  and  15  ins.  at  the  head. 

Average  cost  of  driving  800  piles  with  the  steam-hammer, 
$2  each. 

In  New  York  Harbor  1,800  piles  were  driven  by  a  steam-ham- 
mer, 24  to  26  ft.  into  gravel  and  hard  pan  at  a  cost  of  80  cents 
each. 

*  For  description  of  this  foundation,  see  Engineering  Record  of  July  23, 
1898. 


158  SPREAD  FOUNDATIONS. 

In  Chicago,  40  Norway  pine  piles  were  driven  45  ft.  deep 
every  ten  hours  at  a  cost  (for  driving)  of  55  cts.  each.  Another 
firm  drove  from  60  to  65  piles,  each  45  ft.  long,  15  ft.  deep  into 
hard  sand  each  day  at  a  cost  of  about  30  cts.  each.  In  both 
cases  steam-hammers  were  used.* 

In  Boston,  spruce  piles  from  30  to  45  ft.  long  cost  from  $3  to 
$5  in  place.  Georgia  pine  piles  as  long  as  70  ft.  cost  about  $15 
apiece  for  the  piles  themselves,  and  $2  or  more  each  for  the  driv- 
ing. Oak  piles  from  40  to  50  ft.  long  cost  from  $8  to  $10  each 
in  place. j- 

References. — A  very  valuable  paper  on  "  Some  Instances 
of  Piles  and  Pile-driving,  New  and  Old,"  by  Horace  J.  Howe, 
C.E.,  was  published  in  the  American  Architect  and  Building  News, 
commencing  June  11,  1898.  The  paper  records  a  great  many 
tests  and  gives  several  formulas  and  many  experiences  of  dis- 
tinguished engineers. 

Part  I.  of  Building  Construction  and  Superintendence  also  gives 
much  additional  information  in  regard  to  pile  foundations  and 
experiments  on  the  bearing  power  of  piles. 

Much  valuable  information  on  piles  is  also  given  in  "  A  Prac- 
tical Treatise  on  Foundations,"  by  W.  M.  Patton,  C.E.  John 
Wiley  &  Sons,  publishers. 

SPREAD  FOUNDATIONS. 

Compressible  soils  are  often  met  with  that  will  bear  from  1 
to  2  tons  per  square  foot  with  very  little  settlement,  and  with 
a  uniform  settlement  under  the  same  unit  pressure. 

In  such  cases  it  is  often  cheaper  to  spread  the  foundations  or 
footings  so  as  to  reduce  the  unit  pressure  to  the  capacity  of  the 
soil  than  to  attempt  to  drive  piles,  or  to  go  dowTn  to  hard  pan, 
Spread  footings  may  be  built  of  concrete  with  iron  tension  bars, 
of  steel  beams  or  girders,  and  concrete,  or  of  timber. 

Concrete  with  Iron  Tension  Bars. — When  the  neces- 
sary height  can  be  obtained,  spread  footings  composed  of  Port- 
land cement  concrete,  with  iron  tension  members,  have  many 
qualities  to  recommend  them.  Such  footings  are  easy  of  construc- 
tion, they  are  cheap,  and  their  durability  is  everlasting.  The 
iron  being  so  completely  imbedded  in  the  concrete,  it  cannot 

*  American  Architect,  June  4,  1898,  p.  78. 

t  George  B.  Francis,  C.E.,  in  American  Architect,  July  23,  1898. 


SPREAD  FOUNDATIONS. 


159 


rust,*  and  hence  there  is  no  possibility  of  deterioration  in  the 
footings. 

By  the  use  of  twisted  iron  or  other  forms  of  tension  rods  the 
transverse  strength  of  concrete  footings  may  be  made  equal  to 
that  of  steel  beams,  but  concrete  footings  require  more  height. f 

Fig.  6  shows  the  most  economical  section  for  a  concrete  and 
twisted  iron  footing.  In  building  the  footings  with  steel  beams, 
the  strength  of  the  concrete  is  practically  wasted,  while  in  this 
method  of  construction  it  is  all  utilized.  It  has  been  proved  that 
the  entire  tensile  strength  of  the  twisted  bars  can  be  utilized, 
and,  being  held  continuously  along  their  entire  length  by  the  con- 
crete as  a  screw  bolt  is  held  by  the  nut,  they  neither  draw  nor 
stretch,  except  as  the  concrete  extends  with  them. 


Fig.  6. 


In  building  concrete  footings,  as  shown  in  Fig.  6,  a  layer  of 
concrete  from  3  to  6  inches  thick,  made  in  the  proportion  of  1  to 
3  should  first  be  laid,  and  the  iron  bars  laid  on  and  tamped  down 
into  it.  Another  layer  of  4  inches,  mixed  in  the  same  propor- 
tion, should  then  be  laid,  after  which  the  concrete  may  be  mixed 
in  the  proportion  of  one  to  six.  Each  layer  should  be  laid  before 
the  preceding  layer  has  had  time  to  harden,  otherwise  they  may 
not  adhere  thoroughly. 

The  author  has  prepared  Table  III.,  giving  the  strength  and 
proportions  of  footings  constructed  in  this  way,  which  he  be- 
lieves to  have  a  large  margin  of  safety.  Two  sizes  of  bars  are 

*  In  cutting  through  a  portion  of  a  foundation  built  of  concrete  and  iron, 
and  submerged  in  salt  water,  ten  yeais  after  the  work  was  done,  no  deterio- 
ration to  the  iron  whatever  was  found.  Iron  imbedded  in  concrete,  with 
the  end  projecting,  has  been  found  bright  arid  clean  after  the  projecting 
end  had  completely  rusted  away. 

tFor  description  of  tension  bars  see  Chap.  XXIII. 


160 


SPREAD  FOUNDATIONS. 


:'given,  with  the  corresponding  safe  loads  for  the  footings,  the  other 
measurements  applying  to  both  cases.  The  measurements  in 
the  third  column  refer  to  the  width  of  the  brick  or  stone  footing 
resting  on  the  concrete.  The  greater  the  width  of  this  footing  in 
proportion  to  the  width  of  the  concrete,  the  less  will  be  the  strain 
on  the  tension  rods. 


TABLE  III.— PROPORTIONS  AND  STRENGTH  OF  CON- 
CRETE FOOTINGS  WITH  TWISTED  IRON  TENSION 
BARS. 


Width  of 

Thick- 

Width of 

Distance 

Size  of 

Safe 

Size  of 

Safe 

Footing 

ness  of 

Stone 

between 

square 

load  per 

square 

load  per 

in  feet. 

concrete. 

footing. 

centres 

bar. 

lineal 

bar. 

lineal 

of  bars. 

foot. 

foot. 

Ft.  In. 

Ft.  In. 

Inches. 

Inches. 

Tons. 

Inches. 

Tons. 

20 

3       6 

6     0 

8 

2 

78 

1% 

66 

18 

3       3 

5     6 

8 

2 

76 

1% 

56 

16 

2     10 

5     0 

l-M 

73 

50 

14 

2       8 

4     8 

7 

j^ 

70 

1% 

49 

12 

2       6 

4     4 

6 

1% 

65 

1/4 

48 

10 

2       3 

4     0 

6 

m 

65 

l 

42 

8 

2       0 

4     0 

6 

i 

60 

H 

40 

6 

1       8 

3     6 

6 

H 

55 

Y2 

29 

Piers. — Footings  for  piers  may  be  built  in  the  same  manner, 
with  two  sets  of  bars  laid  crossways  of  each  other,  and  also  diag- 
onally, as  shown  in  Fig.  7.  In  the  case  of  piers  the  pressure  will 
be  more  evenly  distributed  if  the  corners  are  cut  off.  The  same 
size  of  bars  should  be  used  for  a  pier  as  for  a  wall,  whose  footings 
have  the  same  projection  beyond  the  masonry,  and  the  depth 
of  the  concrete  should  be  the  same. 

Fig.  7  represents  the  construction  of  the  pier  footings  under 
the  interior  columns  of  a  four-story  factory  for  the  Pacific  Coast 
Borax  Co.  at  Bayonne,  N.  J.  The  footings  are  computed  to 
resist  an  upward  pressure  of  the  ground  of  2,500  Ibs.  per  square 
foot.* 

This  form  of  construction  has  been  used  to  a  considerable 
extent  in  San  Francisco  and  in  the  eastern  States,  and  twisted 
iron  in  connection  with  concrete  is  being  more  extensively  used 
every  year.  The  right  to  use  twisted  iron  in  concrete  is  pro- 
tected by  letters  patent,  now  owned  by  the  Ransome  Concrete 


*  For  a  description  of  this  building  and  other  illustrations,  see  Engineer* 
ing  Record  of  July  30,  1898, 


SPREAD  FOUNDATIONS. 


161 


Machinery  Co.  of  New  York.*  The  corrugated  bars  controlled 
by  the  St.  Louis  Expanded  Metal  Fireproofing  Co.  are  also  being 
extensively  used  for  spread  footings.  For  detailed  information 
see  1903  catalogue  of  this  company. 

Steel  Beam  Footings.— When  it  is  necessary  to  make  the> 
foundations  from  8  to  15  feet  wide,  with  a  very  small  height  to> 
the  footings,  as  is  the  case  in  Chicago,  steel  beams  must  be  used' 
to  furnish  the  necessary  transverse  strength.  Even  when  build- 


2~belo.vr  floor  line  -~h 


Fig.  7. 

ing  on  solid  ground,  it  is  claimed  that  iron  and  steel  footings  for 
tall  buildings,  at  the  present  price  of  steel,  are  cheaper  than  ma- 
sonry footings.  The  author  doubts,  however,  if  steel  footings 
will  prove  as  durable  as  those  of  masonry. 

When  used  under  walls,  the  beams  are  laid  in  one  course  at 
right  angles  to  the  wall,  and  from  9  to  20  inches  apart  according 
to  the  size  of  the  beams,  thickness  of  the  concrete  and  estimated 

*  Twisted  bars  purchased  from  this  company  may  be  used,  however, 
without  payment  of  further  royalties. 


162 


SPREAD  FOUNDATIONS. 


pressure  per  square  foot.     Over  the  centre  of  the  platform  of 
beams  is  placed  the  brick  or  stone  footings  as  shown  in  Fig.  8. 

When  used  under  piers,  as  is  generally  the  case  in  the  modern 
tall  building,  the  beams  are  usually  arranged  in  two  layers,  as 
shown  in  Fig.  9.  The  bottom  layer  contains  a  sufficient  number 
of  beams  to  cover  the  necessary  bearing  area.  Above  these  is 
laid  a  second  layer  of  beams,  at  right  angles  to  the  first,  and  long 
enough  to  reach  the  extreme  outer  edge  of  the  outer  beams  of  the 
first  layer.  Upon  the  centre  of  the  upper  tier  of  beams  is  placed 


i  .  r 


_L 


i.i    i ,    i 


1.1.1 


i     i 


IP         -11 


SIDE  VIEW 


\^£^q 


Beam. 


CROSS  SECTION, 
Fig.  8. 

the  iron  shoe  of  the  column,  or  a  heavy  stone  base.  Frequently 
the  upper  tier  of  beams  is  so  wide  that  it  cannot  be  well  spanned 
by  a  shoe,  in  which  case  a  third  layer  of  b^ams  or  a  short  riveted 
girder  or  bolster  is  placed  under  the  column. 

When  steel  beam  footings  were  first  used,  rails  were  employed 
for  the  beams  on  account  of  their  lesser  cost,  and  they  were  built 
up  in  five  or  six  layers,  but  now  that  steel  beams  are  so  cheap  it 
is  much  better  to  use  I-beams  for  the  grillage  and  to  build  the 
grillage  in  not  more  than  two  layers,  \yhen  the  upper  layer  is 
composed  of  several  beams,  the  author  believes  that,  owing  to 
the  bending  of  the  beams  in  the  lower  layer,  a  greater  strain  is 


SPREAD  FOUNDATIONS. 


163 


Stone 
Footing 


d 


d 


PLAN 


brought  on  the  two  outer  beams  of  the  upper  layer  than  on  the 
beams  between,  and  that  it  is  impossible  to  determine  the 
amount  of  this  extra  stress.  For  this  reason  the  Author  is 
strongly  of  the  opinion  that  it  is  better  engineering  to  use  but 
two  beams  in  the  upper 
course  of  a  pier  footing,  or  a 
if  sufficiently  large  beams 
cannot  be  obtained,  a 
single  riveted  girder.  , 

In  preparing  the  foot- 
ings, the  ground  is  first 
carefully  leveled  and  the 
bottom  of  the  pier  loca- 
ted .  If  the  ground  is  not 
compact  enough  to  per-  ^ 
mit  of  excavating  for  the 
concrete  bed  without  the 
sides  of  the  pit  or  trench 
falling  in,  heavy  planks  a 
or  timbers  should  be  set 
up  and  fastened  together 
at  the  corners,  and,  if 
necessary,  tied  between 
with  rods,to  hold  the  con- 
crete in  place  and  prevent 
its  spreading  before  it  has 
thoroughly  set.  A  layer 
of  Portland  cement  con- 
crete, made  in  the  propor- 
tion of  1  to  6;  and  from  6  to  12  inches  thick,  according  to  the 
weight  on  the  footings,  should  then  be  filled  in  between  the  tim- 
bers and  well  rammed  and  leveled  off.  If  the  concrete  is  to  be 
12  inches  thick  it  should  be  deposited  in  two  layers.  Upon  this 
concrete  the  beams  should  be  carefully  bedded  in  1  to  2  Portland 
cement  mortar,  so  as  to  bring  them  nearly  level  and  in  line  with 
each  other. 

The  distance  apart  of  the  beams,  from  centre  to  centre,  must 
not  be  so  great  that  the  beams  will  crush  through  the  concrete, 
and  on  the  other  hand  there  must  be  a  space  of  at  least  2  inches 
between  the  edges  of  flanges  to  permit  the  introduction  of  the 
concrete  filling.  As  soon  as  the  beams  are  in  place  the  spaces 
between  them  should  be  filled  with  1  to  6  concrete,  the  stone 


SECTION 
Fig.  9. 


164  SPREAD  FOUNDATIONS. 

being  broken  to  pass  through  a  1  J-inch  ring,  and  the  concrete  well 
rammed  into  place,  so  that  no  cavities  will  be  left  in  the  centre. 
The  concrete  must  also  be  carried  at  least  3  inches  beyond  the 
beams  on  sides  and  ends,  and  kept  in  place  b}^  planks  or  timbers. 

If  two  or  more  layers  of  beams  are  used,  the  top  of  each  layer 
should  be  carefully  leveled  (after  the  concrete  has  been  put  in 
place)  with  1  to  2  Portland  cement  mortar,  not  more  than  \  inch 
thick  over  the  highest  beams,  and  in  this  the  next  layer  of  beams 
should  be  bedded,  and  so  on. 

The  stone  or  metal  base  plate  or  footing  should  also  be  bedded 
in  Portland  cement  mortar,  not  more  than  f  inch  thick,  above 
the  upper  tier  of  beams. 

After  the  base  plate  or  stone  footing  is  in  place  at  least  3 
inches  of  concrete  should  be  laid  above  the  beams  and  at  the 
sides  and  ends,  and  when  this  is  set  the  whole  outside  of  the  foot- 
ings should  be  plastered  with  1  to  2  Portland  cement  mortar. 

Before  the  beams  are  laid  they  should  be  thoroughly  cleaned 
with  wire  brushes,  and,  while  absolutely  dry,  either  painted  with 
iron  paint  or  else  heated  and  coated  with  two  coats  of  asphalt. 
Before  covering  the  beams  with  the  concrete  every  portion  of  the 
metal  should  be  carefully  examined,  and  wherever  the  paint  or 
asphaltum  has  been  scraped  off  in  handling  the  iron  should  be 
thoroughly  dried  and  the  coating  renewed. 

Every  pains  should  be  taken  to  protect  the  beams  from  rust- 
ing for,  when  unprotected,  steel  beams  rust  very  quickly,  and  if 
once  the  beams  were  subjected  to  the  rusting  process  it  would 
probably  not  be  long  before  the  building  commenced  to  settle.* 

Calculations  for  the  Size  of  the  Steel  Beams. 

A.  Beams  under  a  wall. — In  determining  the  size  of  steel 
beams  to  be  placed  under  a  wall,  as  in  Fig.  8,  the  first  step  is  to 
determine  the  necessary  width  of  the  footing,  which  determines 
the  length  of  the  beams,  and  then  the  projection  P  may  be  fixed. 
The  size  of  the  beams  depends  upon  the  projection  P  and  the 
load  to  be  supported. 

The  width  of  the  footing  is  obtained  by  dividing  the  load  per 
lineal  foot  on  the  footing,  by  the  safe  resistance  of  the  soil  per 
square  foot.  This  also  gives  the  length  of  the  beams. 

*  Several  engineers  advocate  placing  the  beams  without  paint,  believing 
that  concrete  is  itself  a  better  preservative  than  paint.  The  New  York  Build- 
ing Code  requires  that  the  beams  be  painted,  while  the  Chicago  law  does  not 


SPREAD  FOUNDATIONS.  165 

Knowing  the  length  of  the  beams,  the  width  of  the  masonry 
footing  may  be  decided  upon.  The  wider  the  stone  footing,  or 
the  smaller  the  projection  P,  the  less  will  be  the  transverse  strain 
on  the  beams. 

The  beams  are  computed  only  for  the  portion  projecting  be- 
yond the  stone  footing,  as  the  load  on  the  beams  directly  under 
the  wall  produces  no  transverse  strain. 

The  beams  are  computed  as  if  they  resisted  an  upward  pres- 
sure of  the  ground,  L  as  if  they  were  supported  as  in  Fig.  10  and 


Distributed  Load  =w  Tons  per  Square  Foot 

'•""•  '':%»^^ 

Beam 


^  Footing  or  Plate 


Fig.  10. 

loaded  with  a  distributed  load  equal,  per  square  foot,  to  the  safe 
resistance  of  the  soil. 

The  formula  for  a  beam  loaded  and  supported  in  this  way  is 
that  for  a  beam  fixed  at  one  end  and  uniformly  loaded  over  its 
projection.  The  readiest  method  of  computing  the  size  of  steel 
beams  thus  loaded  and  supported  is  to  determine  the  necessary 
coefficient  of  strength  for  each  beam,  and  then  from  the  tables 
giving  the  strength  of  steel  beams,  find  the  size  of  beam  having  a 
coefficient  equal  to  or  next  above  the  value  determined.  The 
coefficient  of  strength  is  given  in  the  tables  in  Chapter  XV,  in  the 
column  headed  C. 

The  necessary  coefficient  for  the  beams  is  found  by  the  for- 
mula 

(1) 


in  which  w  represents  the  assumed  bearing  power  of  the  soil  in 
tons  per  square  foot,  P  the  projection  of  the  beam  in  feet,  and 
s  the  spacing  or  distance,  centre  to  centre,  of  beams,  also  in  feet. 
X  denotes  multiplication. 

Owing  to  the  tendency  of  the  beams,  in  bending,  to  concen- 
trate the  load  on  the  outer  edges  of  the  masonry  footing,  and  thus 


166  SPREAD  FOUNDATIONS. 

crush  them,  which  action  would  have  the  same  effect  on  the  beam 
as  lengthening  the  arm  or  projection,  the  author  recommends 
that  when  the  course  above  the  beams  is  of  stone,  brick,  or  con- 
crete, at  least  one-third  the  width  of  the  masonry  footing  be  added 
to  the  actual  projection. 

In  determining  the  width  of  the  footing,  or  the  area  of  a  pier 
footing,  the  loads  from  the  building  should  be  computed  as  de- 
scribed on  page  139.  The  calculations  above  indicated  will  be 
more  clearly  shown  by  the  following  example : 

Example  of  Wall  Footings. — A  building  is  to  be  erected  on 
a  soil  of  which  the  safe  bearing  power  is  but  2  tons,  and  the 
pressure  on  each  lineal  foot  of  the  stone  footing  is  20  tons.  It  is 
decided  to  build  the  footings  as  shown  in  Fig.  8.  What  should 
be  the  dimensions  and  weight  of  the  beams? 

Answer. — As  the  total  pressure  under  each  lineal  foot  of 
wall  is  20  tons,  and  the  safe  bearing  power  of  the  soil  is  2  tons,  the 
footings  must  be  20^2,  or  10  feet  wide.  We  will  use  4-foot 
granite  blocks  for  the  bottom  course  of  the  wall,  which  will  give 
an  actual  projection  (P)  of  3  feet  for  the  beams.  For  making 
the  calculations  we  will  add  to  the  actual  projection  one-third  of 
4  feet  or  16  inches,  making  the  value  of  P  4  J  feet.  We  will  assume 
1  foot  for  the  spacing  of  the  beams,  so  that  s  will  equal  1 .  The 
beams  must  then  have  a  coefficient  of  strength=4XwX-P2Xs= 
4X2X(4-J)2X1=150.22  tons.  Examining  the  table  giving  the 
strength  of  standard  steel  I-beams  (Chapter  XV)  we  find  that  a 
10-inch  35-pound  steel  beam  has  a  coefficient  of  156.2  tons,  and 
a  25-pound  beam  130.2  tons;  therefore  we  must  use  35-pound 
steel  beams  10  feet  long.  If  we  spaced  the  beams  10  inches  on 
centres,  s  would  equal  f  and  C  would  equal  4X2X  (4J)2X  I,  or 
125.1  tons,  which  would  enable  us  to  use  25-pound  beams,  thereby 
effecting  a  saving  of  50  pounds  to  the  lineal  foot  of  wall. 

To  save  making  the  above  calculations  in  each  case  the  Car- 
negie Steel  Company,  Limited,  publishes  the  following  table 
from  which  the  size  of  the  beams  may  be  taken  direct. 

To  apply  the  table,  look  down  the  column  having  a  heading 
equal  to  the  resistance  of  the  soil,  and  take  the  beam  opposite 
the  number  equal  to,  or  just  above,  the  projection  of  the  beam. 

Thus  in  the  above  example  w=2  and  the  working  projection 
is  4.33.  The  nearest  projection  above  4.33  (in  the  column 
headed  2,  Table  IV)  is  4.90,  which  is  opposite  a  12-inch  31.5-lb. 
beam,  which  would  be  cheaper  than  the  10-inch  35-lb.  beam. 

To  use  the  table  for  other  values  of  s  than  1  foot,  w  should  be 


SPREAD  FOUNDATIONS, 


167 


TABLE  IV,  GIVING  SAFE  LENGTHS  OF  PROJECTIONS 
"P"  IN  FEET  (SEE  FIG.  8),  FOR  "s"  =  l  FOOT,  AND 
VALUES  OF  "w,"  RANGING  FROM  1  TO  5  TONS. 


>eam.  1 

Q 

w  (Tons  per  square  foot). 

Denth  of  I 

CD 

a 

.5? 
£ 

1 

* 

fe 

2 

* 

^ 

3 

* 

4 

* 

5 

In. 

24 

80.00 

15.231 

13.61 

12.43 

10.77 

10.16 

9.63 

8.79 

8.14 

7,62 

7.18 

6.81 

20 

80.00 

13.983 

12.50 

11.41 

9.89 

9.32 

8.84 

8.07 

7.47 

6.99 

6.59 

6.25 

20 
18 
15 

65.00 
55.00 
80.00 

12  4S8 
10.857 
11.892 

11.16 
9.71 
10.63 

10.20 
8.86 
9.71 

8.82 
7.68 
8.41 

8.33 
7.23 
7.93 

7.90 
6.87 
7.52 

7.21 
6.27 
6.86 

6.68 
5.80 
6.36 

6.24 
5.43 
5.95 

5.89 
5.12 
5.61 

5.58 
4.86 
5.32 

15 

60.00 

10.405 

9.30 

8.49 

7.36 

6.94 

6.58 

6.01 

5.56 

5.20 

4.90 

4.65 

15 

42.00 

8.861 

7.92 

7.23 

6.27 

5.91 

5.60 

5.12 

4.74 

4.43 

4.18 

3.96 

12 
10 

40.00 
31.50 
25.00 

7.730 
6.925 
5.706 

6.91 
6.19 
5.10 

6.31 
5.65 
4.66 

5.47 
4.90 
4.03 

5.15 
4.55 
3.80 

4.89 
4.38 
3.61 

4.46 
4.00 
3.29 

4.13 
3.70 
3.05 

3.87 
3.46 
2.85 

3.64 
3.26 
2.69 

3.46 
3.10 
2.55 

9 

8 

7 

31.00 
18.00 
15.00 

5.016 
4.354 
3.715 

4.48 
3.8C 
3.32 

4.09 
3.55 
3.03 

3.55 

3.08 
2.63 

3.34 
2.90 

2.48 

3.17 

2.75 
2.35 

2.90 
2.51 
2.14 

2.68 
2.33 
1.98 

2.51 
2.18 
1.86 

2.36 
2.05 
1.75 

2  24 
1.95 

1.66 

6 
5 

4 

12.25 
9.75 
7.50 

3.112 
2.539 
1.994 

2.78 
2.27 
1.78 

2.54 
2.07 
1.63 

2.20 
1.80 
1.41 

2.07 
1.69 
1.33 

1.97 
1.61 
1.26 

1.80 
1.47 
1.15 

1.66 
1.36 
1.07 

1.56 
1.27 
1.00 

1.47 
1.20 
0.94 

1.39 
1.14 
0.89 

increased  or  decreased  in  the  same  ratio  as  5.  Thus  if  &•=  1 J  ft. 
w  should  be  multiplied  by  1J.  Taking  s=10",  ^=2X|=lf. 
The  projection  under  1J  opposite  a  10-inch  25-lb.  beam  is  4.66, 
and  as  our  projection  was  4.33  it  is  evident  that  this  beam  would 
answer  for  a  spacing  of  10  ins. 

In  general,  however,  it  will  be  better  to  calculate  the  beams 
by  formula  (1). 

Beams  under  Piers. — In  this  case  the  size  of  the  lower  beams 
is  determined  in  the  same  way  as  if  under  a  wall,  the  length  of  P 
being  taken  from  the  end  of  the  beam  to  the  centre  of  the  outer 
beam  in  upper  tier. 

For  the  upper  beams  the  load  borne  by  each  beam  should  be 
computed  and  the  coefficient  of  strength  determined  by  the 
formula 

C=4XwXP (2) 

w  being  in  this  case  the  total  distributed  load  on  either  end  of 


168  SPREAD  FOUNDATIONS. 

the  beam  in  pounds,  and  P  the  distance  from  end  of  beam  to  the 
base-plate  above  in  feet. 

Example. — The  basement  columns  of  a  ten-story  building  are 
required  to  sustain  a  permanent  load  of  200  tons. 

What  should  be  the  size  of  the  beams  in  the  footings,  the  sup- 
porting power  of  the  soil  being  but  2  tons? 

Answer, — Dividing  the  load  by  the  bearing  power  of  the  soil 
we  have  100  square  feet,  or  10  X 10  feet,  for  the  area  of  the  foot- 
ing.  We  will  arrange  the  beams  as  shown  in  Fig.  9,  using  a  cast- 
iron  bearing-plate  3  feet  square  under  the  column  (instead  of  the 
stone  block  shown).  The  distance  between  the  centres  of  outer 
beams  in  upper  tier  we  will  make  32  ins.,  thus  making  the  value 

JLQ' 2'    g" 

of  P  for  the  lower  beams  = ^ ,  or  3f  ft.    ^  we  will  make 

12  ins.  or  1. 

Then  by  formula  1,  C=4X2X(3|)2  X  1  =  107.54  tons,  which 
is  a  little  less  than  the  coefficient  for  a  9-inch  25-lb.  beam.  As 
the  10-inch  25-lb.  beam  will  cost  no  more  and  will  be  stiffer  we 
should  use  that. 

For  the  upper  tier  we  will  use  five  beams,  spacing  them  8  in. 
on  centres.  From  an  inspection  of  the  plan  it  is  evident  that 
the  five  beams  must  support,  or  press  down,  an  area  equal  to 
abed,  which  in  this  case  equals  3}XlO  ft.,  or  35  sq.  ft.  As  the 
upward  reaction  is  2  tons  per  square  foot,  the  five  beams  must 
be  figured  to  support  70  tons  (2X35),  or  14  tons  each.  The 
projection  will  be  3J  ft.  Then  by  formula  2 ;— C=  4  X 14  X  3  J  =  196 
tons.  The  coefficient  for  a  12-inch  31J-lb.  beam  is  191.8,  and 
for  a  12-inch  40-lb.  beam  239.  As  it  is  well  to  use  heavy  beams 
for  the  outer  ones  we  will  use  two  12-inch  40-lb.  beams  and 
three  12-inch,  31i-lb.  beams  in  the  upper  tier. 

If  there  were  still  another  tier  of  beams  the  upper  one  would 
be  calculated  in  the  same  way. 

If  the  cap  is  of  stone,  the  value  of  P  should  be  taken  at  least 
6  ins,  greater  than  the  actual  projection,  to  allow  of  any  crushing 
of  the  stone  or  mortar. 

The  deepest  beam  for  the  weight  should  always  be  used,  and 
unless  the  beams  in  the  upper  tier  have  considerable  excess  of 
strength  the  two  outer  beams  should  be  heavy  beams. 

When  the  footings  carry  iron  or  steel  columns  in  the  basement, 
as  is  generally  the  case,  a  cast-iron  or  steel  base-plate  should  be 
used,  as  shown  in  Fig.  11.  This  plate  should  be  bedded  in  Port- 
land cement  directly  above  the  beams,  as  previously  described. 


SPREAD  FOUNDATIONS.  169 

In  placing  the  beams  it  is  essential  that  they  be  arranged  sym- 
metrically under  the  base-plate,  otherwise  they  will  sink  more 
at  one  side  than  at  the  other. 

Combined  Footings. — Two  columns  are  often  supported  on  one 
footing,  as  shown  in  Fig.  11,  and  quite  often  four  columns,  one 
near  each  corner.  The  computations  for  combined  footings 
are  more  complicated  than  for  simple  footings,  especially  when 
the  columns  are  unequally  loaded,  and  require  a  considerable 
knowledge  of  mechanics.  The  best  presentation  of  the  subject 
with  which  the  author  is  acquainted  is  in  Freitag's  Architectural 
Engineering,  second  edition. 

Description  of  Steel-beam  Footing's, — A  very  good 
idea  of  what  has  been  done  in  the  way  of  supporting  buildings 
on  spread  footings  of  steel  beams  and  girders,  and  of  the  various 
arrangements  that  have  been  employed,  may  be  obtained  from 
the  descriptions  of  actual  construction  referred  to  below: 

Surface  Foundations,  Engineering  Record,  July  2,  1898. 


Fig.  II. 

Foundations  of  High  Buildings,  by  W.  B.  Hutton,  Engineer- 
ing Record,  September  23,  1893. 

St.  Paul  Building,  New  York  City,  Engineering  Record,  June 
25,  1898. 

Harrison  Building,  Philadelphia,  Engineering  Record,  Aug.  22, 
1896. 

Franklin  Building  (9  to  15  Murray  Street),  New  York,  Engi- 
neering Record,  May  28,  1898. 

Buek  Building,  New  York  City,  25  ft.  front,  Engineering 
Record,  June  25,  1898. 


170 


SPREAD  FOUNDATIONS. 


Masonic  Temple,  Chicago,  Engineering  Record,  Aug.  13,  1898. 

De  Dino  Building,  New  York  City,  Engineering  Record,  Aug. 
13,  1898. 

The  Wilkes  Building,  New  York  City,  Engineering  Record, 
Juiia  7,  1890. 

American  Exchange  Bank,  New  York  City,  Engineering 
Record,  Oct.  14,  1899. 

Timber  Footing's. — For  buildings  of  moderate  height  tim- 
ber may  be  used  for  giving  the  necessary  spread  to  the  footings, 
provided  water  is  always  present.  The  footings  should  be  built  by 
covering  the  bottom  of  the  trenches,  which  should  be  perfectly 
level,  with  2-inch  plank  laid  close  together  and  longitudinally 
of  the  wall.  Across  these  heavy  timbers  should  be  laid,  spaced 
about  12  inches  from  centres,  the  size  of  the  timbers  being  pro- 
portioned to  the  transverse  strain.  On  top  of  these  timbers 
again  should  be  spiked  a  floor  of  3-inch  plank  of  the  same  width 
as  the  masonry  footings  which  are  laid  upon  it.  A  section  of 
such  a  footing  is  shown  in  Fig.  12. 

All  of  the  timber  work  must  be  kept  below  low-water  mark, 
and  the  space  between  the  transverse  timbers  should  be  filled  with 
sand,  broken  stone,  or  concrete.  The  best  woods  for  such  foun- 
dations are  oak,  Georgia  pine,  and  Norway  pine.  Many  of  the 
old  buildings  in  Chicago  rest  on  timber  footings. 


\2  inch  plank 

Fig.  12 

Calculation  for  the  Size  of  the  Cross  Timbers. — The  size  of  the 
transverse  timbers  should  be  computed  by  the  following  formula : 


Breadth  in  inches—- 


(3) 


w  representing  the  bearing  power  in  pounds  per  square  foot,  P 


SPREAD   FOUNDATIONS.  171 

the  projection  of  the  beam  beyond  the  3-inch  plank  in  feet,  s 
the  distance  between  centres  of  beams  in  feet,  and  D  the  as- 
sumed depth  of  the  beam  in  inches.  A  is  the  constant  for 
strength,  and  should  be  taken  at  90  for  Georgia  pine,  65  for  oak, 
60  for  Norway  pine,  and  55  for  common  white  pine  or  spruce. 

Example.  —  The  side  walls  of  a  given  building  impose  on  the 
foundation  a  pressure  of  20,000  pounds  per  lineal  foot;  the  soil 
will  only  support,  without  excessive  settlement,  2,000  pounds  to 
the  square  foot.  It  is  decided  for  economy  to  build  the  footings 
as  shown  in  Fig.  12,  using  Georgia  pine  timber.  What  should 
be  the  size  of  the  transverse  timbers? 

Answer.  —  Dividing  the  total  pressure  per  lineal  foot  by  2,000 
pounds,  we  have  10  feet  for  the  width  of  the  footings.  The  ma- 
sonry footing  we  will  make  of  granite  or  other  hard  stone,  4  feet 
wide,  and  solidly  bedded  on  the  plank  in  Portland-cement  mor- 
tar. The  projection  P  of  the  transverse  beams  would  then  be  3 
feet.  We  will  space  the  beams  12  inches  from  centres,  so  that 
s=l,  and  will  assume  10  inches  for  the  depth  of  the  beams. 

Then  by  formula   (3),  breadth  in  mches=2X21^.°      ^  =4, 


or  we  should  use  4//XlO//  timbers,  12  inches  from  centres.  If 
common  pine  timber  were  used  we  should  substitute  55  for  90, 
and  the  result  would  be  6J. 

Foundations  for  Temporary  Building's.  —  When 
temporary  buildings  are  to  be  built  over  a  compressible  soil,  the 
foundations  may,  as  a  rule,  be  constructed  more  cheaply  of  tim- 
ber than  of  any  other  material,  and  in  such  cases  the  durability 
of  the  timber  need  not  be  considered,  as  good  sound  lumber  will 
last  two  or  three  years  in  almost  any  place  if  thorough  ventila- 
tion is  provided. 

The  World's  Fair  buildings  at  Chicago  (1893)  were,  as  a  rule, 
supported  on  timber  platforms,  proportioned  so  that  the  maxi- 
mum load  on  the  soil  would  not  exceed  1J  tons  per  square  foot. 
Only  in  a  few  places  over  "  mud-holes"  were  pile  foundations 
used.* 

Masonry  Wells  for  Foundations.  —  Where  the  site 
of  the  building  is  composed  of  compressible  soil  overlaying  bed- 
rock or  hard-pan,  and  especially  where  the  site  has  been  filled 
or  the  conditions  are  not  suitable  for  piling,  wells  of  masonry 


*  A  description  of  the  foundations  of  these  buildings  may  be  found  in 
Part  I,  "Building  Construction  and  Superintendence,"  p.  55. 


172  SPREAD  FOUNDATIONS. 

sunk  to  the  bed-rock  or  hard-pan  will  generally  prove  as  cheap 
as  any  other  equally  good  foundation. 

The  wells  are  formed  by  driving  cylindrical  tubes  of  from  4  to 
6  ft.  in  diameter  through  the  soil  to  the  bearing  stratum.  The 
tubes  are  usually  made  in  short  lengths  and  spliced  as  they  are 
sunk.  After  the  tube  has  reached  the  firm  stratum,  it  is  exca- 
vated and  filled  with  brickwork  or  concrete,  the  masonry  being 
intended  to  support  the  weight,  while  the  steel  shell  merely 
forms  a  wall  around  the  pier  and  enables  it  to  be  built. 

The  wells  are  arranged  as  isolated  piers,  with  the  walls  of  the 
superstructure  supported  by  steel  girders  resting  on  the  piers. 

A  notable  example  of  this  type  of  foundation  is  that  of  the  City 
Hall  of  Kansas  City,  Mo.* 

Such  wells  were  also  used  under  the  new  Stock  Exchange  in 
Chicago.  .For  the  new  Stock  Exchange  Building  in  New  York 
wooden  cylinders  were  employed. 

Caisson  Foundations. — In  the  case  of  the  tall  buildings 
of  New  York  City,  which  as  a  rule^are  built  over  a  soil  composed 
of  mud  and  quicksand,  it  has  been  found,  in  many  cases,  impos- 
sible to  safely  support  the  building  on  the  natural  soil  and  cais- 
sons sunk  to  the  bed-rock  by  th§  pneumatic  process  have  been 
resorted  to  as  the  most  satisfactory  method  of  obtaining  a  foun- 
dation. 

Caissons  have  been  used  for  many  years  in  building  the  foun- 
dations of  bridges,  but  the  first  instance  of  their  use  for  buildings 
is  believed  to  be  in  the  foundations  of  the  Manhattan  Life  In- 
surance Company's  building,  New  York  City,  in  1893.  Since 
that  time  caissons  have  been  used  in  providing  the  foundation 
for  several  buildings  in  that  city.  Caissons  as  used  in  building 
foundations  are  made  both  cylindrical  and  rectangular  in  shape, 
and  they  have  been  built  both  of  wood  and  steel',  the  latter  ma- 
terial being  more  commonly  used.  Cylindrical  caissons  are  the 
most  convenient  and  economical,  but  the  positions  of  the  col- 
umns and  the  necessity  of  supporting  two  and  often  four  col- 
umns on  the  same  caisson  usually  make  it  necessary  to  use  rect- 
angular caissons.  •* 

The  size  of  the  caissons  vary  according  to  the  load  and  number 
of  columns  to  be  supported.  Caissons  as  small  as  5  ft.  in  diame- 
ter have  been  used,  although  from  8  to  10  ft.  is  a  more  common 

*  For  illustrations,  see  Part  I,  "Building  Construction  and  Superin- 
tendence." 


SPREAD  FOUNDATIONS.  173 

size  for  cylindrical  caissons.  Rectangular  caissons  have  been 
used  as  large  as  15JX25  ft.  in  plan.  The  usual  height  of  the 
caissons  that  have  thus  far  been  used  is  from  11  to  12  ft. 

The  caissons  are  sunk  until  they  reach  bed-rock  (which  lies 
from  50  to  60  feet  below  the  Broadway  street-level  in  New  York) ; 
the  surface  of  the  rock  is  then  cleaned  and  dressed  to  level  sur- 
faces and  the  caissons  rammed  full  of  concrete.  On  top  of  the 
caissons,  piers  of  hard-burned  bricks  are  built  to  the  proper 
height  to  receive  the  superstructure,  the  piers  being  generally 
built  as  the  caissons  descend,  so  that  the  top  of  the  masonry  will 
always  be  above  the  water-line.  The  weight  of  the  pier  assists 
in  sinking  the  caisson. 

"Although  this  process  is  costly,  it  has  proved  reliable  and 
applicable  under  the  most  troublesome  conditions  for  carrying 
masonry  piers  to  solid  rock  at  depths  as  great  as  100  feet  below 
the  water-line,  although  such  great  distances  have  not  yet  been 
required  for  buildings.  One  of  the  greatest  advantages  claimed 
for  this  method  is  the  care  and  precision  which  can  be  exercised 
in  preventing  the  inflow  of  quicksand  and  outside  materials  and 
thus  avoiding  any  disturbance  of  the  equilibrium  in  the  sur- 
rounding soils  or  settlements  of  adjacent  loaded  piers  or  the 
undermining  of  walls.  The  pneumatic  caisson  consists  of  a  steel 
or  wooden  box  with  vertical  sides  and  a  flat  top,  but  no  bottom. 
Its  lower  edges  are  provided  with  a  cutting  edge  and  it  is  made 
air-tight  and  filled  with  air  under  any  required  pressure,  which  is 
maintained  by  a  powerful  steam  pump.  Access  is  had  to  the 
interior  or  working  chamber  through  an  extensible  vertical  shaft 
in  the  roof  surmounted  by  a  small  chamber  or  air  lock  with  two 
doors,  the  outer  of  which  is  closed  whenever  the  inner  one  is 
opened  to  give  access  to  the  shaft.  As  both  doors  are  never 
opened  simultaneous!}^  no  direct  communication  is  established 
between  the  atmosphere  and  the  interior  air  pressure,  and  only  u 
small  quantity  of  compressed  air  is  lost  at  each  opening  of  the 
outside  door. 

Two  or  more  shafts  and  air  locks  are  usually  provided  for 
materials  and  for  the  workmen.  The  doors  of  the  material  lock 
are  successively  opened  and  closed  as  quickly  as  possible,  but  in 
the  man  lock  the  operation  is  a  gradual  one,  because  the  pressure 
in  the  lock  must  be  slowly  increased  or  diminished  to  avoid  inju« 
rious  effects  to  the  inmates.  The  men  in  the  working  chamber 
excavate  the  earth  underneath  it  and  undermine  its  edges  so  that 
it  gradually  sinks  under  the  increasing  load  of  the  brick  or  stone 


174  SPREAD  FOUNDATIONS. 

masonry  built  up  on  the  roof  or  heavy  deck  which  forms  the  top 
of  the  working  chamber.  The  excavated  material  is  hoisted  to 
the  surface  of  the  ground  either  in  buckets  through  the  material 
locks,  or,  when  it  is  loose  earth  or  mud,  is  blown  up  with  water 
through  vertical  pipes  open  on  top  and  having  their  lower  ends 
sealed  below  the  surface  of  the  water  in  the  interior  of  the  caisson. 
The  caissons  are  lighted  by  electricity  and  often  have  telephone 
communication  with  the  superintendent's  office  above.  Ex- 
cavation is  carried  on  by  pick  and  shovel,  and  when  necessary 
by  blasting  with  dynamite.  Except  at  considerable  depths 
the  men  work  the  usual  number  of  hours  without  experiencing 
much  evil  effects  from  the  increased  pressure."  * 

A  complete  description  of  the  foundation  of  the  Manhattan 
Life  Insurance  Building  (N.  Y.)  may  be  found  in  the  Engineer- 
ing Record  of  Jan.  20,  1894,  and  an  abstract  of  the  same  in 
"  Building  Construction  and  Superintendence,"  Part  I. 

Descriptions  of  other  caisson  foundations  may  be  found  in  the 
following  numbers  of  the  Engineering  Record,  also  in  Freitag's 
"  Architectural  Engineering." 

July  13,  1896,  American  Surety  Building,  New  York. 

July  11,  1896,  The  Standard  Block,  (N.  Y.). 

Jan.  16,  1897,  The  Gillender  Building  (N.  Y.),  timber  caisson. 

Nov.  27,  1897,  Five-foot  cylindrical  steel  caissons. 

Dec.  11,  1897,  Empire  Building  (N.  Y.) 

Dec.  10,  1898,  Residence  (N.  Y.)  cylindrical  wood  caissons. 

Oct.  28,  1898,  McCready  Building  (N.  Y.),  cylindrical  wood 
caissons. 

Sept.  28,  1901,  Stock  Exchange,  N.  Y.,  wood  caissons,  rec- 
tangular and  cylindrical. 

Cantilever  Foundations. 

When  buildings  of  skeleton  construction  are  erected  without 
a  party  wall  agreement,  it  is  usually  impossible  to  obtain  a  sym- 
metrical foundation  directly  under  the  columns  supporting  the 
side  or  party  wall,  and  in  such  cases  the  foundation  piers  are 
commonly  built  sufficiently  inside  of  the  wall  line  to  give  the 
necessary  spread  to  the  footings,  and  at  the  same  time  have  them 
symmetrical  with  regard  to  the  centre  of  pressure.  Cantilever 
girders  resting  on  these  piers  as  a  fulcrum  are  then  used  to 

*  Engineering  Record,  July  30,  1898. 


SPREAD  FOUNDATIONS. 


175 


carry  the  column  next  to  the  building  line.  By  this  method, 
also,  it  is  sometimes  possible  to  build  without  undermining  the 
adjoining  property. 

Various  arrangements  of  cantilevers  have  been  used  during 
the  past  ten  years,  the  particular  arrangement  being  usually 
determined  by  some  peculiarity  of  the  column  groupings,  or  rela- 
tion to  adjoining  building. 

Figs.  13,  14,  and  15  *  show  three  different  designs  which  illus- 
trate fairly  well  the  different  types  of  cantilevers  as  used  in 
foundations. 


s  tei 


Fig.  13. 


Fig.  13  shows  deep  steel  beams,  used  when  the  load  on  the 
column  resting  on  the  cantilever  produces  such  bending  mo- 
ments as  can  be  taken  up  by  the  beams.  In  this  type  the  long 
end  of  the  cantilever  is  connected  to  an  interior  column  by  means 
of  riveted  connections. 

Fig.  14  shows  a  method  of  cantilever  construction  where  it  is 
not  desirable  to  have  a  separate  foundation  under  each  column, 
and  a  heavy  box  girder  of  suitable  design  is  used  to  transmit  the 
various  column  loads  to  two  independent  foundations.  Owing 
to  danger  of  unequal  settlement  in  the  supporting  piers,  which 
would  affect  the  stresses  in  the  girder,  this  form  of  girder  should 
be  avoided  if  possible. 

Fig.  15  illustrates  one  of  the  latest  types  of  cantilever  founda- 
tions, in  which  the  objection  to  the  continuous  girder  is  over- 
come. 


*  From  the  "Pocket  Companion"  of  the  Carnegie  Pteel  Co.,  Limited,  by 
permission. 


176 


SPREAD   FOUNDATIONS. 


"An  important  feature  in  connection  with  cantilever  construc- 
tion is  to  adopt  a  pin  support  in.  place  of  resting  the  cantilever 


Fig.  14. 

beam  directly  on  the  top  course  of  the  foundation  beams.  For, 
if  the  cantilever  rests  directly  upon  the  upper  course  of  founda- 
tion beams,  without  a  pin  support,  the  outer  beam  nearest  the 
wall  column  will  be  strained  more  than  any  of  the  others,  and 


Fig.  15. 

thus  the  centre  of  pressure  will  not  be  exactly  in  the  middle  of 
the  foundation,  as  it  should  be. 

"The  shoes  for  ordinary  loads  and  conditions  are  made  solid 
of  cast  iron,  and  the  pin  of  steel. 

"  The  height  of  each  shoe  should  not  be  less  than  6  ins.  and  the 
•pin  2J  ins.  in  diameter.  Each  individual  case  should  be  figured 
by  itself,  the  pin  being  figured  for  bearing,  or  crushing  only. 

"A  clearance  of  J"  to  V  is  allowed  between  the  cast  shoes, 
which  are  always  faced,  and  the  hole  bored  to  suit  the  pin."  * 


*  F.  H.  Kindl,  C.E. 


SPREAD  FOUNDATIONS.  177 

Illustrated  descriptions  of  cantilever  foundations  may  be 
found  in  the  following  numbers  of  the  Engineering  Record : 

Cantilever  Foundations  for  Small  Buildings,  Nov.  27,  1897. 

Exchange  Court  Building,  New  York  City,  June  11,  1898. 

Developments  of  Architectural  Construction,  July  30,  1898. 

The  calculations  for  cantilever  foundations  involve  the  deter- 
mination of  bending  moment,  shearing,  and  bucking  in  the  girder 
and  the  reaction  on  the  fulcrum  and  at  the  long  end  of  the  girder. 

The  arrangements  are  so  numerous  that  no  special  rules  can  be 
given,  but  each  case  must  be  calculated  by  means  of  the  general 
principles  relating  to  the  strength  of  girders,  and  for  determining 
supporting  forces,  given  elsewhere  in  this  book, 

Concrete  Piles. — Since  the  year  1902  concrete  piles  have 
been  introduced  in  this  country,  and  for  several  years  previous 
they  had  been  used  to  some  extent  in  Europe.  The  practice  of 
French  and  German  engineers  has  been  to  construct  the  piles  on 
the  ground,  casting  them  in  a  mould  in  which  a  steel  skeleton 
for  reinforcement  is  first  inserted  and  also  a  steel  or  cast-iron 
shoe.  After  the  piles  have  hardened  a  sufficient  length  of  tune 
they  are  driven  like  timber  piles,  a  cushioned  cap  being  placed 
on  top  of  the  pile  to  distribute  the  force  of  the  blow  evenly  over 
the  concrete.* 

In  this  country  the  practice  thus  far  has  been  to  construct  the 
piles  in  place  by  driving  a  hollow  steel  cylinder  which  retains 
the  walls  of  the  hole  in  place  until  the  concrete  has  been  deposited 
and  rammed.  As  the  filling-in  of  the  concrete  progresses,  the 
shell  is  drawn  up,  the  lower  end  of  the  shell  being  always  about 
6  ins.  below  the  top  of  the  concrete.  If  desired,  a  reinforcing 
skeleton  can  be  placed  in  the  shell  before  the  concrete  is  poured, 
but  the  piles  are  very  strong  without  it. 

Thus  far  two  styles  of  shells  have  been  successfully  used,  viz., 
the  "Simplex,"  controlled  by  the  Simplex  Concrete  Piling  Co. 
of  Philadelphia,  and  the  Raymond  Pile,  controlled  by  the  Ray- 
mond Concrete  Pile  Co.  of  Chicago,  from  whom  complete  infor- 
mation as  to  cost,  carrying  capacity,  etc.,  may  be  obtained. 

Concrete  piles,  although  more  expensive  than  timber  piles, 
possess  many  advantages  over  the  latter,  and  can  be  used  in 
places  where  timber  piles  would  not  be  durable. 

They  are  capped  with  concrete  or  steel  grillage  in  the  same 
manner  as  described  for  timber  piles. 

*  For  description  of  several  types  of  cast  piles,  see  the  Engineering  News 
of  March  10,  1904. 


178  MASONRY   WALLS  AND  FOOTINGS, 


CHAPTER  III. 
MASONRY  WALLS  AND  FOOTINGS. 

CEMENTS  AND  CONCRETES. 

Footing  Courses. — Every  foundation  or  bearing  wall 
overlaying  anything  except  solid  rock  should  rest  on  a  footing  or 
base  projecting  beyond  the  wall  on  each  side.  On  wet  or  com- 
pressible soils  these  footings  may  be  built  of  steel  beams  and 
concrete,  concrete  and  twisted  iron,  or  timbers,  as  described  in 
Chapter  II,  but  on  firm  soils  the  footings  are  almost  invariably 
either  of  concrete,  stone,  or  brick. 

Footings  answer  two  important  purposes : 

1st.  By  distributing  the  weight  of  the  structure  over  a  larger 
area  of  bearing  surface,  the  pressure  per  square  foot  on  the 
ground  is  diminished  and  the  liability  to  vertical  settlement 
correspondingly  lessened. 

2d.  By  increasing  the  area  of  the  base  of  the  wall  they  add 
to  its  stability  and  form  a  protection  against  the  danger  of  the 
work  being  thrown  out  of  plumb  by  any  forces  that  may  act 
against  it.  Nearly  every  building  law  requires  that  every  foun- 
dation wall  and  every  pier  shall  have  a  footing  at  least  12  inches 
wider  (6  ins.  on  each  side)  than  the  thickness  of  the  wall  or  pier, 
and  this  may  be  considered  as  the  minimum  projection,  except 
in  rare  instances  where  there  may  be  a  special  reason  for  making 
it  less.  On  firm  soils  a  projection  of  6  ins.  on  each  side  of  the 
wall  will  generally  reduce  the  unit  pressure  *  to  a  point  within 
the  safe  resistance  of  the  soil,  but  it  is  always  wise  to  propor- 
tion the  footings  to  a  uniform  unit  pressure,  as  explained  on 
pages  137-139. 

To  have  any  useful  effect,  footings  must  be  well  bedded  and 
have  sufficient  transverse  strength  to  resist  the  upward  reaction 
on  the  projection. 

Stone  Footings. — Stone  foundation  walls  generally  have 
stone  footings,  although  if  the  wall  is  heavily  loaded  a  bottom 

*  Pressure  per  square  foot. 


MASONRY  WALLS  AND  FOOTINGS.  179 

footing  of  concrete  is  advisable  under  the  stone  footing  If 
practicable,  stone  footings  should  consist  of  stones  having  a 
width  equal  to  that  of  the  footing.  If  impracticable  to  obtain 
stones  of  this  size,  then  two  stones  should  be  used,  meeting  under 
the  centre  of  the  wall.  In  any  event  the  footing  courses  should 
extend  inside  of  the  course  above,  a  distance  equal  to  at  least 
1J  times  the  projection,  otherwise  the  stones  will  not  be  able 
to  transmit  the  necessary  pressure,  but  will  open  at  the  joints 
as  in  Fig.  1. 

Stone  footings  should  be  of  hard,  strong,  and  durable  stone, 
always  laid  on  their  natural  bed 
and  be  solidly  bedded  in  mortar. 
As  a  general  rule,  the  thickness  of 
each  course  should  be  about  equal 
to  its  projection  beyond  the  course 
above.  The  most  common  defect 

[•      ____•  I  in  large  stone  footings   is  that  the 

i  stones  are  not  properly  bedded,  it 


J  /^/  being  more  difficult  to  bed  a  large 


— '   stone    than     a     small     one.      The 
9'  ''  stones  should  be  laid  in  a  thick  bed 

of  mortar  and  worked  with  a  bar  sideways  until  firmly  settled 
into  the  mortar. 

Offsets. — The  projection  of  the  footings  beyond  the  wall,  or 
the  course  above,  is  a  point  that  must  be 
carefully    considered,    whatever    be    the 
material  of  the  footings. 

If  the  projection  of  the  footing  or  offset  ^, 

of  the  courses  is  too  great  for  the  strength      „ A  I    . 

of  the  stone,  brick,  or  concrete,  the  footing — - — V — ' — i 

will  crack,  as  shown  in  Fig.  2.  T  I 

The  proper  offset  for  each  course  will  p'     •> 

depend   upon   the   vertical   pressure,    the 

transverse  strength  of  the  material,  and  the  thickness  of  the 
course.  Each  footing  stone  may  be  considered  as  a  beam  fixed 
at  one  end  and  uniformly  loaded,  and  in  this  way  the  safe  pro- 
jection may  be  calculated. 

Table  I  gives  the  safe  offset  for  masonry  footing  courses,  in 
terms  of  the  thickness  of  the  course,  computed  by  a  factor  of  safety 
of  10. 

It  should  be  borne  in  mind  that  as  each  footing  course  trans- 
mits the  entire  weight  of  the  wall  and  its  load,  the  pressure  will 


180  MASONRY  WALLS  AND    FOOTINGS. 

TABLE  I. 


Kind  of  footing. 

K.  in 
Ibs.  per 
sq.  in.* 

2700 
1800 
1500 
1200 
5400 
1200 

I    150 
(      80 

Offset  for  a  pressure,  in  tons  per 
sq.  ft.  on  the  bottom  of  the  course,  of 

0.5 

3.6 
2.9 
2.7 
2.6 
5.0 
2.6 

0.8 
0.6 

1 

o 

3 

5 

10 

Bluestone  flagging  
Granite  
I>iniestone 

2.6 
2.1 
1.9 
1.8 
3.6 
1.8 

0.6 
0.4 

1.8 
1.5 
1.3 
1.3 
2.5 
1.3 

0.4 
0.3 

1.5 
1.2 
1.1 
1.0 
2.2 
1.0 

1.2 
1 
.9 

.8 
1.5 
.8 

.8 
.7 
.6 
.5 
1.2 
.5 

Sandstone.  .           

Slate  

Best  hard  brick  .... 
I  1  Portland  
Concrete-^  2  sand 

(  3  pebbles.  .  .  . 

(  1  Rosendale.  .  . 
Concrete^  2  sand  
(  3  pebbles 

*  Modulus  of  Rupture,  values  given  by  Prof.  Baker  in  *'  Treatise  on 
Masonry  Construction." 

be  greater  per  square  foot  on  the  upper  courses,  and  the  offsets 
should  be  made  proportionately  less. 

Concrete  Footings. — For  all  buildings  of  any  great  weight, 
and  especially  if  built  on  a  clay  soil,  the  author  believes  that  ce- 
'  ment  concrete  makes  the  best  footing,  and  that  it  is  even  prefer- 
able to  and  generally  cheaper  than  large  slabs  of  stone.  When 
the  concrete  is  properly  made  and  used,  it  attains  a  strength 
equal  to  that  of  most  stones,  and  being  devoid  of  joints,  it  is  like 
a  continuous  beam,  having  sufficient  strength  to  span  any  soft 
spots  that  might  happen  to  be  in  the  foundation.  When  de- 
posited in  thin  layers  and  well  rammed  the  concrete  also  be- 
comes firmly  bedded  on  the  bottom  of  the  trenches,  so  that  there 
is  no  possible  chance  for  settlement  except  that  due  to  the  com- 
pression of  the  soil. 

For  footings,  concrete  should  always  be  mixed  with  cement, 
preferably  Portland  cement,  and  should  have  a  thickness  of  at 
least  8  ins.,  even  under  light  buildings,  and  for  buildings  of  more 
than  two  stories,  a  thickness  of  at  least  12  ins.  In  firm  soils,  such 
as  clay,  the  trenches  should  be  accurately  dug  and  trimmed  to 
the  exact  width  of  the  footing,  so  that  the  concrete  will  fill  the 
trench.  When  the  soil  is  of  loose  gravel  or  sand  it  is  generally 
necessary  to  set  up  planks  to  confine  the  concrete  and  form  the 
sides  of  the  footings.  These  planks  may  be  held  in  place  by 
stakes;  they  should  be  left  in  place  until  the  concrete  has 
become  bard,  which  generally  requires  from  two  to  four  days, 


MASONRY  WALLS  AND  FOOTINGS. 


181 


after  which  they  may  be  pulled  up  and  dirt  filled  in  against  the 
concrete. 

The  proportions  and  manner  of  mixing  concrete  are  described 
in  the  latter  part  of  this  chapter. 

Concrete  should  be  used  as  soon  as  mixed  and  should  always 
be  deposited  in  layers,  which  as  a  rule  should  not  exceed  6  ins. 
in  thickness,  especially  for  the  first  layer.  On  small  jobs  where 
the  work  is  done  by  hand  the  concrete  is  usually  carried  to  the 
trenches  in  wheel-barrows  and  dumped  into  the  trench.  The 
height  from  which  the  concrete  is  dumped,  however,  should  not 
exceed  4  feet  above  the  bottom  of  the  trench,  as  when  falling 
from  a  greater  height  the  heavy  particles  are  apt  to  separate  from 
the  lighter  ones. 

i  As  soon  as  the  concrete  has  been  deposited  in  the  trench,  it 
should  be  levelled  off  and  then  tamped  with  a  wooden  rammer 
I  weighing  about  20  Ibs.,  until  the  water  in  the  concrete  is 
'brought  to  the  surface.  Concrete  should  not  be  permitted  to 
dry  too  quickly,  and  if  twenty-four  hours  elapse  between  de- 
positing the  successive  layers,  the  top  of  each  layer  should  be 
sprinkled  before  the  next  is  deposited. 

For  buildings  over  five  stories  high,  it  is  a  good  idea  to  place  a 
stone  footing  above  the  concrete  footing,  if  suitable  stones  for  the 
purpose  can  be  obtained. 

Brick  Footings. — Where  the  foundation  walls  are  of  brick, 
the  footings  are  usually  either  of  brick  or  concrete.  For  interior 


j  BRLCK 


11  BRICK 


Fig.  3 


Fig.  4 


walls  on  dry  ground,  and  in  many  localities  for  outside  walls, 
brick  footings  are  fully  as  good  as  stone  footings,  provided  good 
hard  bricks  are  used  and  the  footings  are  properly  built. 

Brick  footings  should  always  start  with  a  double  course  and 
then  be  laid  in  single  course  for  ordinary  footings,  the  outside 


182 


MASONRY  WALLS  AND  FOOTINGS. 


of  the  work  being  laid  all  headers,  as  in  the  accompanying  illus- 
trations, and  no  course  projecting  more  than  one  fourth  brick 
beyond  the  one  above  it,  except  in  the  case  of  an  8-  or  9-inch  wall. 
For  brick  footings  under  high  or  heavily  loaded  walls,  each  pro- 
jecting course  should  be  made  double,  the  heading  course  above 
and  the  stretching  course  below.  Figs.  3,  4,  5,  and  6  show  foot- 
ings for  walls  varying  from  one  brick  to  three  bricks  in  thickness. 


2  BRICKS 


Fig.  5 

The  bricks  used  for  footings  should  be  the  hardest  and  sound- 
est that  can  be  obtained,  and  should  be  laid  in  cement  or  hy- 
draulic lime  mortar,  either  grouted  or  thoroughly  slushed  up,  so 
that  every  joint  shall  be  entirely  filled  with  mortar.  The  writer 
favors  grouting  brick  footings,  that  is,  using  thin  mortar  for 


3  BRICKS 


Fig.  6 

filling  the  inside  joints,  as  he  has  always  found  it  to  give  very 
satisfactory  results. 

The  bottom  course  of  the  footing  should  always  be  laid  in  a  bed 
of  mortar  spread  on  the  bottom  of  the  trench,  after  the  latter 


MASONRY  WALLS  AND  FOOTINGS.  183 

has  been  carefully  levelled.  All  bricks  laid  in  warm  or  dry 
weather  should  be  thoroughly  wet  before  laying,  for,  if  laid  dry, 
the  bricks  will  rob  the  mortar  of  a  large  percentage  of  the  moist- 
ure it  contains,  greatly  weakening  the  adhesion  and  strength  of 
the  mortar. 

Too  much  care  cannot  be  bestowed  upon  the  footing  courses 
of  any  building,  as  upon  them  depends  much  of  the  stability  of 
the  work.  If  the  bottom  courses  be  not  solidly  bedded,  if  any 
rents  or  vacuities  are  left  in  the  beds  of  the  masonry,  or  if  the 
materials  themselves  be  unsound,  or  badly  put  together,  the 
effects  of  such  carelessness  are  sure  to  show  themselves  sooner  or 
later,  and  almost  always  at  a  period  when  remedial  efforts  are 
difficult  and  expensive. 

Inverted  Arches. — When  the  external  walls  of  a  building 
are  divided  into  piers,  with  wide  openings  between,  and  the  sup- 
porting power  of  the  soil  is  not  more  than  two  or  three  tons  to  the 
square  foot  it  may  be  desirable  to  connect  the  base  of  the  piers 
by  means  of  inverted  arches,  for  the  purpose  of  distributing  the 
weight  of  the  piers  over  the  whole  length  of  the  footings. 

Examples  of  inverted  arch  footings  are  shown  by  figures  7  and 
8,*  which  represent  respectively  the  construction  employed  in 
the  Drexel  Building  in  Philadelphia  and  the  World  Building  in 
New  York. 

Unless  the  piers  are  about  equally  loaded,  however,  it  will  be 
difficult  to  distribute  the  weight  evenly,  and  if  the  arches  extend 
to  an  angle  of  the  building,  the  end  arch  must  be  provided  with 
ties  of  sufficient  strength  to  resist  the  thrust  of  the  arch,  other- 
wise it  may  push  out  the  corner  pier.  In  the  opinion  of  the 
author,  it  is  usually  better  to  build  the  piers  with  separate  foot- 
ings, projecting  equally  on  all  four  sides  of  the  pier,  and  each  pro- 
portioned to  the  load  supported.  The  intermediate  wall  may 
be  supported  either  by  steel  beams  or  arches  as  preferred.  An 
example  showing  the  method  of  proportioning  inverted  arches  is 
given  in  Chapter  III.  of  Part  I.,  "Building  Construction." 

Foundation  Walls. 

This  term  is  generally  applied  to  those  walls  which  are  below 
the  surface  of  the  ground,  and  which  support  the  superstructure. 
Walls  whose  chief  office  is  to  withhold  a  bank  of  earth,  such  as 
around  areas,  are  called  retaining  walls. 

*  From  the?  Engineering  Record  of  May,  1893,  and  Nov.,  1890. 


184 


MASONRY  WALLS   AND   FOOTINGS. 


Foundation  walls  may  be  built  of  brick;  stone  or  concrete,  the 
former  being  the  most  common.  Brick  walls  for  foundations  are 
only  suitable  in  very  dry  soils  or  in  the  case  of  party  walls,  where 
there  is  a  cellar  or  basement  on  each  side  of  them. 

Portland  cement  concrete  is  an  excellent  material  for  founda- 
tion walls,  and  is  being  more  extensively  used  for  that  purpose 


Colum: 


Fig.  7 


Fig.  8 


every  year.  The  concrete  may  be  filled  in  between  wooden 
forms,  which  hold  it  in  place  until  the  cement  has  set,  or  concrete 
blocks  moulded  so  as  to  form  a  solid  wall  may  be  used. 

If  poured  concrete  is  used  the  forms  should  be  removed  as  soon 
as  the  cement  has  set  and  the  walls  sprinkled  once  or  twice  a  day, 
if  the  weather  is  dry,  so  that  the  concrete  will  not  dry  too  quickly. 

Good  hard  ledge  stone,  especially  if  it  comes  from  the  quarry 
with  flat  beds,  not  only  makes  a  strong  wall  but  if  well  built,  one 
that  will  stand  the  effects  of  moisture  and  the  pressure  of  the 
earth  much  better  than  a  brick  wall.  As  between  a  good  stone 
wall  and  a  wall  of  Portland  cement  concrete,  there  is  probably 
not  much  choice,  except  perhaps  in  the  matter  of  expense,  the 
relative  cost  of  stone  work  and  concrete  varying  in  different 
localities.  A  wall  built  of  soft  stone,  or  stone  that  is  very  irreg- 
ular in  shape,  with  no  flat  surfaces,  is  greatly  inferior  to  a  con- 
crete wall,  or  even  to  a  wall  of  good  hard  brick,  and  should  be  used 
only  for  dwellings  or  light  buildings.  Stone  walls  should  never 
be  less  than  18  ins.  thick,  and  should  be  well  bonded,  with  full  and 
three  quarter  headers,  and  all  spaces  between  the  stones 
filled  solid  with  mortar  and  broken  stone  or  spauls. 


MASONRY  WALLS  AND  FOOTINGS. 


185 


The  mortar  for  stone  work  should  be  made  of  hydraulic  lime 
or  cement ,  and  sharp  and  rather  coarse  sand. 

The  outside  walls  of  cellars  and  basements  should  be  plastered 
smooth  on  the  outside  with  1  to  2,  or  1  to  I J  cement  mortar, 
J  inch  to  f  inches  thick. 

In  heavy  clay  soils  it  is  a  good  idea  to  batter  the  walls  on  the 
outside,  making  the  wall  from  6  ins.  to  a  foot  thicker  at  the  bot- 
tom than  at  the  top. 

The  thickness  of  the  foundation  wall  is  usually  governed  by 
that  of  the  walls  above,  and  also  by  the  depth  of  the  wall. 

Nearly  all  building  regulations  require  that  the  thickness  of 
the  foundation  wail,  to  the  depth  of  12  ft.  below  the  grade  line, 
shall  be  4  ins.  greater  than  the  wall  above  for  brick  and  8  ins.  for 
stone,  and  for  every  additional  10  ft.,  or  part  thereof  deeper,  the 
thickness  shall  be  increased  4  ins.  In  all  large  cities  the  thick- 
ness of  the  walls  is  controlled  by  law.  For  buildings  where  the 
thickness  is  not  so  governed  the  following  table  will  serve  as  a 
fair  guide : 

TABLE  II.— THICKNESS  FOR  FOUNDATION  WALLS. 


Height  of  building. 

Dwellings,  Hotels, 
etc. 

Warehouses. 

Brick. 

Stone. 

Brick. 

Stone. 

Two  stories 

Inches. 
12  or  16 
16 
20 
24 
28 

Inches. 
20 
20 
24 
28 
32 

Inches. 
16 

20 

24 
24 
28 

Inches. 

20 
24 

28 
28 
32 

Three  stories  

Four  stories 

Five  stories.  .  .  . 

Six  stories  

Brick  and  Stone  Walls. — Very  little  is  known  regarding 
the  stability  of  walls  of  buildings  beyond  what  has  been  gained 
by  practical  experience.  The  only  strain  which  comes  upon  any 
horizontal  section  of  such  a  wall,  which  can  be  ascertained,  is 
the  direct  weight  of  the  wall  above,  and  the  pressure  due  to  the 
floors  and  roof. 

In  most  walls,  however,  there  is  more  or  less  tendency  to 
buckle,  to  overcome  which  it  is  necessary  to  make  the  walls 
thicker  than  would  be  required  to  resist  the  direct  crushing  stress. 
The  resistance  to  fire  should  also  be  taken  into  account  in  de- 
ciding on  the  thickness  of  any  given  wall. 


186  MASONRY  WALLS  AND  FOOTINGS. 

The  strength  of  a  wall  also  depends  very  much  upon  the  qual- 
ity of  the  materials  used  and  upon  the  way  in  which  the  wall  is 
built. 

A  wall  bonded  every  twelve  inches  in  height,  and  with  every 
joint  slushed  full  with  good  rich  mortar,  will  be  as  strong  as  a 
poorly  built  wall  four  inches  thicker.  Walls  laid  with  cement 
mortar  are  also  much  stronger  than  those  laid  with  lime  mortar, 
and  a  brick  wall  built  with  bricks  that  have  been  well  wet  just 
before  laying  is  very  much  stronger  than  one  built  with  dry 
bricks. 

Thickness  of  External  Walls. — In  nearly  all  the  larger 
cities  of  the  country  the  minimum  thickness  of  the  walls  is  pre- 
scribed by  law  or  ordinance,  and  as  these  requirements  are  gen- 
erally ample  they  are  commonly  adhered  to  by  architects  when 
designing  brick  buildings.  Table  III.  gives  a  comparison  of  the 
thickness  of  brick  walls  required  for  mercantile  buildings  in  the 
representative  cities  of  the  different  sections  of  the  United  States, 
and  affords  about  as  good  a  guide  as  one  can  have  because  the 
values  given,  as  a  rule,  represent  the  judgment  of  well  qualified 
and  experienced  persons. 

Walls  for  dwellings  are  generally  permitted  to  be  4  ins.  less  in 
thickness  than  for  warehouses,  although  in  some  cities  little  or 
no  distinction  is  made  between  business  blocks  and  dwellings. 

Table  IV.  gives  the  thickness  required  for  the  brick  walls  of 
dwellings,  tenements,  hotels,  and  office  buildings  in  the  city  of 
Chicago,  which  is  as  light  as  such  walls  should  be  built.  Most 
cities  require  13-inch  walls  in  the  upper  story  of  three-story  build- 
ings, and  for  large  two-story  dwellings. 

In  St.  Louis  the  top  two  stories  of  dwellings  are  required  to 
be  13  ins.  thick,  the  next  two,  below,  18  ins.  thick,  the  next  two 
22  ins.,  and  the  next  two  26  ins. 

In  compiling  Table  III.  the  top  of  the  second  floor  was  taken 
at  19  ft.  above  the  sidewalk,  and  the  height  of  the  other  stories 
at  13  ft.  4  ins.,  including  the  thickness  of  the  floor,  as  the  New 
York  and  Boston  laws  give  the  height  of  the  walls  in  feet  instead 
of  in  stories.  When  the  height  of  stories  exceeds  these  measure- 
ments the  thickness  of  the  walls  in  some  cases  will  have  to  be 
increased. 

The  maximum  height  of  stories  permitted  by  the  Chicago 
ordinance  with  these  thicknesses  of  walls  is  18  ft.  in  first  story, 
15  ft.  in  second  story,  13  ft.  6  ins.  in  the  third,  and  12  ft.  in  the 
stories  above. 


MASONRY  WALLS  AND  FOOTINGS. 


187 


TABLE  III.— THICKNESS  OF  WALLS  IN  INCHES,  FOR 
MERCANTILE  BUILDINGS  AND  PUBLIC  STABLES, 
AND,  EXCEPT  IN  CHICAGO,  FOR  ALL  BUILDINGS 
OVER  FIVE  STORIES  IN  HEIGHT. 


Height  of 
Building. 

Stories. 

1st. 

2d. 

3d. 

4th. 

5th. 

6th. 

7th. 

8th. 

16 
16 
16 
12 
13 
17 
13 

i 

Two 

Stories. 

Three 

Stories. 

Four 
Stories. 

Five 

Stories. 

Six 
Stories. 

Seven       , 
Stories.    1 

Eight 
Stories. 

'Boston 

16 
12 
12 
12 
18 
13 
17 
13 

20 

16 
16 
16 
18 
17 
17 
13 

20 
16 
20 
16 
22 
21 
17 
18 

20 
20 
20 
20 
22 
21 
21 
18 

24 
24 
20 
20 
26 
26 
21 
22 

24 
28 
20 
20 
26 
26 
22 

28 
32 
24 
24 
30 
30 
22 

12 
12 
12 
12, 
13 
13 
13 
13 

16 
16 
12 
12 
18 
17 
17 
13 

16 
16 
16 
16 
18 
17 
17 
18 

20 
16 
20 
16 
22 
21 
17 
18 

20 
20 
20 
20 
22 
21 
21 
18 

20 
24 
20 
20 
26 
21 
22 

24 
28 
24 
20 
26 
26 
22 

16 
12 
12 
12 
13 
13 
13 
13 

16 
16 
16 
12 
18 
17 
17 
13 

20 
16 
16 
16 
18 
17 
17 
18 

20 
20 
20 
16 
22 
21 
17 
18 

20 
24 
20 
20 
22 
21 
18 

20 
24 
20 
20 
26 
21 
22 

16 
12 
12 
12 
13 
13 
13 
13 

20 
16 
16 
12 
18 
17 
17 
13 

20 
20 
16 
16 
18 
17 
17 
18 

20 
20 
20 
16 
22 
21 
18 

20 
24 
20 
20 
22 
21 
18 

16 
16 
16 
12 
13 
13 
13 
13 

20 
16 
16 
16 
18 
17 
17 
13 

20 
20 
16 
16 

18 
17 
18 

20 
20 
20 
16 

22 
21 
18 

16 
16 

16 
12 
13 
13 
13 
13 

20 
16 
16 
16 
18 
17 
13 

20 
20 
16 
16 
18 
17 
18 

16 
16 
16 
12 
13 
17 
13 

20 
16 
16 
16 
18 
17 
13 

New  York  

Chicago 

Minneapolis  

St   Louis.  . 

Denver  
San  Francisco.  .... 
New  Orleans 

'Boston 

New  York  

Chicago 

Minneapolis  

St.  Louis.  . 

Denver 

Sari  Francisco  
New  Orleans 

[Boston. 

New  York  
Chicago.  . 

Minneapolis  

St.  Louis  
Denver 

San  Francisco  
.New  Orleans  

rBoston.  .  . 

New  York  

Chicago.  . 

Minneapolis  

St.  Louis  
Denver  
San  Francisco  
[New  Orleans 

[Boston.  .  . 

New  York  

Chicago.  . 

Minneapolis 

St.  Louis  
Denver 

San  Francisco  
i^New  Orleans 

[Boston.  .  . 

New  York  

Chicago.  .        ... 

Minneapolis 

ISt.  Louis  

Denver.  . 

New  Orleans  
'Boston  

New  York 

Chicago  

Minneapolis. 

St.  Louis. 

Denver  

New  Orleans.  .  . 

188 


MASONRY  WALLS  AND  FOOTINGS. 


Height  of 
Building. 

Stories. 

£J 

T3* 
<M 

i 

A 

ji 

,d 

j=! 

A 

j 

,d 

A 

,c 

-t 

»o 

CO 

i^. 

20 
20 
16 
16 
18 
17 

20 
20 
20 
16 
22 
21 

20 
24 
20 
22 
21 

24 
24 
20 
26 
21 

00 

Oi 

o 

^ 

a 

f  Boston.  .  . 

28 
32 
24 
24 
30 
30 

28 
36 
28 
24 
31 
30 

36 
36 

28 
34 
30 

36 
40 
28 
34 
30 

24 
32 
24 
24 
30 
26 

28 
32 
28 
24 
30 
30 

32 
36 
28 
34 
30 

36 
36 
28 
34 
30 

24 
28 
24 
20 
26 
26 

24 
32 
24 
24 
30 
26 

32 
32 

24 
30 
26 

32 
36 
28 
34 
30 

20 
24 
20 
20 
26 
21 

24 

28 
24 
20 
26 
26 

28 
28 
24 
30 
26 

32 
32 
21 
30 

26 

20 
24 

20 
20 
22 
21 

20 
24 
24 
20 
26 
21 

28 
28 
24 
26 
26 

28 
32 
24 
30 
26 

20 
20 
20 
16 

22 
21 

20 
24 
20 
20 
22 
21 

24 
24 
20 
26 
21 

28 
28 
24 
26 
26 

20 
16 
16 
16 
18 
17 

20 
20 
20 
16 
IS 
17 

20 
20 
20 
22 
21 

20 
24 
20 

22 
21 

16 
16 
16 
12 
13 
17 

20 
16 
16 
1.6 
18 
17 

20 
20 
16 
18 
17 

20 
20 
20 
22 
21 

16 
16 
16 
12 
13 
17 

20 
16 
16 
18 
17 

20 
20 
16 
18 
17 

16 
16 
16 
13 
17 

20 
16 
16 
18 
17 

16 
16 
16 
13 
17 

(New  York... 
Nine       j  Chicago  
Stories.     )  Minneapolis  . 
St.  Louis.  ..  . 
I.  Denver 

f  Boston  
1  New  York.  . 
Ten          I  Chicago.  . 

Stories.     ]  Minneapolis. 
1  St.  Louis.  ..  . 
^Denver.  .  . 

f"  Boston  
Eleven      I  New  York... 

stori-  Igftsa.".:: 

^Denver 

!  Boston 

t&Sfti: 

St.  Louis..:. 
Denver  

TABLE  IV.— THICKNESS  OF  ENCLOSING  WALLS,  FOR 
RESIDENCES,  TENEMENTS,  HOTELS,  AND  OFFICE 
BUILDINGS.— CHICAGO  BUILDING  ORDINANCE. 


Basement. 

Stories. 

8 
12 
12 
16 
16 
20 
24 
24 
24 
24 
28 
28 

S 

8 
12 
16 
16 
16 
20 
24 
24 
24 
24 
28 

i 

12 
12 
16 

16 
20 

24 
24 

i 

12 

16 
16 

20 
20 
20 

12 
12 

16 
20 
20 

rC 

00 

A 

| 

,d 

i 

Basement  and  
Two-story  

12 

12 

16 
20 
20 
20 
2J 
24 
28 
28 
28 
32 

8 
12 
16 
18 
20 
20 
20 
24 
21 
24 

12 

16 
16 

20 
20 
24 

12 
12 
16 
16 
20 

12 
12 

16 
16 

1.2 

12 
16 

12 
12 

12 

Three-story  
Four-story  

Five-story  
Six-storv.        .... 

Eight-story  
Nine-story  

Ten-story 

ICleven-story 

Twelve-story  

General  Rule  for  Thickness  of  Walls.— Although 
there  is  a  great  difference  in  the  thicknesses  given  in  Table  III., 
more  indeed  than  there  should  be,  yet  a  general  rule  might  be  de- 


MASONRY  WALLS  AND   FOOTINGS.  189 

duced  from  the  table,  for  mercantile  buildings  over  four  stories 
in  height,  which  would  be  somewhat  as  follows : 

For  brick  equal  to  those  used  in  Boston  or  Chicago,  make  the 
thickness  of  the  three  upper  stories  16  ins.,  of  the  next  three  be- 
low 20  ins.,  the  next  three  24  ins.,  and  the  next  three  28  ins. 
For  a  poorer  quality  of  material  make  only  the  two  upper  stories 
16  ins.  thick,  the  next  three  20  ins.,  and  so  on  down. 

In  buildings  less  than  five  stories  in  height  the  top  story  may 
be  12  ins.  in  thickness. 

In  determining  the  thickness  of  walls  the  following  general 
principles  should  be  recognized : 

First.  That  walls  of  warehouses  and  mercantile  buildings 
should  be  heavier  than  those  used  for  living  or  office  purposes. 

Second.  That  high  stories  and  clear  spans  exceeding  25  ft. 
require  thicker  walls. 

Third.  That  the  length  of  the  wall  is  a  source  of  weakness, 
and  that  the  thickness  should  be  increased  4  ins.  for  every  25  ft. 
over  100  or  125  ft.  in  length.  (In  New  York  the  thickness  in  the 
table  must  be  increased  for  buildings  exceeding  105  ft.  in  depth. 
In  Western  cities  the  tables  are  compiled  for  warehouses  125  ft. 
in  depth,  as  that  is  the  usual  depth  of  lots  in  those  cities.) 

Fourth.  That  walls  containing  over  33  per  cent,  of  openings 
should  be  increased  in  thickness. 

Fifth.  Partition  walls  may  be  4  ins.  less  in  thickness  than  the 
outside  walls  if  not  over  60  ft.  long,  but  no  partition  to  be  less 
than  8  ins.  thick. 

Walls  Faced  with  Ashlar. — "  In  reckoning  the  thickness 
of  walls,  no  allowance  shall  be  made  for  ashlar,  unless  it  is  8 
ins.  or  more  thick,  in  which  case  the  excess  over  4  ins.  shall  be 
reckoned  as  part  of  the  thickness  of  the  wall.  Ashlar  shall  be 
at  least  4  ins.  thick  and  properly  held  by  metal  clamps  to  the 
backing,  or  properly  bonded  to  the  same." — Boston  Building 
law. 

Stone  Walls  should  generally  be  4  ins.  thicker  than  required 
for  brick  walls. 

Hollow  Walls. — Hollow  walls  are  undoubtedly  desirable  for 
dwellings,  and  might  well  be  used  for  other  buildings  not  more 
than  four  or  five  stories  in  height,  on  account  of  the  security 
afforded  from  the  weather.  Owing  to  the  fact  that  they  are 
usually  more  expensive  than  solid  walls,  and  occupy  more  space, 
they  are  not  very  extensively  used  in  this  country,  except  in 
concrete  construction. 


190  MASONRY  WALLS  AND  FOOTINGS. 

The  Boston  building  law  requires  that  "  vaulted  walls  shall 
contain,  exclusive  of  withes,  the  same  amount  of  material  as  is 
required  for  solid  walls,  and  the  walls  on  either  side  of  the  air- 
space shall  be  not  less  than  8  ins.  thick,  and  shall  be  securely 
tied  together  with  ties  not  more  than  2  ft.  apart." 

For  a  description  of  the  construction  of  hollow  brick  walls,  see 
Part  I  of  "  Building  Construction." 

Walls  of  Cement  Blocks. — Blocks  made  of  Portland- 
cement  concrete,  and  formed  in  moulds,  are  rapidly  coming  into 
use  for  building  walls  and  partitions.  Within  the  past  two  years 
several  patents  have  been  taken  out  on  different  forms  of  blocks 
and  on  machines  or  processes  for  making  the  same,  and  many 
buildings  have  been  erected  or  are  now  in  process  of  con- 
struction with  walls  built  of  these  blocks.  Most  of  the  blocks 
are  moulded  so  as  to  form  a  hollow  wall,  and  are  made  to  imitate 
natural  stone. 

Block  construction  has  an  advantage  over  poured  walls,  in  that 
the  blocks  are  thoroughly  seasoned  before  they  are  set  and  hence 
no  provision  is  required  for  expansion  or  contraction.  The 
author  believes  that  such  walls  are  less  liable  to  crack  and  will  be 
more  uniform  in  color  and  texture. 

Concrete  walls  in  various  forms  will  undoubtedly  be  more  ex- 
tensively used  during  the  coming  decade. 

Party  Walls. — There  is  much  diversity  in  building  regu- 
lations regarding  the  thickness  of  party  walls,  although  they  all 
agree  in  that  such  walls  should  never  be  less  than  12  ins.  thick. 
About  one-half  of  the  laws  require  that  party  walls  shall  be  of 
the  same  thickness  as  external  walls;  the  remainder  are  about 
equally  divided  between  making  the  party  walls  4  ins.  thicker 
or  thinner  than  for  independent  side  walls. 

When  the  walls  are  proportioned  by  the  rule  previously  given 
the  author  believes  that  the  thickness  of  the  party  walls  should 
be  increased  4  ins.  on  each  story.  The  floor  load  on  party  walls 
is  obviously  twice  that  on  side  walls,  and  the  necessity  for  thor- 
ough fire  protection  is  greater  in  the  case  of  party  walls  than  in 
other  walls. 

Curtai  n  Walls. — In  buildings  of  the  skeleton  type  the  outer 
masonry  walls  are  usually  supported  either  in  every  story  or 
every  other  story  by  the  steel  framework,  and  carry  nothing  but 
their  own  weight.  Such  walls  may,  therefore,  be  considered  as 
only  one  or  two  stories  high,  and  are  usually  made  only  12  ins. 
thick  for  the  whole  height  of  a  twelve-  or  fifteen-story  building. 


MASONRY  WALLS  AND   FOOTINGS.  191 

"For  skeleton  construction,  the  Chicago  ordinance  allows 
veneer  walls  of  12  ins.  thickness  for  any  height  within  the  max- 
imum limit  of  130  ft.  The  New  York  City  building  law  re- 
quires the  use  of  12-in.  curtain  walls  for  75  ft.  of  the  uppermost 
height  thereof,  and  4  ins.  additional  thickness  for  every  lower 
60  ft.  section  down  to  the  sidewalk  level.  But,  on  account  of  the 
severity  of  these  requirements  as  applied  to  very  high  cage-con- 
struction buildings,  permission  is  frequently  given  by  the  Board 
of  Examiners,  who  are  empowered  to  modify  the  building  laws 
within  certain  limits,  to  reduce  the  above-mentioned  thickness 
to  12  ins.  and  16  ins.  for  buildings  greatly  exceeding  100  ft.  in 
height.  They  have  never,  however,  permitted  a  uniform  thick- 
ness of  12  ins.  for  buildings  over  twelve  stories  in  height."  * 

A  few  of  the  earlier  tall  buildings  were  built  with  self-sustain- 
ing walls,  starting  from  the  foundation,  while  columns  were  in- 
troduced merely  to  support  the  floors  and  to  give  additional 
stiffness. 

"The  'World'  Building,  Few  York  City,  erected  in  1890,  is  an 
extreme  example  of  high-building  construction,  with  self-sustain- 
ing walls.  The  main  roof  is  191  ft.  above  the  street  level,  mak- 
ing thirteen  main  stories,  above  which  is  a  dome  containing  six 
stories — ^n  all,  a  height  of  275  ft.  above  the  street.  The  self- 
sustaining  walls  are  built  of  sandstone,  brick,  and  terra-cotta, 
the  thickness  increasing  from  2  ft.  at  the  top  to  as  much  as  11 
ft.  4  ins.  near  the  bottom,  where  the  walls  are  offset  to  a  con- 
crete footing  15  ft.  wide.  The  walls  are  vertical  on  the  outside 
faces,  the  thickness  being  varied  by  inside  offsets,  so  that  the 
columns  are  recessed  into  the  walls  at  the  bottom,  but  emerge 
and  are  some  distance  clear  of  the  walls  at  the  top." — "Architec- 
tural Engineering,"  p.  148. 

For  a  more  extended  discussion  of  curtain  walls  the  reader  is 
referred  to  Freitag's  "Architectural  Engineering,"  and  to  Birk- 
mire's  "  Planning  and  Construction  of  High  Office  Buildings." 

Durability  of  Iron  Solidly  Imbedded  in  Masonry. 
— T  believe  that,  imbedded  in  lime-mortar  at  such  depth  as  to 
protect  it  from  the  air,  hoop-iron  bond  is  indestructible. — 
M.  C.  MEIGS,  May  17,  1887. 

Iron  ties  imbedded  in  cement  concrete,  even  when  under  water, 
will  not  rust,  and  may  be  considered  as  imperishable,  provided 
that  the  concrete  does  not  crack  so  as  to  admit  the  water. 

*  Architectural  Engineering,  p.  164, 


192  HYDRAULIC  CEMENTS. 

Many  of  our  most  prominent  engineers  consider  Portland  ce- 
ment a  better  preservative  of  iron  or  steel  than  any  paint. 

HYDRAULIC  CEMENTS. 

Two  kinds  of  hydraulic  cement  are  used  in  this  country  in 
laying  up  mason  work,  and  in  making  concrete,  cement  floors, 
walks,  etc.,  viz.,  natural -rock  cement  and  Portland  or  artificial 
cement. 

•  Natural-rock  Cement. — These  cements  are  made  by 
burning  and  finely  grinding  a  natural  rock  whose  principal  in- 
gredients are  carbonate  of  lime,  carbonate  of  magnesia,  and 
alumina  (clay). 

The  principal  localities  in  the  United  States  where  natural 
cements  are  made  for  shipment  are :  Rosendale,  N.  Y. ;  Akron, 
N.  Y.;  Louisville,  Ky.;  Utica,  111.;  La  Salle,  111.;  Milwaukee, 
Wis. ;  Fort  Scott,  Kan. ;  Mankato,  Minn. ;  and  Cement,  Ga. 

Brands. — Natural  cements  are  most  generally  known  by  the 
name  of  the  locality  from  which  the  material  is  obtained,  as,  for 
instance,  Rosendale  Cement,  Utica  Cement,  Louisville  Cement, 
etc.  Each  manufacturer,  however,  has  a  registered  brand  or 
trade-mark  for  his  product.  The  brands  indicated  below  have 
probably  the  largest  sale  amongst  natural  cements. 

"Brooklyn  Bridge,"  " Hoffman,"  " Newark-Rosendale, "  all 
Rosendale  cements.  The  "Utica,"  "Milwaukee,"  "Louisville," 
and  "Fort  Scott"  cements  are  also  extensively  used  in  the  Mid- 
dle West,  and  are  good  cements. 

PROPERTIES    AND    CHARACTERISTICS  OF 
NATURAL   CEMENTS. 

Color. — Natural  cements  are  not  as  uniform  in  color  as  the 
'Portland  cements,  but  vary  from  a  light  to  a  dark  brown,  accord- 
ing to  the  varying  proportions  of  oxide  of  iron  and  impurities 
contained  in  the  stone.  "In  Rosendale  cement  a  light  color 
indicates  an  inferior  underburnt  rock."  Utica  cement  is  almost 
a  cream  color. 

Weight. — The  Rosendale  cements  vary  in  weight  from  49  to 
56  pounds  per  cu.  ft.  Every  barrel  of  the  Newark-Rosendale. 
and  Brooklyn  Bridge  brands  contains  300  Ibs.,  net.  Akron, 
Milwaukee,  Utica,  and  Louisville  cements  weigh  265  Ibs.  per 
barrel,  net, 


NATURAL  CEMENTS.  193 

Time  of  Setting". — The  natural  cements  begin  to  set  quicker 
than  the  Portland  cements,  generally  within  thirty  minutes  and 
always  within  an  hour.  Cement  has  set  when  it  resists  the  im- 
pression of  the  finger-nail. 

Lime  paste  added  to  cement  mortar  will  delay  the  setting  and 
make  it  work  easier,  but  it  also  reduces  its  strength. 

Lime  should  never  be  added  when  the  mortar  is  to  be  used  in 
a  wet  or  damp  place. 

Strength. — A  good  natural  cement  should  show  a  tensile 
strength,  neat,  of  at  least  80  Ibs.  per  sq.  in.  when  one  week  old, 
and  120  Ibs.  at  the  end  of  thirty  days,  or  when  mixed  with  one 
part  sand,  40  Ibs.  at  the  end  of  one  week  and  70  Ibs.  at  the  end 
of  a  month.  The  best  brands  will  give  results  25%  in  excess  of 
these  figures. 

The  strength  of  1  to  2  natural-cement  mortar  is  about  equal 
to  Portland-cement  mortar  1  to  4. 

Proportions  of  Cement  and  Sand  for  Mortar 
and  Concrete. — For  mortar  for  stone  rubble  and  ordinary 
brickwork  one  part  of  natural  cement  may  be  mixed  with  three 
parts  of  sand  by  measure. 

For  brick  piers  and  first-class  brickwork,  not  more  than  two 
parts  sand  to  one  of  cement,  by  measure,  should  be  used,  and  one 
or  one  and  one -half  parts  of  sand  will  make  a  still  stronger 
mortar. 

Any  admixture  of  sand  with  cement  reduces  the  strength. 

For  cement  plastering,  use  equal  parts  of  sand  and  cement. 

For  concrete,  natural  cements  may  be  used  in  the  proportion 
of  one  part  cement  to  two  parts  of  sand  and  four  of  gravel  or 
stone  chips. 

Mortar  that  has  set  should  not  be  re  tempered,  but  should  be 
thrown  away,  as  it  will  not  take  a  true  set  a  second  time. 

Natural-cement  mortar  possesses  sufficient  adhesion  and 
crushing  strength  for  any  ordinary  masonry,  and  when  mixed 
in  the  proportion  of  1  to  2  is  probably  just  as  good  for  masonry 
above  ground  and  for  ordinary  foundations  as  Portland  cement, 
but  at  the  present  price  of  Portland  cement,  it  is  not  much,  if  any, 
cheaper  than  1  to  3  Portland-cement  mortar. 

Effects  of  Freezing  on  Natural  Cement. — It  is  com- 
monly stated  that  natural  cement  should  never  be  used  in  freez- 
ing weather,  but  an  elaborate  series  of  tests  on  frozen  briquettes, 
published  in  the  Engineering  Record  of  Dec.  31,  1899,  would 


194  ARTIFICIAL  CEMENTS. 

seem  to  show  that  Rosendale-cement  mortar  is  not  injured  by 
freezing  in  air,  but  that  it  is  not  safe  to  let  it  freeze  in  water  in 
less  than  two  months. 


ARTIFICIAL  CEMENTS. 

The  artificial  cements  used  in  this  country  for  laying  up 
masonry,  or  in  making  concrete,  are  of  three  varieties,  viz., 
true  Portland  cement,  silica  (sand)  Portland  cement,  and  Puz- 
zolan  (slag)  cement. 

Portland  Cement, — The  true  Portland  cements  are 
made  by  thoroughly  mixing  together,  in  suitable  proportions, 
clay  and  finely  pulverized  carbonate  of  lime  (either  chalk,  marl, 
or  compact  limestone),  burning  the  mixture  in  kilns  at  a  high 
heat  and  then  grinding  the  burnt  product  to  fine  powder. 

"Pure  Portland  cement  as  known  to-day  by  architects  and 
engineers  is  strictly  a  mechanical  mixture.  Some  manufac- 
turers use  as  raw  material  clay  and  chalk,  some  marl  and  clay; 
others  use  argillaceous  limestone  rock  properly  dosed,  while  the 
first  original  Portland  was  made  from  mud  dredged  out  of  the 
river-beds  of  the  lower  Thames  and  the  Medway,  together  with 
limestone." 

True  Portland  cements  are  also  now  made  which  have  slag 
for  their  hydraulic  base,  the  "Universal"  brand  of  Portland 
cement  being  a  prominent  example.  Such  cements  differ  in  no 
way  from  other  standard  Portland  cements,  and  are  accepted 
in  competition  with  them. 

The  chemical  composition  of  a  good  Portland  brand  will  oe 
about  as  follows:  Lime,  60.1;  silica,  23.16;  alumina,  8.5;  ferric 
oxide,  5.3;  with  less  than  five  parts  of  magnesia  and  sulphides. 

Previous  to  the  year  1872,  all  of  the  Portland  cement  used  in 
this  country  was  imported.  In  1895,  2,300,000  Ibs.  of  Portland 
cement  was  made  in  the  United  States,  as  compared  with 
13,500,000  in  Germany  and  8,300,000  in  England.  At  the  pres- 
ent time  more  than  90%  of  the  Portland  cement  used  in  this 
country  is  of  domestic  production,  and  as  American  cements  are 
fully  equal  in  strength  and  durability  to  the  imported  cements,  it 
will  probably  not  be  long  before  the  importation  of  Portland 
cement,  except  a  few  brands  for  special  purposes,  will  practi- 
cally cease. 


ARTIFICIAL  CEMENTS.  195 

Silica-Portland  Cement  is  a  mixture  of  true  Portland 
cement  and  siliceous  sand  ground  together  into  an  impalpable 
powder  in  a  tube-mill. 

A  mixture  of  equal  parts  of  sand  and  cement  thus  ground  to- 
gether possesses  about  the  same  strength  as  ordinary  Portland 
cement  alone. 

A  mixture  of  silica  cement  (one  part  cement  and  one  part 
sand)  with  three  parts  unground  sand  has  the  same  composition 
as  one  part  cement  and  seven  parts  sand,  but  possessing  the 
strength  of  a  mixture  of  one  part  cement  and  three  parts  sand.* 

The  silica-cement  process  was  first  introduced  into  Denmark 
and  has  the  special  advantage  of  making  mortar  that  is  imper- 
meable to  moisture  and  able  to  resist  the  action  of  the  elements. 

During  the  years  1896—1902  a  great  many  silica-Portland  ce- 
ment factories  were  erected  abroad  and  several  companies  were 
formed  in  New  York,  Pennsylvania,  and  Illinois  to  manufacture 
it  on  a  large  scale.  The  author  understands,  however,  that  at 
least  some  of  the  factories  have  been  abandoned,  and  that  this 
material  is  now,  1905,  used  to  a  comparatively  small  extent,  if  at 
all. 

Eight  thousand  barrels  of  silica  cement  were  used  in  the  foun- 
dations of  the  Cathedral  of  St.  John  the  Divine,  New  York  City. 

Puzzolaii  Cement  (sometimes  called  slag  cement)  is 
made  from  granulated  slag  of  a  certain  composition,  both  physi- 
cal and  chemical,  ground  to  exceeding  fineness  with  quicklime 
which  has  been  slaked  with  a  solution  of  caustic  soda.  The 
product  is  a  mechanical  mixture  of  slag  and  slaked  lime,  no 
clinker  being  first  produced  as  in  the  manufacture  of  true  Port- 
land cement.  " Steel  Puzzolan  cement"  is  ground  to  a  fineness 
of  96%  through  a  40,000-mesh  sieve. 

"  Puzzolan  cement  made  from  slag  is  characterized  physically 
by  its  light  lilac  color ;  the  absence  of  grit  attending  fine  grinding 
and  the  extreme  subdivision  of  its  slaked-lime  element ;  its  low 
specific  gravity  (2.6  to  2.8)  compared  with  Portland  (3  to  3.5); 
and  by  the  intense  bluish-green  color  in  the  fresh  fracture  after 
long  submersion  in  water,  due  to  the  presence  of  sulphides,  which 
color  fades  after  exposure  to  dry  air. 

"  Puzzolan  cement  properly  made  contains  no  free  or  anhy- 
drous lime,  stands  storage  well,  does  not  warp  or  swell,  but  is 

*  Addison  H.  Clark,  in  Architects'  Handbook  of  Cements. 


196  ARTIFICIAL  CEMENTS. 

liable  to  fail  from  cracking  and  shrinking  (at  the  surface  only) 
in  dry  air. 

"Mortars  and  concretes  made  from  Puzzolan  approximate 
in  tensile  strength  similar  mixtures  of  Portland  cement,  but 
their  resistance  to  crushing  is  considerably  less.  On  account  of 
its  extreme  fine  grinding  Puzzolan  often  gives  nearly  as  great 
tensile  strength  in  3  to  1  mixtures  as  neat. 

"Puzzolan  permanently  assimilates  but  little  water  com- 
pared with  Portland,  its  lime  being  already  hydrated.  It 
should  be  used  in  comparatively  dry  mixtures,  well  rammed, 

"The  cement  is  well  adapted  for  use  in  sea-water,  and  gener- 
ally in  all  positions  where  it  will  be  constantly  exposed  to  mois- 
ture, such  as  in  foundations,  sewers  and  drains,  and  underground 
works  generally,  and  in  the  interior  of  heavy  masses  of  masonry 
or  concrete."  * 

It  should  not  be  used  for  work  exposed  to  dry  air  or  mechan- 
ical wear,  as  in  floors  and  sidewalks,  nor  should  it  be  used  in  con- 
nection with  iron  or  steel,  unless  the  metal  is  well  protected  by 
some  coating. 

Stainless  Cements. — Mortar  mixed  with  natural-rock  ce- 
ments, or  ordinary  Portland  cements,  are  likely  to  produce  stains 
in  limestone  and  marble,  and  sometimes  in  granite. 

There  are  a  few  Portland  cements  which  do  not  cause  stains, 
and  if  any  cement  at  all  is  to  be  used  in  the  mortar  for  setting 
or  pointing,  one  of  these  brands  should  be  specified. 

Lime  mortar  does  not  stain  the  stones,  but  of  course  it  does 
not  make  as  strong  a  job  as  cement  mortar. 

Leading  Brands  of  Portland  Cement. — The  follow- 
ing are  among  the  leading  brands  of  Portland  cement  now 
on  the  market. 

American  Portland:  "  Atlas,"  f  "  Alpha,"  "  Dragon,"  "  Le- 
high,"  "Iron  Clad,"  "  Saylors,"  "Vulcanite"  (lola,  Colorado 
Portland,  Red  Diamond  {). 

American  Puzzolan:  "  Steel  Puzzolan." 

English  Portland:  "  Brooks,  Shoobridge  &  Co." 

*  Report  of  Board  of  Engineer  Officers,  tJ.  S.  Army,  on  Testing  Hydraulic 
Cements.  1901. 

t  The  output  of  Atlas  cement  in  1901  was  over  3,000,000  barrels. 

t  These  cements  are  made  in  Kansas,  Colorado,  and  Utah,  respectively, 
and  are  extensively  used  in  those  States. 


PORTLAND   CEMENT. 


197 


German  Portland:  "Alsen's,"  "  Dyckerhoff,"  "Mann- 
heimer,"  "Germania." 

Stainless  cements:  "La  Farge,"  French  Portland;  "Puzzo- 
lan,"  H.  H.  Meier  &  Co.,  Bremen;  "Rhinoceros,"  American. 

Cost  of  Portland  Cement. — Portland  cement  can  now  be 
purchased  in  this  country  at  prices  from  $1 .25  to  $2.50  per  barrel, 
the  former  price  being  for  5,000-barrel  lots  at  the  factory.  For 
a  large  order,  in  any  of  the  Central  States,  cement  can  probably 
be  obtained  at  $2.00  per  barrel,  delivered.  The  retail  price  for 
single  barrels  varies  from  about  $2.25  to  $2.75  per  barrel. 

In  Germany  the  average  price  per  barrel  in  the  open  market 
appears  to  be  about  $1.25. 


PROPERTIES  AND  CHARACTERISTICS  OP 
PORTLAND  CEMENT. 

Color. — Portland  cement  should  be  of  a  greenish  gray  color. 
Slag  cements  are  of  a  light  gray  color. 

Weig'lit. — The  weight  of  Portland  cement,  loose,  varies  from 
77  to  95  Ibs.  per  cu.  ft.,  the  average  being  from  85  to  90  Ibs.  A 
barrel  of  Portland  cement  is  supposed  to  contain  3J  cu.  ft. 
(packed),  or  about  380  Ibs.  net  of  cement.  When  put  up  in 
sacks,  each  sack  is  supposed  to  contain  95  Ibs.,  or  four  sacks  to 
the  barrel.* 

"Steel  Puzzolan"  (slag)  cement  weighs  330  Ibs.  net  to  the 
barrel,  or  82J  Ibs.  per  bag  or  sack. 

Fineness. — Fineness  in  cement  is  a  very  important  quality, 
as  fine  grinding  increases  the  strength  and  sand-carrying  capac- 
ity. The  fineness  of  Portland  cement  when  ready  for  the  mar- 
ket should  be  such  that  not  less  than  95%  will  pass  through  a 

*The  actual  weight  per  cubic  foot  and  per  bbl.  of  several  brands  of  Port- 
land cement,  as  tested  by  Chas.  G.  Reid,  is  shown  by  the  following  table: 


Brand. 

Volume 
per  barrel  in 
cubic  feet 
loose  measure 

Weight  per  barrel  in  pounds. 

Weight 
per  cubic  foot 
loose 
measure. 

Gross. 

395 
401 
400.5 
375 
35O 
393 

Net. 

Dyckerhoff  
\tlas 

4.47 
4.45 
4.37 
4.84 
4.96 
4.64 

369.5 
381 
381 
353.5 
333.5 
370.5 

83 
85.5 
86.5 
73.5 
67.5 
79.5 

Alpha  
Meiers 

Steel  .  . 
Hilton  

198  PORTLAND   CEMENT. 

sieve  of  2,500  meshes  to  the  square  inch.  The  U.  S.  Corps  of 
Engineers  requires  that  92%  shall  pass  a  sieve  of  10,000  meshes 
to  the  sq.  inch.  Some  American  cements  will  pass  99%.  The 
finer  a  cement  is  ground  the  more  bulky  it  becomes,  and  the 
less  it  weighs  by  measure. 

Time  of  Setting. — A  true  Portland  cement  is  classed  as 
slow  setting  when  a  cake  of  neat  cement  takes  over  a  half  hour 
to  harden.  Sand  retards  setting,  so  that  cement  which  when 
mixed  neat  would  set  in  half  an  hour  may  not  set  for  one  or  two 
days  if  mixed  with  large  proportions  of  sand. 

Strength. — The  best  test  for  the  strength  of  Portland  cement 
is  the  tensile  strength  of  briquettes  composed  of  1  part  cement 
and  3  parts  standard  sand. 

Such  briquettes  should  show  a  strength  at  seven  days  of  from 
100  to  140  Ibs.,  at  twenty-eight  days  of  from  200  to  300  Ibs.,  and 
at  the  end  of  one  year  of  from  300  to  400  Ibs. 

Briquettes  mixed  neat  (without  sand)  should  break  at  seven 
days,  at  from  250  to  550  Ibs. ;  at  twenty-eight  days,  at  from  400 
to  800  Ibs.,  and  at  the  end  of  a  year,  at  from  500  to  1,000  Ibs. 
The  author  has  made  briquettes  which  gave  a  breaking 
strength  of  over  1,000  Ibs.  when  twenty-eight  days  old.  The 
briquettes  should  be  kept  in  a  damp  box  for  the  first  twenty-four 
hours,  and  then  in  water. 

The  crushing  resistance  of  Portland  cement  varies  from  8  to 
12  times  the  tensile  strength,  the  average  being  10  times  the 
tensile  strength. 

The  greater  the  increase  per  cent,  between  the  seven-day  and 
twenty-eight-day  tests,  the  stronger  and  harder  the  cement  is 
likely  to  become.  This  increase  should  be  at  least  25%. 

Water  Required  in  Mixing'. — Good  Portland  cement 
requires  but  little  water  to  make  a  good  mortar.  Neat  cement 
will  take  17%  to  20%  (by  weight)  of  water,  a  quick-setting 
cement  requiring  more  water  than  one  that  is  slow  setting. 

If  a  greater  quantity  of  water  is  required,  it  indicates  the 
presence  of  an  excess  of  free  lime. 

When  sand  is  mixed  with  cement,  in  the  proportion  of  3  to  1, 
not  more  than  9%  to  12J%  (by  weight)  of  water  will  be  required. 

Natural  rock  and  slag  cements  require  more  water  than  do 
Portland  cements. 

Too  much  water  " drowns"  the  cement,  retards  the  setting,  and 
weakens  the  mortar. 

Ceraent  can  also  be  spoiled  by  a  deficiency  of  water. 


PORTLAND  CEMENT.  199 

Portland-Cement  Mortar.— For  first-class  mortar  not 
more  than  3  bbls  of  sand  should  be  added  to  1  bbl.  of 
cement.  For  rubble  stonework  under  ordinary  conditions  a 
mortar  composed  of  4  parts  sand  to  1  of  cement  will  answer 
every  purpose,  and  be  much  stronger  than  lime  mortar. 

For  the  top  surface  of  floors  and  walks,  from  1  to  1J  parts  of 
sand  may  be  mixed  with  1  part  cement. 

1  to  3  Portland-cement  mortar  has  about  the  same  strength  at 
the  end  of  one  year  as  1  to  1  natural  rock-cement  mortar. 

Mortar  made  with  fine  sand  requires  twice  the  quantity  of 
cement  to  obtain  a  given  strength  as  that  made  with  coarse  sand. 

Effects  of  Freezing  on  Portland -Cement  Mortar, — Numerous 
experiments  and  the  experience  of  engineers  bear  out  the 
assertions, 

1st,  that  the  mortar  is  considerably  injured,  but  not  totally, 
if  frozen  before  it  is  set. 

2d.  That  freezing  only  partially  suspends  chemical  action  in 
the  setting  of  cement. 

3d.  It  is  not  safe  to  allow  a  slow-setting  cement  mortar  to 
freeze  in  less  than  four  days  after  it  has  been  placed,  while  a 
very  quick-setting  mortar  may  freeze  in  twelve  hours  without 
injury,  provided  the  mortar  is  kept  frozen  until  set. 

4th.  That  Portland-cement  mortar  is  injured  more  when  it 
alternately  freezes  and  thaws  than  when  it  remains  frozen  before 
it  has  set  hard.* 

5th.  If  salt  is  added  to  the  water  of  mixture  no  bad  effects 
will  result  from  freezing.  The  rule  for  the  proportion  of  salt 
used  in  the  works  at  Woolwich  Arsenal,  is  said  to  have  been — 
"Dissolve  one  pound  of  rock  salt  in  eighteen  gallons  of  water 
when  the  temperature  is  at  32  degrees  Fahr.,  and  add  three 
ounces  of  salt  for  every  three  degrees  of  lower  temperature." 

6th.  Hot  water  hastens  the  setting  of  Portland-cement  mortar.. 

7th.  2  Ibs.  carbonate  of  soda  in  1  gal.  of  water  boiled  and 
mixed  in  mortar  hastens  the  setting  and  protects  from  freezing. 

Quantity  of  Mortar  required  for  Masonry  and  Plastering.^ — 

"One  barrel  of  Portland  cement  and  three  barrels  of  sand 
thoroughly  and  properly  mixed  will  make  3J  bbls.,  or  12  cu.  ft., 
of  good  strong  mortar.  This  will  be  sufficient  to  lay  up  1 J  cu. 


*  See  Engineering  Record  for  December  24  and  31,  3898. 
t  These  figures  can  be  considered  as  approximate  only,  as  the  amount  of 
mortar  will  vary  on  different  jobs. 


200  CONCRETE. 

yds.  of  rough  stone,  or  about  750  bricks,  with  J  to  f-in.  joints, 
or  cover  125  square  feet  of  surface  1  in.  thick,  or  250  sq.  ft. 
J  in.  thick." 

"One  barrel  of  Rosendale  cement  and  two  barrels  of  lime, 
mixed  with  about  half  a  barrel  of  water,  will  make  8  cu.  ft.  of 
mortar,  sufficient  to  lay  522  common  bricks,  with  J  to  f  in. 
joint,  or  about  1  cu.  yd.  of  rough  rubble." 

For  the  top  coat  of  walks  or  floors. 

1  bbl.  of  Portland  cement  and  1  of  sand  will  cover  75  to  80 
sq.  ft.,  \  in.  thick,  or  50  to  56  sq.  ft.  f  in.  thick. 

1  bbl.  of  Portland  cement  and  1 J  bbls.  of  sand  will  cover  110  to 
120  sq.  ft.  of  floor  J  in.  thick,  or  75  to  80  sq.  ft.  J  in.  thick. 


CONCRETE. 

There  is  probably  no  material  that  is  so  enduring  or  better 
adapted  for  foundations,  walks,  and  basement  floors  than  cement 
concrete,  and  for  a  certain  class  of  buildings  it  may  be  used  with 
advantage  for  the  walls,  floors,  and  interior  supports.  In  fact 
there  are  now  probably  one  hundred  buildings  in  this  country 
in  which  all  of  the  structural  portions  are  formed  of  concrete, 
and  the  use  of  Portland-cement  concrete  for  a  great  variety  of 
purposes  is  rapidly  extending,  due  largely  to  the  reduced  price  of 
Portland-cement,  and  also  to  a  better  appreciation  of  its  merits. 

Concrete  may  be  denned  as  an  artificial  rock,  made  by  unit- 
Ing  sand,  broken  stone,  gravel,  fragments  of  brick,  pottery,  etc., 
by  means  of  lime  or  cement. 

Concrete  made  with  llrne,  however,  is  not  suitable  for  damp 
situations,  and  even  when  used  for  walls  above  ground  it  is 
much  better  to  use  either  a  " Portland"  or  "natural"  cement 
for  the  uniting  material;  in  fact  lime  is  no  longer  used  for  this 
purpose. 

Concrete  made  with  good  Portland  cement,  in  proper  propor- 
tions, becomes  so  hard  and  strong  that  when  pieces  of  the  con- 
crete are  broken  the  line  of  fracture  will  often  be  found  to  pass 
through  the  particles  of  stone,  showing  that  the  adhesion  of  the 
cement  to  the  stone  is  greater  than  the  strength  of  the  stone. 

For  the  aggregates  no  material  is  better  than  clean,  freshly 
broken  stone,  in  size  about  as  large  as  a  hen's  egg.  Granite 
probably  makes  the  best  aggregates,  but  other  hard  stones  will 
answer  for  any  ordinary  concrete.  Soft  sandstones  or  "free- 


CONCRETE.  201 

stones"  are  not  desirable.  Pieces  of  hard  brick  or  dense  terra- 
cotta also  make  good  aggregates. 

Whatever  material  is  used  it  is  essential  that  it  be  free  from 
dirt  and  that  the  particles  be  clean.* 

Good  clean  coarse  gravel  is  also  extensively  used  for  the  mass 
of  the  concrete,  and  some  architects  and  builders  prefer  it  to 
broken  stone,  but  as  all  gravel  has  more  or  less  rounded  and 
smooth  surfaces,  it  would  seem  as  though  the  cement  must  adhere 
more  firmly  to  angular  and  broken  surfaces. f 

A  certain  proportion  of  clean  coarse  sand  is  also  required  to 
fill  the  voids  between  the  particles  of  stone  or  gravel. 

The  best  proportion  of  cement,  sand,  and  aggregates  will  de- 
pend upon  the  kind  and  quality  of  the  cement  used,  the  character 
of  the  aggregates,  and  of  the  work. 

Proportions. — The  proportion  of  sand  to  aggregates  should 
be  such  that  the  sand  will  just  fill  the  voids  in  the  aggregates. 
This  will,  of  course,  vary  with  the  size  of  the  aggregates  and  the 
coarseness  of  the  sand.  For  stone  broken  to  go  through  a  2J- 
inch  ring  about  one-half  as  much  sand  as  stone  is  required,  on 
an  average,  to  fill  the  voids.  After  one  batch  of  concrete  has 
been  deposited  and  rammed  the  inspector  can  generally  tell  by 
the  appearance  whether  too  much  or  too  little  sand  has  been  used. 

Natural-Cement  Concrete. — For  concrete  foundations 
under  buildings  of  moderate  height,  and  for  foundations  for 
cement  pavements,  natural  cement  makes  as  strong  a  concrete 
as  is  required. 


*Mr.  G.  J.  Griesenauer,  cement  tester  for  the  Chicago,  Milwaukee  &  St. 
Paul  Ry.,  reports, in  the  Engineering  News  of  April  16,  1903,  a  very  interest- 
ing series  of  tests  on  the  comparative  strength  of  cement  mortar  made  from 
Trorpedo  sand  and  limestone  and  gravel  screenings.  These  tests  seem  to 
show  that  limestone  screenings  make  very  much  stronger  mortar  than  sand, 
the  increase  in  strength  averaging  about  115  per  cent,  for  proportions  of  1 
to  3.  Gravel  screenings  gave  about  the  same  strength  as  sand. 

Mr.  W.  A.  Rogers,  formerly  with  the  same  railroad,  in  a  very  valuable 
paper  on  concrete,  reports  tests  which  seem  to  show  that  "a  small  amount 
of  dirt  in  the  sand  is  probably  not  seriously  objectionable,  if  suitable  in 
other  ways." 

t  From  some  experiments  carried  out  under  the  direction  of  Captain  Wm. 
Black,  of  the  United  States  Corps  of  Engineers,  for  the  purpose  of  deter- 
mining the  influence  of  different  aggregates  on  the  strength  of  concrete, 
it  would  seem  that  the  gravel  makes  a  much  weaker  concrete  at  the  start 
than  stone,  especially  when  natural  cements  are  used,  but  that  after  a 
period  of  one  year  it  will  probably  attain  the  same  strength  as  that  made 
of  broken  stone.  (See  Engineering  Record  for  April  9,  1898.) 


202  CONCRETE. 

For  the  best  brands  of  natural  cements  1  part  cement,  2  parts 
sand,  and  4  parts  gravel  or  broken  stone  should  be  used. 

(This  proportion  was  used  in  the  foundations  of  the  Brooklyn 
Bridge.) 

Portland-Cement  Concrete. — For  concrete  to  be  used 
under  heavy  buildings  and  under  water  Portland  cement 
should  be  used. 

For  the  best  brands  of  cement  2  parts  of  cement  to  5  of  sand 
and  9  of  broken  stone  will  answer  for  almost  any  building  con- 
struction. Much  larger  proportions  of  sand  and  aggregates 
than  these  are  often  used,  but  the  author  would  not  recommend 
a  greater  proportion  than  the  above  unless  the  quality  of  the 
cement  is  constantly  tested  and  only  the  best  used,  and  the  con- 
crete mixed  under  rigid  inspection. 

Manner  of  Mixing. —  The  most  satisfactory  method  of 
mixing  concrete  by  hand  is  to  first  prepare  a  tight  floor  of  plank, 
or,  better  still,  of  sheet  iron  with  the  edges  turned  up  about 
2  ins.,  for  mixing  the  materials  on. 

Upon  this  platform  should  first  be  spread  the  sand,  and  upon 
this  the  cement.  The  two  should  then  be  thoroughly  and  im- 
mediately mixed  by  means  of  shovels  or  hoes,  and  the  broken 
stone  or  aggregates  then  dumped  on  top  and  the  whole  worked 
over  dry  with  shovels,  and  then  again  worked  over  while  water 
is  added  from  a  sprinkler  on  the  end  of  a  hose.  After  enough 
water  has  been  added  the  mass  should  be  worked  over  at  least 
twice.  Only  as  much  water  should  be  added  as  is  necessary  to 
enable  the  mortar  to  completely  coat  and  cause  to  adhere  all 
the  particles  of  the  aggregates,  and  so  that  when  the  concrete  is 
tamped  the  water  will  just  flush  to  the  surface  without  quaking. 

The  water  should  be  clean  and  at  about  the  temperature  of 
65  degrees. 

There  are  many  machines  for  mixing  mortar  which  for  large 
quantities  of  concrete  effect  a  material  saving  in  the  cost  of  mix- 
ing, and  probably  do  the  work  more  thoroughly  and  evenly. 
As  soon  as  the  concrete  is  mixed  it  should  be  wheeled  to  the 
trenches  in  barrows  and  deposited  in  layers  not  over  6  ins.  thick 
and  well  tamped.  After  it  is  deposited  concrete  should  be  pro- 
tected from  drying  too  rapidly,  as  Portland  cement  reaches  its 
maximum  strength  only  when  kept  damp.  If  the  concrete 
dries  quickly  it  is  also  liable  to  crack  from  contraction,  which 
in  exposed  work  is  likely  to  lead  to  its  destruction  by  weathering. 

Effect  of  Freezing  on  Concrete. — It  would  seem  that 


CONCRETE. 


203 


the  general  opinion  among  railway  engineers  is  that  when  careful 
precautions  are  taken  in  laying  Portland-cement  concrete,  freez- 
ing weather  will  not  cause  any  trouble,  while  the  effect  of  frost 
on  concrete  that  has  set  either  amounts  to  nothing  or  is  confined 
to  surface  cracks.* 

Cost  of  Concrete  and  Materials  Required  per 
Yard, — The  quantities  of  cement,  sand,  and  gravel  required 
to  make  a  yard  (27  cu.  ft.)  of  concrete  will  vary  somewhat 
on  different  jobs.  The  values  given  in  the  following  tables  may 
be  used  as  fair  averages  for  making  'estimates. 

QUANTITIES     REQUIRED     FOR      1      CUBIC     YARD     OF   RAMMED    CON- 
CRETE.     (Compiled  by  Edwin  Thacher,  C.E.) 


1 

Mixture 

s. 

Stone,  f 

Gravel,  t 

Ce- 

Ce- 

Ce- 
ment. 

Sand. 

Stone. 

ment, 
bbls. 

Sand, 
cu.  yds. 

Stone, 
cu.  yds. 

ment, 
bbls. 

Sand, 
cu.  yds. 

Gravel, 
cu.  yds. 

1.0 

2.0 

2.63 

0.40 

0.80 

2.30 

0.35 

0.74 

1.0 

3.0 

2.10 

0.32 

0.96 

.89 

0.29 

0.86 

1.5 

3.0 

.90 

0.43 

0.87 

.71 

0.39 

0.78 

1.5 

4.0 

.61 

0.37 

0.98 

.46 

0.33 

0.88 

2.0 

3.0 

.73 

0.53 

0.79 

.54 

0.47 

0.73 

2.0 

4.0 

.48 

0.45 

0.90 

.34 

0.41 

0.81 

2.0 

5.0 

.29 

0.39 

0.98 

.17 

0.36 

0.89 

2.5 

4.0 

.38 

0.53 

0.84 

1.24 

0.47 

0.75 

2.5 

5.0 

.21 

0.46 

0.92 

1.10 

0.42 

0.83 

2.5 

6.0 

.07 

0.41 

0.98 

0.98 

0.37 

0.89 

3.0 

6.0 

0.91 

0.42 

0.97 

0.84 

0.38 

0.89 

ACTUAL  VOLUME  OF  RAMMED  CONCRETE  RESULTING  FROM  DIF- 
FERENT PROPORTIONS  OF  INGREDIENTS.  (As  determined  by 
Messrs.  A.  W.  Dow  and  W.  J.  Douglas. §) 


Ingredients. 

Propor- 
tions. 

Quantity 
of  Concrete. 

Cement. 

Sand. 

Stone. 

Gravel. 

lbbl.=    [ 
4*cu.ft. 

or         } 
378ilbs.    I 

9    cu.  ft. 

iii    " 
in    - 

13.5     " 

29i  cu.  ft. 
27 
13| 

0 
0 
13*  cu.  ft. 
45 

1:2:5 
1  :  2*  :  6 
1  :  2*  :  3  :  3 
1  :  3  :  10 

21.4    cu.  ft. 
27.66      " 
27.66      " 
45 

For  sand  and  gravel  mixed  as  it  comes  from  the  pit  125  yds. 
will  make  about  100  yds.  of  concrete. 

At  $2  a  day  for  common  labor  the  cost  of  mixing  and  deposit- 
ing concrete,  by  hand,  will  vary  from  $1.25  to  $1.50  a  cu.  yd. 

On  large  jobs  concrete  can  be  mixed  by  machines,  deposited 
and  tamped  by  hand  at  from  .75  to  .90  per  cu.  yd. 

*  Engineering  Record,  October  20,  1900,  also  December  7,  1901. 

t  2£  in.  and  under,  dust  screened  out. 

t  i  in.  and  under. 

§  See  Engineering  News,  March  10,  1904,  p.  226. 


204  CONCRETE. 

For  small  jobs  where  there  are  no  special  disadvantages  $6  per 
cu.  yd.  without  forms  is  perhaps  a  fair  average  price  at  the  pres- 
ent time  (1904),  although  with  wages  at  $2  per  day,  and  on  large 
jobs,  the  work  can  be  done  at  from  $4.00  to  $5.00  a  yard. 

On  the  Boston  subway  the  prices  for  labor  and  materials  were 
as  follows,  per  cu.  yd.* 

Natural  rock-cement  concrete,  $5.00  to  $8.00. 

Portland-cement  concrete,  $6.50  to  $9.50. 

The  following  exact  figures,  giving  the  cost  per  cu.  yd.  of  con- 
crete of  an  arched  culvert  of  26  ft.  span,  with  wring  walls  and 
parapet,  built  near  Pittsburg,  Pa.,  in  1901,  should  be  of  value 
in  estimating  the  cost  of  such  work.  The  proportions  were  1  to 
8  and  1  to  10,  and  the  mixing  was  done  by  hand. 

For  complete  description  of  the  work  see  the  Engineering 
Record  for  April  12,  1902. 

The  finished  structure  contained  1,439  cu.  yds.  of  concrete 
masonry,  the  total  cost  of  which  was  $7,243.24. 

The  cost  per  cu.  yd.  of  concrete  for  material  and  labor  was 
as  follows: 

Material. 

Coarse  gravel,  19  cts.  per  ton,  1.03  tons $0.19$ 

Fine  gravel,  21  cts.  per  ton,  0.40  ton 08$ 

Sand,  36  cts.  per  ton,  0.32  ton 11} 

Cement,  $1.60  per  barrel 1 . 53$ 

Lumber 43 

Tools  and  other  storehouse  accounts 07f 

$2.43f 

Labor. 

Preparing    site   and    cleaning   up   after   comple- 
tion of  structure,  15.5  cts.  per  hour $0.21 

Forms,  23  cts.  per  hour 28 

Platforms  and  buildings,  23  cts.  per  hour 05 

Changing  trestle,  including  service  of  work  train 

and  steam-derrick  car .08$ 

Excavation,  foundations,  15.5  cts.  per  hour 31 

Handling  material,  15.5  cts.  per  hour .03J 

Mixing  and  laying  concrete,  15.5  cts.  per  hour.  ...  1 .44 

$2.41J 

Total  cost  per  cubic  yard  of  concrete $4.85 

Wages  paid  were  as  follows:  Foreman  mason  in  general 
charge,  40  cents  per  hour;  laborers,  15  cents  per  hour;  foreman, 
25  cents  per  hour;  carpenters,  22.5  to  25  cents. 

*  Addison  H.  Clark,  in  "  Architects'  Handbook  of  Cement." 


EXAMPLES  OF  PORTLAND  CEMENT  CONCRETE.  205 


DATA  FOR  ESTIMATING  THE  COST  OF  A  CUBIC  YARD  OF  CON- 
CRETE OF  VARIOUS  PROPORTIONS.  (As  compiled  by  W.  A. 
Rogers,  C.E.) 


Proportion  of 
materials. 

Cost  of  labor, 
mixing  and 
placing  per 
cubic  yard. 

Cost  of  forms 
per  cubic  yard 
(where  forms 
are  required). 

Materials  per 
cubic  yard. 

Cement. 

73 

1 

Is 

22 
pq  * 

1  part  of  natural  ce- 
ment   to    1£    parts 
sand     to     4     parts 
broken    stone  
1    part    Portland    ce- 
ment    to     2     parts 
sand     to     5     parts 
broken  stone 

90  per  cent  of 
the  amount 
paid   per  day 
for  labor. 

From  35  cts. 
to  85  cts.  per 
cubic  yard. 

t« 

bbls. 

1.2 
bbls. 

0.9 
bbls. 

0.35 
cu.  yd. 

0.95 
cu.  yd. 

1  part  Portland  ce- 
ment to  3  parts 
sand  to  7i  parts 
broken  stone. 

EXAMPLES  OP  PORTLAND  CEMENT  CONCRETE. 

Foundation  of  U.  S.  Naval  Observatory,  Georgetown,  D.  C. : 
1  part  cement,  2J  sand,  3  gravel,  5  broken  stone.  (1  barrel  of 
cement,  380  Ibs.,  made  1.18  yds.  of  concrete.) 

Foundations  of  Cathedral  of  St.  John  the  Divine,  New  York : 

1  part  Portland  cement,  2  parts  sand,  3  parts  quartz  gravel,  14 
to  2  ins.  in  diameter.     (17,000  barrels  of  cement  made  11,000 
yards  of  concrete.) 

Manhattan  Life  Insurance  Building,  New  York,  filling  of 
caissons:  1  part  Alsen  Portland  cement,  2  parts  sand,  4  parts 
broken  stone. 

Filling  of  caissons,  Johnston  Building  (15  stories),  New  York: 
1  part  Portland  cement,  3  parts  sand,  7  parts  stone,  finished  on 
top  for  brickwork  with  1  part  cement  and  3  parts  gravel. 

Prof.  Baker  states  that  the  concrete  foundations  under  the 
Washington  Monument  were  made  of  1  part  Portland  cement, 

2  parts  sand,  3  parts  gravel,  and  4  parts  broken  stone,  and  that 
this  mixture  stood,  at  six  months  old,  a  load  of  2,000  Ibs.  per  sq. 
in.,  or  144  tons  per  sq.  ft.     For  the  strength  of  concrete  see 
Chapter  V. 

The  weight  of  concrete  varies  from  130  to  140  Ibs.  per  cu.  ft., 
according  to  the  material  used,  granite  aggregates  making  natu- 
rally the  heaviest  concrete. 


206  RETAINING  WALLS— VAULT  WALLS. 


CHAPTER  IV. 
RETAINING  WALLS— VAULT  WALLS. 

A  Retaining  Wall  is  a  wall  for  sustaining  a  pressure  of 
earth,  sand,  or  other  filling  or  backing  deposited  behind  it  after 
it  is  built,  in  distinction  to  a  brest  or  face  wall,  which  is  a  similar 
structure  for  preventing  the  fall  of  earth  which  is  in  its  undis- 
turbed natural  position,  but  in  which  a  vertical  or  inclined  face 
has  been  excavated. 

Fig.  1  gives  an  illustration  of  the  two  kinds  of  wall. 


Fig.  I 

Retaining  Walls. — A  great  deal  has  been  written  upon  the 
theory  of  retaining  walls,  and  many  theories  have  been  given  for 
computing  the  thrust  which  a  bank  of  earth  exerts  against  a  re- 
taining wall,  and  for  determining  the  form  of  wall  which  affords 
the  greatest  resistance  with  the  least  amount  of  material. 

There  are  so  many  conditions,  however,  upon  which  the  thrust 
exerted  by  the  backing  depends, — such  as  the  cohesion  of  the 
earth,  the  dryness  of  the  material,  the  mode  of  backing  up  the 
wall,  etc., — that  in  practice  it  is  impossible  to  determine  the  exact 
thrust  which  will  be  exerted  against  a  wall  of  a  given  height. 

It  is  therefore  necessary,  in  designing  retaining  walls,  to  be 
guided  by  experience  rather  than  by  theory.  As  the  theory  of 
retaining  walls  is  so  vague  and  unsatisfactory,  we  shall  not  offer 
any  in  this  work,  but  rather  give  such  rules  and  cautions  as  have 
been  established  by  practice  and  experience. 

In  designing  a  retaining  wall  there  are  two  things  to  be  con- 
sidered,— the  backing  and  the  wall. 

The  tendency  of  the  backing  to  slip  is  very  much  less  when  it  is 
in  a  dry  state  than  when  it  is  filled  with  water,  and  hence  every 


RETAINING  WALLS— VAULT  WALLS. 


207 


precaution  should  be  taken  to  secure  good  drainage.  Besides 
surface  drainage,  there  should  be  openings  left  in  the  wall  for 
the  water  which  may  accumulate  behind  it  to  escape  and  run  off. 
The  manner  in  which  the  material  is  filled  against  the  wall  also 
affects  the  stability  of  the  backing.  If  the  ground  be  made  irreg- 
ular, as  in  Fig.  1,  and  the  earth  well  rammed  in  layers  inclined 
from  the  wall,  the  pressure  will  be  very  trifling,  provided  that 
attention  be  paid  to  drainage.  If,  on  the  other  hand,  the  earth 
be  tipped,  in  the  usual  manner,  in  layers  sloping  towards  the  wall, 
the  full  pressure  of  the  earth  wrill  be  exerted  against  it,  and  it 
must  be  made  of  corresponding  strength. 


84 


Fig.2 


Fig.  3 


The  Wall. — Retaining  walls  are  generally  built  with  a  batter- 
ing (sloping)  face,  as  this  is  the  strongest  wall  for  a  given 
amount  of  material;  and,  if  the  courses  are  inclined  towards  the 
back,  the  tendency  to  slide  on  each  other  will  be  overcome,  and 
it  will  not  be  necessary  to  depend  upon  the  adhesion  of  the 
mortar. 

The  importance  of  making  the  resistance  independent  of  the 
adhesion  of  the  mortar  is  obviously  very  great,  as  it  would  other- 
wise be  necessary  to  delay  backing  up  a  wall  until  the  mortar  was 
thoroughly  set,  which  might  require  several  months. 

The  Back  of  the  Wall  should  be  left  Kough.— In 
brickwork  it  would  be  well  to  let  every  third  or  fourth  course 
below  the  frost-line  project  an  inch  or  two.  This  increases  the  fric- 
tion of  the  earth  against  the  back  and  thus  causes  the  resultant  of 
the  forces  acting  behind  the  wall  to  become  more  nearly  vertical, 
and  to  fall  farther  within  the  base,  giving  increased  stability. 
It  also  conduces  to  strength  not  to  make  each  course  of  uniform 
height  throughout  the  thickness  of  the  wall,  but  to  have  some  of 
the  stones,  especially  near  the  back,  sufficiently  high  to  reach  up 
through  two  or  three  courses.  By  this  means  the  whole  masomy 
becomes  more  effectually  interlocked  or  bonded  together  as  one 


208 


RETAINING  WALLS— VAULT  WALLS. 


mass,  and  less  liable  to  bulge.  The  courses  of  masonry  are  also 
often  laid  with  their  beds  sloping  in,  as  in  Fig.  6,  to  overcome 
the  tendency  of  the  courses  to  slide  on  each  other. 

Where  deep  freezing  occurs,  the  back  of  the  wall  should  be 


Fig.5 


Fig.6 


sloped  forwards  for  three  or  four  feet  below  its  top,  as  at  OC 
(Fig.  2),  which  should  be  quite  smooth,  so  as  to  lessen  the  hold 
of  the  frost  and  prevent  displacement. 

Figs.  3,  4,  5,  and  6  show  the  relative  sectional  areas  of  walls  of 
different  shapes  that  would  be  required  to  resist  the  pressure  of 
a  bank. of  earth  twelve  feet  high  ("Art  of  Building,"  E.  Dobson, 
p.  20).  The  first  three  examples  are  calculated  to  resist  the  max- 
imum thrust  of  wet  earth,  while  the  last  shows  the  modified  form 
usually  adopted  in  practice. 


Fig.7 


Rules  for  the  Thickness  of  the  Wall.— As  has  been 
stated,  the  only  practical  rules  for  retaining  walls  which  we 
have  are  empirical  rules  based  upon  experience  and  practice. 


RETAINING  WALLS— VAULT  WALLS, 


209 


Trautwine,  in  his  "Pocket-Book  for  Engineers,"  gives  the 
following  table  for  the  thickness  at  the  base  of  vertical  retaining 
walls  with  a  sand  backing  deposited  in  the  usual  manner. 

The'  first  column  contains  the  vertical  height  CD  (Fig.  7)  of 
the  earth  as  compared  with  the  vertical  height  of  the  wall,  AB', 
which  latter  is  assumed  to  be  1,  so  that  the  table  begins  with 
backing  of  the  same  height  as  the  wall.  These  vertical  walls 
may  be  battered  to  any  extent  not  exceeding  an  inch  and  a  half 
to  a  foot,  or  1  in  8,  without  affecting  their  stability,  and  without 
increasing  the  base. 

Proportion  of  Retaining  Walls. 

(Thickness  of  wall  in  terms  of  the  height,  A  B,  Fig.  7). 


Total  height  of  the  earth  com- 
pared with  the  height  of  the 
wall  above  ground. 

Wall  of 
cut  stone  in 
mortar. 

Good  mortar, 
rubble,  or 
brick. 

Wall  of 
good,  dry 
rubble. 

1 

0.35 

0.40 

0.50 

1.1 

0.42 

0.47 

0.57 

1.2 

0.46 

0.51 

0.61 

1.3 

0.49 

0.54 

0.64 

1.4 

0.51 

0.56 

0.66 

1.5 

0.52 

0.57 

0.67 

1.6 

0.54 

0.59 

0.69 

1.7 

0.55 

0.60 

0.70 

1.8 

0.56 

0.61 

0.71 

2 

0.58 

0.63 

0.73 

2.5 

0.60 

0.65 

0.75 

3 

0.62 

0.67 

0.77 

4 

0.63 

0.68 

0.78 

6 

0.64 

0.69 

0.79 

If  the  wall  is  built  as  in  Fig.  8, 
with  the  ground  practically  level 
with  the  top,  the  top  of  the  wall 
should  be  not  less  than  18  ins.  thick, 
and  the  thickness  at  a,  a,  just  above 
each  step  should  be  from  one-third 
to  two-fifths  of  the  height  from  the 
top  of  the  wall  to  that  point.  If 
the  earth  is  banked  above  the  top 
of  the  wall,  the  thicknesses  should 
be  increased  as  indicated  by  the 
table  given  above. 


Fig.  8 


If  built  upon  ground  that  is  affected  by  frost  or  surface  water, 


210  RETAINING  WALLS— VAULT  WALLS. 

the  footings  should  be  carried  sufficiently  below  the  surface  of 
the  ground  at  the  base  to  insure  against  heaving  or  settling. 

Reinforced  Concrete  may  be  used  to  advantage  in  building 
retaining  walls,  and  often  at  less  expense  than  stone.  Fig.  SA 
shows  a  wall  suggested  by  the  St.  Louis  Expanded  Metal  Fire- 
proofing  Co.  which  reduces  the  masonry  to  a  minimum. 

Brest  Walls  (from  Dobson's  "Art  of  Building").— Where 
the  ground  to  be  supported  is  firm,  and  the  strata  are  horizontal., 
the  office  of  a  brest  wall  is  more  to  protect  than  to  sustain  the 
earth.  It  should  be  borne  in  mind  that  a  trifling  force  skilfully 
applied  to  unbroken  ground  will  keep  in  its  place  a  mass  of  ma- 
terial, which,  if  once  allowed  to  move,  would  crush  a  heavy  wall; 
and  therefore  great  care  should  be  taken  not  to  expose  the  newly 
opened  ground  to  the  influence  of  air  and  wet  for  a  moment  longer 
than  is  requisite  for  sound  work,  and  to  avoid  leaving  the  smallest 
space  for  motion  between  the  back  of  the  wall  and  the  ground. 

The  strength  of  a  brest  wall  must  be  proportionately  in- 
creased when  the  strata  to  be  supported  incline  towards  the  wall; 
where  they  incline  from  it,  the  wall  need  be  little  more  than  a 
thin  facing  to  protect  the  ground  from  disintegration. 

The  preservation  of  the  natural  drainage  is  one  of  the  most 
important  points  to  be  attended  to  in  the  erection  of  brest  walls, 
as  upon  this  their  stability  in  a  great  measure  depends.  No  rule 
can  be  given  for  the  best  manner  of  doing  this:  it  must  be  a 
matter  for  attentive  consideration  in  each  particular  case. 

"Vault  Walls. — In  large  cities  it  is  customary  to  utilize 
the  space  under  the  sidewalk  for  storage  or  other  purposes. 
This  necessitates  a  wall  at  the  curb-line  to  sustain  the  street 
and  also  the  weight  of  the  sidewalk. 

Where  practicable  the  space  should  be  divided  by  partition 
walls  about  every  10  ft.,  and  when  this  is  done  the  outer  wall 
may  be  advantageously  built  of  hard  brick  in  the  form  of  arches, 
as  shown  in  Fig.  9.  The  thickness  of  the  arch  should  be  at  least 
16  ins.  for  a  depth  of  9  ft.,  and  the  "rise"  of  the  arch  from  one- 
eighth  to  one-sixth  of  the  span. 

If  partitions  are  not  practicable  each  sidewalk  beam  may  be 
supported  by  a  heavy  I-beam  column,  with  either  flat  or  seg- 
mental  arches  between  of  either  brick  or  concrete. 

Fig.  10  *  shows  a  detail  of  the  outer  walls  of  the  vault  under 
the  sidewalk  around  the  Singer  Building,  New  York;  Mr.  Er- 

*  Fiqm  The  Engineering  Record  of  February  26, 1898. 


RETAINING  WALLS— VAULT  WALLS. 


211 


•  nest  Flagg,  architect.  These  walls  consisted  of  a  core  formed 
by  two-ring  brick  arches,  with  vertical  axes  built  between  the 
flanges  of  8-inch  vertical  steel  I  beams  spaced  about  5  ft.  apart 
and  bedded  at  the  bottom  in  a  concrete  footing.  Their  tops 


were  joined  by  6-inch  horizontal  I  beams  and  braced  laterally 
by  the  sidewalk   beams  5  ft.  apart.     The    arches    themselves 


Fig.   10 

were  segmental  with  a  rise  of  about  6  ins.,  and  were  built  up 
solid  against  an  8-inch  outside  face  wall.  A  4-inch  plain  cur- 
tain wall  was  built  inside  against  the  flanges  of  the  vertical 
beams  inclosing  segmental  air  chambers  in  front  of  each  arch. 


212    STRENGTH  OP  MASONRY  AND  CONCRETE. 


CHAPTER  V. 
STRENGTH  OP   BRICK  AND  STONE  MASONRY 

AND  CONCRETE. 
'CRUSHING     RESISTANCE    OF     BRICK,    BUILDING 

STONES,     MORTAR,     CONCRETES,     AND     ARCHI- 
TECTURAL  TERRA-COTTA. 

By  the  term  "strength  of  masonry"  is  generally  meant  its 
resistance  to  a  direct  crushing  force  or  load,  and  this  is  the  only 
direct  stress  to  which  masonry  should  be  subjected.  Stone  lin- 
tels and  footings  may  be  subjected  to  a  transverse  stress,  but 
they  can  hardly  be  included  in  the  term  masonry,  as  they  consist 
of  single  pieces.  There  is  also  more  or  less  of  a  tendency  to 
bend  or  split  apart  in  brick  walls  and  piers,  as  they  are  very  high 
in  proportion  to  their  thicknesss,  but  this  is  a  stress  which  cannot 
be  accurately  determined,  and  which  should  be  avoided  as  much 
as  possible.  It  is  impossible  to  fix  values  for  the  strength  of 
brick  or  stone  work  with  anything  like  the  exactness  that  we 
do  for  wood  or  steel,  for  the  reason  that  there  is  not  only  a  great 
variation  in  the  strength  of  brick  and  stone,  even  when  taken 
from  the  same  kiln  or  quarry,  but  the  strength  of  walls  and 
piers  is  also  very  greatly  affected  by  the  kind  and  quality  of  the 
mortar  used,  the  way  in  which  the  work  is  built  and  bonded,  and 
whether  the  brick  or  stone  is  laid  dry  or  wet.  All  that  can  be 
done,  therefore,  is  to  give  values  which  will  be  safe  for  the  differ- 
ent kinds  of  masonry  built  in  the  usual  manner. 
'  "Working-  Strength  of  Masonry. — The  building  laws  of 
most  of  the  larger  cities  of  this  country  specify  the  maximum 
loads  per  sq.  ft.  which  shall  be  placed  upon  different  kinds  of 
masonry,  which  of  course  must  govern  the  architect  when  build- 
ing in  those  places. 

When  there  is  no  restriction  of  this  kind,  Table  I.  will  give  a 
pretty  good  idea  of  the  maximum  loads  which  it  is  safe  to  put 
upon  the  different  kinds  of  work  indicated.  Table  II.  gives  the 
maximum  safe  loads  as  specified  in  the  building  laws  of  seven  dif- 
ferent cities,  and  in  the  latter  part  of  the  chapter  is  given  records 


STRENGTH  OF  MASONRY  AND  CONCRETE.    213 

of  numerous  tests  made  to  determine  the  ultimate  or  breaking 
strength  of  various  kinds  of  brick,  building  stones,  mortars,  and 
concretes,  which  are  of  value  in  determining  the  safe  load  for 
special  cases. 

In  fixing  the  safe  resistance  of  masonry  from  tests  on  the  ulti- 
mate strength  of  work  of  the  same  kind,  a  factor  of  safety  of  at 
least  10  should  be  allowed  for  piers  and  20  for  arches. 

The  Chicago  building  ordinance  fixes  the  maximum  stress 
for  dimension  stone  piers  at  one-thirtieth  of  the  ultimate  strength 
of  the  stone  when  the  beds  are  dressed  to  a  uniform  bearing  over 
their  entire  surface,  and  at  one-fiftieth  of  the  ultimate  strength 
when  the  beds  are  not  dressed. 

When  the  stress  exceeds  one-seventieth  of  the  ultimate 
strength  the  stones  must  be  bedded  in  Portland-cement  mortar. 

TABLE  I.— SAFE  WORKING  LOADS  FOR  MASONRY. 

Brickwork  in  walls  or  piers. 

TONS    PER    SQUARE    FOOT. 

Eastern.  Western. 

Red  brick  in  lime  mortar 7  5 

hydraulic  lime  mortar 6 

natural  cement  mortar,  1  to  3 .   10  8 

Arch  or  pressed  brick  in  lime  mortar 8  6 

"           "            lt          natural  cement.  ...    12  9 

"           "             "         Portland  cement...    15  12J 
Piers  exceeding  in  height  six  times  their  least  dimensions  should 
be  increased  4  ins.  in  size  for  each  additional  6  ft. 

Stonework. 
(Tons  per  square  foot.) 

Rubble  walls,  irregular  stones 3    » 

coursed,  soft  stone 2J 

"  "        hard  stone 5  to  16 

Dimension  stone,  squared  in  cement : 

Sandstone  and  limestone 10  to  20 

Granite 20  to  40 

Dressed  stone,  with  f-inch  dressed  joints  in  cement: 

Granite 60 

Marble  or  limestone,  best 40 

Sandstone 30 

Height  of  columns  not  to  exceed  eight  times  least  diameter. 


214    STRENGTH  OF  MASONRY  AND  CONCRETE. 


Concrete.* 

Portland  cement,  1  to  8,  6  months,  10  tons,  1  year,  15  to  20  tons 
Rosendale  cement,  1  to  6,  6  months,  3  tons,  1  year,    5  to  8  tons 

Hollow  Tile. 
(Safe  loads  per  square  inch  of  effective  bearing  parts.) 

Hard  fire-clay  tiles 80  Ibs.f 

' '     ordinary  clay  tiles 60    ' ' 

Porous  terra-cotta  tiles 40    ' l 

Mortars. 
(In  J-inch  joints,  3  months  old,  tons  per  square  foot.) 

Portland  cement,  1  to  4 40 

Rosendale  cement,  1  to  3 13 

Lime  mortar,  best 8  to  10 

Best  Portland  cement,  1  to  2,  in  J-inch  joints  for  bed- 
ding iron  plates 70 

TABLE  II.— COMPARISON  OF  BUILDING  LAWS. 


i 

. 

.5 

eT  . 

o"  . 

"h 

c 

"3  • 

'i. 

C 

Materials. 

•£05 

§00 

^a 

*l 

il 

fl 

Q}0^ 

pa 

W 

CD 

o^ 

sT 

1 

c- 

Allowable  pressures  in  tons  per  sq.  ft. 

60 

72-172 

40 

Marble  and  limestone,  cut  

40 

50-165 

Sandstone,  hard,  cut  

30 

28-115 

12 

Hard-burned  brick  in  Port,  cement 

18 

'12* 

15 

;     in  nat.  cement  . 

15 

9 

15 

9" 

15 

9 

in  cem't  &  lime. 

12 

in 

"ii* 

12 

1      in  lime  mortar  . 

8 

"e" 

8 

0-^ 

11 

8 

8 

Pressed  brick  in  Portland  cement.  . 

12 

in  natural  cement 

9 

12 

Rubble  stone  in  natural  cement.  .. 

5 

8 

'16' 

12 

Dimension  stone  in  foundations.  .  . 

6 

5-7 

30 

Portland  cement  concrete  in  foun- 

dations   

4 

15 

15 

10 

Natural  cement  concrete   in   foun- 

dations   

8 

4 

4 

Brick  Piers. — As  a  rule  brickwork  is  subject  to  its  full 
safe  resistance  only  when  used  in  piers,  and  in  small  sections  of 
walls,  under  bearing- plates.  In  the  latter  case  but  a  few 

*  See  pp.  226-228. 

t  These  loads  are  those  allowed  by  the  Chicago  Building  Ordinance. 


STRENGTH  OF  MASONRY  AND  CONCRETE.    215 

courses  receive  the  full  load,  and  hence  a  greater  unit  stress  may 
be  allowed  than  for  piers. 

Values  for  computing  the  area  of  bearing  plates  are  given 
in  Chapter  XIII. 

Aside  from  the  quality  of  the  work  and  materials  the  two 
elements  which  most  influence  the  strength  of  brick  piers  are 
the  proportions  of  height  to  least  horizontal  dimensions  and  the 
method  of  bonding.  When  the  height  of  a  brick  pier  exceeds 
six  times  its  least  dimension  the  load  per  square  foot  should  be 
reduced  from  the  values  given  in  Table  I. 

Formulas  for  the  Safe  Strength  of  Brick  Piers  exceeding  six 
diameters  in  height. 

From  the  records  of  numerous  tests  on  the  strength  of  brick 
piers,  from  some  formulas  published  by  Prof.  Ira  O.  Baker  in 
the  Brickbuilder  of  April,  1898,  and  also  from  personal  obser- 
vation, the  author  has  deduced  the  following  formulas  for  the 
maximum  working  loads  of  first-class  brickwork  in  piers  whose 
height  exceeds  six  times  their  least  dimension. 
Piers  laid  with  rich  lime  mortar. 

TT 

Safe  load  per  square  inch  =  110  — 5yr.        ...     (1) 
Piers  laid  with  I  to  2  natural-cement  mortar. 

TT 

Safe  load  per  square  inch  =  140—  5 iyr»     ...     (2) 
Piers  laid  with  I  to  3  Portland-cement  mortar. 

TT 

Safe  load  per  square  inch  =  200— 6yr- (3) 

H  representing  the  height  in  feet,  and  D  the  least  horizontal 
dimension  in  feet.* 

For  a  pier  20  ft.  high  and  2  ft.  sq.  these  formulas  will  reduce 
the  safe  load  to  4.3  tons  per  sq.ft. for  lime  mortar,  6.1  tons  for 
natural  cement  mortar,  and  10  tons  for  Portland  cement  mortar. 
No  pier  over  8  ft.  high,  should  be  less  than  12"X12",  and 
when  from  6  to  8  ft.  in  height  they  should  be  at  least  8"X  12". 

Brick  piers  intended  to  carry  more  than  50  per  cent,  of  the 
safe  loads  given  above  should  not  be  built  in  freezing  weather 
nor  with  dry  bricks.  Lime  mortar  should  not  be  used  for 

*  For  piers  faced  with  pressed  brick,  laid  with  J4"  joint  or  less,  and 
backed  with  common  brick  in  lime  mortar,  only  the  dimensions  of  the  back- 
ing should  be  considered  in  figuring  the  strength  of  the  pier.  If  backing  is 
laid  in  cement  mortar,  and  face  brick  well  tied  to  backing,  the  full  section 
of  pier  may  be  considered. 

For  piers  veneered  with  stone  or  terra-cotta,  4"  thick,  only  the  strength 
of  the  backing  should  be  considered. 


216    STRENGTH  OF  MASONRY  AND  CONCRETE. 

building   piers   that   will   receive   their  full  load  within  three 
months. 
Effect  of  Bond  on  the  Strength  of  Brick  Work.— 

Brick  piers,  loaded  to  the  point  of  destruction,  always  fail  by  the 
splitting  and  bulging  out  of  the  pier,  and  not  by  direct  crushing 
of  the  brick  or  mortar,  showing  that  the  pier  is  weakest  in  the 
bond  and  in  the  tensile  or  transverse  strength  of  the  brick.  It  is 
very  important  therefore  that  the  brickwork  be  well  bonded,  and 
all  joints  filled  with  mortar  or  grouted.  The  strength  of  a  brick 
pier  intended  to  carry  an  extreme  load  would  probably  be 
increased  b}^  bonding  frequently  with  hoop  iron  in  addition 
to  the  regular  brick  bond.* 

Bond  Stones  in  Piers. — Many  competent  architects  and 
builders  consider  that  the  strength  of  a  brick  pier  is  increased 
by  inserting  bond  stones,  from  5  to  8  ins.  in  thickness  and  the 
full  size  of  the  pier,  every  3  or  4  ft.  in  height. 

The  Chicago  Building  Ordinance  requires  that  for  all  piers 
having  a  height  four  or  more  times  their  least  dimension  there 
shall  be  a  bond  stone  at  least  8  ins.  thick  for  each  distance  in 
height  equal  to  double  that  of  the  smallest  dimension  of  such 
pier.  The  Building  Laws  for  the  City  of  New  York  require 
bond  stones  every  thirty  inches  in  height,  and  at  least  4  ins.  thick. 

On  the  other  hand,  there  are  many  first-class  builders  who 
consider  that  bond  stones  in  a  pier  do  more  harm  than  good,  and 
the  author  is  of  the  opinion  that  this  is  generally  the  case.  The 
Boston  Building  Law  does  not  require  bond  stones.  If  bond 
stones  are  used,  they  should  be  bedded  so  as  to  bear  rather  more 
heavily  on  the  inner  portion  of  the  pier  than  on  the  outer  4  ins., 
for  unless  this  is  done  the  outer  shell  will  take  most  of  the  load, 
and  will  be  likely  to  bulge  away  from  the  core. 

Piers  which  support  girders  or  columns  should  have  a  cap- 
stone or  iron  plate  of  sufficient  strength  to  distribute  the  pressure 
over  the  entire  cross-section  of  the  pier. 

Wails  faced  with  Stone,  Terra-cotta,  or  Cement 
Blocks. — Brick  walls  faced  with  blocks  or  ashlar  of  any 
material  should  always  have  the  backing  laid  in  cement — or 
cement  and  lime — mortar  unless  the  backing  is  very  thick,  say 
30  ins.  or  more.  The  aggregate  thickness  of  the  mortar  joints  in 
the  backing  is  so  much  greater  tha-n  in  the  facing,  that  any 
shrinkage  or  compression  of  the  mortar  tends  to  throw  undue 
weight  on  the  facing  and  to  separate  it  from  the  backing. 

*  The  manner  in  which  brick  piers  fail  is  excellently  shown  by  illustra- 
tions on  page  79  of  the  Brickbuilder  for  May,  1896. 


STRENGTH  OF  MASONRY  AND  CONCRETE.     217 

Veneering  of  any  kind  should  be  tied  to  the  backing  at  least 
every  18  ins.  in  height. 

The  New  York  Building  Code  requires  (Sections  28  and  29) 
that  all  bearing  walls  faced  with  brick  laid  in  running  bond, 
and  all  walls  faced  with  stone  ashlar  less  than  8  ins.  thick,  shall 
be  of  such  thickness  as  to  make  the  wall  independent  of  the 
facing  conform  to  that  required  for  unfaced  walls.  Ashlar 
8  ins.  thick  and  bonded  into  the  backing  may  be  counted  as 
part  of  the  thickness  of  the  wall. 

Grouting.* — It  is  contended  by  persons  having  large  ex- 
perience in  building  that  masonry  carefully  grouted,  when  the 
temperature  is  not  lower  than  40°  Fahr.,  will  give  the  most 
efficient  result. 

Many  of  the  largest  buildings  in  New  York  City  have  grouted 
walls. 

The  Mersey  docks  and  warehouses  at  Liverpool,  England,  one 
of  the  greatest  pieces  of  masonry  in  the  world,  were  grouted 
throughout.  It  should  be  stated,  however,  that  there  are  many 
engineers  and  others  who  do  not  believe  in  grouting,  claiming  that 
there  is  a  tendency  of  the  materials  to  separate  and  form  layers. 

Crushing'  Height  of  Brick  and  Stone. — If  we  assume 
the  weight  of  brickwork  to  be  120  pounds  per  cubic  foot,  and  that 
it  would  commence  to  crush  under  700  pounds  per  square  inch, 
then  a  wall  of  uniform  thickness  would  have  to  be  840  ft.  high 
before  the  bottom  courses  would  commence  to  crush  from  the 
weight  of  the  brickwork  above. 

Average  sandstones  at  145  pounds  per  cubic  foot  would  require 
a  column  5,950  ft.  high  to  crush  the  bottom  stones;  an  average 
granite  at  165  pounds  per  cubic  foot  would  require  a  column 
10,470  ft.  high.  The  Merchants'  shot-tower  at  Baltimore  is 
246  ft.  high,  and  its  base  sustains  a  pressure  of  six  tons  and  a 
half  (of  2,240  pounds)  per  square  foot.  The  base  of  the  granite 
pier  of  Saltash  Bridge  (by  Brunei)  of  solid  masonry  to  the  height 
of  96  ft.,  and  supporting  the  ends  of  two  iron  spans  of  455  ft. 
each,  sustains  nine  tons  and  a  half  per  square  foot. 

Stone  Piers. — Piers  of  good  strong  building  stone  laid  in 
courses  the  full  size  of  the  pier,  with  the  top  and  bottom  courses 
bedded  true  and  even,  may  be  used  to  support  very  heavy  loads. 
The  height  of  such  piers,  however,  should  not  exceed  ten  times 
the  least  dimension,  and  when  it  exceeds  eight  times  the  thick- 
ness, the  safe  load  should  be  reduced. 

The  joints  should  not  exceed  f  inch,  and  should  be  spread  with 
*  See  American  Architect,  July  21,  1887,  p.  11, 


218  STRENGTH  OF  MASONRY  AND  CONCRETE. 

1  to  2  Portland-cement  mortar,  kept  back  1  inch  from  the  face 
of  the  pier  to  prevent  spalling  of  the  edges. 

A  test  of  the  strength  of  a  limestone  pier  12  ins.  square  is  de- 
scribed under  Tests  on  the  Crushing  Resistance  of  Stone  in  this 
chapter. 

Rubble-work  should  not  be  used  for  piers  whose  height  ex- 
ceeds five  times  the  least  dimension,  or  in  which  the  latter  is 
less  than  20  ins. 

Records  of  Tests  on  the  Crushing  Resistance  of 
Bricks. — Table  III  gives  the  results  of  some  tests  on  brick, 
made  under  the  direction  of  the  author,  in  behalf  of  the  Mas- 
sachusetts Charitable  Mechanics'  Association. 


TABLE  III.— SHOWING  THE  ULTIMATE  AND  CRACK- 
ING STRENGTH  OF  THE  BRICK,  THE  SIZE  AND 
AREA  OF  FACE. 


Com- 

Name of  brick. 

Size. 

Area  of 
face  in 
sq  ins 

menced 
to  crack 
under 

Net 
strength 
Ibs.  per 

Ibs.  per 

sq.  in. 

sq.  m. 

Philadelphia  Face  Brick  

Whole  brick 

33.7 

4,303 

6,062 

Whole  brick 

32  2 

3,400 

5,831 

t«                                  *4                   4« 

Whole  brick 

34.03 

2,879 

5,862 

Average  

3,527 

5,918 

Cambridge  Brick  (Eastern).  .  .  . 

Half  brick 
Whole  brick 

10.89 
25.77 

3,670 
7,760 

9,825 
12,945 

i«              ««            *• 

Half  brick 

12  67 

3,393 

11,681 

Half  brick 

13.43 

3,797 

14,296 

4,655 

12,186 

Boston  Terra-Cotta  Co/s  Brick 

Half  brick 

11.46 

11,518 

13,839 

Whole  brick 

25.60 

8,593 

11,406 

Whole  brick 

28.88 

3,530 

9,766 

7,880 

11,670 

New  England  Pressed  Brick.  .  . 

Half  brick 
Half  brick 

12.95 
13.2 

3,862 
8,180 

10,270 
13,530 

««                   ««          «« 

Half  brick 

13.30 

2,480 

13,082 

••                   ••          •• 

Half  brick 

13.45 

4,535 

13,085 

4,764 

12,490 

The  specimens  were  tested  in  the  government  testing-machine 
at  Watertown,  Mass.,  and  great  care  was  exercised  to  make  the 
tests  as  perfect  as  possible.  As  the  parallel  plates  between  which 
the  brick  and  stone  were  crushed  are  fixed  in  one  position,  it  is 
necessary  that  the  specimen  tested  should  have  perfectly  parallel 
faces. 


STRENGTH  OF  MASONRY  AND  CONCRETE.    219 

The  bricks  which  were  tested  were  rubbed  on  a  revolving  bed 
until  the  top  and  bottom  faces  were  perfectly  true  and  parallel. 

The  preparation  of  the  bricks  in  this  way  required  a  great  deal 
of  time  and  expense;  and  it  was  so  difficult  to  prepare  some  of 
the  harder  bricks  that  they  had  to  be  broken  and  only  one- 
half  of  the  brick  prepared  at  a  time. 

The  Philadelphia  Brick  used  in  these  tests  were  obtained  from 
a  Boston  dealer,  and  were  fair  samples  of  what  is  known  in  Bos- 
ton as  Philadelphia  Face  Brick.  They  were  a  very  soft  brick. 

The  Cambridge  Brick  were  the  common  brick,  such  as  is  made 
around  Boston.  They  are  about  the  same  as  the  Eastern  Brick, 

The  Boston  Terra-Cotta  Company's  Brick  were  manufactured  of 
a  rather  fine  clay,  and  were  such  as  are  often  used  for  face  brick. 

The  New  England  Pressed  Brick  were  hydraulic-pressed  brick, 
and  were  almost  as  hard  as  iron. 

From  tests  made  on  the  same  machine  by  the  United  States 
Government  in  1884,  the  average  strength  of  three  (M.  W. 
Sands)  Cambridge,  Mass.,  face  brick  was  13,925  pounds,  and  of 
his  common  brick,  18,337  pounds  per  square  inch,  one  brick 
developing  the  enormous  strength  of  22,351  pounds  per  square 
inch.  This  was  a  very  hard-burnt  brick. 

Three  brick  of  the  Bay  State  (Mass.)  manufacture  showed  an 
average  strength  of  11,400  pounds  per  square  inch. 

The  New  England  brick  are  among  the  hardest  and  strongest 
brick  in  the  country,  those  in  many  parts  of  the  West  not  having 
one-fourth  of  the  strength  given  above,  so  that  in  heavy  build- 
ings, where  the  strength  of  the  brick  to  be  used  is  not  known 
by  actual  tests,  it  is  advisable  to  have  the  brick  tested. 

Prof.  Ira  O.  Baker,  of  the  University  of  Illinois,  reported  some 
tests  on  Illinois  brick,  made  on  the  100,000  pound  testing-ma- 
chine at  the  university,  in  1888-89,  which  give  the  crushing 
strength  of  soft  brick  at  674  pounds  per  square  inch,  average  of 
three  face  brick,  3,070  pounds,  and  of  four  paving  brick,  9,775 
pounds. 

In  nearly  all  makes  of  brick  it  will  be  found  that  the  face  brick 
are  not  as  strong  as  the  common  brick. 

Tests  of  the  Strength  of  Brick  Piers  Laid  with 
Various  Mortars.* — These  tests  were  made  for  the  purpose 
of  testing  the  strength  of  brick  piers  laid  up  with  different  cement 
mortars,  as  compared  with  those  laid  up  with  ordinary  mortar. 

*  Made  under  the  direction  of  the  author. 


220    STRENGTH  OF  MASONRY  AND  CONCRETE. 

The  brick  used  in  the  piers  were  procured  at  M.  W.  Sands's  brick- 
yard, Cambridge,  Mass.,  and  were  good  ordinary  brick.  They 
were  from  the  same  lot  as  the  samples  of  common  brick  de- 
scribed above. 

The  piers  were  8"  by  12",  and  nine  courses,  or  about  22J" 
high,  excepting  the  first,  which  was  but  eight  courses  high. 
They  were  built  Nov.  29,  1881,  in  one  of  the  storehouses  at  the 
United  States  Arsenal  in  Watertown,  Mass.  In  order  to  have 
the  two  ends  of  the  piers  perfectly  parallel  surfaces,  a  coat 
about  half  an  inch  thick  of  pure  Portland  cement  was  put  on  the 
top  of  each  pier  and  the  foot  was  grouted  in  the  same  cement. 

March  3,  1882,  three  months  and  five  days  later,  the  tops  of 
the  piers  were  dressed  to  plane  surfaces  at  right  angles  to  the 
sides  of  the  piers.  On  attempting  to  dress  the  lower  ends  of  the 
piers,  the  cement  grout  peeled  off,  and  it  was  necessary  to  re- 
move it  entirely  and  put  on  a  layer  of  cement  similar  to  that  on 
the  top  of  the  piers.  This  was  allowed  to  harden  for  one  month 
and  sixteen  days,  when  the  piers  were  tested.  At  that  time  the 
piers  were  four  months  and  twenty-six  days  old.  As  the  piers 
were  built  in  cold  weather,  the  bricks  were  not  wet. 

The  piers  were  built  by  a  skilled  bricklayer,  and  the  mortars 
were  mixed  under  his  superintendence.  The  tests  were  made 
with  the  government  testing-machine  at  the  Arsenal. 

The  following  table  is  arranged  so  as  to  show  the  result  of  these 
tests,  and  to  afford  a  ready  means  of  comparison  of  the  strength  of 
brickwork  with  different  mortars.  The  piers  generally  failed 
by  cracking  longitudinally,  and  some  of  the  brick  were  crushed. 


,4 

8*S 

"^r^i 

e 

SI 

0 

f-   £   0> 

|s 

8"  X  12"  pier. 

to 

aa>  g^; 

Common  bricks  laid  in  — 

|f 

£§8g 

l! 

P 

£"" 

p 

Lbs. 

Lbs. 

Lbs. 

Lime  mortar  

150,000 

833 

1,562 

Lime  mortar,  3  parts;    Portland  cement,  1 

part.  .  .         .             .             

290,000 

1,875 

3,020 

Lime  mortar  .  3  parts;   Newark  and  Rosen- 

dale  cements,  1  part.                

245,000 

1  ,354 

2,552 

Lime  mortar,  3  parts;  Roman  cement,  1  part 

195,000 

1,041 

2,030 

Portland  cement,  1  part;  sand,  2  parts  

240,000 

1,302 

2,500 

Newark   and    Rosendale    cements,    1    part; 

205  000 

708 

2,135 

Roman  cement,  1  part;  sand,  2  parts  

185,000 

1,770 

1,927 

STRENGTH  OF  MASONRY  AND  CONCRETE.  221 

The  Portland  cement  used  in  these  tests  was  made  by  Brooks, 
Shoobridge  &  Co.,  of  England. 

As  the. actual  strength  of  brick  piers  is  a  very  important  con- 
sideration in  building  construction,  some  tests?>  made  by  the 
United  States  Government  at  Watertown,  Mass.,  and  contained 
in  the  report  of  the  tests  made  on  the  Government  testing- 
machine  for  the  year  1884,  are  given  as  being  of  much  value. 

Three  kinds  of  brick  were  represented  in  the  construction  of 
the  piers,  and  mortars  of  different  composition,  ranging  in 
strength  from  lime  mortar  to  neat  Portland  cement.  The  piers 
Tanged  in  cross-section  dimensions  from  8"X8"  to  16"Xl6", 
and  in  height  from  16  ins.  to  10  ft. 

The  piers  were  tested  at  the  age  of  from  18  to  24  months. 

Table  IV  gives  the  results  obtained  and  memoranda  regard- 
ing the  size  and  character  of  the  piers. 

Test  of  Mortar  Cubes. — Table  V  shows  the  crushing 
strength  of  6"  cubes  of  mortar  made  by  the  United  States 
Government  at  Watertown,  Mass.,  in  the  year  1884. 

The  mortar  cubes  were  allowed  to  season  in  the  open  air  a 
period  of  fourteen  and  a  half  months,  when  they  were  tested. 

The  age  of  the  plaster  cube  was  four  months.  It  should  be 
noticed  that,  while  the  cubes  of  Rosendale  cement  and  lime 
mortar  showed  a  greater  strength  than  when  sand  alone  was 
mixed  with  the  cement,  with  the  cubes  of  Portland  cement  and 
lime  mortar  the  reverse  was  the  case,  differing  from  the  result 
obtained  by  the  author.  This  shows  the  necessity  of  a  number 
and  variety  of  tests. 

Tests  of  the  Crushing   Kesistance  of  Various 
Building  Stones. 

SANDSTONES. 

Long  Meadow  (Mass.)  Stone.* — Reddish-brown  sandstone, 
two  blocks  about  4"  X  4"  in  cross-section  and  8"  high. 

Block  No.  1  commenced  to  crack  at  10,333  Ibs.  per  square  inch, 
and  flew  from  the  machine  in  fragments  at  13,596  Ibs.  per  square 
inch. 

Block  No.  2  commenced  to  crack  at  3,012  Ibs.  per  square  inch 
and  failed  completely  at  9,121  Ibs.  per  square  inch. 

*  These  tests  made  with  U.  S.  testing-machine  at  Watertown  Arsenal, 
Mass. 


222  STRENGTH  OF  MASONRY  AND  CONCRETE. 


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224    STRENGTH   OF  MASONRY  AND  CONCRETE. 
TABLE  V.— TABULATED  RESULTS,  6"  MORTAR  CUBES. 

CRUSHING  STRENGTH. 


No. 
of 
test. 

Composition. 

First 
crack. 

Ultimate 
strength 
persq.  in. 

Weiatht 
per  cu.  ft. 

Lbs. 

Lbs. 

Lbs. 

3a 

1  part  lime,  3  parts  sand 

135 

112 

36 

1     "       "3     " 

119 

111 

3c 

1     "       "      3     " 

118 

106 

4a 

1  part  Portland  cement,  2  part  j  sand 

560 

116 

46 

1     "                            "2      " 

696 

120 

4c 

1     "                            "2      " 

11,500 

383 

115 

5a 

1  part  Rosendale  een.ent,  2  parts  sand 

156 

111 

56 

I     "                               "2     " 

186 

109 

5c 

1     "                              "2     " 

'  4,5()6 

143 

107 

6a 

Neat  Portland  cement 

2,673 

126 

66 

"             "               '* 

95,666 

3.54S 

129 

6c 

44             *'               *4 

4,227 

135 

7a 

Neat  Rosendale  cement 

11,000 

421 

94 

76 

"              "                " 

19,000 

615 

99 

7c 

" 

19,200 

526 

97 

8a 

1  part  Portland  cement,  2  parts  lime  mortar1 

204 

109 

86 

1     "                           "2     "       "           ** 

198 

110 

8c 

1     "                                    2     ' 

175 

103 

9a 

1  part  Rosendale  cement  2  parts  lime  mortar1 

191 

105 

96 

1     "             "               "       2      "       " 

193 

106 

9c 

1     "             "                "       2       "       " 

162 

105 

Plaster-of  -Pari  s 

1,981 

74 

1  Lime  mortar,  1  part  lime,  3  parts  sand. 

Sandstone  from  Norcross  Bros.,  Quarries,  East  Long  Meadow, 
Mass.— Soft  Saulsbury*  Block  No.  1,  4"X4"X8"  high,  com- 
menced to  crack  at  8,250  Ibs.  and  failed  at  8,812  Ibs.  per  square 
inch. 

Block  No.  2,  4"X4"XS"  high,  commenced  to  crack  at  6,500 
Ibs.  and  failed  at  8,092  Ibs.  per  square  inch. 

Hard  Saulsbury  *  Block  No.  1,  4//X4//X8//  high  (about), 
commenced  to  crack  at  12,716  Ibs.  and  failed  at  13,520  Ibs.  per 
square  inch. 

Block  No.  2,  same  size  as  No.  1,  commenced  to  crack  at  13,953 
Ibs.  and  failed  at  14650  Ibs.  per  square  inch. 

Kibbe  Stone*  Block  No.  1,  6"X6"X6",  commenced  to 
crack  at  12,590  Ibs.  and  failed  at  12,619  Ibs.  per  square  inch. 


+  These  tests  made  with  U.  S.  testing-machine  at  Watertown  Arsenal, 
Mass. 


STRENGTH  OF  MASONRY  AND  CONCRETE.    225 


Block  No.  2,  same  size  as  No.  1,  commenced  to  crack  at  12,185 
Ibs.  and  failed  at  12,874  Ibs.  per  square  inch. 

Brown  Stone  from  the  Shaler  &  Hall  Quarry  Co.,  Portland, 
Conn.* 


Dimensions. 

Sectional 
area, 
sq.  ins. 

First 
crack, 
Ibs. 

Ultimate 
strength, 
Ibs.  per 
sq.  in. 

Classification. 

Height, 
ins. 

Compressed 
surface, 
ins. 

2.50 
2.50 
2.98 
2.95 
2.51 
2.48 

2.50 
2.48 
3.00 
2.98 
2.55 
2.48 

2.45 
2.47 
2.95 
2.97 
2  .  53 
2.52 

6.13 
6.13 

8.85 
S.85 
6.45 
6.25 

84,800 
81,700 
123,200 
122,000 
63,850 
58,340 

13,980 
13,330 
13,920 
15,020 
9,900 
9,330 

1st  quality 
1st 
2d 
3d 
Bridge 
Bridge 

Brown  Stone  from  the  Middlesex  Quarry  Co.,  Portland,  Conn.\ 
Four  nearly  cubical  blocks,  about  1J"  square.  Pressure  per 
square  inch  at  time  of  failure:  No.  1, 10,928  Ibs.;  No.  2,  10,322 
Ibs. ;  No.  3,  8,252  Ibs.,  and  No.  4,  6,322  Ibs. 

Red  Sandstone  f  jrom  Greenlee  &  Son's  Quarries  at  Manitou, 
Colo.  One  specimen  failed  at  11,000  Ibs.  per  sq.  inch;  weight  140 
Ibs.  per  cu.  ft. 

Light-red  Laminated  Sandstone^  from  St.  Vrain  Canon,  Colo. 
(a  very  hard  stone,  excellent  for  walks  and  foundations).  Crush- 
ing strength  on  bed  11,505  Ibs.  per  square  inch;  weight  150  Ibs. 
per  cubic  foot. 

Gray  Sandstone  %  (free-working)  from  Trinidad,  Colo.  Crush- 
ing strength  10,000  Ibs.  per  square  inch;  weight  145  Ibs.  per  cubic 
foot. 

Gray  Sandstone  J  from  Fort  Collins,  Colo,  (laminated  and  simi- 
lar in  quality  to  the  St.  Vrain  Stone).  Crushing  strength  on 
bed  11,700  Ibs.  per  square  inch;  weight  140  Ibs.  per  cubic  foot 
(one  ton  of  this  stone  measures  just  a  perch  in  the  wall). 

GRANITE. 

Red  Granite  %  from  Platte  CaTion,  Colo.  Crushing  strength 
per  square  inch  14,000  Ibs.;  weight  per  cubic  foot  164  Ibs. 

*  From  tests  made  by  Colt's  Patent  Fire-arms  Manufacturing  Co. 

t  These  tests  made  with  U.  S.  testing-machine  at  Watertown  Arsenal, 
Mass. 

J  From  tests  made  for  the  Board  of  Capitol  Managers  (of  Colorado)  by 
State  Engineer  E.  S.  Nettleton,  in  1885,  on  two-inch  cubes. 


226  STRENGTH  OF  MASONRY  AND  CONCRETE. 

Lava  Stone  from  the  Kerr  Quarries,  near  Salida,  Colo.      Four 
cubical  blocks.* 


Dimensions. 

Sectional 
area, 
sq.  ins. 

First 
crack, 
Ibs. 

Ultimate  strength, 

Height, 
ins. 

Compressed  sur- 
face, ins. 

Lbs. 

Lbs.  per 
sq.  in. 

4.00 
4.00 
2.00 
1.99 

4.00 
4.00 
2.00 
1.99 

4.00 
4.00 
1.99 
1.99 

16.00 
16.00 
3.98 
3.96 

16f,,900 
174,100 
36,400 
38,200 

165,000 
174,100 
37,100 
38,200 

10,369 
10,881 
9,322 
9,646 

Lava  Stone ,f  Curry's  Quarry,  Douglas  County.  Crushing 
strength,  10,675  ,,lbs.  per  square  "inch;  weight,  119  Ibs.  per 
cubic  foot.  (Experience  has  shown  that  this  stone  is  not  suit- 
able for  piers,  or  where  any  great  strength  is  required,  as  it 
cracks  very  easily.) 

MARBLE. 

White  marble  quarried  at  Sutherland  Falls,  Vermont.  Two 
cubical  blocks  about  6  ins.  square.* 

Block  No.  1  commenced  to  crack  at  9,750  Ibs.  per  square  inch 
and  failed  suddenly  at  11,250  Ibs.  per  square  inch. 

Block  No.  2  did  not  crack  until  it  suddenly  gave  way  at  10,243 
Ibs.  per  square  inch. 

Test  of  a  Limestone  Pier. — A  pier  of  Lemont  limestone  1  ft.  sq. 
in  cross-section  and  9  ft.  high,  composed  of  7  stones  with  bear- 
ing surfaces  planed  perfectly  true  and  parallel  to  natural  bed 
and  the  joints  washed  with  a  thin  grout  of  the  best  English 
Portland  cement,  was  tested  at  the  Watertown  Arsenal  for 
Gen.  Wm.  Sooy  Smith,  and  only  commenced  to  crack  when  the 
full  power  of  the  machine,  400  tons,  was  exerted. 

Crushing  Strength  of  Concrete. — Tests  for  crushing 
strength  made  on  6-in.  cubes  of  concrete,  made  of  one  part  silica 
Portland  cement  (1.1),  two  parts  sand,  and  three  parts  gravel. 
The  concrete  was  taken  from  the  bucket  just  as  it  was  ready  to  be 
laid  in  the  foundations  of  the  Cathedral  of  St.  John  the  Divine. 

Each  result  is  the  average  of  the  crushing  strengths  of  four  sep- 


*  Tested  at  U.  S.  Arsenal,  Watertown,  Mass. 

t  From  tests  made  by  Denver  Society  of  Civil  Engineers  in  1884,  also  on 
two-inch  cubes. 


STRENGTH  OF  MASONRY  AND  CONCRETE.  227 


arate  cubes,  made  under  exactly  the  same  conditions  at  differ- 
ent periods: 

7  days  old  crushed  at  77,162  Ibs.  or  2,143  Ibs.  per  sq.  in. 
14  "  "  "  "  83,225  "  "  2,312  "  "  "  " 
30  "  "  "  "  92,465  "  "  2,568  "  "  "  " 

The  following  table  gives  the  crushing  strength  of  12-in. 
cubes  of  concrete  prepared  and  tested  by  the  Engineering  De- 
partment of  the  District  of  Columbia  in  the  years  1896  and  1897, 
the  loads  being  in  pounds  per  square  foot.  After  the  tests  were 
completed  it  was  found  that  the  machine  used  gave  results  8% 
too  high,  and  the  figures  have  not  been  corrected. 

The  figures  for  1-year  cubes  are  averages  of  5  tests,  all  others 
give  the  mean  of  two  tests. 

A  more  complete  record  of  the  tests  may  be  found  in  the 
Engineering  Record  for  April  9,  1898.* 


No. 

Composition  of  concretes 
by  volume. 

10  days. 

45  days. 

3  mos. 

6  mos. 

1  year. 

1 

1  part  natural  cement, 
2  parts  sand. 

6  parts  average  concrete 
stone.  .  . 

Lbs. 
32,900 

Lbs. 

77,687 

Lbs. 
54,022 

Lbs. 
114  412 

Lbs. 
131  700 

o 

3 

3  parts  average  concrete 
stone,  3  parts  gravel.. 
4  parts  average  concrete 
stone,  2  parts  gravel 

15,500 

52,362 

85,315 

90,965 

121,100 
131  700 

4 

6  parts  (%  average  con- 
crete stone,  J4  grano- 
lithic)    

115  200 

5 
6 

6  parts  average  gravel.  .  . 
6  parts  coarse  concrete 
stone  (no  fine)  .  .    . 

12,500 

60,652 

51  ,980 
85  880 

49,437 

109,900 
119  300 

7 
8 

1  part  (Atlas}  Portland 
cement,  2  parts  sand. 

6  parts  average  concrete 
stone  
3  parts  average  concrete 
stone,  3  parts  gravel.. 

130,750 
136,750 

t343,520 
172,325 

266,962 

324,875 

361,600 
298  037 

440,040 
396  200 

9 

4  parts  average  concrete 
stone,  2  parts  gravel.. 

408  300 

10 

6  parts  (££  average  con- 
crete stone,  J4  grano- 
lithic)   

388  700 

11 
12 

6  parts  average  gravel     . 
G  parts  coarse  concrete 
stone  (no  fine).  . 

99,900 

234,475 

385,612 
234  475 

265,550 
220  350 

406,700 
266  300 

*  Valuable  data  on  the  crushing  strength  of  concretes  ot  different  propor- 
tions may  be  found  in  the  Engineering  News  of  Feb.  4,  1904,  p    114. 

t  Owing  to   the  great  variation  in  the  strength  of  the  two  cubes,  the 

TOfllllffl   for   Hrkt.h    «ro   friirar» 


results  for  both  are  given. 


228  STRENGTH  OF  MASONRY  AND  CONCRETE. 


The  average  crushing  strength  of  four  12-inch  cubes  of  con- 
crete, tested  at  the  U.  S.  Arsenal,  Watertown,  Mass.,  for  the 
city  of  Cleveland,  Ohio,  was  4,286  Ibs.  per  sq.  inch.  The  cubes 
were  composed  of  1  part  Vulcanite  Portland  cement,  2  parts 
lake  sand  and  4  parts  of  broken  limestone,  and  were  85  days  old 
when  tested. 

Strength  of  "Hooped"  Concrete  Columns. — In 
1892,  M.  Considere  conducted  a  series  of  experiments  at  the 
laboratory  of  P&ole  des  Fonts  et  Chaus- 
se*es,  which  demonstrated  conclusively  that 
the  resistance  of  concrete  columns  may 
be  very  greatly  increased  by  winding 
spirally  with  wire  and  then  plastering 
with  cement.  Crushing  resistances  of 
such  columns  as  high  as  9,150  Ibs.  per 
sq.  inch  on  full  section,  and  12,700  Ibs.  per 
sq.  inch  on  core  section,  were  obtained. 
M.  Considere  considers  that  working- 
values  may  be  allowed  for  such  columns  of 
from  950  to  2,150  Ibs.  per  sq.  inch,  accord- 
ing to  the  way  in  which  the  columns  are 
made  and  reinforced.  See  the  Engineer- 
ing Record  of  Jan.  3,  10,  17  and  24,  1903. 

The  accompanying  engraving  shows 
the  method  of  reinforcing  concrete  col- 
umns, employed  by  the  Ransome  Com- 
panies. With  this  reinforcement  it  is  customary  to  allow  a  safe 
stress  in  the  column  of  800  to  1000  Ibs.  to  the  square  inch. 

Architectural  Terra-Cotta — Weight  and  Strength. 

The  lightness  of  terra-cotta,  combined  with  its  enormous  re-= 
sisting  strength,  and  taken  in  connection  also  with  its  durability 
and  absolute  indestructibility  by  fire,  water,  frost,  etc.,  ren- 
ders it  specially  desirable  for  use  in  the  construction  of  all  large 
edifices. 

Terra-cotta  for  building  purposes,  whether  plain  or  ornamental, 
is  generally  made  of  hollow  blocks  formed  with  webs  inside,  so  as 
to  give  extra  strength  and  keep  the  work  true  while  drying.  This 
is  necessitated  because  good,  well-burned  terra-cotta  cannot 
safely  be  made  more  than  about  H  inches  in  thickness, 
whereas,  when  required  to  bond  with  brickwork,  it  must  be 


Re-inforcing  Skeleton 
for  Concrete  Columns. 


STRENGTH  OF  MASONRY  AND  CONCRETE.      229 

at  least  four  inches  thick.  When  extra  strength  is  needed, 
these  hollow  spaces  are  filled  with  concrete  or  brickwork,  which 
greatly  increases  the  crushing  strength  of  terra-cotta,  although 
alone  it  is  able  to  bear  a  very  heavy  weight.  "A  solid  block  of 
terra-cotta  of  one  foot  cube  has  borne  a  crushing  strain  of  500 
tons  and  over." 


TABLE   VI.— CRUSHING   RESISTANCE    OF   BRICK,   STONE,   AND 
CONCRETES.     (PRESSURE  AT  RIGHT  ANGLES  TO  BED.)  * 

Pounds 
per  sq.  in. 

Bride:  Common,  Massachusetts 10,000 

Common,  St.  Louis 6,417 

Common,  Washington,  D.  C 7,370 

Paving,  Illinois 6,000  to  13,000 

Granites:  Blue,  Fox  Island,  Me 14,875 

Gray,  Vinal  Haven,  Me 13,000  to  18,000 

Westerly,  R.  1 15,000 

Rockport  and  Quincy,  Mass 17,750 

Milford,  Conn 22,600 

Staten  Island,  N.  Y 22,250 

East  St.  Cloud,  Minn 28,000 

Gunnison,  Colo 13,000 

Red,  Platte  Caiion,  Colo 14,600 

Limestones:  Glens  Falls,  N.  Y 11,475 

Joliet,  111 12,775 

Bedford,  Ind 6,000  to  10,000 

Salem,  Ind 8,625 

Red  Wing,  Minn 23,000 

Stillwater,  Minn 10,750 

Sandstones:  Dorchester,  N.  B.  (brown) 9,150 

Mary's  Point,  N.  B.  (fine  grain,  dark  brown) 7,700 

Connecticut  brown  stone, t  on  bed 7,000  to  13,000 

Longmeadow,  Mass,  (reddish  brown) 7,000  to  14,000 

' '  average,  for  good  quality 12,000 

Little  Falls,  N.  Y 9,850 

Medina,  N.  Y 17,000 

Potsdam,  N.  Y.  (red) 18,000  to  42,000 

Cleveland,  Ohio 6,800 

North  Amherst,  Ohio 6,212 

Berea,  Ohio 8,000  to  10,000 

Hummelstown,  Pa 12,810 

Fond  du  Lac,  Minn 8,750 

Fond  du  Lac,  Wis 6,237 

Manitou,  Colo,  (light  red) 6,000  to  11,000 

St.  Vrain,  Colo,  (hard  laminated) 11,505 

Marbles:  Lee,  Mass 22,900 

Rutland,  Vt 10,746 

Montgomery  Co.,  Pa.  .  .  10,000 

Colton,  Cal 17,783 

Italy 12,156 

Flagging:   North  River,  N.  Y 13,425 

*  For  more  complete  tables  of  the  strength,  weight,  and  composition  of 
building  stones,  see  Building  Construction  and  Superintendence,  Part  I. 
t  This  stone  should  not  be  set  on  edge. 


230  STRENGTH  OF  MASONRY  AND  CONCRETE. 

Some  exhaustive  experiments  made  by  the  Royal  Institute 
of  British  Architects  give  the  following  results  as  the  crushing 
strength  of  terra-cotta  blocks : 

Crushing  wt. 
per  cu.  ft. 

1.  Solid  block  of  terra-cotta 523  tons 

2.  Hollow  block  of  terra-cotta,  unfilled 186  tons 

3.  Hollow  block  of  terra-cotta,  slightly  made  and  unfilled  80    ' ' 

Tests  of  terra-cotta  manufactured  by  a  New  York  Com- 
pany, which  were  made  at  the  Stevens  Institute  of  Technology 
in  April,  1888,  gave  the  following  results: 

Crushing  wt.  Crushing  wt. 
percu.in.        per  cu.  ft. 

Terra-cotta  block,  2-inch  square,  red.  . . .   6,840  Ibs.  or  492  tons 

Terra-cotta  block,  2-inch  square,  buff 6,236  "    "449    " 

Terra-cotta  block,  2-inch  square,  gray 5,126"    "369    " 

From  these  results,  the  writer  would  place  the  safe  working 
strength  of  terra-cotta  blocks  in  the  wall  at  5  tons  per  square 
foot  when  unfilled,  and  10  tons  per  square  foot  when  filed  solid 
with  brickwork  or  concrete. 

Strength  of  Terra-Cotta  Brackets  or  Consoles. — 
A  cornice  modillion  made  by  the  Northwestern  Terra-Cotta 
Company,  11 J  ins.  high  at  the  wall  line,  8  ins.  wide  on  face,  with  a 
projection  of  2  feet,  was  built  into  a  wall  and  the  upper  sur- 
face loaded  with  pig  iron  to  the  extent  of  two  tons  without 
effect. 

Another  bracket,  5J  ins.  high,  6  ins.  wide,  and  14  ins.  projec- 
tion made  in  the  East,  broke  at  wall  line  under  2,650  Ibs., 
while  a  duplicate  of  it  sustained  2,400  Ibs.  for  one  month  with- 
out breaking.  (See  "The  Brickbuilder,"  Vol.  7,  p.  142.) 

The  weight  of  terra-cotta  in  solid  blocks  is  122  pounds.  When 
made  in  hollow  blocks  1J  inches  thick  the  weight  varies  from 
65  to  85  pounds  per  cubic  foot,  the  smaller  pieces  weighing  the 
most.  For  pieces  12"  X 18"  or  larger  on  the  face,  70  pounds  per 
cubic  foot  will  probably  be  a  fair  average. 

For  the  exterior  facing  of  fireproof  buildings,  terra-cotta  is 
now  considered  as  the  most  suitable  material  available. 


COMPOSITION  OF  FORCES. 


231 


CHAPTER  VI. 

COMPOSITION  AND  RESOLUTION  OP  FORCES- 
CENTRE  OP  GRAVITY. 

LET  us  imagine  a  round  ball  placed  on  a  plane  surface  at  A 
(Fig.  1),  the  surface  being  perfectly  level/so  that  the  ball  will  have 
no  tendency  to  move  until  some  force  is  imparted  to  it.  If,  now, 
we  impart  a  force,  P,  to  the  ball  in  the  direction  indicated  by  the 
arrow,  the  ball  will  move  off  in  the  same  direction.  If,  instead 
of  imparting  only  one  force,  we  impart  two  forces,  P  and  Pt  to 
the  ball,  it  will  not  move  in  the  direction 
of  either  of  the  forces,  but  will  move  off 
in  the  direction  of  the  resultant  of  these 
forces,  or  in  the  direction  Ab  in  the  figure. 
If  the  magnitude  of  the  forces  P  and 
is  indicated  by  the  length  of  the  lines, 
then,  if  we  complete  the  parallelogram 
A  BCD,  the  diagonal  DA  will  represent  the 
direction  and  magnitude  of  a  force  which 
will  have  the  same  effect  on  the  ball  as  the 
two  forces  Pj  and  P.  If,  in  addition  to  the  two  forces  P1  and  P 
we  now  apply  a  third  force,  P,,  the  ball  will  move  in  the  direction 
of  the  resultant  of  all  three  forces,  which  can  be  obtained  by  com- 
pleting the  parallelogram  ADEF,  formed  by  the  resultant  DA 
and  the  third  force  P2.  The  diagonal  R  of  this 
second  parallelogram  will  be  the  resultant  of  all 
three  of  the  forces,  and  the  ball  will  move  in  the 
direction  Ae.  In  the  same  way  we  could  find 
the  resultant  of  any  number  of  forces. 

Again,  suppose  we  have  a  ball  suspended  in 
the  air  whose  weight  is  indicated  by  the  line  W 
(Fig.  2).  Now,  we  do  not  wish  to  suspend  this 
ball  by  a  vertical  line  above  it,  but  by  two  in- 
clined lines  or  forces,  P  and  Pj.  What  shall  be 
the  magnitude  of  these  two  forces  to  keep  the  ball  suspended  in 
just  this  position?  We  have  here  just  the  opposite  of  our  last 


232  COMPOSITION  OF  FORCES. 

case;  and,  instead  of  finding  the  diagonal  of  the  resultant,  we 
have  the  diagonal,  which  is  the  line  W,  and  wish  to  find  the  sides 
of  the  parallelogram.  To  do  this,  prolong  P  and  Plt  and  from  B 
draw  lines  parallel  to  them  to  complete  the  parallelogram.  Then 
will  CA  be  the  required  magnitude  for  P,  and  CB  for  P,. 

Thus  we  see  how  one  force  can  be  made  to  have  the  same  effect 
as  many,  or  many  can  be  made  to  do  the  work  of  one.  Bearing 
the  above  in  mind,  we  are  now  prepared  to  study  the  following 
propositions : 

I.  A  force  may  be  represented  by  a  straight  line. 

In  considering  the  action  of  forces,  either  in  relation  to  struc- 
tures or  by  themselves,  it  is  very  convenient  to  represent  the 
force  graphically,  which  can  easily  be  done  by  a  straight  line  hav- 
ing an  arrow-head,  as  in  Fig.  3.  The  length 
of  the  line,  if  drawn  to  a  scale  of  pounds, 
shows  the  value  of  the  force  in  pounds;  the 
direction  of  the  line  indicates  the  direction 
p.  o  of  the  force;  the  arrow-head  shows  which 

way  it  acts;  and  the  point  A  denotes  the 
point  of  application.  Thus  we  have  the  direction,  magnitude, 
and  point  of  application  of  the  force  represented,  which  is  all 
that  we  need  to  know. 

Parallelogram  of  Forces. — II.  //  two  forces  applied  at 
one  point,  and  acting  in  the  same  plane,  be  represented  by  two 
straight  lines  inclined  to  each  other,  their  resultant  will  be  equal  to 
the  diagonal  of  the  parallelogram  formed  on  these  lines. 

Thus,  if  the  lines  AB  and  AC  (Fig.  4)  represent  two  forces  act- 
ing on  one  point,  A,  and  in  the  same  plane,  / 
then,  to  obtain  the  force  which  would  have  the 
same  effect  as  the  two  forces,  we  complete  the 
parallelogram  ABDC,  and  draw  the  diagonal 
AD.     This  line  will  then  represent  the  result- 
ant of  the  two  forces. 

When  the  two  given  forces  are  at  right  angles  to  each  other, 
the  resultant  will,  by  geometry,  be  equal  to  the  square  root  of  the 
sum  of  the  squares  of  the  other  two  forces. 

The  Triangle  of  Forces. — III.  //  three  forces  acting  on 
a  point  be  represented  in  magnitude  and  direction  by  the  sides 
of  a  triangle  taken  in  order,  they  will  keep  the  point  in  equili- 
brium. 

Thus  let  P,  Q,  and  R  (Fig.  5)  represent  three  forces  acting  on 
the  point  O.  Now,  if  we  can  draw  a  triangle  like  that  shown  at 


COMPOSITION  OF  FORCES.  233 

the  right  of  Fig.  5,  whose  sides  shall  be  respectively  parallel  to 
the  forces,  and  shall  have  the  same  relation  to  each  other  as  do 
the  forces,  then  the  forces  will  keep  the  , 
point  in  equilibrium.  If  such  a  triangle 
cannot  be  drawn,  the  forces  will  be  un- 
balanced, and  the  point  will  not  be  in 
equilibrium. 

The  Polygon  of  Forces.— IV.  // 
any  number  of  forces  acting  at  a  point  can 
be  represented  in  magnitude  and  direction 
by  the  sides  of  a  polygon  taken  in  order, 
they  will  be  in  equilibrium.  Fig. 5. 

This  proposition  is  only  the  preceding 
one  carried  to  a  greater  extent. 

Moments. — In  considering  the  stability  of  structures  and 
the  strength  of  materials,  we  are  often  obliged  to  take  into  con- 
sideration the  moments  of  the  forces  acting  on  the  structure  or 
piece ;  and  a  knowledge  of  what  a  moment  is,  and  the  properties 
of  moments,  is  essential  to  the  proper  understanding  of  these 
subjects. 

When  we  speak  of  the  moment  of  a  force,  we  must  have  in 
mind  some  fixed  point  about  which  the  moment  is  taken. 

The  moment  of  a  force  about  any  given  point  may  be  defined  as 
the  product  of  the  force  into  the  perpendicular  distance  from  the 
point  to  the  line  of  action  of  the  force;  or,  in  other  words,  the 
moment  of  a  force  is  the  product  of  the  force  by  the  arm  with  which 
it  acts. 

Thus  if  we  have  a  force  F  (Fig.  6),  and  wish  to  determine  its 

PK^  /  moment  about  a  point  P,  we  determine  the  perpen- 

Xx\^    /    dicular  distance  Pa,  between  the  point  and  the  line 

/&      of  action  of  the  force,  and  multiply  it  by  the  force 

/p         in  pounds.     For  example,  if  the  force  F  were  equal 

Fig  6          ^°  a  wei»ht  °f  500  pounds,  and  the  distance  Pa 

were  2  inches,  then  the  moment  of  the  force  about 

the  point  P  would  be  1,000  inch-pounds. 

The  following  important  propositions  relating  to  forces  and 
moments  should  be  borne  in  mind  in  calculating  the  strength  or 
stability  of  structures. 

V. — //  any  number  of  parallel  forces  act  on  a  body,  that  the 
body  shall  be  in  equilibrium,  the  sum  of  the  forces  acting  in  one 
direction  must  equal  the  sum  of  the  forces  acting  in  the  opposite 
direction. 


234  COMPOSITION  OF  FORCES. 


IP* 

L_R 


Thus  if  we  have  the  parallel  forces  P1,  P2,  P3,  and  P4,  acting 
on  the  rod  AB  (Fig.  7),  in  the 
opposite  direction  to  the  forces 
PI,  PI,  P3)  then,  if  the  rod  is  in 
B  equilibrium,  the  sum  of  the  forces 
P1,  P2,  P3,  and  P4,  must  equal  the 
sum  of  the  forces  Plf  P2,  and  P3. 

VI.  //   any   number  of   parallel 
forces    act   on   a   body   in  opposite 
directions,  then,  for    the  body  to  be 
Fig.  7  in    equilibrium,    the     sum    of    the 

moments  tending  to  turn  the  body 

in  one  direction  must  equal  the  sum  of  the  moments  tending  to  turn 
the  body  in  the  opposite  direction  about  any  given  point. 

Thus  let  Fig.  8  represent  three  par-  *t> 

allel  forces  acting  on  a  rod  AB.     Then 
for  the  rod  to  be  in  equilibrium,  the  sum  .  *      ~®~'    T      '^~2     *r  - 


for  the  rod  to  be  in  equilibrium,  the  sum 

of  the  forces  F2  and  F3  must  be  equal  to    <= *— - 

Ft.  Also,  if  we  take  the  end  of  the  rod, 
A,  for  our  axis,  then  must  the  moment 
of  Ft  be  equal  to  the  sum  of  the  mo- 
ments of  F2  and  F3  about  that  point,  be- 
cause the  moment  of  F^  tends  to  turn 

the  rod  down  to  the  right,  and  the  moments  of  F-£  and  F3  tend  to 
turn  the  rod  up  to  the  left,  and  there  should  be  no  more  tendency 
to  turn  the  rod  one  way  than  the  other.  For  example,  let  the 
forces  F3,  F2,  each  be  represented  by  5,  and  let  the  distance  Aa 
be  represented  by  2,  and  the  distance  Ac  by  4.  The  force  F1 
must  equal  the  sum  of  the  forces  Fs  and  F2,  or  10;  and  its  mo- 
ment must  equal  the  sum  of  the  moments  of  F3  and  F2.  If  we  take 
the  moments  around  A,  then  the  moment  of  .F3=5X2=10,  and 
of  F2  =  5  X  4  =  20.  Their  sum  equals  30 :  hence  the  moment  of  Fl 
must  be  30.  Dividing  the  moment  30  by  the  force  10,  we  have 
for  the  arm  3 ;  or  the  force  Fl  must  act  at  a  distance  3  from  A  to 
keep  the  rod  in  equilibrium. 

If  we  took  our  moments  around  b,  then  the  force  F1  would  have 
no  moment,  not  having  any  arm,  and  so  the  moment  of  F2  about 
b  must  equal  the  moment  of  F3  about  the  same  point;  or,  as  in 
this  case  the  forces  are  equal,  they  must  both  be  applied  at  the 
same  distance  from  6,  showing  that  b  must  be  halfway  between 
a  and  c,  as  was  proved  before. 


COMPOSITION   OF   FORCES. 


235 


Fig.9a 


The  Principle  of  the  Lever. — This  principle  is  based 
upon  the  two    preceding   propositions, 
and  is  of  great  importance  and  conveni- 
ence. 

VII.  //  three  parallel  forces  acting  in 
one  plane  balance  each  other  y  then  each 
force  must  be  proportional  to  the  distance  A 
between  the  other  two. 

Thus,  if  we  have  a  rod  AB  (Figs.  9a, 
9b,  and  9c),  with  three  forces,  Plt  P2, 
P:j,  acting  on  it,   that  the  rod  shall  be 
balanced,  we  must  have  the  following  relation  between  the  forces 
and  their  points  of  application;  viz., 

Jj.  •  IL  •  Us.. 

CB  '  AB  '  AC' 

or 

PI  '  P2  :P3  "BC  :AB  :AC. 

This  is  the  case  of  the  common  lever,  and  gives  the  means  of 
determining  how  much  a  given  lever  will  raise. 


p         F!g.9b 
! 

C 

F 

Pt 

PI        Fig.  9c 


The  proportion  is  also  true  for  any  arrangement  of  the  forces 
(as  shown  in  Figs,  a,  b,  and  c),  provided,  of  course,  the  forces  are 
lettered  in  the  order  shown  in  the  figures. 

EXAMPLE. — Let  the  distance  AC  be  6  inches,  and  the  distance 
CB  be  12  inches.  If  a  weight  of  500  pounds  is  applied  at  the 
point  B.  how  much  will  it  raise  at  the  other  end,  and  what  sup- 
port will  be  required  at  C  (Fig.  9b)  ? 

Ans.  Applying  the  rule  just  given,  we  have  the  proportion: — 

P3  :  P!  ::  AC  :  CB,  or  500  :  (PJ  ::  6  : 12. 

Hence  Pj=  1,000  pounds;  or  500  pounds  applied  at  B  will  lift  1,000 
suspended  at  A.     The  supporting  force  at  C  must,  by  proposi- 


236  CENTRE  OF  GRAVITY. 

tion  V.,  be  equal  to  the  sum  of  the  forces  Pt  and  P3,  or  1,500 
pounds  in  this  case. 

Centre  of  Gravity. — The  lines  of  action  of  the  force  of 
gravity  converge  towards  the  centre  of  the  earth;  but  the  dis- 
tance of  the  centre  of  the  earth  from  the  bodies  which  we  have 
occasion  to  consider,  compared  with  the  size  of  those  bodies,  is 
so  great,  that  we  may  consider  the  lines  of  action  of  the  forces  as 
parallel.  The  number  of  the  forces  of  gravity  acting  upon  a  body 
may  be  considered  as  equal  to  the  number  of  particles  compos- 
ing the  body. 

The  centre  of  gravity  of  a  body  may  be  defined  as  the  point 
through  which  the  resultant  of  the  parallel  forces  of  gravity, 
acting  upon  the  body,  passes  in  every  position  of  the  body. 

If  a  body  be  supported  at  its  centre  of  gravity,  and  be  turned 
about  that  point,  it  will  remain  in  equilibrium  in  all  positions. 
The  resultant  of  the  parallel  forces  of  gravity  acting  upon  a  body 
is  obviously  equal  to  the  weight  of  the  body,  and  if  an  equal  force 
be  applied,  acting  in  a  line  passing  through  the  centre  of  gravity 
of  the  body,  the  body  will  be  in  equilibrium. 

Examples  of  Centres  of  Gravity. — Centre  of  Gravity 
of  Lines.  Straight  Lines. — By  a  line  is  here  meant  a  material  line 
whose  transverse  section  is  very  small,  such  as  a  very  fine  wire. 

The  centre  of  gravity  of  a  uniform  straight  line  is  at  its  middle 

point.     This  proposition  is  too  evident  to  require  demonstration. 

The  centre  of  gravity  of  the  perimeter  of  a  triangle  is  at  the 

centre  of  the  circle  inscribed  in  the  lines  joining  the  centres  of 

the  sides  of  the  given  triangle. 

Thus,  let  ABC  (Fig.  10)  be  the  given 
triangle.  To  find  the  centre  of  gravity 
of  its  perimeter,  find  the  middle  points, 
D,  E,  and  F,  and  connect  them  by 
straight  lines.  The  centre  of  the  circle 
inscribed  in  the  triangle  formed  by 
p  C  these  lines  will  be  the  centre  of  gravity 

Fi9-ia  sought. 

Symmetrical    Lines. — The    centre    of 

gravity  of  lines  which  are  symmetrical  with  reference  to  a  point 
will  be  at  that  point.  Thus  the  centre  of  gravity  of  the  circum- 
ference of  a  circle  or  an  ellipse  is  at  the  geometrical  centre  of 
those  figures. 

The  centre  of  gravity  of  the  perimeter  of  an  equilateral  triangle, 
or  of  a  regular  polygon,  is  at  the  centre  of  the  inscribed  circle. 


CENTRE  OF  GRAVITY.  237 

The  centre  of  gravity  of  the  perimeter  of  a  square,  rectangle,  or 
parallelogram,  is  at  the  intersection  of  the  diagonals  of  those 
figures. 

Centre  of  Gravity  of  Surfaces.  Definition. — A  surface  here 
means  a  very  thin  plate  or  shell. 

Symmetrical  Surfaces. — If  a  surface  can  be  divided  into  two 
symmetrical  halves  by  a  line,  the  centre  of  gravity  will  be  on  that 
line :  if  it  can  be  divided  by  two  lines,  the  centre  of  gravity  will 
be  at  their  intersection. 

The  centre  of  gravity  of  the  surface  of  a  circle  or  an  ellipse  is 
at  the  geometrical  centre  of  the  figure,  of  an  equilateral  triangle 
or  a  regular  polygon,  it  is  at  the  centre  of  the  inscribed  circle;  of 
a  parallelogram,  at  the  intersection  of  the  diagonals;  of  the  sur- 
face of  a  sphere,  or  an  ellipsoid  of  revolution,  at  the  geometrical 
centre  of  the  body;  of  the  convex  surface  of  a  right  cylinder  at 
the  middle  point  of  the  axis  of  the  cylinder. 

Irregular  Figures. — Any  figure  may  be  divided  into  rectangles 
and  triangles,  and,  the  centre  of  gravity  of  each  being  found,  the 
centre  of  gravity  of  the  whole  may  be  determined  by  treating  the 
centres  of  gravity  of  the  separate  parts  as  particles  whose  weights 
are  proportional  to  the  areas  of  the  parts  they  represent. 

Triangle. — To  find  the  centre  of  gravity  of  a  triangle,  draw  a 
line  from  each  of  two  angles  to  the  middle  of  the  side  opposite : 
the  intersection  of  the  two  lines  will  give  the  centre  of  gravity. 

Quadrilateral. — To  find  the  centre  of  gravity  of  any  quadrilat- 
eral, draw  diagonals,  and,  from  the  end  of  each  farthest  from 
their  intersection,  lay  off,  toward  the  intersection,  its  shorter 
segment :  the  two  points  thus  formed  with  the  point  of  intersec- 
tion will  form  a  triangle  whose  centre  of  gravity  is  that  of  the 
quadrilateral. 

Thus,  let  Fig.  11  be  a  quadrilateral  whose  centre  of  gravity  is 
sought.  Draw  the  diagonals  AD 
and  BC,  and  from  A  lay  off  AF= 
ED,  and  from  B  lay  off  BH=EC. 
From  E  draw  a  line  to  the  middle 
of  FH,  and  from  F  a  line  to  the 
middle  of  EH.  The  point  of  inter- 
section of  these  two  lines  is  the 
centre  of  gravity  of  the  quadri- 
lateral.  This  is  a  method  com- 
monly used  for  finding  the  centre  of  gravity  of  the  voussoirs  of 
an  arch. 


238 


CENTRE   OF   GRAVITY. 


D= 


D=RX 


chord3 
12  X  area 
2  X  chord 

3  X  arc 


~  =  0.42447? 

O7T 


Table  of  Centres  of  Gravity. — Let  a  denote  a  line 
drawn  from  the  vertex  of  a  figure  to  the  middle  point 
of  the  base,  and  D  the  distance  from  the  vertex  to  the 
centre  of  gravity.  Then 

In  an  isosceles  triangle       .      .      .      .     D=%a 
In  a  segment  of  a  circle  | 
Vertex  at  centre  of  circle  f 
In  a  sector  of  a  circle,  the  ver- 1 
tex  being  at  the  centre  j 

In  a  semicircle,  vertex  being) 
at  the  centre  f 

In  a  quadrant  of  a  circle     . 
In  a  semi-ellipse,  vertex  being ) 
at  the  centre  f 

In  a  parabola,  vertex  at  intersection  of)  n_s 

axis  with  curve  f 

In  a  cone  or  pyramid D=$a 

In  a  frustum  of  a  cone  or  pyramid,  let  h  =  height  of  complete 
cone   or  pyramid,  /ix=  height  of  frustum,  and  the  vertex  be  at 

apex  of  complete  cone  or  pyramid ;  then  D  =  -j-— — r-^ . 

Centre  of  Gravity  of  Heavy  Particles. — Centre  of 


Sector. 


Gravity  of  Two  Particles. — Let  P  be  the 
weight  of  a  particle  at  A  (Fig.  12),  and  W 
that  at  C. 

The  centre  of  gravity  will  be  at  some/ 
point,  B,  on  the  line  joining  A   and  C.  * 
The  point  B  must  be  so  situated,  that  if 
the  two  particles  were  held  together  by  a 


W 


W 


Fig.  12 


stiff  wire,  and  were  supported  at  B  by  a  force  equal  to  the  sum 
of  P  and  W,  the  two  particles  would  be  in  equilibrium. 

The  problem  then  comes  under  the  principle  of  the  lever,  and 
hence  we  must  have  the  proportion  (see  proposition  VII.). 

P  +  W  :P  \:AC  :BC, 
or 

PXAC 


BC= 


P+W 


If  W=P,  then  BC=AB,  or  the  centre  of  gravity  will  be  half- 
way between  the  two  particles.  This  problem  is  of  great  im- 
portance, for  it  presents  itself  in  many  practical  examples, 


CENTRE  OF  GRAVITY. 


239 


Centra  of  Gravity  of  Several  Heavy  Particles.— Let  W1}  W2j  W3, 
Wt  and  W5  (Fig.  13)  be  the  weights  of  the  particles. 

Join  Wl  and  W2  by  a  straight  line,  and 
find  their  centre  of  gravity  A,  as  in  the  pre- 
ceding problem.  Join  A  with  W%,  and  find 
the  centre  of  gravity  B,  which  will  be  the 
centre  of  gravity  of  the  three  weights  Wt, 
W2,  and  TF3.  Proceed  in  the  same  way  with 
each  weight,  and  the  last  centre  of  gravity 
found  will  be  the  centre  of  gravity  of  all  the 
particles. 

In  both  of  these  cases  the  lines  joining  the  particles  are  sup- 
posed to  be  horizontal  lines,  or  else  the  horizontal  projection  of 
the  real  straight  line  which  would  join  the  points. 

Centre  of  Gravity  of  Compound  Sections  Found 
by  Moments. — To  determine  the  strength  of  a  beam  having 
an  unsymmetrical  section,  it  is  first  necessary  to  determine  the 
distance  of  the  centre  of  gravity  of  the  section  from  the  bottom 
of  the  beam.  Various  other  computations  also  involve  finding 
the  centre  of  gravity  of  an  irregular  figure,  so  that  the  problem 
is  one  of  practical  importance. 

If  the  figure  of  which  the  centre  of  gravity  is  sought  can  be 
divided  into  regular  figures  the  readiest  and  simplest  method  of 
finding  the  distance  of  the  centre  of  gravity  from  one  edge  is 
by  means  of  moments. 

To  explain  this  method  we  will  assume  a  T-shape  section  of 
uniform  thickness  pivoted  on  a  wire,  XX,  as  in  Fig.  14.  The  T 


Fig,  14 


is  made  up  of  two  rectangles,  one  forming  what  we  will  call  the 
flange,  the  other  the  web.     The  centre  of  gravity  of  each  oi 


240  CENTRE  OF  GRAVITY. 

these  rectangles  will  be  at  their  centre,  which  can  easily  be 
found. 


Fig.  15 

Now,  if  the  T  were  placed  horizontally,  as  in  the  figure,  the 
axis  XX  being  fixed,  it  would  immediately  revolve  about 
the  axis  until  it  became  vertical,  and  the  moments  causing  the 
revolution  would  be  A'd'  +  A"d",  A'  representing  the  weight 
of  the  web  and  A"  the  weight  of  the  flange.  To  hold  the  T  in 
a  horizontal  position,  there  must  be  a  moment  acting  in  the 
opposite  direction  just  equal  to  the  sum  of  the  two  moments 
acting  downwards,  and  if  the  force  in  this  upward  moment,  rep- 
resented by  A,  is  equal  to  the  weight  of  the  entire  T,  then  the 
force  must  be  applied  at  the  centre  of  gravity  of  the  entire  figure 
to  make  its  moment  just  equal  to  the  sum  of  the  two  moments. 

But  the  moment  of  A  will  be  Ad,  therefore  d  must  denote  the 
distance  from  the  end  of  the  web  to  the  centre  of  gravity  of  the 
entire  figure,  and  as  Ad*=  A'd'-^- A^d" ,  d  must  equal 

A'd'  +  A"d" 

~^         ' 

and  A  is  equal  to  A'  +  A".  As  the  weight  of  any  homogeneous 
material  of  uniform  thickness  is  proportional  to  the  area;  A,  A', 
and  A"  may  be  used  to  represent  areas  as  well  as  weights. 

To  reduce  formula  1  to  a  rule  we  have : 

VIII.  The  distance  of  the  centre  of  gravity  of  a  compound  figure 
from  any  line,  taken  as  a  base,  is  equal  to  the  sum  of  the  products, 
found  by  multiplying  the  areas  of  the  simple  figures  of  ichich  the 
compound  figure  is  composed  by  the  distance  of  their  centres  of 
gravity  fro?n  the  base  line,  divided  by  the  area  of  the  entire  figure. 
This  rule  applies  to  any  compound  figure. 

EXAMPLE  I. — Assume  that  the  T  shown  in  Fig.  14  has  the  di- 
mensions indicated  in  the  figure.  Then  A'  will  equal  6,  A",  8, 
and  A,  14.  d'  will  equal  3  and  d"  6J. 

The  sum  of  the  products  of  A'  by  d'  and  A"  by  d'  will  be 
18  +  52  or  70,  and  this  divided  by  14,  the  area  of  the  entire  figure, 
gives  5  ins.  for  the  distance  d. 

The  distance  d  of  the  centre  of  gravity  from  the  top  of  the 


CENTRE  OF  GRAVITY. 


241 


webs,  in  any  of  the  figures  shown  in  Fig.  15,  may  be  found  by 
the  following  formula: 


d=- 


df 
area  of  webs  X^-+  area  of  flange 

area  of  webs  +  area  of  flange 


(2) 


For  a  section  like  that  shown  in  Fig.  16,  in  which  A',  A",  A'" 
represent  the  area  of  the  respective  rectangles,  the  distance  d 
of  the  centre  of  gravity  from  the  top  may  be  found  by  the 
formula 


d= 


(3) 


EXAMPLE  IT. — To  show  the  application  of  proposition  VIII. 
to  any  compound  figure,  we  will  take  that  shown  by  Fig.  17  and 
find  the  distance  d  of  the  centre  gravity  of  the  entire  figure  from 
the  vertex  o.  The  area  of  the  triangle  is  36  sq.  ins.  and  of  the 
semicircle  56.5. 


U/v 


Fig.  16 


o 

Fig.  17 


From  the  table  on  page  238  we  find  that  the  distance  of  the 
centre  of  gravity  of  an  isosceles  triangle  from  the  vertex  is  f  its 
height,  which  gives  4  as  the  value  for  d'.  The  centre  of  gravity 
for  a  semicircle  is  0.4244  r  from  its  base,  so  that  d"  equals  8.54. 
Then 

36X4  +  56.5X8.54 


36  +  56.5 


=  6.77. 


This  method  of  finding  the  centre  of  gravity  is  the  same  as 
that  given  in  Chapter  IX.  for  finding  supporting  forces,  except 
that  in  the  latter  case  the  problem  is  to  find  the  balancing  force 
instead  of  the  arm. 


242      STABILITY  OF  PIERS  AND  BUTTRESSES, 


CHAPTER  VII. 
STABILITY  OF  PIERS  AND  BUTTRESSES. 

A  PIER  or  buttress  may  be  considered  stable  when  the  forces 
acting  upon  it  do  not  cause  it  to  rotate  or  "tip  over,"  or  any 
course  of  stones  or  brick  to  slide  on  its  bed.  When  a  pier  has  to 
sustain  only  a  vertical  load,  it  is  evident  that  the  pier  must  be 
stable,  although  it  may  not  have  sufficient  strength. 

It  is  only  when  the  pier  receives  a  thrust,  such  as  that  from  a 
rafter  or  an  arch,  that  its  stability  must  be  considered. 

In  order  to  resist  rotation,  we  must  have  the  condition  that  the 
moment  of  the  thrust  of  the  pier  about  any  point  in  the  outside  of 
the  pier  shall  not  exceed  the  moment  of  the  weight  of  the  pier 
about  the  same  point. 

To  illustrate  let  us  take  the  pier  shown  in  Fig.  1. 

Let  us  suppose  that  this  pier  receives  the  foot  of  a  rafter  which 
exerts  a  thrust  T  in  the  direction  AB.  The  tendency  of  this 
thrust  will  be  to  cause  the  pier  to  rotate  about  the  outer  edge 
&!,  and  the  moment  of  the  thrust  about  this  point  will  be  Ty<.a'blf 
ab^  being  the  arm.  Now,  that  the  pier  shall  be  just  in  equilibrium, 
the  moment  of  the  weight  of  the  pier  about  the  same  edge  must 
just  equal  TXa'b^  The  weight  of  the  pier  will,  of  course,  act 
through  the  centre  of  gravity  of  the  pier  (which  in  this  case  is  at 
the  centre),  and  in  a  vertical  direction;  and  its  arm  will  be  b^c,  or 
one-half  the  thickness  of  the  pier. 

Hence,  to  have  equilibrium,  we  must  have  the  equation 


But  under  this  condition  the  least  additional  thrust,  or  the 
crushing  off  of  the  outer  edge,  would  cause  the  pier  to  rotate; 
hence,  to  have  the  pier  in  safe  equilibrium,  we  must  use  some 
factor  of  safety. 

This  is  generally  done  by  making  the  moment  of  the  weight 
equal  to  that  of  the  thrust  when  referred  to  a  point  in  the  bottom 
of  the  pier,  a  certain  distance  in  from  the  outer  edge. 

This  distance  for  piers  or  buttresses  should  not  be  less  than  one- 
fourth  of  the  thickness  of  the  pier, 


STABILITY  OF  PIERS  AND   BtJTT&ESSES       243 

Representing  this  point  in  the  figure  by  b,  we  have  the  neces- 
sary equation  for  the  safe  stability  of  the  pier, 


t  denoting  the  width  of  the  pier. 

We  cannot  from  this  equation  determine  the  dimensions  of  a 
pier  to  resist  a  given  thrust,  because  we  have  the  distance  ab,  t, 
and  Wj  all  unknown  quantities.  Hence  we  must  first  guess  at 
the  size  of  the  pier,  then  find  the  length  of  the  line  ab,  and  see  if 
the  moment  of  the  pier  is  equal  to  that  of  the  thrust.  If  it  is  not 
we  must  guess  again. 


Graphic  Method  of  Determining  the  Stability  of  a 
Pier  or  Buttress. — When  it  is  desired  to  determine  if  a  given 
pier  or  buttress  is  capable  of  resisting  a  given  thrust,  the  prob- 
lem can  easily  be  solved  graphically  in  the  following  manner. 

Let  ABCD  (Fig.  2)  represent  a  pier  which  sustains  a  given 
thrust  T  at  B. 

To  determine  whether  the  pier  will  safely  sustain  this  thrust, 
we  proceed  as  follows. 

Draw  the  indefinite  line  BX  in  the  direction  of  the  thrust. 
Through  the  centre  of  gravity  of  the  pier  (which  in  this  case  is  at 
the  centre  of  the  pier)  draw  a  vertical  line  until  it  intersects  the 
line  of  the  thrust  at  e.  As  a  force  may  be  considered  to  act  any- 
where in  its  line  of  direction,  we  may  consider  the  thrust  and  the 
weight  to  act  at  the  point  e,  and  the  resultant  of  these  two  forces 
can  be  obtained  by  laying  off  the  thrust  T  from  e  on  eX,  and  the 
weight  of  the  pier  W,  from  e  on  the  line  eY,  both  to  the  same 
scale  (pounds  to  the  inch),  completing  the  parallelogram,  and 
drawing  the  diagonal.  If  this  diagonal  prolonged  cuts  the  base 
of  the  pier  at  less  than  one-fourth  of  the  width  of  the  base  from 
the  outer  edge,  the  pier  will  be  unstable  and  its  dimensions  must 
be  changed. 


244      STABILITY  OF  PIERS  AND   BUTTRESSES. 


The  stability  of  a  pier  may  be  increased  by  adding  to  its  weight 
(by  placing  some  heavy  material  on  top)  or  by  increasing  its 
width  at  the  base  by  means  of  "off-sets,"  as  in  Fig.  3A. 

Figs.  3  (A  and  B)  show  the  method  of  determining  the  stability 
of  a  buttress  with  offsets. 

The  first  step  is  to  find  the  vertical  line  passing  through  the 
centre  of  gravity  of  the  whole  pier.  This  is  best  done  by  divid- 
ing the  buttress  up  into  quadrilaterals,  as  A  BCD,  DEFG,  and 
GHIK  (Fig.  3 A),  finding  the  centre  of  gravity  of  each  quadri- 
lateral by  the  method  of  diagonals  explained  in  Chapter  VI.  and 
then  measuring  the  perpendicular  distances  X1}  X.2,  X3  from  the 
different  centres  of  gravity  to  the  line  KL 

Multiply  the  area  of  each  quadrilateral  by  the  distance  of  its 
centre  of  gravity  from  the  line  KI  and  add  together  the  areas 
and  the  products.  Divide  the  sum  of  the  latter  by  the  sum  of 
the  former  and  the  result  will  be  the  distance  of  the  centre  of 
gravity  of  the  whole  buttress  from  KI.  This  distance  we  denote 
by  XQ.  f  ^ 

I 


H 


Fig.3A  Fig.3B 

EXAMPLE  I. — Let  the  buttress  shown  in  Fig.  3A  have  the 
dimensions  given  between  the  cross-marks.  Then  the  area  of 
the  quadrilaterals  and  the  distances  from  their  centres  of  gravity 
to  KI  would  be  as  follows: 

1st  area=35  sq.  ft.  Xl=Q/ 
2d  area=23  sq.  ft.  X,  =  2' 
3d  area=ll  sq.  ft.  Xz=4' 


1st 

2d  areaXX2=67.85 

3d  area  X  X3  =  54. 45 


Total  area,  69  sq.  ft.  Total  moments,  155.55 

The  sum  of  the  moments  is  155.55,  and,  dividing  this  by  the 
total  area,  we  have  2.25  as  the  distance  XQ.     Measuring  this  to 


STABILITY  OF  PIERS  AND  BUTTRESSES.      245 


the  scale  of  the  drawing  from  KI,  we  have  a  point  through  which 
the  vertical  line  passing  through  the  centre  of  gravity  must  pass. 
After  this  line  is  found,  the  method  of  determining  the  stability  of 
the  pier  is  the  same  as  that  given  for  the  pier  in  Fig.  2.  Fig.  3B 
also  illustrates  the  method.  If  the  buttress  is  more  than  one  foot 
thick  (at  right  angles  to  the  plane  of  the  paper),  the  cubic  con* 
tents  of  the  buttress  must  be  obtained  to  find  the  weight.  It 
is  easier,  however,  to  divide  the  real  thrust  by  the  thickness  of  the 
buttress,  which  gives  the  thrust  per  foot  of  buttress. 

Line  of  Resistance. — Definition.  The  line  of  resistance 
or  of  pressures  of  a  pier  or  buttress  is  a  line  drawn  through  the 
centre  of  pressure  of  each  joint. 

The  centre  of  pressure  of  any  joint  is  the  point  where  the  re- 
sultant of  the  forces  acting  on  that  portion  of  the  pier  above  the 
joint  cuts  it. 

The  line  of  pressures,  or  of  resistance,  when  drawn  in  a  pier, 
shows  how  near  the  greatest  stress  on  any  joint  comes  to  the 
edges  of  that  joint. 

It  can  be  drawn  by  the  following  method: 

Let  ABCD  (Fig.  4)  be  a  pier 
whose  line  of  resistance  we  wish 
to  draw.  First  divide  the  pier  in 
height,  into  portions  two  or  three 
feet  high,  by  drawing  horizontal 
lines.  It  is  more  convenient  to 
make  the  portions  all  of  the  same 
size. 

Prolong  the  line  of  the  thrust, 
and  draw  a  vertical  line  through 
the  centre  of  gravity  of  the  pier, 
intersecting  the  line  of  thrust  at 
the  point  a.  From  a  lay  off  to  a 
scale  the  thrust  T  and  the  weights 
of  the  different  portions  of  the  pier, 
commencing  with  the  weight  of  the 
upper  portion.  Thus  Wi  represents 
the  weight  of  the  portion  above  the 
first  joint;  w2  represents  the  weight 
of  the  second  portion;  and  so  on. 
The  sum  of  the  w's  will  equal  the  p.  4 

whole  weight  of  the  pier. 

Having  proceeded  thus  far,  complete  a  parallelogram,  with  T 


246       STABILITY  OF  PIERS  AND  BUTTRESSES. 

and  Wi  for  its  two  sides.  Draw  the  diagonal,  and  prolong  it. 
Where  it  cuts  the  first  joint  will  be  a  point  in  the  line  of  resist- 
ance. Draw  another  parallelogram,  with  T  and  wl  +  w2  for  its 
two  sides.  Draw  the  diagonal  intersecting  the  second  joint  at 
2.  Proceed  in  this  way,  when  the  last  diagonal  will  intersect  the 
base  in  4.  Join  the  points  1,  2,  3,  and  4,  and  the  resulting  line 
will  be  the  line  of  resistance. 

We  have  taken  the  simplest  case  as  an  example;  but  the  same 
principle  is  true  for  any  case. 

Should  the  line  of  resistance  of  a  pier  at  any  point  approach 
the  outside  edge  of  the  joint  nearer  than  one-quarter  the  width 
of  the  joint,  the  pier  should  be  considered  unsafe. 

As  an  example  embracing  all  the  principles  given  above  we  will 
take  the  following  case. 

EXAMPLE  II. — Let  Fig.  5  represent  the  section  of  a  side  wall 
of  a  church,  with  a  buttress  against  it.  Opposite  the  buttress,  on 
the  inside  of  the  wall,  is  a  hammer-beam  truss,  which  we  will  sup- 
pose exerts  an  outward  thrust  on  the  walls  of  the  church  amount- 
ing to  about  9600  pounds.  We  will  further  consider  that  the 
resultant  of  the  thrust  acts  at  P,  and  at  an  angle  of  60°  with  a 
horizontal.  The  dimensions  of  the  wall  and  buttress  are  given  in 
Fig.  5A,  and  the  buttress  is  two  feet  thick. 

QUESTION. — Is  the  buttress  sufficient  to  enable  the  wall  to 
withstand  the  thrust  of  the  truss? 

The  first  point  to  decide  is  if  the  line  of  resistance  cuts  the 
joint  CD  Sit  a  safe  distance  in  from  C.  To  ascertain  this  we 
must  find  the  centre  of  gravity  of  the  wall  and  buttress  above  the 
joint  CD  (Fig.  5).  We  can  find  this  easiest  by  the  method  of 
moments  around  KM  (Fig.  5A),  as  already  explained. 

The  distance  X1  is,  of  course,  half  the  thickness  of  the  wall, 
or  one  foot.  We  next  find  the  centre  of  gravity  of  the  portion 
CEFG  (Fig.  5A)  by  the  method  of  diagonals,  and,  scaling  the 
distance  X2,  we  find  it  to  be  2.95  feet. 

The  area  of  CEFG=A2=10  square  feet;  and  of  G1KL=^A1 
=  26  square  feet. 

Then  we  have 

Z2=2.95     A2=10     .4,  X  ^2=29. 5 
36  36)55.5 


STABILITY   OF   PIERS   AND   BUTTRESSES.      247 

Or  the  centre  of  gravity  is  at  a  distance  1.5  feet  from  the  line 
ED  (Fig.  5).  Then  on  Fig.  5  measure  the  distance  XQ—  1.5  feet, 
and  through  the  point  a  draw  a  vertical  line  intersecting  the  line 
of  the  thrust  prolonged  at  0.  Now,  if  the  thrust  is  9600  pounds 
for  a  buttress  two  feet  thick,  it  would  be  half  that,  or  4800 
pounds,  for  a  buttress  one  foot  thick.  We  will  call  the  weight  of 
the  masonry  of  which  the  buttress  and  wall  is  built  150  pounds 
per  cubic  foot.  Then  the  thrust  is  equivalent  to  4800  -f- 150,  or  32 
cubic  feet  of  masonry.  Laying  this  off  to  a  scale  from  0,  in  the 
direction  of  the  thrust  and  the  area  of  the  masonry,  36  square  feet 
from  0  on  the  vertical  line,  completing  the  rectangle,  and  draw- 
ing the  diagonal,  we  find  it  cuts  the  joint  CD  at  t,  within  the 
limits  of  safety. 

We  must  next  find  where  the  line  of  resistance  cuts  the  base 
AB. 

First  find  the  centre  of  gravity  of  the  whole  figure,  which  is 
found  by  ascertaining  the  distances  X2',  X3',  in  Fig.  5A,  and 
making  the  following  computation. 

37=1'  A1'=40     A/xX/=40 

AY  =  2'.98     A2'=24     42'X-Xy=71.52 


76  76)170.92 


Then  from  the  line  EB  (Fig.  5)  lay  off  the  distance  A0'=2'.25, 
and  draw  through  d  a  vertical  line  intersecting  the  line  of  the 
thrust  at  0'  '.  On  this  vertical  from  0'  measure  down  the  whole 
area  76,  and  from  its  extremity  lay  off  the  thrust  T=32  at  the 
proper  angle.  Draw  the  line  O'e  intersecting  the  base  at  c.  This 
is  the  point  where  the  line  of  resistance  cuts  the  base;  and,  as  it 
is  at  a  safe  distance  in  from  A,  the  buttress  has  sufficient  stability. 

If  there  were  more  offsets,  we  should  proceed  in  the  same  way, 
finding  where  the  line  of  resistance  cuts  the  joint  at  the  top  of 
each  offset.  The  reason  for  doing  this  is  because  the  line  of  re- 
sistance might  cut  the  base  at  a  safe  distance  from  the  outer  edge, 
while  higher  up  it  might  come  outside  of  the  buttress,  so  that  the 
buttress  would  be  unstable. 

The  method  given  in  these  examples  is  applicable  to  piers  of 
any  shape  or  material. 

Should  the  line  of  resistance  make  an  angle  less  than  30°  with 


248      STABILITY  OF   PIERS  AND   BUTTRESSES. 


any  joint,  it  might  cause  the  stones  above  the  joint  to  slide  on 
their  bed.  This  can  be  prevented  either  by  dowelling,  or  by 
inclining  the  joint. 


Fig.5 


Fig.SA 


It  is  very  seldom  in  architectural  construction  that  such  a  ease 
would  occur,  however. 


THE  STABILITY   OF  ARCHES.  249 


CHAPTER  Vin. 
THE  STABILITY  OP  ARCHES. 

THE  arch  is  an  arrangement  for  spanning  large  openings  by 
means  of  small  blocks  of  stone,  or  other  material,  arranged  in  a 
particular  way.  As  a  rule,  the  arch  answers  the  same  purpose 
as  the  beam,  but  it  is  widely  different  in  its  action  and  in  the  effect 
that  it  has  upon  the  appearance  of  an  edifice.  A  beam  exerts 
merely  a  vertical  force  upon  its  supports,  but  the  arch  exerts  both 
a  vertical  load  and  an  outward  thrust.  It  is  this  thrust  which 
requires  that  the  arch  should  be  used  with  caution  where  the 
abutments  are  not  abundantly  large. 

Before  taking  up  the  principles  of  the 
arch,  we  will  define  the  many  terms  relat- 
ing to  it.  The  distance  ec  (Fig.  1)  is 
called  the  span  of  the  arch;  ai,  its  rise;  6, 
its  crown;  its  lower  boundary  line,  eac,  its 
soffit  or  intrados;  the  outer  boundary  line, 
its  back  or  extrados.  The  terms  "soffit" 
and  "back"  are  also  applied  to  the  entire  lower  and  upper  curved 
surfaces  of  the  whole  arch.  The  ends  of  the  arch,  or  the  sides 
which  are  seen,  are  called  its  faces.  The  blocks  of  which  the  arch 
itself  is  composed  are  called  voussoirs:  the  centre  one,  K,  is  called 
the  keystone;  and  the  lowest  ones,  SS,  the  springers.  In  seg- 
mental  arches,  or  those  whose  intrados  is  not  a  complete  semi- 
circle, the  springers  generally  rest  upon  two  stones,  as  RR,  which 
have  their  upper  surface  cut  to  receive  them:  these  stones  are 
called  skewbacks.  The  line  connecting  the  lower  edges  of  the 
springers  is  called  the  springing-line;  the  sides  of  the  arch  are 
called  the  haunches;  and  the  load  in  the  triangular  space,  between 
the  haunches  and  a  horizontal  line  drawn  from  the  crown,  is 
called  the  spandrel. 

The  blocks  of  masonry,  or  other  material,  which  support  two 
successive  arches,  are  called  piers:  the  extreme  blocks,  which,  in 
the  case  of  stone  bridges,  generally  support  on  one  side  embank- 
ments of  earth,  are  called  abutments. 

A  pier  strong  enough  to  withstand  the  thrust  of  either  arch 
should  the  other  fall  down,  is  sometimes  called  an  abutment  pier 


250  THE  STABILITY  OF  ARCHES. 

Besides  their  own  weight,  arches  usually  support  a  permanent 
load  or  surcharge  of  masonry  or  of  earth. 

In  using  arches  in  architectural  constructions,  the  form  of  the 
arch  is  generally  governed  by  the  style  of  the  edifice,  or  by  a  lim- 
ited amount  of  space.  The  semicircular  and  segmental  forms  of 
arches  are  the  best  as  regards  stabilty,  and  are  the  simplest  to 
Construct.  Elliptical  and  three-centred  arches  are  not  as  strong 
as  circular  arches,  and  should  only  be  used  where  they  can  be 
given  all  the  strength  desirable. 

The  strength  of  an  arch  depends  very  much  upon  the  care  with 
which  it  is  built  and  of  the  quality  of  the  work. 

In  stone  arches,  special  care  should  be  taken  to  cut  and  lay 
the  beds  of  stones  accurately,  and  to  make  the  bed-joints  thin 
and  close,  in  order  that  the  arch  may  be  strained  as  little  as  pos- 
sible in  settling. 

To  insure  this,  arches  are  sometimes  built  dry,  grout  or  liquid 
mortar  being  afterwards  run  into  the  joints;  but  the  advantage 
of  this  method  is  doubtful. 

Brick  Arches  may  be  built  either  of  wedge-shaped  bricks, 
moulded  or  rubbed  so  as  to  fit  to  the  radius  of  the  soffit,  or  of 
bricks  of  common  shape.  The  former  method  is  undoubtedly 
the  best,  as  it  enables  the  bricks  to  be  thoroughly  bonded,  as  in 
a  wall;  but,  as  it  involves  considerable  expense  to  make  the 
bricks  of  the  proper  shape,  this  method  is  very  seldom  employed. 
Where  bricks  of  the  ordinary  shape  are  used,  they  are  accommo- 
dated to  the  curved  figure  of  the  arch  by  making  the  bed-joints 
thinner  towards  the  intrados  than  towards  the  extrados;  or,  if 
the  curvature  is  sharp,  by  driving  thin  pieces  of  slate  into  the 
outer  edges  of  those  joints;  and  different  methods  are  followed 
for  bonding  them.  The  most  common  way  is  to  build  the  arch 
in  concentric  rings,  each  half  a  brick  thick;  that  is,  to  lay  the 
bricks  all  stretchers,  and  to  depend  upon  the  tenacity  of  the 
mortar  or  cement  for  the  connection  of  the  several  rings.  This 
method  is  deficient  in  strength,  unless  the  bricks  are  laid  in  ce- 
ment at  least  as  tenacious  as  themselves.  Another  way  is  to 
introduce  courses  of  headers  at  intervals,  so  as  to  connect  pairs 
of  half-brick  rings  together.  • 

This  may  be  done  either  by  thickening  the  joints  of  the  outer 
of  a  pair  of  half-brick  rings  with  pieces  of  slate,  so  that  there  shall 
be  the  same  number  of  courses  of  stretchers  in  each  ring  between 
two  courses  of  headers,  or  by  placing  the  courses  of  headers  at 
such  distances  apart,  that  between  each  pair  of  them  there  shall 


THE  STABILITY  OF  ARCHES. 


251 


be  one  course  of  stretchers  more  in  the  outer  than  in  the  inner 
ring. 

The  former  method  is  best  suited  to  arches  of  long  radius;  the 
latter,  to  those  of  short  radius.  Hoop  iron  laid  round  the  arch, 
between  half-brick  rings,  as  well  as  longitudinal^  and  radially, 
is  very  useful  for  strengthening  brick  arches.  The  bands  of  hoop 
iron  which  traverse  the  arch  radially  may  also  be  bent,  and  pro- 
longed in  the  bed-joints  of  the  backing  and  spandrels. 

By  the  aid  of  hoopriron  bond,  Sir  Marc-Isambard  Brunei  built 
a  half-arch  of  bricks  laid  in  strong  cement,  which  stood,  project- 
ing from  its  abutment  like  a  bracket,  to  the  distance  of  sixty  feet, 
until  it  was  destroyed  by  its  foundation  being  undermined. 

The  New- York  City  Building  Laws  make  the  following  re- 
quirements regarding  brick  arches: — 

"All  arches  shall  be  at  least  four  inches  thick.  Arches  over 
four-foot  span  shall  be  increased  in  thickness  toward  the  haunches 
by  additions  of  four  inches  in  thickness  of  brick.  The  first  addi- 
tional thickness  shall  commence  at  two  and  a  half  feet  from  the 
centre  of  the  span,  the  second  addition  at  six  and  a  half  feet 
from  the  centre  of  the  span;  and  the  thickness  shall  be  in- 
creased thence  four  inches  for  every  additional  four  feet  of  span 
towards  the  haunches. 

"The  said  brick  arches  shall  be  laid  to  a  line  on  the  centres  with 
a  close  joint,  and  the  bricks  shall  be  well  wet,  and  the  joints  filled 
with  cement  mortar  in 
proportions  of  not  more 
than  two  of  sand  to  one 
of  cement  by  measure. 
The  arches  shall  be  well 
grouted  and  pinned,  or 
chinked  with  slate,  and 
keyed."  * 

Rule  for  Radius  of  Brick 
Arches. — A  good  rule  for 
the  radius  of  segment al 
brick  arches  over  win- 
dows, doors,  and  other 
small  openings  is  to  make 
the  radius  equal  to  the  width  of  the  opening.  This  gives  a  good 
rise  to  the  arch  and  makes  a  pleasing  proportion  to  the  eye. 

*  For  illustrations  of  the  different  ways  of  building  brick  arches,  see 
Chapter  VII.  of  Part  I.,  "Building  Construction  and  Superintendence." 


Fig.  2 


252  THE  STABILITY   OF  ARCHES. 

Segmental  Arches  with  Tie  Rods. — It  is  often  desirable  to  span 
openings  in  a  wall  by  means  of  an  arch  when  there  is  not  suffi- 
cient abutments  to  withstand  the  thrust  or  kick  of  the  arch.  In 
such  a  case  the  arch  can  be  formed  on  two  cast-iron  skewbacks, 
which  are  held  in  place  by  iron  rod,3,  as  is  shown  in  Fig.  2. 

When  this  is  done,  it  is  necessary  to  proportion  the  size  of  the 
rods  to  the  thrust  of  the  arch.  The  horizontal  thrust  of  the  arch 
is  very  nearly  represented  by  the  following  formula: 

TT    .       *  i  ,1  load  on  arch X span 

Horizontal  thrust  =- -. T. /  .  ^ — r. 

8  X  rise  ot  arch  in  ieet 

If  the  load  is  concentrated  at  the  centre  of  the  arch,  the  thrust 
will  be  twice  that  given  by  above  formula. 

The  stress  in  the  rod  or  rods  will  equal  the  horizontal  thrust 
of  the  arch ;  if  there  are  two  rods,  the  stress  in  each  will  be  one- 
half  the  thrust ;  if  there  are  three  rods,  then  each  must  be  capable 
of  resisting  J  of  the  thrust.  Knowing  the  stress  in  the  rods,  theii 
size  may  be  readily  determined  from  Table  III.  of  Chapter  XI. 

Centres  for  Arches. — A  centre  is  a  temporary  structure, 
generally  of  timber,  by  which  the  voussoirs  of  an  arch  are  sup^ 
ported  while  the  arch  is  being  built.  It  consists  of  parallel 
frames  or  ribs,  placed  at  convenient  distances  apart,  curved  on 
the  outside  to  a  line  parallel  to  that  of  the  soffit  of  the  arch,  and 
supporting  a  series  of  transverse  blanks,  upon  which  the  arch 
stones  rest. 

The  most  common  kind  of  centre  is  one  which  can  be  lowered, 
or  struck  all  in  one  piece,  by  driving  out  wedges  from  below  it, 
so  as  to  remove  the  support  from  every  point  of  the  arch  at  once. 

The  centre  of  an  arch  should  not  be  struck  until  the  solid  part 
of  the  backing  has  been  built  and  the  mortar  has  had  time  to  set 
and  harden;  and,  when  an  arch  forms  one  of  a  series  of  arches 
with  piers  between  them,  no  centre  should  be  struck  so  as  to 
leave  a  pier  with  an  arch  abutting  against  one  side  of  it  only,  un- 
less the  pier  has  sufficient  stability  to  act  as  an  abutment. 

When  possible,  the  centre  of  a  large  brick  arch  should  not  be 
struck  for  two  or  three  months  after  the  arch  is  built. 

Mechanical  Principles  of  the  Arch. — In  designing  an 
arch,  the  first  question  to  be  settled  is  the  form  of  the  arch ;  and 
in  regard  to  this  there  is  generally  but  little  choice.  Where  the 
abutments  are  abundantly  large,  the  segmental  arch  is  the  strong- 
est form;  but  where  it  is  desired  to  make  the  abutments  of  the 


THE  STABILITY  OF  ARCHES.  253 

arch  as  light  as  possible,  a  pointed  or  semicircular  arch  should  be 
used.  \ 

Depth  of  Keystone. — Having  decided  upon  the  form  of  the  arch, 
the  depth  of  the  arch-ring  must  next  be  decided.  This  is  gen- 
erally determined  by  computing  the  required  depth  of  keystone, 
and  making  the  whole  ring  of  the  same  or  a  little  larger  depth. 

In  considering  the  strength  of  an  arch,  the  depth  of  the  key- 
stone is  considered  to  be  only  the  distance  from  the  extrados  to 
the  intrados  of  the  arch;  and  if  the  keystone  projects  above  the 
arch-ring,  as  in  Fig.  1,  the  projection  is  considered  as  a  part  of 
the  load  on  the  arch. 

There  are  several  rules  (or  determining  the  depth  of  the  key- 
stone, but  all  are  empirical ;  and  they  differ  so  greatly  that  it  is 
difficult  to  recommend  any  particular  one.  Professor  Rankine's 
rule  is  often  quoted,  and  is  probably  true  enough  for  most  arches. 
It  applies  to  both  circular  and  elliptical  arches,  and  is  as  fol- 
lows: 

Raiikiiie's  Rule. — For  the  depth  of  the  keystone,  take  a  mean 
proportional  between  the  inside  radius  at  the  crown,  and  0.12 
of  a  foot  for  a  single  arch,  and  0.17  of  a  foot  for  an  arch  forming 
one  of  a  series.  Or,  if  represented  by  a  formula, 

Depth  of  keytsone  for  a  single  arch  in  feet 


«=  \/(0. 12  X  radius  at  crown). 
Depth  of  keystone  for  an  arch  of  a  series  in  feet 


=  V (0.17  X radius  at  crown). 

This  rule  seems  to  agree  very  well  with  actual  cases  in  arches 
of  a  certain  kind.  By  it,  however,  the  depth  of  keystone  is  the 
same  for  spans  of  any  length,  provided  the  radius  is  the  same; 
and  in  this  particular,  it  seems  to  us,  the  rule  is  not  satisfactory. 

Trautwine's  Rule. — Mr.  Trautwine,  from  calculations 
made  on  a  large  number  of  arches,  deduced  an  original  rule  for 
the  depth  of  keystone,  which  is  more  agreeable  to  theory  than 
Rankine's.  His  rule  is,  for  cut  stone, 

TA     4-u     c  i        •     f    4      l^  radius  +  half  span\   IA1, 
Depth  of  key  in  feet=  (  -  — —          -  )  +0.2  foot. 

For  second-class  work  this  depth  may  be  increased  about  one- 
eighth  part,  or  for  brick  or  fair  rubble,  about  one-fourth. 

The  following  table  gives  a  few  examples  of  the  depth  of  key- 
stone of  some  existing  bridges,  together  with  the  depth  which 


254 


THE  STABILITY   OF  ARCHES. 


would  be  required  by  Trautwine's  or  Rankine's  Rule.  From 
this  table  it  will  be  seen  that  both  rules  agree  very  well  with 
practice. 

TABLE  I.— SHOWING  DEPTH  OF  KEYSTONE  OF  SOME 
EXISTING  ARCHES. 


Calculated 

o 

depth  of 

IM 

key. 

ro 

0 

Bridge  (circular  arc). 

Span. 

Rise. 

1 

0> 

"o> 

c    * 

jn 

Engi- 
neer. 

P4 

*c 

1 

II 

••!! 

3 
o 

r 

r 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Cabin  John  ,  Washing- 
ton Aqueduct. 

220.0 

57.25 

134.25 

4.60 

4.11 

4.00 

Meigs. 

Grosvenor  Bridge, 

Chester,  Eng.  . 

200.0 

42.00 

140.00 

4.00 

4.07 

4.10 

Hartley. 

Dora  Riparia,  Turin, 

Italy 

148.0 

18  00 

160.10 

4  92 

4  03 

4  38 

Mosca. 

Tongueland,  England  . 
Dea.n  Bridge,  Srotl'nd, 

118  0 

38.00 

64.80 

3.50 

3.00 

2.79 

Telford. 

in  a  series  

90.0 

30.00 

48.90 

3.00 

2.62 

2.88 

Telford. 

Falls    Bridge,    Phila- 

delphia &   Reading 
Railroad  

78.0 

25.00 

43.00 

3.00 

2.46 

2.27 

Steele. 

Chestnut    St.  Bridge, 

Philadelphia,   brick 

in  cement  

60.0 

18  00 

34  .  00 

2.50 

2.20 

2.00 

Kneass. 

Philadelphia  &  Read- 

ing Railroad  

44.0 

8.00 

34.30 

2.50 

2.08 

2.02 

Steele. 

Philadelphia  &  Read- 

ing Railroad  

31.2 

5.00 

26.80 

1.66 

1.83 

1.79 

Steele. 

Table  II.,  taken  from  Trautwine's  "Civil  Engineers'  Hand- 
book," gives  the  depth  of  keystone  for  arches  of  first-class  cut- 
stone,  according  to  Trautwine's  Rule.  For  second-class  cut- 
stone  add  about  one-eighth  part  and  for  good  rubble  or  brick, 
about  one-fourth  part. 

Having  decided  what  the  thickness  of  the  arch-ring  will  be  it 
remains  to  determine  whether  such  an  arch  would  be  stable  if 
built. 

The  following  example  will  illustrate  the  method  of  determin- 
ing this  point : 

EXAMPLE  I. — Unloaded  semicircular  arch  of  20- foot  span. 

First,  to  find  the  depth  of  keystone,  we  will  take  Rankine's 
Rule,  and  by  it  we  have 

Depth  of  key  =  \/07l2~Xlb=  vT2  =  *  • X  feet- 


THE  STABILITY   OF  ARCHES. 


255 


TABLE  II.— TABLE  OF  KEYSTONES  FOR  ARCHES  OF 
FIRST-CLASS  CUT-STONE. 


Span 
in 
feet. 

"Rise  in  parts  of  the  span. 

M 

M 

M 

% 

-% 

y* 

Mo 

key.  ft. 

key.  ft. 

key.  ft. 

key.  ft. 

key.  ft. 

key.  ft. 

key.  ft. 

2 

0.55 

0.56 

0.58 

0.60 

0.61 

0  64 

0.68 

4 

0.70 

0.72 

0.74 

0.76 

0.79 

0.83 

0  88 

6 

0.81 

0.83 

0.86 

0.89 

0  92 

0.97 

1.03 

8 

0.91 

0.93 

0  96 

1.00 

1.03 

1.09 

1.16 

10 

0.99 

1.01 

1.04 

1.07 

.11 

1.18 

1.26 

15 

.17 

1.19 

1.22 

1.26 

.30 

1.40 

1.50 

20 

.32 

1.35 

1.38 

1.43 

.48 

1.59 

1.70 

25 

.45 

1.48 

1.53 

1.58 

.64 

1.76 

1.88 

30 

.57 

1.60 

1.65 

1.71 

.78 

1.91 

2.04 

35 

.68 

1.70 

1.76 

1.83 

1.90 

2.04 

2.19 

40 

.78 

1.81 

1.88 

1.95 

2.03 

2.18 

2.33 

50 

1.97 

2.00 

2.08 

2.16 

2.25 

2.41 

2.58 

60 

2.14 

2.18 

2.26 

2.35 

2.44 

2.62 

2.80 

80 

2.44 

2.49 

2.58 

2.68 

2.78 

2.98 

3.18 

100 

2.70 

2.75 

2.86 

2.97 

3.09 

3.32 

3.55 

120 

2,91 

2.99 

3.10 

3.22 

3.35 

3.61 

3.88 

140 

3.16 

3.21 

3.33 

3.46 

3.60 

3.87 

1.15 

160 

3.36 

3.44 

3.58 

3.72 

3.87 

4.17 

180 

3.56 

3.63 

3.75 

3.90 

4.03 

4.38 

200 

3.74 

3.81 

3.95 

4.12 

4.29 

220 

3.91 

4.00 

4.13 

4.30 

4.48 

210 

4.07 

4.15 

4.30 

4.48 

260 

4.23 

4.31 

4.47 

4.66 

280 

4.38 

4.46 

4.63 

300 

4.53 

4.62 

4.80 

Trautwine's  Rule  would  give  nearly  the  same,  or 


foot=ai:3 


But  if  we  should  compute  the  stability  of  a  semicircular  arch 
of  20-foot  span  and  1.3-foot  depth  of  keystone,  we  should  find 
that  the  arch  was  very  unstable;  hence,  in  this  case,  we  must 
throw  the  rule  aside  and  go  by  our  own  judgment.  In  the  opin- 
ion of  the  author,  such  an  arch  should  have  at  least  2|  feet  depth 
of  arch-ring,  and  we  will  try  the  stability  of  the  arch  with  that 
thickness. 

In  all  calculations  on  the  arch,  it  is  customary  to  consider  the 
arch  to  be  one  foot  thick  at  right  angles  to  its  face;  for  it  is  evi- 
dent that  if  an  arch  one  foot  thick  is  stable,  any  number  of 
arches  of  the  same  dimensions  built  alongside  of  it  would  be 
stable. 


256 


THE   STABILITY   OF   ARCHES. 


Graphic  Solution  of  the  Stability  of  the  Arch.— 

The  most   convenient  method  of   determining  the   stability  of 
the  arch  is  by  the  graphic  method,  as  it  is  called. 

IST  STEP. — Draw  one-half  the  arch  to  as  large  a  scale  as  con* 
venient  and  divide  it  up  into  voussoirs  of  equal  size.  In  this 
example,  shown  in  Fig.  3,  we  have  divided  the  arch-ring  into  ten 
equal  voussoirs.  (It  is  not  necessary  that  these  should  be  the 
actual  voussoirs  of  which  the  arch  is  built.)  The  next  step  is  to 
find  the  area  of  each  voussoir.  Where  the  arch-ring  is  divided 
into  voussoirs  of  equal  size,  this  is  easiest  done  by  computing 
the  area  of  the  arch-ring  and  dividing  by  the  number  of  voussoirs, 


SPAN -20  FT.  - 

DEPTH  OF  KEY— 2  fi 


Fig.3 


Rule  for  area  of  one-half  of  arch-ring  is  as  follows : 

Area  in  square  f eet=0. 7854  X  (outside  radius  squared— inside 
radius  squared). 

In  this  example  the  whole  area  equals  0.7854X(12.52  — 102) 
=  44.2  square  feet.  As  there  are  ten  equal  voussoirs,  the  area  of 
each  voussoir  is  4.4  square  feet. 

Having  drawn  out  one-half  of  the  arch-ring,  we  divide  each 
joint  into  three  equal  parts;  and  from  the  point  A  (Fig.  3)  we 
lay  off  to  a  scale  the  area  of  each  voussoir,  one  below  the  other, 
commencing  with  the  top  voussoir.  The  whole  length  of  the 
line  A  E  will  equal  the  whole  area  drawn  to  same  scale. 

The  next  step  is  to  find  the  vertical  line  passing  through  the 
centre  of  gravity  of  the  whole  arch-ring.  To  do  this,  it  is  first 
necessary  to  draw  vertical  lines  through  the  centre  of  gravity  of 
each  voussoir.  The  centre  of  gravity  of  one  voussoir  may  be 
found  by  the  method  of  diagonals,  as  in  the  second  voussoir  from 


THE  STABILITY  OF  ARCHES.  257 

the  top  (Fig.  3).  Having  the  centre  of  gravity  of  one  voussoir, 
the  centres  of  gravity  of  the  others  can  easily  be  obtained  from  it. 

Next,  from  A  and  E  (Fig.  3)  draw  lines  at  45°  with  AE,  inter- 
secting at  0.  Draw  01 ,  02,  03,  etc.  Then,  where  AO  intersects 
the  first  vertical  line  at  a,  draw  a  line  parallel  to  01,  intersecting 
the  second  vertical  at  6.  Draw  be  parallel  to  02,  cd  parallel  to 
03,  and  so  on  to  kn  parallel  to  010;  prolong  this  line  downward 
until  it  intersects  AO,  prolonged,  at  D,  Then  a  vertical  line 
drawn  through  D  will  pass  through  the  centre  of  gravity  of  the 
arch-ring. 

2o  STEP. — Draw  a  horizontal  line  through  A  (the  upper  part 
of  the  middle  third),  and  a  vertical  line  through  D,  the  two 
lines  intersecting  at  C  (Fig.  3). 

Now,  that  the  arch  shall  be  stable,  it  is  considered  necessary 
that  it  shall  be  possible  to  draw  a  line  of  resistance  of  the  arch 
within  the  middle  third.  We  will,  then,  first  assume  that  the 
line  of  resistance  shall  act  at  A  and  come  out  at  B. 

Then  draw  the  line  CB,  and  a  horizontal  line  opposite  the 
point  10,  between  Q  and  p.  This  horizontal  line  represents  the 
horizontal  thrust  at  the  crown. 

Draw  AP  equal  to  Qp,  and  the  lines  PI,  P2,  P3,  etc. 

Then,  from  the  point  where  AC  prolonged  intersects  the  first 
vertical,  draw  a  line  to  the  second  vertical  parallel  to  PI ;  from 
this  point  a  line  to  the  third  vertical  parallel  to  P2;  and  so 
on.  The  last  line  should  pass  through  B.  If  these  lines,  which 
we  will  call  the  line  of  resistance,  all  lie  within  the  middle  third, 
the  arch  may  be  considered  to  be  stable.  Should  the  line  of  re- 
sistance pass  outside  of  the  arch-ring,  the  arch  should  be  con- 
sidered unstable.  In  Fig.  3  this  line  does  not  all  lie  in  the  middle 
third,  and  we  must  see  if  a  line  of  resistance  can  yet  be  drawn 
within  that  limit. 

2o  TRIAL. — The  line  of  resistance  in  Fig.  3  passes  farthest  from 
the  middle  third  at  the  seventh  joint  from  the  top;  and  we  will 
next  pass  a  line  of  resistance  through  A  and  where  the  lower  line 
of  the  middle  third  cuts  the  seventh  joint,  or  at  D  (Fig.  4). 

To  do  this  we  must  prolong  the  line  gh,  parallel  to  07  (Fig.  4), 
until  it  intersects  AO.  In  this  case  it  intersects  it  at  O,  but  this 
is  merely  a  coincidence;  it  would  not  always  do  so.  Through  O 
draw  a  vertical  intersecting  PA  prolonged  at  C.  Draw  a  line 
through  C  and  D,  and  the  horizontal  line  pQ,  opposite  the  point 
7;  this  line  represents  the  new  horizontal  thrust  H^  Draw  AP 
=  pQ,  and  the  lines  PI,  P2,  etc. ;  then  draw  the  line  of  resistance 


258 


THE  STABILITY  OF  ARCHES. 


as  before.  It  should  pass  through  D  if  drawn  correctly.  This 
time  we  see  that  the  line  of  resistance  lies  within  the  middle  third, 
except  for  just  a  short  distance  at  the  springing;  and  hence  we 
may  consider  the  arch  stable.  If  it  had  gone  outside  the  middle 
third  this  time,  to  any  great  extent,  we  should  have  considered 
the  arch  unstable. 

The  above  is  the  method  of  determining  the  stability  of  an 
unloaded  semicircular  arch.  Such  a  case  very  seldom  occurs  in 
practice ;  but  it  is  a  good  example  to  illustrate  the  method,  which 
applies  to  all  other  cases,  with  a  little  difference  in  the  method 
of  determining  the  centre  of  gravity  of  loaded  arches. 


Fig.4 


EXAMPLE  II. — Loaded  or  surcharged  semicircular  arch. 

We  will  take  the  same  arch  as  in  Example  I.  and  suppose  it  to 
be  loaded  with  a  wall  of  masonry  of  the  same  thickness  and 
weight  per  square  foot  as  that  of  the  arch-ring,  the  horizontal 
surface  of  the  wall  being  3  feet  6  inches  above  the  arch-ring  at 
the  crown. 

1st  STEP. — Find  centre  of  gravity. 

Commencing  at  the  crown,  divide  the  load  and  arch-ring  into 
strips  two  feet  wide,  making  the  last  strip  the  width  of  the  arch- 
ring  at  the  springing.  Then  draw  the  joints  as  shown  in  Fig.  5. 
Measure  with  the  scale  the  length  of  each  vertical  line,  A  a,  Bb, 
etc. ;  then  the  area  o/'  A  a  *tb  is  equal  to  the  length  of  A  a  +  Bb,  as 
the  distance  between  them  is  just  two  feet.  The  area  of  FfKk 
is,  of  course,  Ff  X  width  of  arch-ring. 

In  this  case  the  areas  of  the  slices  are  as  shown  by  the  figures 
on  their  faces  (Fig.  5) . 

Now  divide  the  arch-ring  into  thirds,  and  from  the  top  of  the 


THE   STABILITY   OF   ARCHES. 


259 


middle  third,  at  R,  lay  off  in  succession,  to  a  scale,  the  areas  of 
the  slices,  commencing  with  the  first  slice  from  the  crown,  AaBb. 
These  areas,  when  measured  off,  will  be  represented  by  the  line 
Rl,  2,  3  ...  6  (Fig.  5).  From  the  extremities  of  this  line,  R 
and  6,  draw  lines  at  45°  with  a  vertical,  intersecting  at  0.  From 
0  draw  lines  to  1,  2,  3,  4,  5,  and  6.  Next  draw  a  vertical  line 
through  the  centre  of  each  slice  (these  lines,  in  Fig.  5,  are  num- 
bered 1,  2,  3,  etc.).  From  the  point  in  which  the  line  RO  inter- 
sects vertical  1,  draw  a  line  parallel  to  01,  to  the  line  2.  From 
this  point  draw  a  line  to  vertical  3,  parallel  to  02,  and  so  on.  The 
line  parallel  to  05  will  intersect  vertical  6  at  Y.  Then  through 
Y  draw  a  line  downwards  at  45°,  intersecting  OR  at  X.  A  ver- 
tical line  drawn  through  X  will  pass  through  the  centre  of 
gravity  of  the  arch-ring  and  its  load. 


SPAN— 20  FT. 
-DEPTH  OF  KEY-2'6* 


2o  STEP. — To  find  the  thrust  at  the  crown  and  at  the  springing. 

To  find  the  thrust  at  the  crown,  draw  a  vertical  line  through  X, 
and  a  horizontal  line  through  R,  intersecting  at  V.  Now,  the 
weight  of  arch  and  load,  and  the  resultant  thrust  of  arch,  must 
act  through  this  point.  We  will  also  make  the  condition  that 
the  thrust  shall  pass  through  Q,  the  outer  edge  of  the  middle 
third.  Then  the  thrust  of  the  arch  must  act  in  the  line  VQ. 
Opposite  6,  on  the  vertical  line  through  7?,  draw  a  horizontal  line 
H,  between  VX  and  VQ.  This  horizontal  line  represents  a  hori- 


260  THE  STABILITY   OF  ARCHES. 

zontal  thrust  at  R,  which  would  cause  the  resultant  thrust  of  the 
arch  to  pass  through  Q.  Now  draw  the  horizontal  line  RP,  equal 
in  length  to  //,  and  from  P  draw  lines  1,  2,  3  .  .  .  6.  The  line 
P6  represents  the  thrust  of  the  arch  at  the  springing.  Its  amount 
in  cubic  feet  of  masonry  can  be  determined  by  measuring  its 
length  to  the  proper  scale. 

3D  STEP. — To  draw  the  line  of  resistance. 

The  lines  PI,  P2,P3,  etc.,  represent  the  magnitude  and  direction 
of  the  thrust  at  each  joint  of  the  arch.  Thus  PI  represents  the 
thrust  of  the  first  voussoir  and  its  load,  P2  that  of  the  first  two 
voussoirs  and  their  loads,  and  so  on.  Then  from  the  point  a't 
where  the  line  RP,  prolonged,  intersects  the  vertical  line  1,  draw 
a  line  a'  b'  parallel  to  PI ;  from  6',  on  2,  draw  a  line  b'cf  parallel 
to  P2,  and  so  on.  The  last  line  should  pass  through  Q  and  be 
parallel  to  P6. 

Now,  if  we  connect  the  points  where  the  lines  a'b',  bfc',  etc., 
cut  the  joints  of  the  arch,  we  shall  have  a  broken  line,  which  is 
known  as  the  line  of  resistance  of  the  arch.  If  this  line  lies  within 
the  middle  third  of  the  arch,  then  we  conclude  that  the  arch  is 
stable.  If  the  line  of  resistance  goes  far  outside  of  the  middle, 
we  must  see  if  it  be  possible  to  draw  another  line  of  resistance 
within  the  middle  third;  and  if,  after  a  trial,  we  find  that  it  is 
not  possible,  we  must  conclude  that  the  arch  is  not  safe,  or  un- 
stable. 

In  the  example  which  we  have  just  been  discussing,  the  line  of 
resistance  goes  a  little  outside  of  the  middle  third ;  but  it  is  very 
probable  that  on  a  second  trial  we  should  find  that  a  line  of  resist- 
ance passed  through  R  and  Q'  would  lie  almost  entirely  within 
the  middle  third. 

The  method  of  drawing  the  second  line  of  resistance  was  ex- 
plained under  Example  I. ;  and,  as  the  same  method  applies  to 
all  cases,  we  will  not  repeat  it. 

The  method  given  for  Example  II.  would  apply  equally  well 
for  a  semi-elliptical  arch. 

EXAMPLE  III. — Segmented  arch,  with  load  (Fig.  6). 

IST  STEP. — To  determine  the  centre  of  gravity. 

In  this  case  we  proceed,  the  same  as  in  the  latter,  to  divide  the 
arch-ring  and  its  load  into  vertical  slices  two  feet  wide,  and  com- 
pute the  area  of  the  slices  by  measuring  the  length  of  the  vertical 
lines  Aa,  Bb,  etc.  Having  computed  the  areas  of  the  slices,  we 
lay  them  off  in  order  from  R  to  a  convenient  scale  and  then  pro- 
ceed exactly  as  in  Example  II.,  the  remaining  steps  to  determine 


THE  STABILITY   OF  ARCHES. 


261 


the  thrust  and  the  lines  of  resistance  are  also  the  same  as  given 
under  Example  IT. 

In  a  flat  segmental  arch  there  is  practically  no  need  of  dividing 
the  arch-ring  into  voussoirs  by  joints  radiating  from  a  centre,  but 


to  consider  the  joints  to  be  vertical.     Of  course,  when  built,  they 
must  be  made  to  radiate. 

Fig.  6  shows  the  computation  for  an  arch  of  40-foot  span  and 
with  a  load  13|  feet  high  at  the  centre.  The  depth  of  the  arch- 
ring  is  2  feet  6  inches. 


262 


CAST-IRON  ARCH-GIRDERS. 


It  will  be  seen  that  the  curve  of  pressures  lies  entirely  within 
the  middle  third,  and  hence  the  arch  is  abundantly  safe,  or 
stable.  It  should  be  remarked  that  the  line  of  resistance  in  a 
segments!  arch  should  be  drawn  through  the  lower  edge  of  the 
middle  third  at  the  springing. 

It  will  be  noticed  that  the  horizontal  thrust,  and  the  thrust  T, 
at  the  springing,  are  very  great  as  compared  with  those  in  a  semi- 
circular arch;  and  hence,  although  the  scgmental  arch  is  the 
stronger  of  the  two,  it  requires  much  heavier  abutments. 

These  three  examples  serve  to  show  the  method  of  determining 
the  stability  and  thrust  of  any  arch  such  as  is  used  in  building. 

Concrete- Steel  Arches. — Many  arches  are  now  built  of  concrete 
reinforced  by  steel  ribs.  A  very  comprehensive  and  practical 
paper  on  such  arches,  by  Mr.  Edwin  Thacher,  C.E.,  was  pub- 
lished in  the  Engineering  News  of  September  21,  1899. 

Cast-iron  Arch-girders  with  Wrought-iron 
Tension-rods. 

Cast-iron  arch-girders  were  at  one  time  quite  extensively  used 
in  some  parts  of  this  country  for  supporting  brick  walls  over, 
store  fronts  or  other  wide  openings,  but  now  that  structural  steel 
has  become  so  cheap  they  are  seldom  used.  Occasionally,  how- 
ever, the  conditions  are  such  as  to  make  their  use  desirable. 

Fig.  7  shows  the  usual  form  of  such  a  girder,  the  section  of  the 
casting  and  rod  being  shown  in  Fig.  8. 


Fig.!7 


Fig.  8 


The  casting  is  made  in  one  piece  with  box  ends,  the  latter  hav- 
ing grooves  and  seats  to  receive  the  wrought-iron  tie-rod. 

The  tie-rod  is  made  from  one-eighth  to  three-eighths  of  an  inch 
shorter  than  the  casting,  and  has  square  ends  forming  shoulders 
so  as  to  fit  into  the  castings.  The  rod  has  usually  one  weld  on 
its  length,  and  great  care  should  be  taken  that  this  weld  be  perfect. 


CAST-IRON  ARCH-GIRDERS.  263 


The  rod  is  expanded  by  heat,  and  then  placed  in  position  in  the 
casting,  and  allowed  to  contract  in  cooling;  thus  tying  the  two 
ends  of  the  casting  together  to  form  abutments  for  receiving  the 
horizontal  thrust  of  the  arch.  If  the  rod  is  too  long,  it  will  not 
receive  the  full  proportion  of  the  strain  until  the  cast-iron  has  so 
far  deflected,  that  its  lower  edge  is  subjected  to  a  severe  tensile 
strength,  which  cast-iron  can  feebly  resist.  If  the  tie-rod  is  made 
too  short,  the  casting  is  cambered  up,  and  a  severe  initial  strain 
put  upon  both  the  cast  and  wrought  iron,  which  enfeebles  both 
i'or  carrying  a  load.  The  girders  should  have  a  lise  of  about  two 
feet  six  inches  on  a  length  of  twenty-five  feet.* 

Bules  for  Calculating   Dimensions  of  Girder 
and  Rod. 

A  cast-iron  arch-girder  is  considered  as  a  long  column,  subject 
to  a  certain  amount  of  bending-strain ;  and  the  resistance  will  be 
governed  by  the  laws  affecting  the  strength  of  beams,  as  well  as 
by  those  relating  to  the  strength  of  columns. 

If  we  regard  the  arch  as  flexible,  or  as  possessing  no  inherent 
stiffness,  and  the  rod  as  a  chord  without  weight,  the  horizontal 
thrust  or  stress  will  be  represented  by  the  formula. 

Hor.  thrust  _  load  on  girder  in  Ibs.Xspan  in  feet         .  . 
or  stress  (Ibs.)  ~~  8  X  rise  of  girder  in  feet 

From  this  rule  we  can  calculate  the  required  diameter  of  the 
tension-rod,  which  may  be  expressed  thus 


-rv  .    .     ,       .       t  /  load  on  girder  X  span  in  feet      /ON 

Diameter  in  inches  f  =  i/  - —     — £—. — T —  j .     (2) 

8Xnsemfeetx7854 

The  rise  should  be  measured  from  the  centre  of  the  rod  to  the 
centre  of  the  cast-iron  arch;  the  load  should  be  in  pounds. 

The  rule  generally  used,  however,  in  proportioning  the 
wrought-iron  tie  to  the  cast-iron  arch  is  to  allow  one  square  inch 
of  cross-section  of  tie-rod  for  every  ten  net  tons  of  load  imposed  upon 
the  span  of  the  arch. 

The  following  table,  taken  from  Mr.  Fryer's  book  on  "Archi- 
tectural Iron-Work,  shows  the  section  of  the  cast-iron  arch  re- 

*  "Architectural  Iron-Work  for  Buildings,"  William  J.  Fryer,  Jr.,  p.  38. 
t  For  i  working  stress  of  10000  Ibs.  per  square  inch.      For  rods  of  mild 
steel,  use  9800  in  place  of  7854. 


264 


CAST-IRON  ARCH-GIRDERS. 


quired  to  support  solid  brick  walls,  and  having  a  span  of  from  13 
to  26  feet. 


Height  of 
wall. 

Thickness  of 
wall. 

Dimensions  of  section. 

Top  flange. 

Centre  web. 

Bulb. 

40  feet 
50     " 
40     " 
50     " 

12  inches 
12       " 
16       " 
16       " 

12"  XI" 
12"  X  11A" 

12"  XW 

1o/'X^ 

3"     X  2" 
3"  fi  X  2" 

3V6"  X  2" 

12"Xl" 

4       X^ 

EXAMPLE  I. — It  is  desired  to  support  a  12-inch  brick  wall  40 
feet  high  over  an  opening  20  feet  wide,  with  a  cast-iron  arch- 
girder.  What  should  be  the  dimensions  of  the  girder? 

For  the  casting,  we  find  from  the  table  that  the  cross-section 
of  the  flange  should  be  12  inches  by  1  inch;  of  the  web,  12 
inches  by  f  inch;  and  of  the  bulb,  3  inches  by  2  inches.  We  will 
make  the  rise  of  the  girder  2  feet  and  6  inches,  and  from  Formula 
2  we  find  * 


TV  -      -,  .    .     ,  . 

Diam.  of  rod  in  inches  =  4 

r 


/        weight  of  wall  X  span 

of  arch  infeetX7854 


Figs.  9  and  10  show  a  cast-iron  arched  girder  that  was  used  to 


-294- 


Fig,  9 

support  a  central  tower  over  the  crossing  of  the  nave  and  transept 

*  Considering  that  the  girder  would  only  support  about  twenty  feet  of 
the  wall  in  height,  the  wall  above  that  supporting  itself.  See  "  Beams  Sup- 
porting Brick  Walls,"  Chapter  XV. 


CAST-IRON  ARCH-GIRDERS. 


265 


of  St.  John's  Church,  Stockton,  California, 
Mr.  A.  Page  Brown, 
architect.  The  clear 
span  is  29 J  feet,  and  the 
height  of  the  wall  above 
the  girder  18  feet.  One 
object  in  using  such  a 

SECTION^AT  CENTER.    girder  jn  ^    place    wag 

to  get  the  height  in  the 
centre  without  also  raising  the  supports, 
which  could  not  be  obtained  with  a  steel 
plate  girder.  The  church  has  a  vaulted 
ceiling  which  comes  just  below  the  arch  of 
the  girder,  the  tie-rod  being  exposed. 

The  rise  of  the  casting  in  thic  case  is  rather 
more  than  common,  the  usual  rise  being 
jl  from  yV  to  J  of  the  span. 

Fig.  11  shows  an  arch  girder,  with  the 
casting  in  three  sections,  with  pin  joints, 
the  head  of  the  suspending  pieces  AA,  form- 
ing the  pin.  The  flexible  bolt  connections 
serve  to  hold  the  sections  in  place  laterally. 

Mr.  Peter  H.  Jackson,  C.E.,  of  San  Fran- 
cisco, who  has  had  an  extended  experience 
with  this  form  of  construction,  says  of  it: 
"The  Franklin  girder  is  unequaled  for 
strength  in  the  application  of  the  same 
amount  of  metal  in  any  other  form.  This 
cast-iron  arch  is  in  effect  a  device  for  em- 
ploying cast  iron  compressively,  neutralizing 
the  tensile  strain  due  to  transverse  strain. 
It  has  been  favorably  commented  on  by 
the  scientific  papers  of  the  United  States. 
London  and  Paris." 


266 


BENDING-MOMENTS. 


CHAPTER  IX. 

BENDING-MOMENTS    AND    SUPPORTING 
FORCES. 

THE  bending-moment  of  a  beam  or  truss  represents  the  de- 
structive energy  of  the  load  on  the  beam  or  truss  at  any  point  for 
which  the  bending-moment  is  computed. 

The  moment  of  a  force  around  any  given  axis  is  the  product 
of  the  force  into  the  perpendicular  distance  between  the  line  of 
action  of  the  force  and  the  axis,  or  the  product  of  the  force  into 
its  arm. 

In  a  beam  the  forces  or  loads  are  all  vertical  and  the  arms  hori- 
zontal. 

The  bending-moment  at  any  cross-section  of  a  beam  is  the  alge- 
braic sum  of  the  moments  of  the  forces  tending  to  turn  the  beam 
around  the  horizontal  axis  passing  through  the  centre  of  gravity  of 
the  section. 

EXAMPLE. — Suppose  we  have  a  beam  with  one  end  securely 
fixed  into  a  wall  and  the  other  end  projecting  from  it,  as  in  Fig.  1. 

Let    us    now   suppose    we   have   a 
weight  which  if  placed  at  the  end 
the  beam  will  cause  it  to  break 
the  point  of  support. 
Then,   if  we   were  to  place  the 
weight    on    the    beam    at   a   point 
v\near    the    wall,    the    beam    would 
<  support   the  weight   easily;   but  as 
we  move   the   weight  towards  the 
outer  end  of  the  beam,  the  beam 
bends   more    and    more,  and  when 
the  weight  is  at  the  end,  the  beam 
breaks,  as  shown  by  the  dotted  lines,  Fig.  1 . 

Now,  it  is  evident  that  the  destructive  energy  of  the  weight  is 
greater  the  farther  the  weight  is  removed  from  the  wall-end  of  the 
beam,  although  the  weight  itself  remains  the  same  all  the  time. 
The  reason  for  this  is  that  the  moment  of  the  weight  tends  to 


Fig.1 


BENDING-MOMENTS. 


267 


turn  the  beam  about  the  point  A ,  and  thus  produces  a  pull  on  the 
upper  fibres  of  the  beam  and  compresses  the  lower  fibres.  As  the 
weight  is  moved  out  on  the  beam,  its  moment  becomes  greater, 
and  hence  also  the  pull  and  compression  on  the  fibres;  and 
when  the  moment  of  the  weight  produces  a  greater  tension  or 
compression  on  the  fibres  than  they  are  capable  of  resisting,  they 
fail  and  the  beam  breaks.  Before  the  fibres  break,  however, 
they  commence  to  stretch,  and  this  allows  the  beam  to  bend; 
hence  the  name  "bending-moment"  has  been  given  to  the  mo- 
ment which  causes  a  beam  to  bend,  and  perhaps  ultimately  to 
break. 

There  may,  of  course,  be  several  loads  on  a  beam,  and  each  one 
having  a  different  moment  tending  to  bend  the  beam;  and  it 
may  also  occur  that  some  of  the  weights  may  tend  to  turn  the 
beam  in  different  directions ;  the  algebraic  sum  of  their  moments 
(calling  those  tending  to  turn  the  beam  to  the  right  +  and  the 
others  —  )  would  be  the  bending-moment  of  the  beam. 

Knowing  the  bending-moment  of  a  beam,  we  have  only  to  find 
the  section  of  the  beam  that  is  capable  of  resisting  it,  as  is  shown 
in  the  general  theory  of  beams,  Chapter  XV. 

To  determine  the  bending-moments  of  beams  mathematically 
requires  considerable  training  in  mechanics  and  mathematics; 
but,  as  most  beams  may  be  placed  under  some  one  of  the  follow- 
ing cases,  we  shall  give  the  bending-moment  for  these  cases  and 
then  show  how  the  bending-moment  for  any  other  methods  of 
loading  may  be  easily  obtained  by  a  scale  diagram. 


Examples  of  Bending-Moments. 


CASE  I. 

Beam  fixed   at  one   end  and  loaded 
with  concentrated  load  W. 


Bending-moment   =    W   X    L. 


may,  or  may  not,  be  the  whole  length 
of  the  beam    according  to  where  the  ^ 
weight  is  located.) 


Fig.  2 


268 


BENDING-MOMENTS. 


CASE  II. 

Beam  fixed  at  one  end,  loaded  with 
a  distributed  load  W. 


Bending-moment  =  W  X  77. 


Fig.  3 


NOTE. — If  L  is  in  feet,  the  bending-mo- 
ment will  be  foot-pounds;  if  L  is  in  inches, 
the  bending-moment  will  be  in  inch-po  .inds. 
See  general  formula  for  beams,  Chapter  XV. 


CASE  III. 


Beam  fixed  at  one  end}  loaded  with 
both  a  concentrated  and  a  distributed 
load. 


Bending-moment = P  X  L2  +  W  X  -£. 


Li 


Tl 


Fig.4 


CASE  IV. 
Beam  supported  at  both  ends,  loaded  with  concentrated  load  at 


centre. 


W 

(H 


Bending-moment 


Fig.  5 

CASE  V. 
Beam  supported  at  both  ends,  loaded  with  a  distributed  load  W. 


BENDING-MOMENTS. 


269 


CASE  VI. 

Beam  supported  at  both  ends,  loaded  with  concentrated  load  not 
at  centre. 


-m- 


Fig.  7 


Bending-moment 

mXn 


-wx- 


L    * 


CASE  VII. 

Beam  supported  at  both  ends,  loaded  with  two  equal  concen- 
trated loads,  equally  distant  from  the  centre. 


Bending-moment 
—  WXm. 


Wfl 


-  m- 
>W 


Fig.    8 


From  these  examples  it  will  be  seen  that  all  the  quantities  which 
enter  into  the  bending-moment  are  the  weight,  the  span,  and  the 
distance  of  point  of  application  of  concentrated  load  from  each 
end. 

CASE  VIII. 

Beam  supported  at  both  ends,  loaded  with  a  distributed  load  over 
only  a  portion  of  the  span. 


-Lr 


Bending-moment 


8 


Fig.  9 


When  m  and  n  are  equal,  bending-moment  =  —  ^— '. 


270 


BENDING-MOMENTS. 


EXAMPLE.— Let  W=  800  Ibs.;  w=8';w=12';  L=20';L1=8/. 
Then  bending-moment  = 
800X8X12  _  800X  8  _  ^^  _  ^  _  ^    foot.pounds    of 

2i(j  o 

36,480  inch-pounds. 

EXAMPLE    II.— Let   n=m=10ft;  L=20ft.;    1^=4  ft.;   TF=* 
600  Ibs.     Then  bending-moment  = 
600X20  _  600X4  =  3000_300  =  2700  ft.  Ibs.  or  32,400  in.-lbs. 

The  bending-moment  for  any  case  other  than  the  above  may 
easily  be  obtained  by  the  graphic  method,  which  will  now  be 
explained. 


Graphic  Method  of  Determining  Beiicling-- 
Moments. 

The  bending-moment  of  a  beam  supported  at  both  ends  and 
loaded  with  one  concentrated  load  may  be  shown  graphically,  as 
follows : 

Let  W  be  the  weight  applied,  as  shown.  Then,  by  rule  under 
Case  VI.,  the  bending-moment  directly  under 


w=wx' 


_ 


Draw  the  beam,  with  the  given  span,  accurately  to  scale,  and 
measure  down  the  line  AB  (to  a  scale  of  pounds  .to  the  inch) 
equal  to  the  bending-moment.  Connect  B  with  each  end  of 
the  beam.  If,  then,  we  wished  to  find  the  bending-moment 
at  any  other  point  of 
the  beam,  as  at  o, 

draw  the  vertical  line 

y    to    BC,    and     its  x—  '    ^  rA 

length,  measured    to  \ 
the  same  scale  as  A  B, 
will  give  the  bending 
moment  at  o. 

Beam  with  two 
concentrated  loads. 
(Fig.  11.) 

To  draw  the  bending-moment  for  a  beam  with  two  connected 
loads,  first  draw  the  dotted  lines  ABD  and  ACD,  giving  the  out- 


Fig.  10 


BENDING-MOMENTS. 


271 


line  of  the  bending-moment  for  each  load  separately;  EB  being 
equal  to  JFX-  and  FC  equal  to  ^X 


Now,  the  bending-moment  at  the  point  E  equals  EB,  due  to 
the  load  W,  and  Eb,  due  to  the  load  P;  hence  the  bending- 
moment  at  E  should  be  drawn  equal  to  EB  +  Eb^EB^-,  and 
at  F  the  bending-moment  should  equal  FC  +  Fc=FC1.  The 
outline  for  the  bending-moment  due  to  both  loads,  then,  would 
be  the  line  ABfiiD  and  the  greatest  bending-moment  would, 
in  this  particular  case,  be  FC^ 

Beam  with  three  concentrated  loads.     (Fig.  12.) 
Proceed  as  in  the  last  case,  and  draw  the  bending-moment 
for    each    load    separately.     Then    make    AD=A1+A2  +  A3, 


Fig.  12 

and  CF=Cl+C2  +  C3.     The  line  HDEFI 
will  then  be  the  outline  for  the  bending-moment  due  to  all  the 


272 


BENDING-MOMENTS. 


weights.     The  bending-moment  for  a  beam  loaded  with  any 
number  of  concentrated  weights  may  be  drawn  in  the  same  way. 
Beam  with  uniformly  distributed  load.     (Fig.  13.) 


Fig.  13 

Draw  the  beam  with  the  given  span,  accurately  to  a  scale,  as 
before,  and  at  the  middle  of  the  beam  draw  the  vertical  line  AB 

equal   to   WX-^-,  W  representing  the  whole   distributed  load. 

o 

Then  connect  the  points  C,  B,  D  by  a  parabola  and  it  will  give 
the  outline  of  the  bending-moments.  If,  now,  we  wanted  the 
bending-moment  at  the  point  a,  we  have  only  to  draw  the  verti- 
cal line  ab,  and  measure  it  to  the  same  scale  as  AB,  and  it  will 
be  the  moment  desired.  Methods  for  drawing  the  parabola 
may  be  found  in  "  Geometrical  Problems,"  Part  I. 

Beam  loaded  with  both  distributed  and  concentrated  loads.  (Fig  14.) 
To  determine  the  bending-moment  in  this  case,  we  have 
only  to  combine  the  methods  for  concentrated  loads  and  for 
the  distributed 
load,  as  shown  in 
the  accompany- 
ing figure.  The 
bending  -  moment 
at  any  point  on 
the  beam  will 
then  be  limited 
by  the  line  ABC 
on  top  and 
CDEFA  on  the 
bottom;  and  the 
greatest  bending- 
moment  will  be 
the  longest  verti- 
cal line  that  can  be  drawn  between  these  two  bounding  lines. 


-"K 


BENDING-MOMENTS. 


273 


For  example,  the  bending-moment  at  X  would  be  BE.  The 
position  of  the  greatest  bending-moment  will  depend  upon  the 
position  of  the  concentrated  loads,  and  it  may  and  may  not 
occur  at  the  centre. 

EXAMPLE. — What  is  the  greatest  bending-moment  in  a  beam 
of  20  feet  span,  loaded  with  a  distributed  load  of  800  pounds 
and  a  concentrated  load  of  500  pounds  6  feet  from  one  end,  and 
a  concentrated  load  of  600  pounds  7  feet  from  the  other  end? 

Ans.  1st.  The  moment  due  to  the  distributed  load  is  JFX7T, 

800  X  20 


2000  pounds. 
We,  therefore, 
lay  off  to  a 
scale,  say  4000 
pounds  to  the 
inch,  £1  =  2000 
pounds,  and 
draw  a  parabola 
between  the 
points  A,  B,  and 
C. 


Fig.  15 


2d.  The  bending-moment   for   the  concentrated  load  of  500 


pounds  is 


500X6X14 
20 


;,  or  2100  pounds.    Hence  we  draw  E2=  2100 


pounds  to  the  same  scale   as  Bl,  and  then  draw  the  lines  AE 
and  CE. 

3d.  The  bending-moment  for  the  concentrated  load  of  600 


pounds  is 


600X7X13 
20 


:,  or  2730  pounds;   and  we  draw  D3  =  2730 


pounds  and  connect  D  with  A  and  C. 

4th.  Make  EH=2-4,  and  D<3=3-5,  and  connect  G  and  H 
with  C  and  A  and  with  each  other. 

The  greatest  bending-moment  will  be  represented  by  the 
longest  vertical  line  which  can  be  drawn  between  the  parabola 
ABC  and  the  broken  line  A  HOC.  In  this  example  we  find 
the  longest  vertical  line  which  can  be  drawn  is  xy;  and  by 
scaling  it  we  find  the  greatest  bending-moment  to  be  5550  foot- 
pounds, applied  10  feet  11  inches  from  the  point  A. 

In  this  case  the  position  of  the  line  Xy  was  determined  by 


274  SUPPORTING  FORCES. 

drawing  the  line  T7\  parallel  to  HG,  and  tangent  to  ABC.     The 
line  Xy  is  drawn  through  the  point  of  tangency. 

NOTE.  —  If  we  wish  the  bending-moment  in  inch-pounds,  multiply  the 
moment  in  foot-pounds  by  12. 

Supporting  Forces. 

It  is  a  fundamental  principle  of  mechanics  that  for  a  body  to 
be  in  equilibrium  the  forces  acting  upon  it  must  balance  each 
other.  When,  therefore,  a  body,  such  as  a  beam,  girder,  or 
truss,  is  subjected  to  loads  acting  downwards  in  a  vertical  direc- 
tion, that  the  beam  or  truss  shall  keep  its  position  there  must 
be  an  equal  resistance  in  the  opposite  direction.  This  resistance 
is  furnished  by  the  supports,  which  may  be  either  of  masonry, 
columns,  or  another  beam  or  truss. 

From  the  above  propositions  it  follows  that  the  supports  must 
react  against  the  beam  or  truss  with  a  combined  resistance  equal  to 
the  sum  of  the  loads  acting  downwards. 

It  is  often  necessary  to  determine  the  amount  of  each  reac- 
tion, and  in  computing  the  shearing  stress  in  a  beam  or  girder, 
or  in  drawing  a  strain  diagram  for  a  truss,  this  is  the  first  step 
of  the  problem. 

The  following  rules  will  enable  one  to  determine  the  support- 
ing forces  or  reactions,  for  any  manner  of  loading,  when  the 
beam,  girder,  or  truss  is  supported  at  both  ends. 

These  rules  apply  either  to  a  beam,  girder,  or  truss,  and  to 
any  style  of  truss. 

1.  When  the  loads  are  symmetrically  disposed  between  the  sup- 
ports, each  supporting  force  is  equal  to  one-half  of  the  total  load. 

2.  For  a  single  concentrated  load  applied  at  any  point,  as  in 
Fig.  16, 


t 


Fig.  16 


i=  p^W-P*  (1) 

3.  For  a  distributed  load  applied  over  only  a  portion  of  the  span, 


SUPPORTING  FORCES. 


275 


as  in  Fig.  17,  assume  the  load  to  be  concentrated  at  its  centre, 
and  use  formula  (1). 


I         Fig.  17 
EXAMPLE.— Let     n=8,    m=12,    and    TF=&00;     then    P^ 

cnn  v  1  2 

*      =  480.     When  n  and  m  are  equal,  then  P^P2=  %W. 

4.  For  any  number  of  concentrated  forces,  indicate  the  distances 
from  the  right-hand  support,  as  in  Fig.  18;  then 


2n  +  W3o  +  W,r  +  W,s  +  W6t 


(2) 


The  same  result  would  be  obtained  by  finding  the  reaction  of 
j.  for  each  load  by  formula  (1)  and  adding  the  reactions. 


w, 


W2 


r        0 __.», 
L_..^,__  ___>, 

^i  Wt"      ^F:r-1 


pt._  .£.__ 


Fig.  18 

When  a  truss  is  loaded  unsymmetrically ,  the  supporting  forces 
will  be  found  by  formula  (2),  keeping  the  same  notation,  and 
using  the  same  number  of  terms  in  the  formula  as  there  are  loads 
on  the  truss. 

It  should  always  be  borne  in  mind  that  the  sum  of  the  reactions 
is  equal  to  the  sum  of  the  loads. 


276 


SUPPORTING  FORCES. 


//  the  beam  or  girder  supports  a  distributed  load  and  also  con- 
centrated loads,  to  each  of  the  reactions  obtained  by  formulas  (1) 
or  (2)  add  one-half  of  the  distributed  load. 

EXAMPLE  1. — A  beam  16  ft.  long  is  supported  at  each  end  by 
the  tie  beam  of  a  truss,  the  distance  between  the  centres  of  the 
trusses  being  15  ft.  4  ins.;  at  a  point  4  ft.  4  ins.  from  the  centre 
of  the  left-hand  support  the  beam  sustains  a  concentrated  load 
of  12  tons.  What  part  of  the  load  is  supported  by  each  truss? 

Ans.  Let  P!  denote  the  portion  of  the  load  borne  by  the  truss 
at  the  left,  P2  that  borne  by  the  truss  at  the  right,  and  L  the  dis- 
tance between  the  centres  of  the  trusses;  then,  by  formula  (1), 
we  have 


12X11 
151    ' 


=  8.6  tons      and 


EXAMPLE  2. — A  girder  of  30  feet  span  is  loaded  with  a  dis- 
tributed load  of  15  tons  and  with  six  concentrated  loads  of  5, 
6,  4,  8,  3,  and  2  tons,  arranged  consecutively  from  left  to  right. 


Fig.  19 

The  distances  from  the  right-hand  support,  corresponding  to 
those  in  Fig.  18,  are:  m  =  28,  n=22,  o=16,  r=12,  s=10,  t=Q. 
What  will  be  the  reaction  at  each  support? 

Ans.  First  find  reactions   for  concentrated  loads.     By  for- 
mula (2) 


D      5X28  +  6X22  +  4X16  +  8X12  +  3X10  +  2X6 
/!=  —  —  — 

P2=5-i-6-f  4  +  8  +  3  +  2-  15.8-  12.2  tons. 


_ 

-lo.o  tons; 


SUPPORTING  FORCES.  277 

One-half  of  the  distributed  load  is  7.5  tons;  then  P1  for  whole 
load=  15.8 +  7.5=  23.3  tons  and  P2=19.7  tons. 

The  reactions  obtained  for  the  concentrated  loads  may  be 
verified  by  multiplying  each  load  by  its  distance  from  the  other 
support  and  dividing  the  sum  of  the  products  by  the  span. 
The  result  will  be  P2.  Thus  in  the  above  example 

p   5X2  +  6X8  +  4X14  +  8X18  +  3X20  +  2X24 
P*~  "30~ 

which  proves  the  former  calculation. 

EXAMPLE  3. — A  truss  is  loaded  in  such  a  way  that  the  loads 
correspond  to  3  tons  for  Wl  (Fig.  19),  3  tons  for  W2,  5  tons  for 
Ws,  6  tons  for  TF4,  and  5  tons  for  TF5;  the  distance  L  is  48  feet; 
ra,  40  feet;  n,  32  feet;  o,  24  feet;  r,  16  feet,  and  s,  8  feet.  What 
is  the  reaction  at  each  support? 

4         p     3X40  +  3X32  +  5X24  +  6X16  +  5X8     0  QQ 
Ana.  PI=  —  ~~4% —  —=9.83  tons; 

-9.83=12.17tons. 


278    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


CHAPTER  X. 

MOMENTS  OP  INERTIA  AND  RESISTANCE,  AND 
RADIUS  OP  GYRATION. 

DIMENSIONS  AND  PROPERTIES  OF  STRUCTURAL 
SHAPES. 

MOMENT  OF  INERTIA. 

THE  strength  of  sections  to  resist  strains,  either  as  girders  or  as 
posts,  depends  not  only  on  the  area,  but  also  on  the  form  of  the 
cross-section.  The  property  of  the  section  which  represents  the 
effect  of  the  form  upon  the  strength  of  a  beam  or  post  is  its 
moment  of  inertia,  usually  denoted  by  I.  The  moment  of  inertia 
for  any  cross-section  is  the  sum  of  the  products  obtained  by  multi- 
plying the  area  of  each  particle  in  the  cross-section  by  the  square 
of  its  distance  from  the  neutral  axis. 

The  neutral  axis  of  a  beam  is  the  line  on  which  there  is  neither 
tension  nor  compression,  and  when  the  stresses  are  within  the 
elastic  limit  of  the  material,  it  can  be  shown  that  the  neutral 
axis  passes  through  the  centre  of  gravity  of  the  cross-section. 

For  most  forms  of  cross-section  the  moment  of  inertia  is  best 
found  by  the  aid  of  the  calculus ;  though  it  may  be  obtained  by 
dividing  the  figure  into  small  squares  or  triangles,  and  multi- 
plying their  areas  by  the  squares  of  the  distance  of  their  centres 
of  gravity  from  the  neutral  axis.  The  sum  of  all  the  products 
will  be  the  moment  of  inertia  of  the  section. 

MOMENT  OF  RESISTANCE. 

The  resistance  of  a  beam  to  bending  and  cross-breaking  at  any 
given  cross-section  is  the  moment  of  the  two  equal  and  opposite 
forces,  consisting  of  the  thrust  along  the  longitudinally  com- 
pressed layers,  and  the  tension  along  the  longitudinally  stretched 
layers. 

This  moment,  called  the  "moment  of  resistance,"  is,  for  any 
given  cross-section  of  a  beam,  equal  to 

/         moment  of  inertia        \ 

,.  ,  — r-  )  X  modulus  of  rupture  or  fibre  stress. 

\extreme  distance  from  axis/ 


RADII  OF   GYRATION.  279 

The  moment  of  resistance  forms  a  part  of  all  formulas  for  the 
strength  of  beams.  The  portion  of  the  above  formula  included 
in  parenthesis  is  sometimes  erroneously  designated  the  moment 
of  resistance;  in  the  handbooks  published  by  the  manufacturers 
of  structural  steel  shapes,  it  is  now  designated  as  the  section 
modulus,  and  for  the  sake  of  uniformity,  the  author  has  adopted 
the  same  term. 

RADIUS  OF  GYRATION. 

The  effect  of  the  form  or  section  of  a  column  upon  its  strength 
is  determined  by  a  property  called  the  radius  of  gyration.  The 
value  of  the  radius  of  gyration  of  any  section  is  determined  by 
the  formula,  r=\/ moment  of  inertia  4- section  area.  , 

The  moment  of  inertia  and  radius  of  gyration  of  a  section  are 
always  taken  about  an  axis  passing  through  the  centre  of  gravity 
of  the  section.  For  all  sections  except  circles  there  will  be  at 
least  two  radii  of  gyration;  the  least  of  these  will  be  that  taken 
about  the  axis  around  which  the  column,  strut,  or  beam  is  most 
likely  to  bend. 

Formulas  for  the  moment  of  inertia,  radius  of  gyration,  and 
section  modulus  of  the  principal  elementary  sections  are  given 
below.  In  the  case  of  hollow  or  re-entering  sections,  the  moment 
of  the  hollow  portion  is  to  be  subtracted  from  that  of  the 
enclosing  area. 

Moments  of  inertia  when  referred  to  the  same  axis  can  be 
added  or  subtracted  like  any  other  qualities  which  are  of  the 
same  kind. 

Moments  of  Inertia,  Section  Modulus,  and  Radii 
of  Gyration. 

/  =  moment  of  inertia. 

R  =  section  modulus. 

r  =  radius  of  gyration. 

A  =  area  of  the  section. 

Position  of  neutral  axis  represented  by  broken  line. 

fc-fc-H,  rbd* 

12' 


'12' 


280    MOMENTS  OF  INERTIA  AND   RESISTANCE. 


T 


bd* 


1 


7= 


12 

27 
d' 
I_ 

bd — bjd/ 


7 
i 


^ 


36' 


18' 


2 
ffi . 

~ 


y- — &- *. 


1 

i 


r 

1_ 


RADII    OF   GYRATION. 

y&  y& 

• 

i=- 


281 


s\ 


r2==& 

/=  0.0491  (D4-cF). 
J?=  0.0982  (l)3-^. 


)  (a  very  close 


5.64  )         approximation), 


12 


6-1 


*  To  find  the  value  of  d,  see  page  240. 


282    MOMENTS   OF  INERTIA  AND   RESISTANCE. 


A^bd-d^b-f). 

W-dW-t) 
1=         —    --  -      d^d-s  +  y 


=  *L  A/  I 

d  •     T~V  X' 


12 


I  I    s       j       b'x*-(V-t)X(x-s)* 


3      . 


To  find  x  and  a/  see  page  239. 


Moments  of  Inertia  of  Compound  Shapes. 

The  moment  of  inertia  of  any  combination  of  single  shapes  is 
equal  to  the  sum  of  the  moments  of  inertia  of  the  individual 
shapes  taken  about  an  axis  passing  through  the  centre  of  gravity 
of  the  combination. 

The  moment  of  inertia  of  the  individual  sections  may  be 
obtained  by  the  following  rule: 

The  moment  of  inertia  of  any  section  about  an  axis  other  than 
through  its  centre  of  gravity  is  equal  to  its  m.oment  of  inertia  about 
a  parallel  axis  passing  through  its  centre  of  gravity  plus  the  area  of 
the  section  multiplied  by  the  square  of  the  distance  between  the  axes. 

Thus,  the  moment  of  inertia  of  the  angle  (Fig.  1)  about  the 


RADII  OP  GYRATION. 


283 


ORMULAS    USED    FOR    COMPUTING    MOMENTS    OF 
INERTIA     FOR     STANDARD     SECTIONS. 


Tan2a=-i 


7,  Axis  1-1=2 


I"  minimum,  Axis  3  —  3  = 


12 

I'  cos2  a  —  7  sin2  a 
cos  2a 


;j« 


a?, 


7,Axisl-l=- 


36 


144 


area  of  head. 


rfc2/,    2s  +  fr\2l  ,  ta+s'} 

,  Axis  l-l  =  e    va+  Vrf o — /  J  + ^ — 

i_  jtj      >  jt  ' '.      .  o 

-A(x-s): 


',  Axis  2-2  =  rr^-  + 


36 


284    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


FORMULAS    USED    FOR    COMPUTING    MOMENTS    OF 
INERTIA    FOR    STANDARD    SECTIONS— Continued. 


,    .    .    ,      , 

/,  Axis  1  —  1  =    ^ 


(&-Q2 

12    ' 
M-l* 


Slope  of  flange  =g-*=j—  =  «  for  standard  sections. 


6 


n 


T      A      •      1          .  < 

I,  Axis  1-    =-^ 
/'.Axis  2-2=-2 
Slope  of  flange  =  g 


~         —  for  standard  sections. 


— 


/.Axis  1-1  = 


/"fAxis2-2  =  - 


^^  2(2a-0  ' 

(q  -  a;)9  4  arr3  -  (a  -  Q  (x  -  O3 
~~~~ 


2— 


,_ 
' 


tf-:-* 

^a- 


Tan2a  = 


2(o/  H 
[(2z  -  Ob(b  -  2s')  +  ( 2a;r  -  Q(a  -  Q(o  +  <  -  2a;)]< 


2(1' -I) 


^aVH 

r  \ 


/.  Axis  1  —  1  = 
/',  Axis  2-2  = 


Ka  -  aQ 


/  cos2  a -r  sin2  a 
/".AxisS-^-          cos2a< . 


RADII  OF  GYRATION. 


285 


axis  AB  is  equal  to  its  moment  of  inertia  about  the  axis  ab 
plus  the  product  of  its  area  by  x2.     The  mo- 
ment of    inertia   for  the    standard  merchant  a~         •>— J--J----6 
shapes  of  structural  steel  may  be  found  from 
the   tables  given  in   this   chapter.     The  dis- 
tance d  may  be  found  from  columns  IX.  and 
X.,  " Properties    of    Angles."     This    distance 
subtracted  from  D  will  give  the  distance  x.      *~~ 

The  method  of  finding  the  moment  of  inertia  Fi9- 

for  the  most  common  combinations  is  indicated  below.  The 
column  numbers  refer  to  the  columns  in  the  table  giving  the 
properties  of  the  section  under  consideration.  A  period  be- 
tween letters  denotes  multiplication. 

Fig  2.  Moment  of  Inertia  of  Combination  about  Axis  AB 


=  twice  the  moment  of  inertia  for    A. 
beam    a    (col.    II.)  +  that    for 
beam  b  (col.  III.). 


Fig.  2 
Fig.  3.  Moment  of  Inertia  of  Combination  about  Axis  CD 

=  twice  the  area  of  beam  a  (col.  |T  y 

I)X^2  +  twice  moment  of  in- 
ertia  for  beam  a  (col.  III.)  + 
that  for  beam  b  (col.  II.). 

r 

Fig.  3 

Fig.  4.  Moment  of  Inertia  of  Combination  about  Axis  AB 

Xcdlice 


=  twice    the    moment    of    single 
channel  in  col.  II. 


Fig.  4 


286    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


Fig.  5.  Moment  of  Inertia  of  Combination  about  Axis  CD 

—  twice    area     of    one     channel H ML 

(col.    I.)  Xd24- twice    moment 
of  inertia  (col.  III.). 
d=  distance  of  centre  of  gravity  of 

the  channel  from  centre  line       J^.. 
of  the  combination. 

Fig.  5 
Fig.  6.  Moment  of  Inertia  of  Combination  about  Axis  AB 


§ 


,  -. 

=  sum  of  j  \  12 

(.1  for  channels  =  twice  the  moment  in  col.  II. 


— 

i 

i      \i 

A—  - 

]___ 

V 
J-B 

*.-.U-« 

i 

X 

i 

^__J 

i 

ll^ 

f 

1 

D 

Fig.  6 

Fig.  6.  Moment  of  Inertia  about  Axis  CD 
I  for  plates  =  - 


=  sum  of^J 


12 


i  /  for  channels  =  2  X  (area  of    one    channel  X  I2  +  mo- 
ment  of  inertia,  col.  III.). 


r,  col.  IX. 

Fig.  7.  Moment  of  Inertia  of  Combination  about  Axis  AB 
=  sum  of 

'/for  plates  P=  (jTr+b.t.x2)  X2; 

/moment  of  one     area  of  one  angle\ 

/  for  four  angles  =  4  X  (        -,         •.  TTT   +         *•  2          ! 

\angle,  col.  III.  times  y2        J  ' 


/ 
for  plate  P^^. 


=$d-l,     col.  IX. 


RADII   OF  GYRATION. 


287 


Fig.  7.  Moment  of  Inertia  about  Axis  CD 
=  sum  of 

2tb* 

/for  plates  P=—^  ; 
i« 

/moment  of  one  ,  area  of  one  angle\ 

/lor  four  angles  =  4X  (          i         i   TT    +          ±-         72          )  > 
\  angle,  col.  II,  times  Z2          /  ' 


[/for  plate 


. 


(col. 


Moment  of  inertia  for  Four  Angles  connected  by  Lattice  and 
without  Cover-plates.  —  Same  as  in  middle  line  of  above. 


r    '  rrrj. 

fTT 

[ 

J  !    ! 

ffc 

% 

>  i  i 

. 

i  i 

Q 

H- 

n 
J« 

\ 

J 

Fig 

p 

3 
.  7 

C 
-5-i- 


— B 


D 
Fig.  8 

Fig.  8.  Moment  of  Inertia  of  Combination  about  Axis  AB. 
Same  as  for  Fig.  7,  letting  ^  equal  total  thickness  of  web- 
plates. 

Fig.  8.  Moment  of  Inertia  about  Axis  CD 
=  sum  of 

/  for  flange-pi  ares  =  -—- ; 
\.  2i 


I  for  four  angles=4X 
/  for  web-plates = 2  X 


/moment  of  one     area  of  one  angle\  m 


\  angle,  col.  II. 


times  Z2 


.  X.). 


288     MOMENTS  OF  INERTIA  AND   RESISTANCE. 

Fig.  9.  Moment  of  Inertia  of  Two  Angles. 
About  axis  AB  :  7=  twice  the  moment  of  single  angle,  col.  IL 


.    ~~    T     Ov.  /moment  of  one     area  of  one  angle\ 
About  axis  CD:  7=  2X  (        T          ,    TTT -f 

\angle,  col.  III.  times  xl         /' 


EXAMPLE  I.—  Fig.  7,  Let  6=12;  t=%.  d=30;  ^=4.  An- 
gles 5X3JXJ.  Find  moment  of  inertia  of  the  girder  about 
axis  AB. 

From  table  of  properties  of  standard  angles,  unequal  legs, 
we  find  area  of  one  angle  to  be  4.  Moment  of  inertia  of  angle 
about  axis  parallel  to  long  flange  =  4.  05;  distance  from  centre 
of  gravity  to  back  of  long  flange  =.91. 

Then 


7forflange-plates=2X  +  12XiX(15i)       =    2790.96 

/  for  four  angles  =4X[4.05  +  4X(15-.91)2]  =     3192.20 

/  for  web-plate    =^  1125.00 


/  for  whole  section  =  7108.16 

It  will  be  noticed  that  the  moment  of  inertia  of  the  flange- 
plates  and  angles  about  their  own  axes  is  so  small,  compared 
with  the  moment  of  the  girder,  that  they  might  be  omitted 
without  any  appreciable  error. 

In  calculating  the  moment  of  inertia  of  riveted  girders  it  is 
the  custom  with  many  engineers  to  let  7=  area  of  flange-plates 

and  angles  X  1^~)   t  which  in  this  case  would  give 
7=28X152=6300. 


RADII  OF  GYRATION  289 

EXAMPLE  II.— Find  the  moment  of  inertia  of  two  6X4 X| 
nch  angles,  placed  as  in  Fig.  9,  d  being  made  1  inch. 

Ans.  Moment  of  inertia  about  axis  45=2X13.47  (see  col. 
EL,  p.  303)  =  26. 94 

For  moment  about  axis  CD  we  have 

Area  of  one  angle  from  col.  I.,  p.  303,  =3.61]  7=4.90; 
X"=.5  +  .94  (col.  IX.)  =  1.44;  then 

/  for  both  angles= 2  X[4.90  + 3.61  X  1.44  2]=  24.76. 


Radius  of  Gyration  of  Compound  Shapes. 

A.  By  Moment  of  Inertia. 

The  radius  of  gyration  of  any  combination  is  found  by  divid- 
ing the  moment  of  inertia  of  the  shape  by  the  total  metal  area 
and  taking  the  square  root  of  the  product. 

Thus,  the  radius  of  gyration  of  the  two  angles  in  Example  II., 


about  A  B  =  =  1 .93 ; 


about  CD=  ==  1.85. 

t  .2i2i 


B.  Without  Moment  of  Inertia. 

In  the  case  of  a  pair  of  any  shape  without  a  web  the  value  of 
fthe  radius  of  gyration  can  always  be  readily  found  without  con- 
rsidering  the  moment  of  inertia. 

The  radius  of  gyration  for  any  section  around  an  axis  parallel 
to  another  axis  passing  through  its  centre  of  gravity  is  found  as 
follows : 

Let  r  =  radius  of  gyration  around  axis  through  centre  of 
gravity;  R  =  radius  of  gyration  around  another  axis  parallel  to 
tabove;  d=  distance  between  axes;  then 


Thus,  in  Example  II.,  the  radius  of  gyration  about  the  axis 
CD  could  have  been   obtained   as    follows:    r=  radius  of   one 


290    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


angle  about  its  own   axis  parallel  to  CD=1.17    (Column    V.), 
d=x  (Fig.  9)  =  .5  +  .94  (Column  IX.)  =  1.44. 

.R  =  \/1.442  +  1.172=1.85,  the  same  result  that  we  obtained 
by  using  the  moment  of  inertia. 

The  radius  about  AB,  Fig.  9,  is  the  same  as  for  one  angle 
(Column  II.). 

When  r  is  small  compared  with  d,  as  is  generally  the  case  in 
latticed  girders  and  columns,  R  may  be  taken  as  equal  to  d 
without  material  error. 

EXAMPLE  III. — Two  9-inch,  15-pound  standard  channel-bars 
are  placed  4.6  inches  apart,  as  in  the  figure;  required  the  radius 
of  gyration  around  axis  CD   for  combined 
section. 

.4ns.  Find  r,  in  Column  V.,  p.  298  = 
0.665;    and   r2=.4422. 

B  Distance  from  base  of  channel  to  neutral 

axis,   Column  IX.,   is  0.59.     One-half  of 
4.6  =  2.3  +  .59=  2.89,     the     distance     be- 
tween neutral  axis  of  single  channel  amd 
of  combined  section;   hence 
JR=\/8.3521  +  . "4422=  2.96;   or,   for  all  practical  purposes,  R=  d. 
EXAMPLE  IV. — Four  3X3Xi-inch  standard  angles  placed  as 
shown  form  a  column  10  inches  square;  find  the  radius  of  gyra- 
tion. 


L,  J 


Ans.  From  Column  IV.,  p.  310,  we  find  r=0.93  and  ra=.8649. 
The  distance  from  base  of  angle  to  neutral  a-xis,  Column  IX.,  is 
.84*  hence,  d=5-.84  =  4.16,  or,  d2=  17.3056,  and 

R=  \/17.3056  +  .8649  =  4.26. 

Table  I.  will  be  found  of  considerable  assistance  when  com- 
puting the  moment  of  inertia  of  sections  built  with  plates. 


RADII  OF  GYRATION. 


291 


TABLE  I. 
MOMENTS   OF  INERTIA  OF..         i         ..RECTANGLES. 


I 


c 

"-1  m 

3% 

ZZ 
£>rH 

Width  of  rectangle  in  inches. 

| 

& 

1 

A 

i 

A 

8. 

j» 

2 

.17 

.21 

.25 

.29 

.33 

.38 

.42 

3 

56 

.70 

.84 

.98 

1.13 

1.27 

1.41 

4 

1.33 

1.67 

2.00 

2.33 

2.67 

3.00 

3.33 

5 

2.60 

3.26 

3.91 

4.56 

5.21 

5.86 

6.51 

6 

4.50 

5.63 

6.75 

7.88 

9.00 

10.13 

11.25 

7 

7.15 

8.93 

10.72 

12.51 

14.29 

16.08 

17.86 

8 

10.67 

13  .  33 

16.00 

18.67 

21.33 

24.00 

26.67 

9 

15.19 

18.98 

22.78 

26.58 

30.38 

34.17 

37.97 

10 

20.83 

26.04 

31.25 

36.46 

41.67 

46.  87 

52.08 

11 

27.73 

34.66 

41.  £9 

48  .  o3 

55.46 

62.39 

69.32 

12 

36.00 

45.00 

54.00 

63.00 

72.00 

81.00 

90.00 

13 

45.77 

57.21 

68.66 

80.10 

91  .  54 

102.98 

114.43 

14 

57.17 

71.46 

85.75 

100.04 

114.33 

128  63 

142.92 

15 

70.31 

87.89 

105.47 

123.05 

140.63 

158.20 

175.78 

16 

85.33 

106.67 

128.00 

149.33 

170.67 

192.00 

213.33 

17 

102  .  35 

127.94 

1  53  .  53 

179.12 

204.71 

230.30 

255.  S9 

18 

121.50 

151.88 

182.25 

2i2.63 

243.00 

273  .  38 

303.75 

19 

142.90 

178.62 

214.34 

250.07 

285.79 

321.52 

357.24 

20 

166.67 

208.33 

250.00 

291.67 

333.33 

375.00 

416.67 

21 

192.94 

2-11.17 

289  Ml 

337.64 

385.88 

434.11 

482.34 

22 

221.83 

277  29 

332  .  75 

388.21 

443.67 

499.13 

554.58 

23 

253.48 

316.85 

380  .  22 

443.59 

506.96 

570.33 

633.70 

24 

288.00 

360.00 

432.00 

504.00 

576.00 

648.00 

720.00 

25 

325.52 

406.90 

488.28 

569.66 

651.04 

732.42 

813.80 

26 

3^6  .  17 

457.71 

549  .  25 

640.79 

732.33 

823.88 

915.42 

27 

410.06 

512.58 

6i5.09 

717.61 

8^0.13 

922.64 

1025.16 

28 

457.33 

571.67 

6X6.00 

800.33 

9i4.67 

1029.00 

\  143  .  33 

29 

508.10 

6,55.13 

7b2  .  16 

889.18 

1016.21 

1143.23 

1270.26 

30 

562.50 

703.13 

843.75 

984  .  38 

1125.00 

1265.63 

1406.25 

32 

682.67 

853.33 

1024.00 

H94.67 

1365.33 

1536.00 

1706.67 

34 

818.83 

1023.54 

1228.25 

1432.96 

1637.67 

1842.38 

2047.08 

36 

972.00 

12  J  5.  00 

1458.00 

1701.00 

1944.00 

2187.00 

2430.00 

38 

1143.17 

1428.96 

1714.75 

2000.54 

22X6.33 

2572.13 

2857.92 

40 

1333.33 

1666.67 

2000  .  00 

2333.33 

2666.67 

3000.00 

3333.33 

42 

1543.50 

1929.38 

2315.25 

2701  .  13 

3087.00 

3472.88 

3858.75 

44 

1774.67 

2218.33 

2662  .  00 

3105.67 

3549.33 

3993.00 

4436.67 

46 

2027.  «3 

2534.79 

3041.75 

3548.71 

4055  .  67 

4562.63 

5069.58 

48 

2304.00 

2880.00 

3456  .  00 

4032  .  00 

4608.00 

5184.00 

5760.00 

50 

2604.17 

3255.21 

3906.25 

4557.29 

5208.33 

5859.38 

6510.42 

52 

2929.33 

3661.67 

4394.00 

5126.33 

6591.00 

5858.67 

7323  .  33 

54 

3280  .  50 

4100.63 

4920.75 

5740.88 

6561.00 

7381  .  13 

8201.25 

56 

3658.67 

4573.33 

5488.00 

6402  .  67 

7317.33 

8232.00 

9146.67 

58 

4064  .  S3 

5081.04 

6U97.25 

7113.46 

8129.67 

9145.87 

10162.08 

60   4500.00 

5625.00 

6750.00 

7875.00 

9000.00 

10125.00 

11250.00 

292    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


TABLE    I—Continued. 
MOMENTS  OF  INERTIA  OF..         S         ..RECTANGLES 


I 


Width  of  rectangle  in  inches. 

d 
"H  <n 
•^  2 

•4^X1 

D,  o 

|.i 

« 

i 

ft 

£ 

if 

1 

.46 

.50 

.54 

.58 

.63 

.67 

2 

1.55 

1.69 

1.83 

1.97 

2.11 

2.25 

3 

3.67 

4.00 

4.33 

4.67 

5.00 

5.33 

4 

7.16 

7.81 

8.46 

9.11 

9.77 

10.42 

5 

12.38 

13.50 

14.63 

15.75 

16.88 

18.00 

6 

19.05 

21.44 

23.22 

25.  01 

26.80 

28.58 

7 

29.33 

32.00 

34.67 

37.33 

40.00 

42.67 

8 

41.77 

45.56 

49.36 

53.16 

56.95 

60.75 

9 

57.29 

62.50 

67.71 

72.92 

78.13 

83.33 

10 

76.26 

83.19 

90.12 

97.05 

103.98 

110.92 

11 

99.00 

108.00 

117.00 

126.00 

135.00 

144.00 

12 

125.87 

137.31 

148.75 

160.20 

171.64 

183.08 

13 

157.21 

171.50 

185.79 

200.08 

214.38 

228.67 

14 

193.36 

210.94 

228  .  52 

246.09 

263.67 

281  .  25 

15 

234.67 

256  .  00 

277.33 

298.67 

320.00 

341.33 

16 

281.47 

307.06 

332  .  65 

358.24 

383.83 

409.42 

17 

334.13 

364.50 

394.88 

425.25 

455.63 

486.00 

18 

392.96 

428.69 

464.41 

500.14 

535.86 

571.58 

19 

45S.33 

500.00 

541.67 

583.33 

625.00 

666.67 

20 

530.58 

578.81 

627.05 

675.28 

723.52 

771.75 

21 

610.04 

665  .  50 

720  .  96 

776.42 

831.87 

887.33 

22 

697.07 

760.44 

823.81 

887.18 

950.55 

1013.92 

23 

792.00 

864.00 

936.00 

1008.00 

1080.00 

1152.00 

24 

895.18 

976  .  56 

1057.94 

1139.32 

1220.iO 

1302.08 

25 

1006.96 

1098.50 

1190.04 

1281.58 

1373.13 

1464.67 

26 

1127.67 

1230.19 

1332.70 

1435.22 

1537.73 

1610.25 

27 

1257.67 

1372.00 

1486.33 

1600.67 

1715.00 

1829.33 

28 

1397.29 

1524.31 

1651  .  34 

1778.36 

1905.39 

2032.42 

29 

1546.88 

1687.50 

1828.13 

1968.75 

2109.38 

2250.00 

30 

1877.33 

2048.00 

2218.67 

2389  .  33 

2560.00 

2730.67 

32 

2251.79 

2456.50 

2661.21 

2865  .  92 

3070.63 

3275  .  33 

34 

2673.00 

2916.00 

3159.00 

3402.00 

3645.00 

3888.00 

36 

3143.71 

2429.50 

3715.29 

4001.08 

4286.88 

4572.67 

38 

3666.67 

4000.00 

4333.33 

4666  .  67 

5000.00 

5333.33 

40 

4244.63 

4630.50 

5016.38 

5402  .  25 

5788.13 

6174.00 

42 

4880.33 

5324.00 

5767.67 

6211.33 

6655.00 

7098.67 

44 

5576.54 

6083.50 

6590  .  46 

7097  .  42 

7604  .  38 

8111.33 

46 

6336.00 

6912.00 

7488.00 

8064.00 

8640.00 

9216.00 

48 

7161.46 

7812.50 

8463  .  54 

9114.58 

9765.63 

10416.67 

50 

8055  .  67 

8788.00 

9520.33 

10252  .  67 

10985.00 

11717.33 

52 

9021.38 

9841.50 

10661.03 

11481.75 

12301.88 

13122.00 

54 

10061.33 

10976.00 

11890.67 

12805.33 

13720.00 

14634.67 

56 

11178.  2Q 

12194.50 

13210.71 

14226.92 

15243.12 

16259.33 

58 

12375.00 

13500.00 

14625.00 

15750.00 

16875.00 

1  SOOO  .  00 

60 

RADII  OF  GYRATION.  293 

TABLE  II.— RADII  OF  GYRATION  FOR  ROUND  COLUMNS 


Thickness  in  inches  varying  by  tenths. 

Outside 
diameter 
Of  column 

•1 

.2 

•3 

•  4 

•5 

.6 

•7 

.8 

•9 

10 

Corresponding  radius  of  gyration  in  inches. 

2 

.67 

.64 

.61 

.58 

.56 

.54 

.52 

.51 

.50 

.50 

3 

1.03 

.99 

.96 

.93 

.90 

.88 

.85 

.83 

.81 

.79 

4 

1.38 

1.35 

1.31 

1.28 

1.25 

1.22 

1.19 

1.16 

1.14 

1.12 

5 

1.73 

1.70 

1.66 

1.63 

1.60 

1.57 

1.54 

1.51 

1.48 

1.46 

6 

2.08 

2.05 

2.02 

1.98 

1.95 

1.92 

1.89 

1.86 

1.83 

1.80 

7 

2.43 

2.40 

2.36 

2.33 

2.30 

2.27 

2.24 

2.21 

2.18 

2.15 

8 

2.79 

2.76 

2.72 

2.69 

2.66 

2.62 

2.59 

2.56 

2.53 

2.50 

9 

3.15 

3.11 

3.08 

3.04 

3.01 

2.97 

2.94 

2.91 

2.88 

2.85 

10 

3.51 

3.47 

3.44 

3.40 

3.37 

3.33 

3.30 

3.27 

3.23 

3.20 

11 

3.86 

3.82 

3.79 

3.75 

3.72 

3.68 

3.65 

3.62 

3.58 

3.55 

13 

4.21 

4.18 

4  15 

4.11 

4.08 

4.04 

4.01 

3.97 

3.94 

3.90 

TABLE     III.— RADII 


OF     GYRATION 
COLUMNS. 


FOR     SQUARE 


Thickness  in  inches  varying  by  tenths. 

Outside 
of  column 

.1 

-2 

.3 

•4 

.5 

•6 

•7 

.8 

.9 

1.0 

in  inches. 

Corresponding  radius  of  gyration  in  inches. 

2 

.78 

.74 

.71 

.68 

.65 

.63 

.61 

.59 

.58 

.58 

3 

1.18 

1.14 

1.11 

1.08 

1.04 

1.01 

.98 

.96 

.93 

.91 

4 

1.59 

1.55 

1.51 

1.47 

1.44 

1.41 

1.38 

1.35 

1.32 

1.29 

5 

2.00 

1.96 

1.92 

1.89 

1.85 

1.81 

1.78 

1.75 

1.71 

1.68 

6 

2.41 

2.37 

2.33 

2.29 

2.25 

2.21 

2.18 

2.15 

2.11 

2.08 

7 

2.82 

2.78 

2.74 

2.70 

2.66 

2.62 

2.58 

2.55 

2.51 

2.48 

8 

3.23 

3.19 

3.15 

3.11 

3.07 

3.03 

2.99 

2.96 

2.92 

2.89 

9 

3.63 

3.59 

3.55 

3.51 

3.48 

3.44 

3.40 

3.36 

3.32 

3.29 

1O 

4.04 

4.00 

3.96 

3.92 

3.88 

3.84 

3.80 

3.77 

3.73 

3.70 

11 

4.45 

4.41 

4.37 

4.33 

4.29 

4.25 

4.21 

4.17 

4.13 

4.10 

12 

4.86 

4.82 

4.78 

4.74 

4.70 

4.66 

4.62 

4.58 

4.54 

4.51 

Dimensions,  Moments  of  Inertia,  Radii  of  Gyra- 
tion and  Section  Modulus  of  Standard  Struc- 
tural Shapes. 

As  in  using  steel  in  structural  shapes  one  is  practically  con- 
fined to  the  choice  of  such  shapes  as  are  rolled  by  the  mills,  it  is 
necessary  to  have  at  hand  the  dimensions  and  properties  of 
those  shapes  to  be  able  to  calculate  the  necessary  size  to  meet 


294    MOMENTS  OF  INERTIA   AND   RESISTANCE. 

special  requirements  for  strength  and  the  practical  conditions 
of  economy  and  framing.  During  the  past  fifteen  years  great 
changes  have  been  made  both  in  the  material  and  shape  of 
structural  bars  of  steel  and  iron.  At  the  present  time  the  New 
Jersey  Steel  and  Iron  Company  is  the  only  manufacturer  of 
wrought-iron  beams  in  the  country,  to  the  writer's  knowledge, 
all  other  mills  rolling  steel  shapes,  only,  except  perhaps  small 
angles  and  bars. 

The  rolling  mills  which  manufacture  the  most  complete  line 
of  structural  shapes  are  those  of  the  Carnegie  Steel  Co.,  Cambria 
Iron  Co.,  Jones  &  Laughlins,  Passaic  Rolling  Mill  Co.,  Pencoyd 
Iron  Works,  and  the  Phoenix  Iron  Co.  In  general,  the  products 
of  these  mills  agree  in  shape  quite  closely,  especially  for  beams 
and  channels.  This  is  particularly  true  of  the  shapes  rolled 
by  the  first  three  of  the  companies  named  above. 

The  standard  steel  beams  and  channels  given  in  the  following 
pages  are  rolled  by  all  six  of  the  mills,  with  the  exception  of  the 
24-inch  beams  which  are  not  rolled  by  the  Passaic  and  Phoenix 
mills.  Some  of  the  mills  also  roll  additional  weights.  Thus 
the  Pencoyd  Iron  Works  rolls  18-inch  beams  up  to  90  Ibs., 
and  6-inch  beams  up  to  46  Ibs.  per  foot.  Except  for  the  18-inch 
beams,  only  the  properties  of  the  standard  sizes  are  given  in 
this  book. 

The  following  tables  of  properties  of  structural  shapes  have 
been  compiled  from  the  1900  publication  of  the  Carnegie  Steel 
Company,  except  in  the  case  of  shapes  not  rolled  by  them.  It 
may  be  well  to  state  that  the  tables  of  properties  for  the  various 
structural  shapes,  published  by  the  companies  named  above, 
do  not  agree  exactly,  even  for  the  same  weights,  but  the  differ- 
ences are  not  of  practical  importance.  The  tables  of  the  Cam- 
bria Iron  Company  and  of  the  Carnegie  Steel  Company  agree  the 
closest,  for  beams  and  channels.  As  angles  are  very  extensively 
used  for  a  great  many  purposes,  the  properties  for  all  sizes  rolled 
are  given,  and  also  a  table  showing  from  which  mills  the  different 
sizes  may  be  obtained.  Naturally  it  will  generally  be  advan- 
tageous to  use  a  size  that  is  rolled  by  several  mills. 

The  properties  for  grooved  steel,  given  on  p.  300,  were  com- 
puted by  the  author  from  the  dimensions  given  by  the  manu- 
facturers. These  small  channels  are  quite  extensively  used  in 
connection  with  suspended  ceilings,  and  other  fireproof  con- 
structions, and  it  is  believed  that  the  table  will  be  found  useful 
by  many.  The  Tables  A,  B,  C,  and  D  will  be  found  very  con- 


RADII  OF  GYRATION. 


295 


venient  when  computing  the  strength  of  struts  formed  of  a  pair 
of  channels  and  angles. 


Standard  Steel  Beams  and  Channels* 


— Z- 1 

•— h— 
k- d •** 

The  following  data  are  common  to  all  standard  I  beams  and 
channels,  with  the  exceptions  stated: 

c=  ^  minimum  web; 
C=  minimum  web  4-  yV  inch. 

s=  thickness  of  web  =  £,  minimum  for  all  beams  except  20" 
I's  and  24"  I's. 


*T 


For  20"  beam  s=  .55",  t=  .50". 
For  24"  beams  s=  .60",  t=  .50". 
For  20"  beam,  80  Ibs.,  s=  .65",  *=  .60". 

The  slope  of  flange  of  all  beams  and  channels  is  16f  per  cent. 
=  9° -27' -44"  =  2"  per  foot. 
Weight  per  foot=areaX3.4. 

When  ordering  I  beams,  channels,  or  angles,  the  weight  or 
thickness  should  be  given,  but  not  both. 


296    MOMENTS  OF  INERTIA  AND  RESISTANCE. 


PROPERTIES  OF  STANDARD  STEEL  I  BEAMS. 

A 


I. 

II.         III. 

IV.       V. 

VII. 

Depth 
of 
beam. 

W'ght 
per 
foot, 
Ibs. 

Area, 
sq.  in. 

Thick- 
ness of 
web, 
in. 

Width 
of 
flange, 
in. 

Moment  of 
inertia. 

Radius  of 
gyration. 

Sec- 
tion 
mod- 
ulus. 
Axis 
AB. 
R. 

Axis 
AB. 
7. 

Axis 
CD. 
/'. 

Axis 
AB. 
r. 

Axis 
CD. 
r'. 

24 

80.00 
85.00 
90.00 
95.00 
100.00 

65.00 
70.00 
75.00 

80.00 
85.00 
90.00 
95.00 
100.00 

55.00 
60.00 
65.00 
70.00 

75.00 
80.00 
85.00 
90.00 

42.00 
45.00 
50.00 
55.00 

60.00 
65.00 
70.00 
75.00 

80.00 
85.00 
90.00 
95.00 
100.00 

31.50 
35.00 

23.32 
25.00 
26.47 
27.94 
29.41 

19.08 
20.59 
22.06 

23.73 
25.00 
26.47 
27.94 
29.41 

15.93 
17.65 
19.12 
20.59 

22.05 
23.53 
25.00 
26.46 

12.48 
13.24 
14.71 
16.  18 

17.67 
19.12 
20.59 
22.06 

23.81 
25.00 
26.47 
27.94 
29.41 

9.26 
10.29 

0.500 
0.570 
0.631 
0.692 
0.754 

0.500 
0.575 
0.649 

0.600 
0.663 
0.737 
0.810 
0.884 

0.460 
0.555 
0.637 
0.719 

0.71 
0.79 
0.74 
0.82 

0.410 
0.460 
0.558 
0.656 

0.590 
0.686 
0.784 
0.882 

0.810 
0.889 
0.987 
1.085 
1.184 

0.350 
0.436 

7.000 
7.070 
7.131 
7.192 
7.254 

6.250 
6.325 
6.399 

7.000 
7.063 
7.137 
7.210 

7.284 

6.000 
6.095 
6.177 
6.259 

6.58 
6.66 
7.00 
7.08 

5.500 
5.550 
5.648 
5.746 

6.000 
6.096 
6.194 
6.292 

6.400 
6.479 
6.577 
6.675 
6.774 

5.000 
5.086 

2087  .  9 
2i68.6 
2239.1 
2309  .  6 
2380.3 

1169.6 
1219.9 

1268.9 

1466  .  5 
1508.7 
1557.8 
1606.8 
1655.8 

795.6 

841.8 
881.5 
921.3 

1023.5 
1063.4 
1149.6 
1188.0 

441.7 
455.8 
483.4 
511.0 

609.0 
636.0 
663.6 
691.2 

795.5 

817.8 
845.4 
872.9 
900.5 

215.8 

228.3 

42.86 
44.35 
45.70 
47.10 
48.56 

27.86 
29.04 
30.25 

45.81 
47.25 
48.98 
50.78 
52.65 

21.19 
22.38 
23.47 
24.62 

31.67 
33.12 
44.18 
46.03 

14.62 
15.09 
16.04 
17.06 

25.96 
27.42 
29.00 
30.68 

41.76 
43.57 
45.91 

48.37 
50.98 

9.50 
10.07 

9.46 
9.31 
9.20 
9.09 
9.00 

7.83 

7.70 
7.58 

7.86 
7.77 
7.67 
7.58 
7.50 

7.07 
6.91 
6.79 
6.69 

6.81 
6.72 

6.78 
6.70 

5.95 

5.87 
5.73 
5.62 

5.87 
5.77 
5.68 
5.60 

5.78 
5.72 
5.65 
5.59 
5.53 

4.83 
4.71 

1.36 
1.33 
1.31 
1.30 
1.28 

1.21 
1.19 
1.17 

1.39 
1.37 
1.36 
1.35 
1.34 

1.15 
1.13 
1.11 
1.09 

1.20 
1.19 
1.33 
1.32 

1.08 
1.07 
1.04 
1.02 

1.21 
1.20 
.19 
.18 

.32 
.32 
.32 
.32 
1.31 

1.01 
0.99 

174.0 
180.7 
186.6 
192.5 
198.4 

117.0 
122.0 
126.9 

146.7 
150.9 
155.8 
160.7 
165.6 

88.4 
93.5 
97.9 
102.4 

113.7 

118.2 
127.7 
132.0 

58.9 

60.8 
64.5 
68.1 

81.2 

84.8 
88.5 
92.2 

106.1 
109.0 
112.7 
116.4 
120.1 

36.0 
38.0 

20 

20 
18 

18* 

15 

15 

15 

12 

*  Rolled  only  by  Pencoyd  and  Passaic  Mills. 


RADII   OF  GYRATION. 


297 


PROPERTIES  OF  STANDARD  STEEL  I    BEAMS. 
(Continued.) 


I. 

II.         III. 

IV.       V. 

VII. 

Moment  of 

Radius  of 

Sec- 

Depth 
of 
beam. 

W'ght 
per 
foot, 
Ibs. 

Area, 
sq.  in. 

Thick- 
ness of 
web, 
in. 

Width 
of 
flange, 
in. 

inertia. 

gyration. 

tion 
mod- 
ulus, 

Axis 

A  TD 

Axis 

Axis 

Axis 

Axis 

AB. 

CD. 

AB. 

CD. 

Ar>. 
p 

/. 

/'. 

r. 

r'. 

/»• 

40.00 

11.84 

0.460 

5.250 

268.9 

13.81 

4.77 

1.08 

44.8 

45.00 

13.24 

0.576 

5.366 

285.7 

14.89 

4.65 

1.06 

47.6 

12 

50.00 

14.71 

0.699 

5.489 

303.3 

16.12 

4.54 

1.05 

50.6 

55.00 

16.18 

0.822 

5.612 

321.0 

17.46 

4.45 

1.04 

53.5 

25.00 

7.37 

0.310 

4.660 

122.1 

6.89 

4.07 

0.97 

24.4 

10 

30.00 

8.82 

0.455 

4.805 

134.2 

7.65 

3.90 

0.93 

26.8 

35.00 

10.29 

0.602 

4.952 

146.4 

8.52 

3.77 

0.91 

29.3 

40.00 

11.76 

0.749 

5.099 

158.7 

9.50 

3.67 

0.90 

31.7 

21.00 

.    6.31 

0.290 

4.330 

84.9 

5.16 

3.67 

0.90 

18.9 

9 

25.00 

7.35 

0.406 

4.446 

91.9 

5.65 

3.54 

0.88 

20.4 

30.00 

8.82 

0.569 

4.609 

101.9 

6.42 

3.40 

0.85 

22.6 

35.00 

10,29 

0.732 

4.772 

111.8 

7.31 

3.29 

0.84 

24.8 

18.00 

5.33 

0.270 

4.000 

56.9 

3.78 

3.27 

0.84 

14.2 

8 

20.50 

6.03 

0.357 

4.087 

60.6 

4.07 

3.17 

0.82 

15.1 

23.00 

6.76 

0.449 

4.179 

64.5 

4.39 

3.09 

0.81 

16.1 

25.50 

7.50 

0.541 

4.271 

68.4 

4.75 

3.02 

0.80 

17.1 

15.00 

4.42 

0.250 

3.660 

36.2 

2.67 

2.86 

0.78 

10.4 

7 

17.50 

5.15 

0.353 

3.763 

39.2 

2.94 

2.76 

0.76 

11.2 

20.00 

5.88 

0.458 

3.868 

42.2 

3.24 

2.68 

0.74 

12.1 

12.25 

3.61 

0.230 

3.330 

21.8 

1.85 

2.46 

0.72 

7.3 

6 

14.75 

4.34 

0.352 

3.452 

24.0 

2.09 

2.35 

0.69 

»8.0 

17.25 

5.07 

0.475 

3.575 

26.2 

2.36 

2.27 

0.68 

8.7 

9.75 

2.87 

0.210 

3.000 

12.1 

1.23 

2.05 

0.65 

4.8 

5 

12.25 

3.60 

0.357 

3.147 

13.6 

1.45 

1.94 

0.63 

5.4 

14.75 

4.34 

0.504 

3.294 

15.2 

1.70 

1.87 

0.63 

6.1 

7.50 

2.21 

0.190 

2.660 

6.0 

0.77 

1.64 

0.59 

3.0 

8.50 

2.50 

0.263 

2.733 

6.4 

0.85 

1.59 

0.58 

3.2 

4 

9.50 

2.79 

0.337 

2.807 

6.7 

0.93 

1.55 

0.58 

3.4 

10.50 

3.09 

0.410 

2.880 

7.1 

1.01 

1.52 

0.57 

3.6 

5.50 

1.63 

0.170 

2.330 

2.5 

0.46 

1.23 

0.53 

1.7 

3 

6.50 

1.91 

0.263 

2.423 

2.7 

0.53 

1.19 

0.52 

1.8 

7.50 

2.21 

0.361 

2.521 

2.9 

0.60 

1.15 

0.52 

1.9 

298     MOMENTS   OF   INERTIA  AND   RESISTANCE. 


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RADII   OF   GYRATION. 


299 


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300    MOMENTS   OF  INERTIA  AND   RESISTANCE. 


DIMENSIONS  AND  PROPERTIES  OF 

GROOVED  STEEL,  OR  SMALL 

CHANNELS. 


1 


No. 
of 
Sec. 

d 

& 

I 

e 

a 

W'ght 
per 
foot. 

Area. 

Mo- 
ment 
of  in- 
ertia.1 

Sec- 
tion- 
mod- 
ulus.1 

Coeffi- 
cient 
of 
str'th.2 

ins. 

ins. 

ins. 

ins. 

ins. 

Ibs. 

sq.  ins. 

Ibs. 

1 

*2*4 

1.37 

.25 

.25 

.25 

3.80 

1.12 

0.80 

0.71 

7570 

2 

*2 

1.09 

.22 

.31 

.18 

2.90 

0.87 

.48 

.48 

5120 

3 

*2 

1   18 

31 

3  60 

1  06 

54 

54 

5760 

4 

t2 

1.25 

.25 

.31 

.25 

3.60 

1.062 

.585 

.585 

6240 

5 

*2 

1.00 

8/16 

.25 

.22 

2.6 

0.756 

.423 

.423 

4512 

6 

J2 

% 

.25 

.19 

H 

2.0 

0.619 

.2665 

.266 

2836 

7 

*!•% 

0.59 

.09 

.25 

.09 

1.13 

0.33 

.15 

.17 

1815 

8 

tl^ 

0.75 

H 

^ 

^ 

1.32 

0.344 

.1083 

.144 

1536 

9 

U^ 

% 

.19 

.2 

.14 

1.46 

0.433 

.1194 

.159 

1736 

10 

tm 

0.5 

YB 

8/16 

Ni 

0.94 

0.273 

.0557 

.089 

950 

11 

n& 

0.56 

.19 

.19 

/^ 

1.12 

0.330 

.0500 

.088 

939 

12 

tU6 

% 

M 

tt 

Jl 

1.00 

0.266 

.0462 

.082 

874 

13 

n 

0.5 

H 

8/16 

^ 

0.83 

Q.242 

.0315 

.063 

672 

14 

n 

0.39 

^0 

8/16 

/^ 

0.68 

0.208 

.0253 

.050 

532 

15 

He 

/^ 

.16 

.  11 

0.67 

0.183 

.0185 

.042 

448 

16 

tsl 

0.42 

11 

8/16 

^ 

0.69 

0.193 

.0189 

.043 

458 

17 

19 

% 

'fc 

.16 

.09 

0.53 

0.156 

.0095 

.025 

266 

1  Axis  AB. 

2  Computed  for  fibre  stress  of  16,000  Ibs.  per  square  inch. 
*  Rolled  by  the  Pencoyd  Iron  Works. 

t  "    Illinois  Steel  Company. 

J       *'       °     •*    Jones  &  Laughlins.  Ltd. 

DIMENSIONS    OF    CAR    TRUCK    CHANNELS, 

(Rolled  by  Carnegie  Steel  Co.  and  Jones  &  Laughlins,  Ltd.) 


d 

b 

t 

e 

a 

Weight. 

Area. 

13 

4 

0.375 

0.88 

0.34 

32 

9.41 

12 

2.64 

0.31 

0.75 

0.34 

21  .  33 

6.27 

ANGLES. 

The  following  table  has  been  compiled  to  show  all  the  various 
sizes  of  angles  that  are  rolled,  and  also  by  what  companies. 
The  abbreviations  indicate  the  companies  that  roll  that  particu- 
lar size.  The  word  all  shows  that  the  size  is  rolled  by  all  of  the 
five  companies  included  in  the  list.  The  abbreviations  refer 


RADII   OF   GYRATION. 


301 


to  the  following  companies:  Cam.,  Cambria  Iron  Co.;  Car., 
The  Carnegie  Steel  Co.;  J.  &  L.,  Jones  &  Laughlins;  Pas., 
Passaic  Rolling  Mill  Co.;  Pen.,  Pencoyd  Iron  Works. 


WITH  UNEQUAL  LEGS. 

ANGLES  WITH  EQUAL  LEGS. 

Size. 

Pen. 

8  X8  Car.,  Pen. 

Car.,  Pen. 

6  X6 

All. 

Pen. 

5  X5 

All. 

All. 

4JX4J 

Cam. 

Cam.,  Car.,  J.  &  L., 

4   X4 

All. 

Pen. 

3iX3| 

All. 

Cam. 

3iX3i 

J.  &L. 

Pen. 

3   X3 

All. 

Cam.,  Car.,  J.  &  L.,      i  2JX2J 

Cam.,    Car.,    J.    &   L., 

Pen. 

Pen. 

All. 

2JX2J 

All. 

All. 

2JX2J 

All. 

Cam.,  Car.,  Pas.,  Pen. 

2   X2 

All. 

All. 

liXlf 

AIL 

All. 

14X14 

All. 

J.  &L. 

Hxii 

All. 

All. 

1    XI 

All. 

All. 

I-x  1- 

Car.,  Pas. 

Pen. 

ix  I 

Cam.,    Car.,   J.    &   L., 

Car.,  J.  &  L. 

Pas. 

All. 

All. 

All. 

Cam. 

Cain. 

Cam. 

Car.,  Pas.,  Pen. 

Pas. 

Cam.,  Pen. 

Cam.,  Car. 

Pen. 

Pas. 

Car, 

J.  &L. 

J.  &L. 

302     MOMENTS  OF   INERTIA   AND   RESISTANCE. 


. 

a 


* 

Perpendicular  dis- 
tances from  centre 
of  gravity  to  back 
of  flanges. 

To  back 
of  shorter 
flange,  d. 

ass  csssagssra  ss 

<N  W  <N       <M<M<NCq<NC^<N<N<N<N       (M  <N 

To  back 
of  longer 
flange,  I. 

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PROPERTIES   OF  STANDARD   AND   SPECIAL  ANGLES. 

ANGLES   WITH   EQUAL   LEGS. 


A--— 


I. 

II. 

IV. 

VI. 

VII. 

IX. 

Distance 

Moment 

Radii  of  gyra- 

Section 
modu- 

of centre 
of 

Size,  in 
inches. 

Thick- 
ness of 
metal. 

W'ght 
per  ft. 

Area 
in 
sq.  ins. 

of 
inertia. 

tion. 

lus, 
R. 

gravity 
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Axis 

Axis 

Axis 

Axis 

j 

AB. 

AB. 

EF. 

AB. 

a. 

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56.9 

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97.97 

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1  1/16 

54.0 

15.87 

93.53 

2.43 

1.56 

16.67 

2.39 

1 

51.0 

15.00 

88.98 

2.44 

1.56 

15.80 

2.37 

15/16 

48.0 

14.12 

84.33 

2.44 

1.56 

14.91 

2.34 

7/8 

45.0 

13.23 

79.58 

2.45 

1.57 

14.01 

2.32 

8     X8 

13/16 

42.0 

12.34 

74.71 

2.46 

1.57 

13.11 

2.30 

3/4 

38.9 

11.44 

69.74 

2.47 

1.57 

12.18 

2.28 

11/16 

35.8 

10.53 

64.64 

2.48 

1.58 

11.25 

2.25 

5/8 

32.7 

9.61 

59.42 

2.49 

1.58 

10.30 

2.23 

9/16 

29.5 

8.68 

54.09 

2.50 

1.58 

9.34 

2.21 

1/2 

26.4 

7.75 

48.63 

2.50 

1,58  i     8.37 

2.19 

1 

37.4 

11.00 

35.46 

1.80 

1.16 

8.57 

1.86 

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35.3 

10.37 

33.72 

1.80 

1.16 

8.11 

1.84 

7/8 

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9.74 

31.92 

1.81 

1.17 

7.64 

1.82 

13/16 

30.9 

9.09 

30.06 

1.82 

1.17 

7.15 

.80 

3/4 

28.7 

8.44 

28.15 

1.83 

1.17 

6.66 

.78 

6     X6 

11/16 

26.5 

7.78 

26.19 

1.83 

1.17 

6.17 

.75 

5/8 

24.2 

7.11 

24.16 

1.84 

1.18 

5.66 

.73 

9/16 

21.9 

6.43 

22.07 

1.85 

1.18 

5.14 

.71 

1/2 

19.6 

5.75 

19.91 

1.86 

1.18 

4.61 

.68 

7/16 

17.2 

5.06 

17.68 

1.87 

1.19 

4.07 

.66 

3/8 

14.8 

4.36 

15.39 

1.88 

1.19 

3.53 

.64 

1 

30.6 

9.00 

19.64 

1.48 

0.96 

5.80 

.61 

15/16 

28.9 

8.50 

18.71 

1.48 

0.96 

5.49 

.59 

7/8 

27.2 

7.99 

17.75 

1.49 

0.96 

5.17 

.57 

13/16 

25  .4 

7.46 

16.77 

1.50 

0.97 

4.85 

.55 

3/4 

23.6 

6.94 

15.74 

1.51 

0.97 

4.53 

.52 

5     X5 

11/16 

21.8 

6.42 

14.68 

1.51 

0.97 

4.20 

.50 

5/8 

20.0 

5.86 

13.58 

1.52 

0.97 

3.86 

.48 

9/16 

18.1 

5.31 

12.44 

1.53 

0.98 

3.51 

.46 

1/2 

16.2 

4.75 

11.25 

1.54 

0.98 

3.15 

.43 

7/16 

14.3 

4.18 

10.02 

1  .55 

0.98 

2.79 

.41 

3/8 

12.3 

3.6] 

8.74 

1   56 

0.99 

2.42 

.39 

310     MOMENTS   OF  INERTIA   AND   RESISTANCE. 


PROPERTIES  OF  STANDARD  AND   SPECIAL  ANGLES. 

ANGLES    WITH    EQUAL   LEGS  (continued). 


I. 

II. 

IV. 

VI. 

VII. 

IX. 

Size,  in 
inches. 

Thick- 
ness of 
metal. 

W'ght 
per  ft. 

Area 
in 
sq.  ins. 

Moment 

of. 
inertia. 

Radii  c 
ti 

>f  gyra- 
on. 

Section 
modu- 
lus, 
R. 

Distance 
of  center 
of 
gravity 
from 
bark  of 

Axis 
AB. 

Axis 
AB. 

Axis 
EF. 

Axis 
AB. 

flange. 
d. 

4^X4^ 

5/8 
9/16 
1/2 
7/16 
3/8 
5/16 

17.8 
16.1 
14.5 
12.7 
11.0 
9.2 

5.23 
4.75 
4.25 
3.75 
3.23 
2.71 

9.71 
8.91 
8.07 
7.20 
6.30 
5.36 

1.36 
1.37 
1.38 
1  .  39 
1.40 
1.40 

0.87 
0.88 
0.88 
0.88 
0.89 
0.89 

3.09 
2.81 
2  .  53 
2.24 
1.95 
1.64 

1.35 
1.33 
1.31 
1.29 
1026 
1.24 

4     X4 

13/16 
3/4 

11/16 
5/8 
9/16 
1/2 
7/16 
3/8 
5/16 

19.9 
18.5 
17.1 
15.7 
14.3 
12.8 
11.3 
9.8 
8.2 

5.84 
5.44 
5.03 
4.61 
4.18 
3.75 
3.31 
2.86 
2.40 

8.14 
7.67 
7.17 
6.66 
6.12 
5.56 
4.97 
4,36 
3.71 

1.18 
1.19 
1.19 
1.20 
1.21 
1.22 
1.23 
1  .  23 
1.24 

0.77 
0.77 
0.77 
0.77 
0.78 
0.78 
0.78 
0.79 
0.79 

3.01 
2.81 
2.61 
2.40 
2.19 
1.97 
1.75 
1.52 
1.29 

.29 
.27 
.25 
.23 
.21 
.18 
.16 
.14 
1.12 

3KX3H 

3MX3M 

13/16 
3/4 
11/16 
5/8 
9/16 
1/2 
7/16 
3/8 
5/16 

3/4 

3/8 

17.1 
16.0 
14.8 
13.6 
12.3 
11.1 
9.8 
8.5 
7.1 

14.7 
7.8 

5.03 
4.69 
4.34 
3.98 
3.62 
3.25 
2.87 
2.48 
2.09 

4.32 
2.29 

5.25 
4.96 
4  65 
4.33 
3.99 
3  64 
3.26 
2.87 
2.45 

2.96 
2.27 

1.02 
1.03 
1.04 
1.04 
1.05 
1.06 
1.07 
1.07 
1.08 

0.79 
0.99 

0.67 
0.67 
0.67 
0.67 
0.68 
0.68 
0.68 
0.69 
0.69 

0.53 
0.68 

2.25 
2.11 
1.96 
1.81 
1.65 
1.49 
1.32 
1.15 
0.98 

1.36 
0.99 

1.17 
1.15 
1.12 
1.10 
1.08 
1.06 
1.04 
1.01 
0.99 

1.08 
0.95 

3     X3 

5/8 
9/16 
1/2 
7/16 
3/8 
5/16 
1/4 

11.4 
10.4 
9.4 
8.3 
7.2 
6.1 
4.9 

3.36 
3.06 
2.75 
2.43 
2.11 
1.78 
1.44 

2.62 
2.43 
2.22 
1.99 
1.76 
1.51 
1.24 

0.88 
0.89 
0.90 
0.91 
0.91 
0.92 
0.93 

0.57 
0.58 
0.58 
0.58 
0.58 
0.59 
0.59 

1.30 
1.19 
1.07 
0.95 
0.83 
0.71 
0.58 

0.98 
0.95 
0.93 
0.91 
0.89 
0.87 
0.84 

2HX2H 

1/2 
7/16 
3/8 
5/16 
1/4 

8.5 
7.6 
6.6 
5.5 
4.5 

2.50 
2.22 
1.92 
1.62 
1.31 

1.67 
1.51 
1.33 
1.15 
0.93 

0.82 
0.82 
0.83 
0.84 
0.85 

0.52 
0.53 
0  .  53 
0.54 
0.55 

0.89 
0.79 
0.69 
0.59 
0.48 

0.87 
0.85 
0.82 
0.80 
0.78 

2^X2^ 

1/2 
7/16 
3/8 
5/16 
1/4 
3/16 

7.7 
6.8 
5.9 
5.0 
4.1 
3.1 

2.25 
2.00 
1.73 
1.47 
1.19 
0.90 

1.23 
1.11 
0.98 
0.85 
0.70 
0.55 

0.74 
0.74 
0.75 
0.76 
0.77 
0.78 

0.47 
0.48 
0.48 
0.49 
0.49 
0.49 

0.73 
0.65 
0.57 
0.48 
0.40 
0.30 

0.81 
0.78 
0.76 
0.74 
0.72 
0.69 

RADII   OF  GYRATION. 


311 


PROPERTIES  OF  STANDARD  AND  SPECIAL   ANGLES. 

ANGLES    WITH    EQUAL    LEGS 


I. 

Area 
in 
sq.ins. 

II. 

IV. 

VI. 

VII. 

Section 
modu- 
lus, 
R. 

Axis 
AB. 

IX. 

Size,  in 
inches- 

Thick- 
ness of 
metal. 

W'ght 
per  ft. 

Moment 
of 
inertia. 

Axis 
AB. 

Radii  of  gyra- 
tion. 

Distance 
of  centre 
of 
gravity 
from 
back  of 
flange, 

d. 

Axis 
AB. 

Axis 
EF. 

2^X2^ 

1/2 
7/16 
3/8 
5/16 
1/4 
3/16 

7/16 

3/8 
5/16 
1/4 
3/16 

7/16 

3/8 
5/16 
1/4 
3/16 

3/8 
5/16 
1/4 
3/16 

1/8 

5/16 
1/4 
3/16 
1/8 

1/4 

3/16 
1/8 

3/16 
1/8 

3/16 
1/8 

6.8 
6.1 
5.3 
4.5 
3.7 
2.8 

5.3 
4.7 
4.0 
3.2 
2.5 

4.6 
4.0 
3.4 
2.8 
2.1 

3.4 
2.9 
2.4 
1.8 
1.2 

2.4 
.9 
.5 
.0 

.5 
.2 
0.8 

1.0 
0.7 

0.8 
0.6 

2.00 
1.78 
1.55 
1.31 
1.06 
0.81 

1.56 
1.36 
1.15 
0.94 
0.72 

1.30 
1.17 
1.00 
0.81 
0.62 

0.99 
0.84 
0.69 
0.53 
0.36 

0.69 
0.56 
0.43 
0.30 

0.44 
0.34 
0.24 

0.29 
0.21 

0.25 
0.17 

0.87 
0.79 
0.70 
0.61 
0.51 
0.39 

0.54 
0.48 
0.42 
0.35 
0.28 

0.35 
0.31 
0.27 
0.23 
0.18 

0.19 
0.16 
0.14 
0.11 
0.08 

0.09 
0.077 
0.061 
0.044 

0.037 
0.030 
0.022 

0.019 
0.014 

0.012 
0.009 

0.66 
0.67 
0.67 
0.68 
0.69 
0.70 

0.59 
0.59 
0.60 
0.61 
0.62 

0.51 
0.51 
0.52 
0.53 
0.54 

0.44 
0.44 
0.45 
0.46 
0.46 

0.36 
0.37 
0.38 
0.38 

0.29 
0.30 
0.31 

0.26 
0.26 

0.22 
0.23 

0.43 
0.43 
0.43 
0.44 
0.44 
0.44 

0.39 
0.39 
0.39 
0.39 
0.40 

0.33 
0.34 
0.34 
0.34 
0.35 

0.29 
0.29 
0.29 
0.29 
0.30 

0.23 
0.24 
0.24 
0.25 

0.19 
0.19 
0.20 

0.18 
0.19 

0.16 
0.17 

0.58 
0.52 
0.45 
0.39 
0.32 
0.24 

0.40 
0.35 
0.30 
0.25 
0.19 

0.30 
0.26 
0.23 
0.19 
0.14 

0.19 
0.162 
0.134 
0.104 
0.070 

0.109 
0.091 
0.071 
0.049 

0.056 
0.044 
0.031 

0.033 
0.023 

0.024 
0.017 

0.74 
0.72 
0.70 
0.68 
0.66 
0.63 

0.66 
0.64 
0.61 
0.59 
0.57 

0.59 
0.57 
0.55 
0.53 
0.51 

0.51 
0.49 
0.47 
0.44 
0.42 

0.42 
0.40 
0.38 
0,35 

0.34 
0.32 
0.30 

0.29 
0.26 

0.26 
0.23 

2     X2 

1»X1« 

iHxiK 

U4X1M 

1     XI 

fcxjfc 

«x« 

312     MOMENTS   OF  INERTIA  AND   RESISTANCE. 


PROPERTIES    OF    CARNEGIE    DECK-BEAMS    AND 
BULB  ANGLES. 

DECK-BEAMS . STEEL. 


Deck-beam. 


Bulb  angle. 


m 

d 

1 

I. 

II. 

III. 

IV. 

V. 

VII. 

a 

| 

1 

i 

.2 

Moments  of 

Radii  of 

l|« 

CD 

A 

1 

"o 

02 

te 

i 

~O    32 

inertia, 
7. 

gyration, 
r. 

s]H 

° 

C 

*o 

«H""- 

.2  "~ 

a 

i 

1 

1 

i"2 

Axis 

Axis 

Axis 

Axis 

|!« 

Q 

^ 

H 

£ 

5 

AB. 

CD. 

AB. 

CD. 

R. 

11.5" 

37.00 

.55 

5.30 

10.9 

194.7 

6.60 

4.23 

0.78 

30.6 

11.5" 

32.20 

.42 

5.17    9.5 

178.7 

6.06 

4.34 

0.80 

27.6 

10' 

35.70 

.63 

5.5010.5 

139.9 

7.41 

3.64 

0.84 

25.7 

10' 

27.23 

.38 

5.25    8.0 

118.4 

6.12 

3.83 

0.87 

21.2 

9' 

30.00 

.57 

5.07    8.8 

93.2 

5.18 

3.25 

0  75 

19.6 

9' 

26.00 

.44 

4.94 

7.6 

85.2 

4.61 

3.35 

0.76 

17.7 

8' 

24.48 

.47 

5.16 

7.2 

62.8 

4.45 

2.97 

0.79 

14.1 

8' 

20.15 

.31 

5.00    5.9 

55.6 

3.90 

3.08 

0.82 

12.2 

7' 

23.46 

.54 

5.10 

6.9 

45.5 

4.30 

2.57 

0.79 

11.7 

r 

18.11 

.31 

4.87 

5.3 

38.8 

3.55 

2.70 

0.82 

9.7 

6' 

17.16 

.43 

4.53 

5.0 

24.4 

2.66 

2.20 

0.73 

7.2 

6' 

14.10 

.28 

4.38 

4.1 

21.6 

2.22 

2.28 

0.72 

6.1 

BULB    ANGLES. STEEL. 


10" 

32.00 

.63 

3.5 

9.41 

116.0 

3.51 

21  .(> 

10" 

26.50 

.48 

3.5 

7.80 

104.2 

3.66 

19.9 

9" 

21.80 

.44 

3.5 

6.41 

69.3 

3.33 

14.5 

8" 

19.23 

.41 

3.5 

5.66 

48.8 

2.95 

11.7 

7" 

18.25 

.44 

3.0 

5.37 

34.9 

2.56 

9.6 

7" 

16.00 

.34 

3.0 

4.71 

32.2 

6.61 



8.7 

6" 

17.20 

.50 

3.0 

5.06 

23.9 

2.16 

7.6 

6" 

13.75 

.38 

3.0 

4.04 

20.1 

2.21 



6.6 

6"      12.30 

.31 

3.0 

3.62 

18.6 

..... 

2.28 



5.7 

5" 

10.00 

.31 

2.5 

2.94 

10.2 



1.86 



4.1 

RADII   OF   GYRATION. 


313 


PROPERTIES    OF    CARNEGIE    T    SHAPES.— STEEL. 

Thickness  varies  slightly ,  that  given  being  the  minimum. 


d 

.2 

I. 

II. 

III. 

IV. 

V. 

VII. 

VIII 

IX. 

& 
o 

<D" 

& 

"OQ 

| 

it* 

Moments  of 

Radii  of 

Section 

,fl 

i 

o 

inertia, 

gyration, 

modulus, 

3 

1 

•s 

o 

i 

L 

r. 

R. 

h 

03 

i 

1 

• 

+"'x 

5 

1 

1 

2 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

I03 

c 

OQ 

_§_ 

1 

1 

AB. 

CD. 

AB. 

CD. 

AB. 

CD. 

W 

5     X3 

1/2 

13.6 

3.99 

2.6 

5.6 

0.82 

1.19 

1.18 

2.22 

0.75 

5     X2J4 

3/8 

11.0 

3.24 

1.6 

4.3 

0.71 

1.16 

0.86 

.70 

0.65 

4!4X3i4 

7/16 

15.8 

4.65 

5.1 

3.7 

1.04 

0.90 

2.13 

.65 

1.11 

414X3 

5/16 

18.5 

2.55 

1.8 

2.6 

0.87 

1.03 

0.81 

.16 

0.73 

414X3 

3/8 

10.0 

3.00 

2.1 

3.1 

0.86 

1.04 

0.94 

.38 

0.75 

4J4X2J4 

5/16 

8.0 

2.40 

1.1 

2.6 

0.69 

1.07 

0.56 

.16 

0.58 

4J4X2J4 

3/8 

9.3 

2.79 

1.2 

3.1 

0.68 

1.08 

0.65 

.38 

0.60 

4     X5 

1/2 

15.6 

4.56 

10.7 

2.8 

.54 

0.79 

3.10 

1.41 

1.56 

4     X5 

3/8 

12.0 

3.54 

8.5 

2.1 

.56 

0.78 

2.43 

1.06 

1.51 

4     X4J4 

1/2 

14.6 

4.29 

8.0 

2.8 

.37 

0.81 

2.55 

1.41 

1.37 

4     X4J4 

3/8 

11.4 

3.36 

6.3 

2.1 

.38 

0.80 

1.98 

1.06 

1.31 

4     X4 

1/2 

13.7 

4.02 

5.7 

2.8 

.20 

0.84 

2.02 

1.40 

1.18 

4     X4 

3/8 

10.9 

3.21 

4.7 

2.2 

.23 

0.84 

1.64 

1.09 

1.15 

4     X3 

3/8 

9.3 

2.73 

2.0 

2.1 

0.86 

0.88 

0.88 

1.05 

0.78 

4     X2J4 

3/8 

8.6 

2.52 

1.2 

2.1 

0.69 

0.92 

0.62 

1.05 

0.63 

4     X2J4 

5/16 

7.3 

2.16 

1.0 

1.8 

0.70 

0.91 

0.55 

0.88 

0.60 

4     X2 

3/8 

7.9 

2.31 

0.60 

2.1 

0.52 

0.96 

0.40 

1.05 

0.48 

4     X2 

5/16 

6.6 

1.95 

0.54 

1.8 

0.51 

0.95 

0.34 

0.88 

0.51 

314X4 

1/2 

12.8 

3  .  75 

5.5 

1.89 

1.21 

0.72 

1.98 

1.08 

1.25 

314X4 

3/8 

9.9 

2.91 

4.3 

1.42 

1.22 

0.70 

1.55 

0.81 

1.19 

314  x  314 

1/2 

11.7 

3.45 

3.7 

1.89 

1.04 

0.74 

1.52 

1.08 

1.06 

3)4  X  3^t 

3/8 

9.2 

2.7( 

3.0 

1.42 

1.05 

0.73 

1.19 

0.81 

1.01 

3!4  X  3 

1/2 

10.9 

3.21 

2.4 

1.88 

0.87 

0.77 

1.13 

1.08 

0.88 

314X3 

3/8 

8.5 

2.49 

1.9 

1.41 

0.88 

0.75 

0.88 

0.81 

0.83 

314X3 

5/16 

7.8 

2.28 

1.6 

1.18 

0.89 

0.76 

0.72 

0.68 

0.78 

3     X4 

1/2 

11.8 

3.48 

5.2 

1.21 

1.23 

0.59 

1.94 

0.81 

1.32 

3     X4 

7/16 

10.6 

3.12 

4.8 

1.09 

1.25 

0.60 

1.78 

0.72 

1.32 

3     X4 

3/8 

9.3 

2.73 

4.3 

0.93 

1.26 

0.59 

1.57 

0.62 

1.29 

3     X3!4 

1/2 

10.9 

3.21 

3.5 

1.20 

1.06 

0.62 

1.49 

0.80 

1.12 

3     X  3!4 

7/16 

9.8 

2.88 

3.3 

1.31 

1.08 

0.68 

1.37 

0.88 

1.11 

314     MOMENTS  OF   INERTIA  AND   RESISTANCE. 


PROPERTIES    OF    CARNEGIE    T    SHAPES.— STEEL 

(concluded) . 


W 

.9 

I. 

II. 

III. 

IV. 

V. 

VII. 

VIII. 

IX. 

g 

„ 

m 

1 

W) 

£ 

Moments  of 

Radii  of 

Section 

_H 

^ 

o3 

"o 

inertia, 

gyration, 

modulus, 

1 

,0 

t*H 

«£ 

TO 

/. 

r. 

R. 

I*- 

& 

5 

fl 

1 

M 

0 

ft 

"S 

•S'S 

,§ 

1 

"1 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

1s 

e 

cc 

.2 

| 

u 

1 

AB. 

CD. 

AB. 

CD. 

AB. 

CD. 

P9 

3     X3J4 

3/8 

8.5 

2.49 

2.9 

0.93 

1.09 

0.61 

1.21 

0.62 

1.09 

3     X3 

1/2 

10.0 

2.94 

2.3 

1.20 

0.88 

0.64 

1.10 

0.80 

0.93 

3     X3 

7/16 

9.1 

2.67 

2.1 

1.08 

0.90 

0.64 

1.01 

0.72 

0.92 

3     X3 

3/8 

7.8 

2.28 

1.8 

0.90 

0.90 

0.63 

0.86 

0.60 

0.88 

3     X3 

5/16 

6.6 

1.95 

1.6 

0.75 

0.90 

0.62 

0.74 

0.50 

0.86 

3     X2!4 

3/8 

7.2 

2.10 

1.1 

0.89 

0.72 

0.66 

0.60 

0.60 

0.71 

3     X2J4 

5/16 

6.1 

1.80 

0.94 

0.75 

0.73 

0.65 

0.52 

0.50 

0.68 

2-MX2 

5/16 

7.4 

2.16 

1.1 

0.62 

0.71 

0.54 

0.75 

0.45 

0.53 

2J4X3 

3/8 

7.2 

2.10 

1.8 

0.54 

0.92 

0.51 

0.87 

0.43 

0.97 

2J4X  3 

5/16 

6.1 

1.80 

1.6 

0.44 

0.94 

0.51 

0.76 

0.35 

0.92 

2}4X2% 

3/8 

6.7 

1.98 

1.4 

0.66 

0.84 

0.58 

0.73 

0.53 

0.87 

5/16 

5.8 

1.71 

1.2 

0.44 

0.83 

0.51 

0.60 

0.35 

0.83 

2J4  X2J4 

3/8 

6.4 

1.89 

1.0 

0.52 

0.74 

0.53 

0.59 

0.42 

0.76 

2^<3  X2J4 

5/16 

5.5 

1.62 

0.87 

0.44 

0.74 

0.52 

0.50 

0.35 

0.74 

2.V6X1J4 

3/16 

2.9 

0.84 

0.09 

0.29 

0.31 

0.58 

0.09 

0.23 

0.29 

2!4X2i4 

5/16 

4.9 

1.44 

0.66 

0.33 

0.68 

0.48 

0.42 

0.30 

0.69 

2/4  X  214 

1/4 

4.1 

1.20 

0.51 

0.25 

0.67 

0.47 

0.32 

0.22 

0.66 

2     X2 

5/16 

4.3 

1.26 

0.45 

0.23 

0.60 

0.43 

0.33 

0.23 

0.63 

2     X2 

1/4 

3.7 

1.08 

0.36 

0.18 

0.60 

0.42 

0.25 

0.18 

0.59 

2     X1J4 

1/4 

3.1 

0.90 

0.16 

0.18 

0.42 

0.45 

0.15 

0.18 

0.42 

i%xi% 

1/4 

3.1 

0.90 

0.23 

0.12 

0.51 

0.37 

0.19 

0.14 

0.54 

1MX1M 

3/8 

3.6 

1.05 

0.12 

0.19 

0.33 

0.41 

0.15 

0.22 

0.91 

1^x1*4 

1/4 

2.4 

0.75 

0.15 

0.08 

0.49 

0.34 

0.14 

0.10 

0.42 

1^X1J4 

3/16 

1.84 

0.54 

0.11 

0.06 

0.45 

0.31 

0.11 

0.07 

0.44 

1!4X1M 

1/4 

2.04 

0.60 

0.08 

0.05 

0.36 

0.27 

0.10 

0.07 

0.40 

1^x1*4 

3/16 

1.53 

0.45 

0.06 

0.03 

0.37 

0.26 

0.07 

0.05 

0.38 

1     XI 

3/16 

1.23 

0.36 

0.03 

0.02 

0.29 

0.21 

0.05 

0.04 

0.32 

1     XI 

1/8 

0.87 

0.26 

0.02 

0.01 

0.29 

0.21 

0.03 

0.02 

0.29 

RADII   OF  GYRATION. 


315 


PROPERTIES    OF    CAMBRIA    AND 
CARNEGIE    STEEL    Z-BARS. 


-B 


a 

d 

0) 

.  02 
.fl 

I. 

II. 

III. 

IV. 

V. 

VI. 

1 

03 

a 

1 

0) 

•  s 

Moments  of 
inertia. 

Radii  of  gyration. 

a 

a 

T. 

o 

O 

1 

Q     J" 

•3 

•^ 

1 

o3  O 

o. 

12 

•g«9 

'« 

B« 

Axis 

Axis 

Axis 

Axis 

Axis 

p 

f 

H 

£ 

< 

AB. 

CD. 

AB. 

CD. 

EF. 

6 

3V£ 

3/8 

15.6 

4.59 

25.32 

9.11 

2.35 

1.41 

0.83 

39/16 

7/16 

18.3 

5.39 

29.80 

10.95 

2.35 

1.43 

0.84 

6>6 

Si 

1/2 

21.0 

6.19 

34.36 

12.87 

2.36 

1.44 

0.84 

6 

3i^ 

9/16 

22.7 

6.68 

34.64 

12.59 

2.28 

1.37 

0.81 

3%  6 

5/8 

25.4 

7.46 

38.86 

14.42 

2.28 

1.39 

0.82 

6J4 

3^ 

11/16 

28.0 

8.25 

43.18 

16.34 

2.29 

1.41 

0.84 

ft 

3V6 

3/4 

29.3 

8.63 

42.12 

15.44 

2.21 

1.34 

0.81 

6Vi6 

39/16 

13/16 

32.0 

9.40 

46.13 

17.27 

2.22 

1.36 

0.82 

6^ 

3% 

7/8 

34.6 

10.17 

50.22 

19.18 

2.22 

1.37 

0.83 

5 

314 

5/16 

11.6 

3.40 

13.36 

6.18 

.98 

.35 

0.75 

3%  6 

3/8 

13.9 

4.10 

16.18 

7.65 

.99 

.37 

0.76 

5)4 

3% 

7/16 

16.4 

4.81 

19.07 

9.20 

.99 

.38 

0.77 

5 

3J4 

1/2 

17.8 

5.25 

19.19 

9.05 

.91 

.31 

0.74 

5Vl6 

3%6 

9/16 

20.2 

5.94 

21.83 

10.51 

.91 

.33 

0.75 

SYs 

3H 

5/8 

22.6 

6.64 

24.53 

12.06 

.92 

.35 

0.76 

5 

3!4 

11/16 

23.7 

6.96 

23.68 

11.37 

1.84 

.28 

0.73 

5H6 

3%6 

3/4 

26.0 

7.64 

26.16 

12.83 

1.85 

.30 

0.75 

3% 

13/16 

28.3 

8.33 

28.70 

14.36 

1.86 

.31 

0.76 

4 

3Vi6 

1/4 

8.2 

2.41 

6.28 

4.23 

1.62 

.33 

0.67 

41/16 

5/16 

10.3 

3.03 

7.94 

5.46 

1.62 

.34 

0.68 

4^ 

3%6 

3/8 

12.4 

3.66 

9.63 

6.77 

1.62 

.36 

0.69 

4 

3Vie 

7/16 

13.8 

4.05 

9.66 

6.73 

1.55 

1.29 

0.66 

4  Vie 

1/2 

15.8 

4.66 

11.18 

7.96 

1.55 

1.31 

0.67 

4>6 

38/?6 

9/16 

17.9 

5.27 

12.74 

9.26 

1.55 

1.33 

0.69 

4 

3#e 

5/8 

18.9 

5.55 

12.11 

8.73 

1.48 

1.25 

0.66 

4M.6 

3V6 

11/16 

20.9 

6.14 

13.52 

9.95 

1.48 

1.27 

0.67 

4^ 

33/i6 

3/4 

22.9 

6.75 

14.97 

11.24 

1.49 

1.29 

0.69 

3 

2iy16 

1/4 

6.7 

1.97 

2.87 

2.81 

1.21 

1.19 

0.55 

3Vie 

2% 

5/16 

8.4 

2.48 

3.64 

3.64 

1.21 

1.21 

0.56 

3 

2iy16 

3/8 

9.7 

2.86 

3.85 

3.92 

1.16 

1.17 

0.55 

3VlQ 

2M 

7/16 

11.4 

3.36 

4.57 

4.75 

1.17 

1.19 

0.56 

3 

21^6 

1/2 

12.5 

3.69 

4.59 

4.85 

1.12 

1.15 

0.55 

Stte 

2% 

9/16 

14.2 

4.18 

5.26 

5.70 

1.12 

1.17 

0.56 

316    MOMENTS   OF   INERTIA   AND   RESISTANCE. 


TABLE    A.— RADII    OF    GYRATION    FOR    A    PAIR    OF 
ANGLES  PLACED  BACK  TO  BACK. 

ANGLES    WITH    EQUAL    LEGS. 


Radii  of  gyration  given  correspond  to  directions  indicated  by  arrow-heads. 


Size,  in 
inches. 

Weight  per 
foot  of 
single  angle, 
in  Ibs. 

*Area  of 
section, 
in  ins. 

Radii  of  gyration. 

TO. 

n- 

r2. 

r» 

8   X8   Xl 

26.4 

15.50 

2.50 

3.32 

3.49 

3.58 

8   X8  XH 

56.9 

33.46 

2.42 

3.42 

3.60 

3.69 

6   X6   X   1 

14.8 

8.72 

1.88 

2.49 

2.67 

2.76 

6   X6   X   i 

19.6 

11.50 

1.86 

2.52 

2.70 

2.80 

6   X6   X   } 

28.7 

16.88 

1.83 

2.55 

2.73 

2.83 

6   X6   Xl 

37.4 

22.00 

1.80 

2.59 

2.77 

2.87 

5   X5  X   1 

12.3 

7.22 

1.56 

2.09 

2.26 

2.35 

5  X5  X   i 

16.2 

9.50 

1.54 

2.11 

2.29 

2.38 

5   X5   X   J 

23.6 

13.88 

1.51 

2.15 

2.33 

2.43 

5   X5   Xl 

30.6 

18.00 

1.48 

2.19 

2.38 

2.48 

4   X4   X   % 

8.2 

4.80 

1.24 

1.67 

1.85 

1.94 

4   X4  X   | 

9.8 

5.72 

1.23 

1.69 

1.88 

1.97 

4   X4   X   f 

15.7 

9.22 

1.20 

1.72 

1.91 

2.00 

4X  4   X  % 

19.9 

11.68 

1.18 

1.75 

1.94 

2.04 

O  2  X  O'J  X     /16 

7.1 

4.18 

1.08 

1.47 

1.65 

1.74 

O  1  v/  O  1  v/      3 
O^  /\  O  2  /\      8 

8.5 

4.96 

1.07 

1.49 

1.67 

1.77 

13.6 

7.96 

1.04 

1.52 

1.70 

1.81 

3iX3iX  % 

17.1 

10.06 

1.02 

1.55 

1.74 

1.85 

3   X3   X   i 

4.9 

2.88 

0.93 

1  25 

1.43 

1.53 

3   X3   X   I 

7.2 

4.22 

0.91 

'1.27 

1.45 

1.56 

3   X3   X   i 

9.4 

5.50 

0.90 

1.29 

1.48 

1.59 

3   X3   X   | 

11.4 

6.72 

0.88 

1.32 

1.51 

1.62 

2fX2fX  i 

4.5 

2.62 

0.85 

1.15 

1.34 

1.44 

2fX2JX   i 

8.5 

5.00 

0.82 

1.19 

1.39 

1.49 

2JX2JX   % 

3.1 

1.80 

0.78 

1.04 

1.22 

1.32 

2JX2JX   i 

7.7 

4.50 

0.74 

1.10 

1.29 

1.40 

2  J  X  2^  X  Jie 

2.8 

1.62 

0.70 

0.94 

1.12 

1.23 

2  J  X  2^  X   i 

6.8 

4.00 

0.66 

0.99 

1.19 

1.30 

2  X2  X   i 

3.2 

1.88 

0.61 

0.85 

1.03 

1.14 

*  The  figures  in  this  column  give  the  area  of  both  angles. 


RADII   OF   GYRATION. 


317 


TABLE    B.— RADII    OF    GYRATION    FOR    A    PAIR    OF 
ANGLES  PLACED  BACK  TO  BACK. 

ANGLES    WITH    UNEQUAL    LEGS LONG    LEG    VERTICAL. 

r, 


Radii  of  gyration  given  correspond  to  directions  indicated  by  arrow-heads. 


Size,  in 
inches. 

Weight  per 
foot  of 
single  angle, 
in  Ibs. 

f  Area  of 
section, 
in  ins. 

Radii  of  gyration. 

ro. 

n- 

f2- 

r-3- 

*8  X6   X   4 

23.0 

13.52 

2.56 

2.32 

2.49 

2.57 

*8  X6   XI 

45  .  6 

26.82 

2.53 

2.47 

2.65 

2.74 

6   X4   X   f 

12.3 

7.22 

1.93 

1.50 

1.67 

1.76 

6   X4   X  % 

25.4 

14.94 

1.87 

1.55 

1.74 

1.84 

6   X3iX   f 

11.7 

6.84 

1.94 

1.26 

1.43 

1.53 

6   X3|X   i 

15.3 

9.00 

1.92 

1.28 

1.46 

1.56 

6   X34X   f 

18.9 

11.10 

1.90 

1.30 

1.49 

1.59 

6   X3iX  % 

24.0 

14.12 

1.88 

1.33 

1.52 

1.62 

5  X4  X  i 

11.0 

6.46 

1.59 

1.58 

1.75 

1.85 

5   X4   X    i 

21.1 

12.38 

1.54 

1.62 

1.81 

1.91 

5   X3JX   f 

10.4 

6.10 

1.60 

1.33 

1.51 

1.60 

5   X3JX   f 

19.8 

11.62 

1.55 

1.39 

1.59 

1.68 

5   X3   X   f 

9.8 

5.72 

1.61 

1.10 

1.27 

1.37 

5   X3   X   i 

12.8 

7.50 

1..59 

1.12 

1.30 

1.39 

5   X3   X   f 

15.7 

9.22 

1.57 

1.14 

1.33 

1.42 

5   X3   X   i 

18.5 

10.88 

1.55 

1.17 

1.36 

1.46 

4   X3iX    1 

9.1 

5.34 

1.25 

1.43 

1.60 

1.70 

4   X3|X   J 

17.2 

10.12 

1.20 

1.44 

1.62 

1.72 

4   X3   X   f 

8.5 

4.96 

1.26 

1.46 

1.64 

1.74 

4   X3   X   i 

16.0 

9.38 

1.22 

1.48 

1.67 

1.77 

3|X2JX   i 

4.9 

2.88 

1.12 

0.96 

1.13 

1.23 

3^X2£X   $   • 

7.2 

4.22 

1.10 

0.98 

1.16 

1.26 

3iX2^X   \ 

9.4 

5.50 

1.09 

1.00 

1.19 

1.29 

3iX2|X  % 

12.4 

7.30 

1.06 

1.03 

1.23 

1.33 

3   X2   X   i 

4.0 

2.38 

0.95 

0.75 

0.93 

1.03 

3   X2   X   4 

7.7 

4.50 

0.92 

0.80 

1.00 

1.10 

2iX2   X  % 

2.8 

1.62 

0.79 

0.79 

0.97 

1.07 

2iX2   X   i 

6.8 

4.00 

0.75 

0.84 

1.04 

1.15 

*  Rolled  only  by  the  Pencoyd  Iron  Co.  Works. 

t  The  figures  in  this  column  give  the  area  of  both  angles. 


318     MOMENTS   OF   INERTIA  AND   RESISTANCE. 


TABLE    C.— RADII    OF    GYRATION    FOR  A     PAIR    OF 
ANGLES  PLACED  BACK  TO  BACK. 

ANGLES   WITH   UNEQUAL   LEGS. — SHORT   LEG   VERTICAL. 


Radii  of  gyration  given  correspond  to  directions  indicated  by  arrow-heads. 


Weight 
per  foot 

*  Area  of 

Radii  of  gyration. 

Size  in  inches. 

of  single 

section 

angle, 

in  inches. 

1.17 

2.92 

3.01 

6     X4     X    % 

12.3 

7.22 

2.74 

6     X4     X    K 

16.2 

9.50 

1.15 

2.76 

2.94 

3.04 

0     X4     X    % 

23.6 

13.88 

1.12 

2.80 

2.99 

3.09 

6     X4     XI 

30.6 

18.00 

1.09 

2.85 

3.04 

3.14 

6     X33/X    % 

11.7 

6.84 

0.99 

2.81 

3.00 

3.10 

6     X3j|xl  8 

28.9 

17.00 

0.92 

2.93 

3.13 

3.23 

5     X4     X    % 

11.0 

6.46 

1.20 

2.20 

2.38 

2.48 

5     X4     X    V& 

24.2 

14.22 

1.14 

2.29 

2.48 

2.58 

5     X334X    G/i6 

8.7 

5.12 

1  .03 

2.26 

2.44 

2.54 

5     X334X    % 

22.7 

13.34 

0.96 

2.36 

2.55 

2.65 

5     X3     X    %e 

8.2 

4.80 

0.85 

2.33 

2.51 

2.61 

5     X3     X    13A6 

19.9 

11.68 

0.80 

2.42 

2.62 

2.72 

4     X3V6X    5/i6 

7.7 

4.50 

1.07 

1.73 

1.91 

2.00 

11.9 

7.00 

1.04 

1.76 

1.95 

2.04 

4     X  334X    % 

14.6 

8.60 

1.03 

1.78 

1.98 

2.07 

4     X334X    13/ie 

18.5 

10.86 

1.01 

1.81 

2.01 

2.11 

4     X3     X   5/i« 

7.1 

4.18 

0.89 

1.79 

1.97 

2.07 

4     X3     X    13/i6 

17.1 

10.06 

0.83 

1.88 

2.08 

2.18 

3^X3     X    5/ie 

6.6 

3.86 

0.90 

1.52 

1.71 

1.80 

3^X3     X    13/io 

15.7 

9.24 

0.85 

1.61 

1.81 

1.91 

3J/X2V6X  V* 

4.9 

2.88 

0.74 

1.58 

1.76 

1.86 

3i/X2V£X     1-Vift 

12.4 

7.30 

0.67 

1.66 

1.86 

1.96 

3     X2J4X    34 

4.5 

2.62 

0.75 

1.31 

1.50 

1.59 

3     X234X   9/i6     ' 

9.5 

5.56 

0.72 

1.37 

1.56 

1.66 

3     X2     X    34 

4.0 

2.38 

0.57 

1.38 

1.56 

1.66 

3     X2     X    34 

7.7 

4.50 

0.55 

1.42 

1.62 

1.73 

234X2     X    %e 
234X2     X    34 

2.8 
6.8 

1.62 
4.00 

0.60 
0.56 

1.10 
1.16 

1.28 
1.35 

1.39 
1.46 

18  The  figures  in  this  column  give  the  area  of  both  angles. 


RADII   OF  GYRATION. 


319 


TABLE    D.— RADII    OF    GYRATION    FOR    A    PAIR    OF 
STANDARD  CHANNELS  PLACED  BACK  TO  BACK. 


Radii  of  gyration  given  correspond  to  directions  indicated  by  arrow-heads. 


Depth  in 
inches. 

Thickness 
of  web. 

Weight 
per  foot 
of  one 
channel. 

Area  of 
two 
channels. 

Radii  of  gyration. 

r0. 

r\. 

r2. 

rs- 

0.40 

33.00 

19.80 

5.62 

1.38 

1.48 

1.58 

0.43 

35.00 

20.58 

5.58 

1.38 

1.47 

1.57 

0.52 

40.00 

23.52 

5.43 

1.37 

1.46 

1.56 

15 

0.62 

45.00 

26.48 

5.32 

1.37 

1.45 

1.56 

0.72 

50.00 

29.42 

5.23 

1.37 

1.46 

1.56 

0.82 

55.00 

32.36 

5.16 

1.38 

1.47 

1.58 

0.28 

20.50 

12.06 

4.61 

1.24 

1.34 

1.44 

0.39 

25.00 

14.70 

4.43 

1.21 

1.31 

1.41 

12 

0.51 

30.00 

17.64 

4.28 

1.20 

1.30 

1.40 

0.64 

35.00 

20.58 

4.17 

1.21 

1.31 

1.41 

1.76 

40.00 

23.52 

.09 

1.23 

1.32 

1.43 

0.24 

15.00 

8.92 

3.87 

1.14 

1.24 

1.34 

0.38 

20.00 

11.76 

3.66 

1.10 

1.20 

1.31 

10 

0.53 

25.00 

14.70 

3.52 

1.10 

1.20 

1.31 

0.68 

30.00 

17.64 

3.42 

1.12 

1.22 

1.33 

0.82 

35.00 

20.58 

3.35 

1.16 

1.26 

1.37 

0.23 

13.25 

7.78 

3.49 

1.09 

1.19 

1.29 

0.29 

15.00 

8.82 

3.40 

1.07 

1.17 

1.28 

0.45 

20.00 

11.76 

3.21 

1.05 

1.15 

1.26 

0.62 

25.00 

14.70 

3.10 

1.07 

1.17 

1.28 

320    MOMENTS  OF  INERTIA  AND   RESISTANCE. 


TABLE    D.— RADII    OF    GYRATION    FOR    A    PAIR   OF 
STANDARD  CHANNELS  PLACED  BACK  TO    BACK 

(continued) . 


I' 


Radii  of  gyration  given  correspond  to  directions  indicated  by  arrow-heads. 


fl    . 

si 

a  « 
|l 

Thickness 
of  web. 

Weight 
per  foot 
of  one 
channel. 

Area 
of  two 
channels. 

Radii  of  gyration. 

r* 

f|. 

r2- 

r3- 

8 

0.22 

11.25 

6.70 

3.11 

1.04 

1.14 

1.25 

8 

0.31 

13.75 

8.08 

2.98 

1.04 

1.14 

1.25 

8 

0.40 

16.25 

9.56 

2.89 

1.03 

1.14 

1.24 

8 

0.49 

18.75 

11.02 

2.82 

1.03 

1.14 

1.24 

8 

0.58 

21.25 

12.50 

2.77 

1.03 

1.14 

1.24 

7 

0.21 

9.75 

5  70 

2.72 

0.99 

1.09 

1.20 

7 

0.32 

12.25 

7.20 

2.59 

0.99 

1.09 

1.20 

7 

0.42 

14.75 

8.68 

2.50 

0.99 

1.10 

1.21 

7 

0.53 

17.25 

10.14 

2.44 

1.00 

1.10 

1.21 

7 

0.63 

19.75 

11.62 

2.39 

1.00 

1.10 

1.22 

6 

0.20 

8.00 

4.76 

2.34 

0.94 

1.05 

1.15 

6 

0.32 

10.50 

6.18 

2.21 

0.94 

1.05 

1.16 

6 

0.44 

13.00 

7.64 

2.13 

0.95 

1.06 

1.16 

6 

0.56 

15.50 

9.12 

2.07 

0.95 

1.06 

1.17 

5 

0.19 

6.50 

3.90 

1.95 

0.89 

1.00 

1.10 

5 

0.33 

9.00 

5.30 

1.83 

0.90 

1.00 

1.11 

5 

0.48 

11.50 

6.76 

1.75 

0.91 

1.01 

1.12 

4 

0.18 

5.25 

3.10 

1.56 

0.84 

0.95 

1.06 

4 

0.25 

6.25 

3.68 

1.51 

0.84 

0.95 

1.06 

4 

0.32 

7.25 

4.26 

1.46 

0.84 

0.95 

1.06 

3 

0.17 

4.00 

2.38 

1.17 

0.80 

0.91 

1.02 

3 

0.26 

5.00 

2.94 

1.12 

0.81 

0.92 

1.03 

3 

0.36 

6.00 

3.52 

1.08 

0.83 

0.93 

1.05 

RESISTANCE  TO  TENSION.  321 


CHAPTER   XL 
RESISTANCE  TO  TENSION. 

PHYSICAL  PROPERTIES  AND  SPECIFICATIONS  OF  IRON 
AND    STEEL. 

STRENGTH  OF  RODS,  ROPES,  AND  CABLES.       PROPORTIONS  OF  UPSET 
SCREW  ENDS,    EYE-BARS,   TTJRNBUCKLES,   ETC. 

THE  resistance  which  any  material  offers  to  being  pulled  apart 
is  due  to  the  tenacity  of  its  fibres,  or  the  cohesion  of  the  particles 
of  which  it  is  composed. 

It  is  evident  that  the  amount  of  resistance  to  tension  which  any 
cross-section  of  a  body  will  exert  depends  only  upon  the  tenacity 
of  its  fibres,  or  the  Cohesion  of  its  particles,  and  upon  the  number 
of  fibres  or  particles  in  the  cross-section. 

As  the  number  of  the  fibres,  or  particles,  in  the  section  is  pro- 
portional to  the  area,  the  strength  of  any  piece  of  material  must 
be  as  the  area  of  its  cross-section;  and  hence,  if  we  know  the 
tenacity  of  the  material  per  square  inch  of  cross-section,  we  can 
obtain  the  total  strength  by  multiplying  it  by  the  area  of  the  sec- 
tion in  inches. 

The  tenacity  of  different  building  materials  per  square  inch  has 
been  found  by  pulling  apart  a  bar  of  the  material  of  known 
dimensions,  and  dividing  the  breaking  force  by  the  area  of  the 
cross-section  of  the  bar. 

Table  I.  gives  the  allowable  safe  values  for  the  tenacity  of 
building  materials,  as  recommended  by  the  best  authorities. 

Knowing  the  tenacity  of  one  square  inch  of  the  material  all 
that  is  necessary  to  determine  the  tenacity  of  a  piece  of  any  uni- 
form size  is  to  multiply  the  area  of  its  cross-section,  in  square 
inches,  by  the  number  in  the  table  opposite  the  name  of  the 
material;  or: 

For  a  rectangular  bar, 

Safe  load  in  Ibs.  =  breadth  X  depth  X  T.  (1) 

For  a  round  bar, 

Safe  load  in  Ibs.  =  0. 7854  X  diameter  squared  X  T0          (2) 


322  RESISTANCE   TO  TENSION. 

If  the  size  of  the  bar  is  desired  we  have 

Area  of  cross-section  =  ~r-.  (3) 

For  a  round  bar,  

/     i««  j 

(4) 

T=  values  for  the  material,  given  in  Table  I. 
TABLE  I. 

Allowable   Safe    Tensile   Stress   per   Square   Inch  for  Building 
Materials. 

Safe  Strength  in 

Material.  Ibs.  per  sq.  in. 

T 

Cement,  natural,  one  week  old 60  to  100 

Cement,  Portland,  one  week,  fair  average 350 

METALS. 

Cast  iron 3,000 

Copper,  cast 2,000 

"        forged  or  rolled 5,500 

"        wire 9,000 

Wrought  iron  * 10,000  to  14,000 

Wrought  steel,  soft 12,000  to  16,000 

"  "      medium  f 12,500  to  18,000 

Steel  wire 20,000 

WOODS.     (Factor  of  safety  of  five  to  six.)J 

Ash,  white 2,000 

Ash,  brown 1,500 

Chestnut 1,500 

Hemlock. 1,200 

Oak,  white 2,000 

Pine,  Georgia  yellow 2,000 

Pine,  Oregon  (Douglas  Fir) 1,800 

Pine,  Norway 1,600 

Pine,  white 1,400 

Redwood 800 

Spruce 1,600 

Whitewood 1,200 

*  See  page  324.  t  See  page  331. 

t  The  Building  Law  for  Greater  New  York  fixes  the  permissible  unit 
stress  in  yellow  pine  at  1200  Ibs.  per  sq.  inch;  in  oak  at  1000  Ibs.;  in  white 
pine  and  spruce  at  800  Ibs.,  arid  in  hemlock  at  600  Ibs.  These  values  are 
about  one-tenth  of  the  ultimate  strength. 


RESISTANCE  TO  TENSION.  323 

EXAMPLE  I. — The  strain  in  the  tie-beam  of  a  truss  has  been 
found  to  be  120,000  Ibs.  What  should  be  the  size  of  the  beam, 
if  made  of  white  pine? 

Ans.  By  formula  (3)  we  have 

120  000 
Area  of  cross-section  =        ?       =85.7  sq.  inches. 

If  we  make  the  depth  of  the  beam  12  inches  then  the  thickness 
must  be  ^-,  or  7.2  inches.  As  the  beam  is  horizontal  its  own 

weight  would  produce  an  additional  strain  in  the  fibres,  for  which 
some  allowance  must  be  made. 

Allowance  must  also  be  made  for  any  cutting  of  the  beam  or 
for  holes  for  truss  rods.  If  there  is  a  two-inch  hole  through  the 
beam,  we  should  use  a  10X12  inch  beam,  which  will  allow  for 
the  hole,  and  for  the  weight  of  the  beam. 

For  the  calculation  of  tie-beams  subject  to  a  transverse  load  see 
Chapter  XV. 

EXAMPLE  II. — What  size  angle  bar  should  be  used  to  resist  a 
tensile  stress  of  60,000  Ibs.,  the  material  being  medium  steel? 

60,000 

Ans.  Sectional  area=-          =4  sq.  in. 
lo,00u 

From  the  tables  giving  the  properties  of  angles,  Chapter  X.,  we 
find  that  a  4  X  4  X  f  angle  has  an  area  of  4.61  square  inches.  This 
would  be  reduced  by  one  f-inch  hole,  for  a  f-inch  rivet,  which 
gives  the  net  area  4.61  -  JX  1  =  4.06  square  inches,  or  just  above 
that  required. 

[The  tensile  strength  of  the  sizes  of  angles  most  commonly  used 
in  trusses  is  given  in  Table  X.  For  reduction  in  net  area  caused 
by  rivet-holes  see  Table  XI.,  also  Table  I.,  Chapter  XX.] 

Wrought  Iron. 

Wrought  iron  is  no  longer  used  for  the  manufacture  of  struc- 
tural shapes,  such  as  angles,  channels,  beams,  etc.,  except  in  case 
of  special  orders,  its  use  in  structural  work  being  practically 
limited  to  rods,  bars,  and  bolts.  Nearly  all  bolts  are  made  of 
wrought  iron,  and  truss  rods  are  generally  furnished  in  wrought 
iron  unless  steel  is  specified.  Flat  tie-bars  are  made  both  of  iron 
and  steel.  The  cost  of  bars  and  rods  is  about  the  same  in 
wrought  iron  or  mild  steel,  but  wrought  iron  is  easier  to  work 
than  steel. 


324  RESISTANCE  TO  TENSION. 

Tensile  Strength  and  Quality.  —  The  best  American  rolled  iron 
has  a  breaking  tensile  strength  of  from  fifty  thousand  to  sixty 
thousand  pounds  per  square  inch  for  specimens  not  exceeding 
one  square  inch  in  section.  Ordinary  bar  iron  should  not  break 
under  a  less  strain  than  fifty  thousand  pounds  per  square  inch, 
and  should  not  take  a  set  under  a  stress  less  than  twenty-five 
thousand  pounds  per  square  inch.  A  bar  one  inch  square  and 
one  foot  long  should  stretch  fifteen  per  cent,  of  its  length  before 
breaking,  and  should  be  capable  of  being  bent,  cold,  90°  over  the 
edge  of  an  anvil  without  sign  of  fracture,  and  should  show  a 
fibrous  texture  when  broken. 

Iron  that  wrill  not  meet  these  requirements  is  not  suitable  for 
structures  ;  but  nothing  is  gained  by  specifying  more  severe  tests, 
because,  in  bars  of  the  sizes  and  shapes  usually  required  for  such 
work,  nothing  more  can  be  attained  with  certainty,  and  conscien- 
tious makers  will  be  unwilling  to  agree  to  furnish  that  which  it  is 
not  practicable  to  produce. 

The  working  strength  of  wrought-iron  ties  in  trusses  is  gener- 
ally taken  at  ten  thousand  pounds  per  square  inch.  In  places 
where  the  load  is  perfectly  steady  and  constant  twelve  thousand 
pounds  may  be  used. 

The  extension  of  iron,  for  all  practical  purposes,  is  as  follows  : 

Wrought  iron,  ^^  of  its  length  per  ton  per  square  inch. 

Cast  iron,  -^D  of  its  length  per  ton  per  square  inch. 


Appearance  of  the  Fractured  Surface  of  Wrought 

Iron. 

At  one  time  it  was  thought  that  a  fibrous  fracture  was  a  sign  of 
good  tough  wrought  iron,  and  that  a  crystalline  fracture  showed 
that  the  iron  was  bad,  hard,  and  brittle.  Mr.  Kirkaldy's  experi- 
ments, however,  show  conclusively  that,  whenever  wrought  iron 
breaks  suddenly,  it  invariably  presents  a  crystalline  appearance  ; 
and,  when  it  breaks  gradually,  it  invariably  presents  a  fibrous 
appearance.  From  the  same  experiments  it  was  also  shown  that 
the  appearance  of  the  fractured  surface  of  wrought  iron  is,  to  a 
certain  extent,  an  indication  of  its  quality,  provided  it  is  known 
how  the  stress  was  applied  which  produced  the  fracture. 

Small,  uniform  crystals,  of  a  uniform  size  and  color,  or  fine, 
close,  silky  fibres,  indicate  a  good  iron. 

Coarse  crystals,  blotches  of  color  caused  by  impurities,  loose 
and  open  fibres,  are  signs  of  bad  iron;  and  flaws  in  the  fractured 


RESISTANCE   TO   TENSION.  325 

surface  indicate  that  the  piling  and  welding  processes  have  been 
imperfectly  carried  out. 

Kirkaldy's  Conclusions.* 

Mr.  David  Kirkaldy  of  England,  who  made  some  of  the  most 
valuable  experiments  on  record  on  the  strength  of  wrought  iron, 
came  to  some  conclusions,  many  of  which  differed  from  what  had 
previously  been  supposed  to  be  true.  , 

The  following  are  of  special  importance  to  the  student  of  build- 
ing construction,  and  should  be  carefully  studied : 

"The  breaking-strain  does  not  indicate  the  quality,  as  hitherto 
assumed. 

"  A  high  breaking-strain  may  be  due  to  the  iron  being  of  supe- 
rior quality,  density,  fine,  and  moderately  soft,  or  simply  to  its 
being  very  hard  and  unyielding. 

"A  low  breaking-strain  may  be  due  to  looseness  and  coarseness 
in  the  texture;  or  to  extreme  softness,  although  very  close  and 
fine  in  quality. 

"The  contraction  of  area  at  fracture,  previously  overlooked, 
forms  an  essential  element  in  estimating  the  quality  of  specimens. 

"The  respective  merits  of  various  specimens  can  be  correctly 
ascertained  by  comparing  the  breaking -strain  jointly  with  the 
contraction  of  area. 

"Inferior  qualities  show  a  much  greater  variation  in  the  break- 
ing-strain than  superior. 

"Greater  differences  exist  between  small  and  large  bars  in 
coarse  than  in  fine  varieties. 

"The  prevailing  opinion  of  a  rough  bar  being  stronger  than  a 
turned  one  is  erroneous. 

"Rolled  bars  are  slightly  hardened  by  being  forged  down. 
i    "The  breaking-strain  and  contraction  of  area  of  iron  plates  aro 
[greater  in  the  direction  in  which  they  are  rolled  than  in  a  trail  s- 
(verse  direction. 

"Iron  is  less  liable  to  snap  the  more  it  is  worked  and  rolled. 

"The  ratio  of  ultimate  elongation  may  be  greater  in  short  than 
in  long  bars,  in  some  descriptions  of  iron;  whilst  in  others  the 
ratio  is  not  affected  by  difference  in  the  length. 

"Iron,  like  steel,  is  softened,  and  the  breaking-strain  reduced, 
by  being  heated,  and  allowed  to  cool  slowly. 

*  Kirkaldy's  Experiments  on  Wrought  Iron  and  Steel. 


326  RESISTANCE   TO   TENSION. 

"A  great  variation  exists  in  the  strength  of  iron  bars  which 
have  been  cut  and  welded.  Whilst  some  bear  almost  as  much  as 
the  uncut  bar,  the  strength  of  others  is  reduced  fully  a  third. 

"The  welding  of  steel  bars,  owing  to  their  being  so  easily 
burned  by  slightly  overheating,  is  a  difficult  and  uncertain  opera- 
tion. 

"Iron  is  injured  by  being  brought  to  a  white  or  welding  heat,  if 
not  at  the  same  time  hammered  or  rolled. 

"The  breaking  strain  is  considerably  less  when  the  strain  is 
applied  suddenly  instead  of  gradually,  though  some  have  imagined 
that  the  reverse  is  the  case. 

"The  specific  gravity  is  found  to  generally  indicate  pretty  cor- 
rectly the  quality  of  specimens. 

"The  density  of  iron  is  decreased  by  the  process  of  wire-drawing 
and  by  the  similar  process  of  cold  rolling,*  instead  of  increased, 
as  previously  imagined. 

"The  density  of  iron  is  decreased  by  being  drawn  out  under  a 
tensile  strain,  instead  of  increased,  as  believed  by  some. 

"It  must  be  abundantly  evident,  from  the  facts  that  have  been 
produced,  that  the  breaking-strain,  when  taken  alone,  gives  a 
false  impression  of,  instead  of  indicating,  the  real  quality  of 
iron,  as  the  experiments  which  have  been  instituted  reveal  the 
somewhat  startling  fact,  that  frequently  the  inferior  kinds  of  iron 
actually  yield  a  higher  result  than  the  superior.  The  reason  of 
this  difference  was  shown  to  be  due  to  the  fact  that,  whilst  the  one 
quality  retained  its  original  area  only  very  slightly  decreased  by 
the  strain,  the  other  was  reduced  to  less  than  one-half.  Now, 
surely  this  variation,  hitherto  unaccountably  completely  over- 
looked, is  of  importance  as  indicating  the  relative  hardness  or  soft- 
ness of  the  material,  and  thus,  it  is  submitted,  forms  an  essential 
element  in  considering  the  safe  load  that  can  be  practically  applied 
in  various  structures.  It  must  be  borne  in  mind  that,  although 
the  softness  of  the  material  has  the  effect  of  lessening  the  amount 
of  the  breaking-strain,  it  has  the  very  opposite  effect  as  regards 
the  working-strain.  This  holds  good  for  two  reasons:  first,  the 
softer  the  iron,  the  less  liable  it  is  to  snap ;  and,  second,  fine  or  soft 


*  The  conclusion  of  Mr.  Kirkaldy  in  respect  to  cold  rolling  is  undoubtedly 
true  when  the  rolling  amounts  to  wire-drawing;  but,  when  the  compression 
of  the  surface  by  rolling  diminishes  the  sectional  area  in  greater  proportion 
than  it  extends  the  bar,  the  result,  according  to  the  experience  of  the 
Pittsburgh  manufacturers,  is  a  slight  increase  in  the  density  of  the  iron. 


RESISTANCE  TO  TENSION.  327 

iron,  being  more  uniform  in  quality,  can  be  more  depended  upon 
in  practice.  Hence  the  load  which  this  description  of  iron  can 
suspend  with  safety  may  approach  much  more  nearly  the  limit 
of  its  breaking-strain  than  can  be  attempted  with  the  harder  or 
coarser  sorts,  where  a  greater  margin  must  necessarily  be  left. 

"As  a  necessary  corollary  to  what  we  have  just  endeavored  to 
establish,  the  writer  now  submits,  in  addition,  that  the  working- 
strain  should  be  in  proportion  to  the  breaking-strain  per  square 
inch  of  fractured  area,  and  not  to  the  breaking-strain  per  square 
inch  of  original  area,  as  heretofore.  Some  kinds  of  iron  experi- 
mented on  by  the  writer  will  sustain  with  safety  more  than  double 
the  load  that  others  can  sustain,  especially  in  circumstances 
where  the  load  is  unsteady,  and  the  structure  exposed  to  concus- 
sions, as  in  a  ship  or  railway  bridge." 

Cast  Iron. 

Cast  iron  has  only  about  one-third  the  tensile  strength  of 
wrought  iron;  and  as  it  is  liable  to  air-holes,  internal  strains  from 
unequal  contraction  in  cooling,  and  other  concealed  defects, 
reducing  its  effective  area  for  tension,  it  should  never  be  used 
where  it  is  subjected  to  any  great  tensile  stress. 

STANDARD  SPECIFICATIONS  FOR  STRUCTURAL  CAST  IRON. — 
Except  where  chilled  iron  is  specified,  all  castings  shall  be  tough 
gray  iron,  free  from  injurious  cold-shuts  or  blow-holes,  true  to 
pattern,  and  of  a  workmanlike  finish.  Sample  pieces  one  inch 
square,  cast  from  the  same  heat  of  metal  in  sand  moulds,  shall 
be  capable  of  sustaining  on  a  clear  span  of  4  feet  8  inches  a  cen- 
tral load  of  500  pounds  when  tested  in  the  rough  bar. 

Structural  Steel.* 

The  strength  of  structural  steel  depends  largely  on  the  amount 
of  the  constituent  elements  that  are  associated  with  the  iron,  and 
each  of  which  affect  more  or  less  the  hardness  and  strength  of  the 
metal. 

The  principal  of  these  are  carbon,  manganese,  silicon,  phos- 
phorus, and  sulphur,  the  first-named  being  purposely  retained  as 
useful  or  necessary,  the  others  being  rejected,  as  far  as  practi- 

*  Mr.  James  Christie  in  "Steel  in  Construction,"  published  by  the  A.  &  P. 
Roberts  Company,  proprietors  of  the  Pencoyd  Iron  Works. 


32S  RESISTANCE  TO  TENSION. 

cable,  as  objectionable  when  in  excess  of  certain  minute  pro- 
portions. 

The  grade  and  character  of  steel  is  usually  known  by  the 
percentage  of  contained  carbon.  Steel  used  in  structures  usually 
varies  in  tensile  strength  from  55,000  to  70,000  Ibs.  per  square 
inch  of  section,  or  from  .10  to  .25  per  cent,  of  carbon. 

Table  II.  exhibits  the  physical  characteristics  of  open-hearth 
basic  steel  of  the  various  grades,  the  results  derived  from  an 
extensive  series  of  tests  indicating  the  tendency  of  a  total  average 
of  the  composition  hereafter  described  to  approximate  to  the 
figures  given  in  table. 

The  predominant  elements  other  than  carbon  averaged 
throughout  the  series  as  follows :  manganese,  .54 ;  phosphorus,  .05; 
sulphur,  .05  per  cent.  Any  increase  of  these  elements  is  attended 
with  an  increase  of  tensile  strength  and  reduced  ductility,  and 
vice  versa.  The  tensile  strength  of  the  steel  is  also  affected  to 
some  extent  by  the  temperature  at  which  it  is  finished,  arid  the 
rate  of  cooling,  these  influences  being  more  apparent  in  the 
grades  containing  highest  carbon.  Therefore  the  values  given 
have  only  a  general  significance,  and  individual  tests  may  vary 
widely  above  or  below  the  figures  in  the  table. 

For  Bessemer  or  open-hearth  acid  process  steel  the  tensile 
strength  will  ordinarily  be  greater  for  the  same  percentage  of 
carbon  given  in  this  table,  for  the  reason  that  the  proportions  of 
phosphorus  and  sulphur,  and  sometimes  manganese,  are  usually 
higher  than  in  open-hearth  basic  steel,  each  of  these  elements 
contributing  to  strength  and  hardness  in  the  steel. 

For  convenient  distinguishing  terms,  it  is  customary  to  classify 
steel  in  three  grades,  "mild  or  soft,"  "medium,"  and  "hard"; 
and  although  the  different  grades  blend  into  each  other,  so  that 
no  line  of  distinction  exists,  in  a  general  sense  the  grades  below 
.15  carbon  may  be  considered  as  "soft."  steel,  from  .15  to  .30  car- 
bon as  "medium,"  and  above  that  "hard"  steel.  Each  grade 
has  its  own  advantages  for  the  particular  purpose  to  which  it  is 
adapted.  The  soft  steel  is  well  adapted  for  boiler-plate  and  simi- 
lar uses,  where  its  high  ductility  is  advantageous.  The  medium 
grades  are  used  for  general  structural  purposes,  while  harder  steel 
is  especially  adapted  for  axles  and  shafts,  and  any  service  where 
good  wearing  surfaces  are  desired.  Mild  steel  has  superior  weld- 
ing property  as  compared  to  hard  steel,  and  will  endure  higher 
heat  without  injury.  Steel  below  .10  carbon  should  be  capable  of 
doubling  flat  without  fracture,  after  being  chilled  from  a  red  heat 


RESISTANCE  TO  TENSION.  329 

TABLE  II.— OPEN-HEARTH  BASIC  STEEL. 


Percentage 
of  carbon. 

Tensile  strength  in  pounds 
per  square  inch. 

Ductility. 

Ultimate 
strength. 

Elastic 
limit. 

Stretch  in 
8  inches. 

Reduction  of 
fractured  area. 

.08 

54,000 

32.500 

32  per  cent. 

60  per  cent. 

.09 

54,800 

33,000 

31 

58 

.10 

55,700 

33,500 

31 

57 

.11 

56,500 

34,000 

30 

56 

.12 

57,400 

34,500 

30 

55 

.13 

58,200 

35,000 

29 

54         ' 

.14 

59,100 

35,500 

29 

53 

.15 

60,000 

36,000 

28 

52 

.16 

60,800 

36,500 

28 

51 

.17 

61,600 

37,000 

27 

50 

.18 

62,500 

37.500 

27 

49         < 

.19 

63,300 

38,000 

26 

48 

.20 

64,200 

38,500 

26 

47 

.21 

65,000 

39,000 

25 

46         l 

.22 

65,800 

39,500 

25 

45 

.23 

66,600 

40,000 

24 

44 

.24 

67,400 

40,500 

24 

43 

.25 

68.200 

41,000 

23 

42 

in  cold  water.  Steel  of  .  1 5  carbon  will  occasionally  submit  to  the 
same  treatment,  but  will  usually  bend  around  a  curve  whose 
radius  is  equal  to  the  thickness  of  the  specimen;  about  90  per 
cent,  of  specimens  stand  the  latter  bending  test  without  fracture. 
As  the  steel  becomes  harder,  its  ability  to  endure  this  bending 
test  becomes  more  exceptional,  and  when  the  carbon  ratio 
becomes  .20,  little  over  twenty-five  per  cent,  of  specimens  will 
stand  the  last-described  bending  test.  Steel  having  about  .40 
per  cent,  carbon  will  usually  harden  sufficiently  to  cut  soft  iron 
and  maintain  an  edge. 

Elasticity  of  Steel. 

As  the  material  elongates  or  shortens  under  stress,  the  change 
of  length  is  directly  proportionate  to  the  stress,  and  the  material 
recovers  its  original  length  after  removal  of  the  stress,  until  the 
elastic  limit  is  reached,  when  changes  of  length  are  no  longer  regu- 


330  RESISTANCE  TO  TENSION. 

lar,  and  permanent  set  takes  place,  or  the  destruction  of  the 
material  has  begun. 

In  good  material  the  stress  at  elastic  limit,  for  either  tension  or 
compression,  is  usually  about  six-tenths  of  the  ultimate  tenacity. 

The  ductility  under  tensile  strength,  is  usually  measured  by  the 
total  elongation  in  a  given  length,  or  by  the  percentage  of  reduc- 
tion of  the  fractured  area,  or  by  both. 

The  elasticity  is  measured  by  the  change  of  length  under  stress 
below  the  elastic  limit  of  the  material.  The  elasticity  of  the 
various  grades  of  steel  are  practically  uniform,  that  is,  each 
material  will  exhibit  a  uniform  change  of  length  under  uniform 
stress  below  the  elastic  limit;  but,  as  the  elastic  limit  of  the 
higher  grades  is  greater  than  that  of  the  lower  or  softer  grades, 
the  former  will  elongate  or  shorten  to  a  greater  extent  than  the 
latter  before  its  elasticity  is  injured.  This  property  is  expressed 
by  a  modulus,  which  for  either  material  will  average  about 
29,000,000  Ibs.  That  is,  if  the  change  of  length  could  be  extended 
sufficiently,  it  would  require  29,000,000  Ibs.  per  square  inch  of 
section  to  double  the  original  length  under  tensile  strain,  or  to 
shorten  the  length  one-half  under  compression.  Therefore,  steel 
will  extend  or  shorten  ^^^-QQ-Q-Q-Q  part  of  its  normal  length  for 
every  pound  per  sectional  inch  in  change  of  load. 

Expausion  by  Heat. 


Soft  steel  or  iron  will  extend  about  r^Vinr  part  of  its  length  for 
each  degree  F.  of  elevation  of  temperature.  For  a  variation  in 
temperature  of  100  degrees  F.,  the  change  in  length  will  be  about 
one  inch  in  125  feet. 


Weight  or  Specific  Gravity  of  Steel. 

The  specific  gravity  of  steel  varies  according  to  the  purity  of 
the  metal,  and  also  according  to  the  degree  of  condensation 
imparted  by  the  process  of  rolling  or  forging. 

As  a  rule,  mild  steel  has  a  higher  specific  gravity  than  hard 
steel,  and  both  are  lower  than  perfectly  pure  iron,  but  about  two 
per  cent,  higher  than  ordinary  commercial  iron.  Structural  steel 
in  comparatively  small  sections,  having  the  composition  denoted 
in  the  previous  table  of  tensile  strength,  has  the  following  specific 
gravity,  corresponding  to  given  carbon  ratio : 


RESISTANCE  TO  TENSION.  331 


Carbon,  per  cent. 

Specific  gravity. 

Weight  per  cubic  foot 
in  pounds. 

.10 

7.860    ' 

489.92 

.20 

7.858 

489.80 

.30 

7.856 

489.67 

In  the  form  of  rolled  beams  and  largest  commercial  sections  the 
weight  will  be  slightly  less  than  this. 

The  weights  for  steel  sections  given  in  this  book  are  all  calcu- 
lated on  a  basis  of  489.6  Ibs.  per  cubic  foot,  or  the  sectional  area 
in  square  inches  multiplied  by  3.4  equals  the  weight  in  pounds 
per  foot. 

Working  Strength  of  Steel. 

In  designing  steel  roof  trusses  engineers  generally  allow  about 
16,000  Ibs.  per  square  inch  for  the  working  tensile  strength  of 
steel  shapes,  such  as  angles  or  channels,  and  about  18,000  Ibs.  for 
round  or  flat  bars,  when  the  quality  of  the  material  is  to  be  tested, 
and  it  is  known  that  the  work  will  be  first-class.  For  wind 
bracing  a  stress  of  20,000  Ibs.  is  often  used.  (See  page  268  of 
Freitag's  ". Architectural  Engineering.") 

Where  the  material  is  not  to  be  tested,  the  author  would  not 
recommend  the  use  of  greater  unit  strains  than  14,000  Ibs.  for 
shapes  and  15,000  Ibs.  for  bars.  For  truss-rods  obtained  of  an 
ordinary  blacksmith,  and  which  have  perhaps  been  welded,  not 
over  12,500  Ibs.  should  be  used. 

The  "New  York  and  Chicago  building  laws  fix  the  limit  of  tensile 
stress  in  steel  at  16,000  Ibs. ;  the  Boston  law  at  15,000  Ibs. 

MANUFACTURERS'  SPECIFICATIONS  GOVERN- 
ING THE  PHYSICAL  PROPERTIES  OF 
STRUCTURAL  STEEL. 

Revised  Oct.  23,  1896. 
PROCESS    OF   MANUFACTURE. 

(1)  Steel  may  be  made  by  either  the  open-hearth  or  Bessemer 
process. 

TEST-PIECES. 

(2)  All  tests  and  inspections  shall  be  made  at  place  of  manufac- 
ture prior  to  shipment. 


332 


RESISTANCE  TO  TENSION. 


(3)  The  tensile  strength,  limit  of  elasticity,  and  ductility  shall 
be  determined  from  a  standard  test-piece  cut  from  the  finished 
material.  The  standard  shape  of  the  test-piece  for  sheared 
plates  shall  be  as  shown  by  the  following  sketch: 


1  TO  3  RADIUS 


PIECE  TO  BE  THE  SAME  THICKNESS  AS  THE  PLATE 


On  tests  cut  from  other  material  the  test-piece  may  be  either 
the  same  as  for  plates,  or  it  may  be  planed  or  turned  parallel 
throughout  its  entire  length.  The  elongation  shall  be  measured 
on  an  original  length  of  8  inches,  except  when  the  thickness  of  the 
finished  material  is  %  inch  or  less,  in  which  case  the  elongation 
shall  be  measured  in  a  length  equal  to  sixteen  times  the  thickness  ; 
and  except  in  rounds  of  f  inch  or  less  in  diameter,  in  which  case 
the  elongation  shall  be  measured  in  a  length  equal  to  eight  times 
the  diameter  of  section  tested.  Two  test-pieces  shall  be  taken 
from  each  melt  or  blow  of  finished  material,  one  for  tension  and 
one  for  bending. 

ANNEALED  TEST  PIECES. 

(4)  Material  which  is  to  be  used  without  annealing  or  further 
treatment  is  to  be  tested  in  the  condition  in  which  it  comes  from 
the  rolls.     When  material  is  to  be  annealed  or  otherwise  treated 
before  use,  the  specimen  representing  such  material  is  to  be  sim- 
ilarly treated  before  testing. 

MARKING. 

(5)  Every  finished  piece  of  steel  shall  be  stamped  with  the 
blow  or  melt  number,  and  steel  for  pins  shall  have  the  blowT  or 
melt  number  stamped  on  the  ends.     Rivet  and  lacing  steel,  and 
small  pieces  for  pin  plates  and  stiffeners,  may  be  shipped  in 
bundles  securely  wired  together,  with  the  blow  or  melt  number 
on  a  metal  tag  attached. 


FINISH. 


(6)  Finished  bars  must  be  free  from  injurious  seams,  flaws, 
cracks,  and  have  a  workmanlike  finish. 


or 


RESISTANCE  TO  TENSION.  333 


CHEMICAL    PROPERTIES. 

(7)  Steel   for   buildings,    train   sheds,    highway   bridges   and 
similar  structures  shall  not  contain  more  than  0.10  per  cent,  of 
phosphorus.     Steel  for  railway  bridges  shall  not  contain  more 
than  0.08  per  cent,  of  phosphorus. 

GRADES  OF  STEEL. 

(8)  Structural  steel  shall  be  of  three  grades :  RIVET,  SOFT,  and 
MEDIUM. 

RIVET    STEEL. 

(9)  Ultimate  strength,  48,000  to  58,000  pounds  per  square  inch. 
Elastic  limit,  not  less  than  one-half  the  ultimate  strength. 
Elongation,  26  per.  cent. 

Bending  test,  180  degrees  flat  on  itself,  without  fracture  on  out- 
side of  bent  portion. 

SOFT    STEEL. 

(10)  Ultimate  strength,  52,000  to  62,000  pounds  per  square 
inch. 

Elastic  limit  not  less  than  one-half  the  ultimate  strength. 
Elongation,  25  per  cent. 

Bending  test,  180  degrees  flat  on  itself,  without  fracture  on  out- 
side of  bent  portion. 

MEDIUM    STEEL 

(11)  Ultimate  strength,  60,000  to  70,000  pounds  per  square 
inch. 

Elastic  limit,  not  less  than  one-half  the  ultimate  strength. 
Elongation,  22  per  cent. 

Bending  test,  180  degrees  to  a  diameter  equal  to  thickness  of 
piece  tested,  without  fracture  on  outside  of  bent  portion. 

PIN  STEEL. 

(12)  Pins  made  from  either  of  the  above-mentioned  grades  of 
steel  shall,  on  specimen  test-pieces  cut  at  a  depth  of  one  inch  from 
surface  of  finished  material,  fill  the  physical  requirements  of  the 
grade  of  steel  from  which  it  is  rolled  for  ultimate  strength,  elastic 
limit,  and  bending,  but  the  required  elongation  shall  be  decreased 
5  per  cent. 


334  RESISTANCE  TO  TENSION. 

EYE-BAR    STEEL. 

(13)  Eye-bar  material,  1 J  inches  and  less  in  thickness,  made  of 
either  of  the  above-mentioned  grades  of  steel,  shall,  on  test- 
pieces  cut  from  finished  material,  fill  the  requirements  of  the 
grade  of  steel  from  which  it  is  rolled.  For  thicknesses  greater  than 
1J  inches  there  will  be  allowed  a  reduction  in  the  percentage  of 
elongation  of  1  per  cent,  for  each  J  of  an  inch  increase  of  thick- 
ness, to  a  minimum  of  20  per  cent,  for  medium  steel  and  22  per 
cent,  for  soft  steel. 

FULL-SIZE    TEST    OF    STEEL   EYE-BARS. 

(14)  Full-size  test  of  steel  eye-bars  shall  be  required  to  show 
not  less  than  10  per  cent,  elongation  in  the  body  of  the  bar,  and 
tensile  strength  not  more  than  5,000  pounds  below  the  minimum 
tensile  strength  required  in  specimen  tests  of  the  grade  of  steel 
from  which  they  are  rolled.     The  bars  will  be  required  to  break 
in  the  body,  but  should  a  bar  break  in  the  head,  but  develop  10 
per  cent,  elongation  and  the  ultimate  strength  specified  it  shall 
not  be  cause  for  rejection,  provided  not  more  than  one-third  of 
the  total  number  of  bars  tested  break  in  the  head ;  otherwise  the 
entire  lot  will  be  rejected. 

VARIATION   IN   WEIGHT. 

(15)  The  variation  in  cross-section  of  weight  of  more  than  2J 
per  cent,  from  that  specified  will  be  sufficient  cause  for  rejection, 
except  in  the  case  of  sheared  plates  which  will  be  covered  by  the 
following  permissible  variations: 

a.  Plates  12  J  pounds  per  square  foot,  or  heavier,  when  ordered 
to  weight,  shall  not  average  more  than  2J  per  cent,  variation 
above,  or  2J  per  cent,  below  the  theoretical  weight. 

b.  Plates  under  12  J  pounds  per  square  foot,  when  ordered  to 
weight,  shall  not  average  a  greater  variation  than  the  following : 

Up  to  75  inches  wide,  2  J  per  cent,  above,  or  2  J  per  cent,  below 
the  theoretical  weight. 

75  inches  and  over,  5  per  cent,  above,  or  5  per  cent,  below  the 
theoretical  weight. 

c.  For  all  plates  ordered  to  gauge,  there  will  be  permitted  an 
average  excess  of  weight  over  that  corresponding  to  the  dimen- 
sions on  the  order  equal  in  amount  to  that  specified  in  the  fol- 
lowing table. 


RESISTANCE  TO   TENSION. 


335 


TABLE  OF  ALLOWANCES  FOR  OVERWEIGHT  FOR 
RECTANGULAR  PLATES  WHEN  ORDERED  TO 
GAUGE. 

THE  WEIGHT  OF  ONE  CUBIC  INCH  OF  ROLLED  STEEL  IS  ASSUMED 
TO  BE  .2833  POUND. 

(Plates  J"  and  over  in  thickness.) 


Width  of  plate. 

Thickness 
of  plate. 

Up  to  57  inches. 

75  in.  to  100  in. 

Over  100  inches. 

i  inch 

10  percent. 

14  percent. 

18  percent. 

%0 

8 

12 

16 

f 

7 

10 

13 

Jfe 

6 

8 

10 

^ 

5 

7 

9 

% 

44 

64 

84 

I 

4 

6 

8 

Over  f 

34 

5 

64 

For  Ordinary  Building  Construction  the  following  form  of  speci- 
fication for  the  quality  and  testing  of  the  steel  work  is  recom- 
mended : 


Specifications  for  Structural  Steel  Work. 

Material  and  Workmanship. — The  entire  structural  frame- 
work as  indicated  by  the  framing  plans,  or  as  specified,  is  to  be 
of  wrought  steel,  of  quality  hereinafter  designated ;  all  material 
to  be  provided  and  put  in  place  by  this  contractor  unless  specific- 
ally stated  to  the  contrary.  All  work  to  be  done  in  a  neat  and 
skilful  manner,  as  per  detail  or  specified,  and  if  not  detailed  or 
specified,  as  directed  by  the  superintendent. 

Quality  and  Material. — Steel  may  be  made  by  either  the 
Bessemer  or  open-hearth  process,  but  must  be  uniform  in  quality, 
and  in  no  case  contain  over  -^  of  one  per  cent,  of  phosphorus. 

The  grade  of  steel  used  (except  for  rivets)  shall  fill  the  following 
requirements  when  tested  in  small  specimens: 

[He re  should  be  inserted  section  (11)  of  the  foregoing  specifica- 
tions.] 

Inspection. — All  steel  work  is  to  be  inspected  from  the  melt  to 
final  delivery  of  finished  material  on  board  cars.  The  inspection 


336  RESISTANCE  TO  TENSION. 

will  include  surface,  mill,  and  shop  inspection  by  an  inspector 
satisfactory  to  the  architect  or  his  engineer,  to  whom  all  reports 
are  to  be  made.  No  work  shall  be  delivered  until  approved  and 
stamped  by  the  inspector.  All  inspection  shall  be  at  the  expense 
of  this  contractor. 

Tests. — [Sections  (3)  and  (4)  in  preceding  specification  to  be 
inserted  here.] 

Eye-bars. — To  determine  the  strength  of  the  eyes  two  full-size 
eye-bars  with  eyes  shall  be  tested  to  destruction.  These  tests 
shall  show — [Section  14  in  preceding  specification  to  follow.] 

Finish. — Finished  bars  must  be  free  from  injurious  seams, 
flaws,  or  cracks,  and  have  a  workmanlike  finish. 

Rivet  Steel. — [Same  as  section  (9),  preceding  specification.] 

Rivets. — The  pitch  of  rivets  shall  never  be  less  [than  1J"  nor 
more  than  6",  while  the  minimum  distance  from  the  centre  of 
any  rivet  to  the  edge  of  the  shape  shall  be  \\".  'No  rivets  to  be 
used  in  tension.  An  excess  of  25  per  cent,  shall  be  allowed  in 
proportioning  field  rivets. 

Rivet-holes  may  be  punched  or  drilled,  but  -  must  not  be 
more  than  Ty  larger  than  diameter  of  rivet. 

Rivet-holes  must  be  accurately  spaced,  as  drift-pins  will  be 
allowed  for  assembling  only. 

The  rivets  shall  completely  fill  the  holes,  with  full  heads  con- 
centric with  the  rivets,  and  in  full  contact  with  the  surface  of 
the  metal. 

Tie-bars,  Eye-bars,  Screw   Ends,  Clevises,  Sleeve- 
nuts,  and  Turn-buckles. 

The  best  shape  for  an  iron  or  steel  tie  is  largely  determined  by 
the  manner  in  which  the  tie  is  to  be  secured  at  the  ends.  If  the 
tie  is  to-be  secured  by  rivets,  either  channels  or  angles  are  gen- 
erally used,  except  where  only  a  very  small  bar  is  required,  in 
which  case  a  plain  rectangular  bar  may  be  used.  In  figuring  the 
strength  of  such  ties,  it  is  customary  to  use  the  net  sectional  area 
of  the  tie  at  the  point  where  the  area  is  most  reduced  by  rivet- 
holes. 

For  figuring  the  reduction  in  sectional  area  by  rivet-  or  bolt- 
holes,  Table  XI.  of  this  chapter  will  be  found  very  convenient. 

Eye-bars. — For  pin-connected  trusses,  the  ties  almost  invars 
ably  consist  of  eye-bars,  i.e.,  a  rectangular  bar  with  an  eye  at 
each  end.  "  Eye-bars  are  now  generally  made  of  mild  steel,  of 


RESISTANCE  TO   TENSION.  337 

an  ultimate  strength  of  from  56,000  to  66,000  Ibs.  per  square 
inch,  the  methods  of  manufacture  securing  a  more  satisfactory 
and  reliable  product  from  that  metal  than  from  iron.  Steel  eye- 
bars  are  made  by  forging  or  upsetting  the  eye  or  head  of  the  bar 
in  a  die,  and  subsequently  reheating  and  annealing  the  finished 
bars  previous  to  boring  the  pin-holes.  Wrought-iron  bars  are 
made  by  piling  and  welding,  which  is  always  an  unreliable 
process. 

For  economy  in  dies,  the  same  head  or  eye  is  used  for  two  or 
three  different  pin-holes,  and  for  this  reason  it  is  often  cheaper 
to  use  a  slightly  larger  head  than  would  be  really  necessary  for 
strength,  rather  than  to  have  a  special  die  made  to  order.  Table 
V.  gives  the  principal  dimensions  of  the  standard  sizes  of  steel 
eye-bars  manufactured  by  the  Edge  Moor  Bridge  Works.  Eye- 
bars  made  by  other  companies  vary  slightly  from  those  dimen- 
sions and  from  each  other,  but  not  to  any  great  extent.  The 
thickness  of  the  bar  for  any  given  width  should  not  be  less  than 
the  minimum  thickness  given  in  the  table,  because  thinner  bars 
are  difficult  to  manufacture,  and  are  liable  to  buckle  in  the  head 
when  under  strain.  "The  thickness  of  the  bar  may  be  made 
anything  greater  than  this  minimum,  but  a  thickness  of  two 
inches  for  bars  six  inches  wide  and  under  is  rarely  exceeded." 
The  thicker  the  bar  the  greater  will  be  the  bending  moment  on 
the  pin. 

"It  is  always  better  to  use  an  eye  the  diameter  of  which  is 
about  two  and  one-quarter  times  the  width  of  the  bar.  In 
extreme  cases  the  diameter  of  the  eye  may  be  made  two  and 
one-half  times  the  width  of  the  bar,  but  it  is  never  desirable  to 
exceed  this,  as  the  cost  and  difficulty  of  manufacture  increase 
rapidly  if  larger  eyes  are  used.  Eye-bars  are  now  made  as  large 
as  12X3  inches,  with  eyes  27  to  30  inches  in  diameter."* 


•Fig.  1. — Eye-bar  with  screw  ends  for  sleeve-nut  or  turn-buckle. 


Eye-bars  are  sometimes  made   with  upset  screw  ends  and 
sleeve-nuts,  or  turn-buckles  in  the  centre,  as  shown  by  Fig.  1. 

*  C.  W.  Bryan,  C.E.,  Engineer  of  the  Edge  Moor  Bridge  Works. 


338 


RESISTANCE   TO   TENSION. 


Light  square  rods,  secured  to  large  pins,  are  often  made  with  loop 
eyes,  as  shown  by  Figs.  2  and  3,  as  for  such  eyes  the  diameter  of 
the  pin  is  not  limited. 

Loop  eyes  are  made  by  welding,  and  as  satisfactory  welds  can- 


Fig.  2. — Loop-eyes  and  sleeve-nuts. 

not  be  generally  secured  with  steel,  loop-ended  rods  are  usually 
made  of  wrought  iron. 

When  two  single  tie-rods  balance  each  other  on  a  pin,  to  avoid 
eccentricity  one  of  the  rods  must  either  have  a  clevis  on  the  end, 


Fig.  3. — Forked  loop. 

as  shown  at  the  head  of  Table  VI.,'  or  a  forked  loop,  as  in  Fig.  3. 
Clevises  also  afford  means  of  adjusting  the  length  of  the  tie. 

Sleeve-nuts  and  Turn-buckles. — For  adjusting  the  length  of  the 
tie-bars  or  rods,  which  pass  over  a  pin,  sleeve-nuts  or  turn- 
buckles  are  used,  and  even  when  the  end  of  the  rod  is  held  by  a 
nut,  as  in  wooden  trusses,  it  is  often  desirable  to  place  the  turn- 
buckle  in  the  centre  of  the  rod,  for  adjusting  after  the  truss  has 
seasoned,  as  it  is  then  generally  inconvenient  if  not  impossible 
to  get  at  the  nut.  The  open  turn-buckle,  Table  VII.,  possesses 
the  advantages  that  the  ends  of  the  rod  are  visible,  and  it  may  be 
easily  inspected  and  the  position  of  the  rods  noted;  also,  that 
they  may  be  adjusted  by  running  a  bar  through  the  link.  Tables 
VII.  and  VIII.  give  dimensions  of  sleeve-nuts  and  turn-buckles 
which,  while  not  the  same  with  all  manufacturers,  are  very 
nearly  so. 

Upset  Screw  Ends. — When  a  screw  thread  is  cut  on  a  rod  or 
bolt,  the  strength  of  the  rod  or  bolt  is  measured  bv  the  sectional 


RESISTANCE  TO  TENSION.  339 

area  at  the  root  of  the  thread,  and  consequently  there  is  a  con- 
siderable excess  of  metal  in  the  body  of  the  rod  that  is  practically 
wasted.  For  long  rods,  therefore,  and  especially  where  there 
are  many  of  a  kind,  the  end  of  the  rod  is  enlarged  or  upset  by 
forging,  so  that,  when  the  screw  is  cut,  the  diameter  of  the  screw 
at  the  root  of  the  thread  is  left  a  little  larger  than  the  body  of  the 
rod.  Frequent  trials  with  such  rods  have  proven  that  they  will 
pull  apart  in  tension  anywhere  else  but  in  the  screw ;  the  threads 
remaining  perfect,  and  the  nut  turning  freely  after  having  been 
subjected  to  such  a  severe  test.  By  this  means  the  net  section 
required  in  tension  is  made  available  with  the  least  excess  of 
material,  and  no  more  dead  weight  is  put  upon  the  structure 
than  is  actually  needed  to  carry  the  loads  imposed. 

Only  the  larger  machine  shops,  however,  are  equipped  for  up- 
setting, so  that  in  small  towns  and  cities  it  is  often  necessary  to 
send  to  a  considerable  distance  for  upset  rods.  For  this  reason 
it  is  often  cheaper  to  use  a  slightly  larger  rod  without  upsetting, 
than  to  specify  the  theoretical  size  with  upset  ends.  Upset  rods 
also  require  a  larger  hole  to  pass  through. 

Dimensions  of  upset  screw  ends  are  given  in  Table  IV. 

Tables. — The  following  tables  will  be  found  useful  when  design- 
ing ties  of  steel  or  iron,  or  for  drawing  turn-buckles,  sleeve-nuts, 
clevises,  etc.  The  strength  of  the  plain  rods  in  Table  III.  are 
based  on  the  sectional  area  at  the  root  of  the  thread. 


340 


RESISTANCE  TO  TENSION. 


TABLE  III.— STRENGTH   OF  ROUND   RODS   OF  IRON 
AND  STEEL. 


.2 

&  03 

-M  O> 

0>rCj 

11 
ffi 

NOT  UPSET. 
Allowed  strain  per  sq.  in.* 

UPSET. 
Allowed  strain  per  sq.  in.* 

10  ,000  Ibs. 

12,5001bs. 

15,000  Ibs. 

10  ,000  Ibs. 

12,500  Ibs. 

15,000  Ibs. 

i 

268 

335 

402 

491 

613 

736 

k 

452 

.  565 

678 

767 

958 

1150 

i 

679 

848 

1,018 

1,104 

1,380 

1,656 

% 

929 

1,160 

1,393 

1,503 

1,878 

2,254 

* 

1,256 

1,570 

1,884 

1,963 

2,453 

2,944 

% 

1,618 

2,022 

2,427 

2,485 

3,106 

3,727 

i 

1,963 

2,453 

2,944 

3,068 

3,835 

4,600 

3,000 

3,750 

4,500 

4,418 

5,520 

6,627 

i- 

4,200 

5,250 

6,300 

6,013 

7,516 

9,020 

i 

5,430 

6,780 

8,140 

7,854 

9,815 

11,780 

H 

6,860 

8,570 

10,290 

9,940 

12,425 

14,900 

ii 

8,850 

11,060 

13,270 

12,270 

15,330 

18,400 

if 

10,700 

13,370 

16,050 

14,840 

18,550 

22,260 

ii 

12,870 

16,080 

19,300 

17,670 

22,080 

26,500 

if 

15,000 

18,750 

22,500 

20,730 

25,910 

31,090 

if 

17,600 

23,000 

26,400 

24,050 

30,060 

36,070 

*i 

20,200 

25,250 

30,300 

27,610 

34,500 

41,400 

2 

22,800 

28,500 

34,200 

31,420 

39,270 

47,130 

2J 

26,400 

33,000 

39,600 

35,460 

44,320 

53,190 

2i 

30,000 

37,500 

45,000 

39,760 

49,700 

59,680 

2f 

33,500 

41,870 

50,250 

44,300 

55,370 

66,450 

2l 

37,200 

46,500 

55,800 

49,080 

61,350 

73,620 

2| 

46,400 

58,000 

69,800 

59,390 

74,230 

89,080 

3 

54,000 

67,500 

81,000 

70,680 

88,350 

106,000 

3i 

65,000 

81,250 

97,500 

82,950 

103,690 

124,400 

31 

75,400 

94,250 

113,100 

96,210 

120,260 

144,300 

3J 

85,600 

107,000 

128,400 

110,450 

138,060 

165,600 

4 

99,000 

123,750 

148,500 

125,660 

157,000 

188,490 

4i 

113,400 

141,700 

170,100 

141,800 

177,250 

212,700 

41 

126,000 

157,500 

189,000 

159,000 

198,750 

238,500 

4f 

141,800 

177,250 

212,700 

177,200 

221,500 

265,800 

5 

157,600 

197,000 

236,400 

196,300 

245,370 

298,400 

5i 

175,900 

219,870 

263,850 

216,400 

270,500 

324,000 

5* 

192,600 

240,750 

288,900 

237,500 

296,800 

356,000 

5i 

212,300 

265,370 

318,400 

259,600 

324,500 

389,000 

6 

231,000 

288,750 

346,500 

282,700 

353,300 

424,000 

"'  For  first-class  work  and  material  12,500  Ibs.  may  be  allowed  for  iron 
and  15,000  Ibs.  for  steel.  If  the  rods  are  to  be  welded  or  are  made  by  an 
ordinary  blacksmith  use  10,000  Ibs.  for  iron  and  12,500  Ibs.  for  steel. 


RESISTANCE  TO  TENSION. 


341 


TABLE     IV.— STANDARD     PROPORTIONS     OF     UPSET 
SCREW-ENDS   FOR   ROUND    AND    SQUARE    BARS. 


<0 

rg 

ROUND  BARS. 

SQUARE  BARS. 

Is- 

"S 

.a 

j 

1  , 

o> 

"§ 

pd- 

0) 

J5 

02 

££ 

fH 

n 

a  . 
t4_  a 

| 

111 

*O  o* 

H^ 

££ 

o 

ft 

0>   02    SH 

O  V 

M^ 

Ok 

«^^  « 

<0  <+4 

^    <u 

'o'o 

•73 

°   °    O 

®  w 

O*O 

•3 

°  °  o 

"8  ° 

11 

oJ 

1! 

g 

I 

||| 

Q)    S-" 

|B 

11 

c3 

pi 

5 

3 

5 

H 

P 

S 

a~ 

H 

W 

Inches 

Inches 

Inches. 

No. 

Per  cent 

Inches 

Inches. 

No. 

Per  cent 

\ 

"4 

0.620 

10 

54 

| 

0.620 

10 

21 

% 

1 

0.620 

10 

21 

0.731 

9 

33 

f 

i 

0.731 

9 

37 

1 

0.837 

S 

41 

l^ 

0.837 

8 

48 

1 

0.837 

8 

17 

f 

1 

0.837 

8 

25 

IJL 

0.940 

7 

23 

H 

0.940 

7 

34 

It 

1.065 

7 

35 

| 

It 

1.065 

7 

48 

If 

1.160 

6 

38 

H 

1.065 

7 

29 

If 

1.160 

6 

20 

1 

If- 

1  .  160 

6 

35 

l-i 

1.284 

6 

29 

1% 

if 

1.160 

6 

19 

If 

1.389 

5} 

34 

1| 

11 

1  .  284 

6 

30 

If 

1.389 

5J 

20 

1.284 

6 

17 

If 

1.490 

5 

24 

it 

if 

1.389 

6} 

23 

if 

1.615 

5 

31 

if 

1.490 

5 

29 

1| 

1.615 

5 

19 

if 

if 

1.490 

5 

18 

2 

1.712 

44- 

22 

1# 

H 

1.615 

5 

26 

2J 

1.837 

4| 

28 

1| 

2 

1.712 

41- 

30 

2| 

1.837 

4| 

18 

2 

1.712 

4J 

20 

2i 

1.962 

24 

If 

2-1 

1.837 

41 

28 

2| 

2.087 

4^ 

30 

2* 

1.837 

4J 

18 

21 

2.087 

4J 

20 

If 

21 

1.962 

4J 

26 

2* 

2.175 

4 

21 

21 

1.962 

4} 

17 

2f 

2.300 

4 

26 

11 

2| 

2.087 

4} 

24 

2f 

2.300 

4 

18 

1% 

2J 

2.175 

4 

26 

2f 

2.425 

4 

23 

2 

2i 

2.175 

4 

18 

2| 

2.550 

4 

28 

2^6 

2| 

2.300 

4 

24 

21- 

2.550 

4 

20 

2i 

21 

2.300 

4 

17 

3 

2.629 

3J 

20 

2% 

2f 

2.425 

4 

23 

3J 

2.754 

3i 

24 

342  RESISTANCE  TO  TENSIO^. 

TABLE   IV.— UPSET  SCREW-ENDS— (concluded). 


r§ 

ROUND  RARS. 

SQUARE  BARS. 

o    . 

-gs 

"S 

•*» 

^ 

f-d 

o 

"§     • 

^ 

s 

p"^ 

en 
C, 

£*§ 

o 

c 

O     I 

I* 

ll 

1 

'-£  ^  P 

"of 

2? 

43  £ 

1 

£  &  * 

Sl-2 

J.I 

Oi  ^ 

I 

III 

QJ   W 

_o>  £ 

'o'o 

•i 

O  w  <u 

<U   <£ 

"o1© 

OQ 

'o'o  o" 

•8*0 

p 

si 

i 

w  ®  o 

~£   O 
fl    02 

il 

c3  O 

1 

pfl 

5 

3 

p 

H 

^§ 

P 

5" 

H 

H 

Inches 

Inches 

Inches 

No. 

Per  cent 

inches 

Inches 

No. 

Per  cent 

2T 

91 

^ 

2.550 

4 

28 

3! 

2.754 

3J 

18 

2% 

2J 

2.550 

4 

22 

2.879 

22 

2f 

3 

2.629 

3J 

23 

3f 

3.004 

31 

26 

3* 

2.754 

3J 

28 

3} 

3.004 

3i 

19 

21 

3i 

2  .  754 

3^ 

21 

3} 

3.100 

31 

21 

2% 

3i 

2.879 

3i 

26 

3| 

3.225 

3i 

24 

2f 

3i 

2.879 

3i 

20 

31 

3  .  225 

3i 

19 

2% 

3| 

3.004 

3i 

25 

3f 

3.317 

3 

20 

2J 

3| 

3.004 

3i 

19 

3| 

3.442 

3 

23 

2% 

3i 

3  .  100 

3i 

22 

3.442 

3 

18 

2^1 

3| 

3.225 

3i 

26 

4 

3.567 

3 

21 

2% 

3f 

3.225 

3i 

21 

4J 

3.692 

3 

24 

3 

3| 

3.317 

3 

22 

4* 

3.692 

3 

19 

34 

3.442 

3 

21 

4f 

3.923 

2$ 

24 

3i 

4 

3  .  567 

3 

20 

4i 

4.028 

2f 

21 

3f 

4J 

3.692 

3 

20 

4| 

4.153 

2f 

19 

3^ 

4J 

3.798 

2| 

18 

3f 

4i 

4.028 

2f 

23 

3| 

4f 

4.153 

2f 

23 

4.255 

2f 

21 

REMARKS.  —  As  upsetting  reduces  the  strength  of  iron,  bars  having  the 
same  diameter  at  root  of  thread  as  that  of  the  bar  invariably  break  in  the 

screw-end,  when  tested  to  destruction,  without  developing  the  full  strength 

of  the  bar.     It  is  therefore  necessary  to  make  up  for  this  loss  in  strength 
by  an  excess  of  metal  in  the  upset  screw-ends  over  that  in  the  bar. 

The  above  table  is  the  result  of  numerous  tests  on  finished  bars  made 

at  the  Keystone  Bridge  Company's  Works  in  Pittsburgh,  and  gives  pro- 
portions that  will  cause  the  bar  to  break  in  the  body  in  preference  to  the 

upset  end. 

The  screw-threads  in  above  table  are  the  Franklin  Institute  standard. 

To  make  one  upset  end  for  five  inches  length  of  thread  allow  six  inches 

length  of  rod  additional. 

RESISTANCE  TO   TENSION. 


343 


TABLE  V.— STEEL  EYE-BARS. 
EDGE  MOOR  BRIDGE  WORKS'  STANDARD. 


A 

Width 
of  bo  ly 
of  bar. 

T 
Minimum 
thickness 
of  bar. 

E 
Diameter 
of  head  of 
bar. 

D 

Diameter 
of  largest 
pin-hole. 

Sectional 
area  of  the 
head  on  line 
S-S  in  excess 
of  that  in 

Safe  strength 
at  15,000 
Ibs.  per 
sq.  in. 

body  of  bar. 

Inches. 

Inches. 

Inches. 

Inches. 

Per  cent. 

Pounds. 

2 

} 

44 

if 

33 

15,000 

2 

i 

54 

2J 

33 

15,000 

2* 

i 

54 

2i 

33 

23,430 

2* 

64 

3J 

33 

23,430 

3 

J 

6i 

21 

33 

33,750 

3 

| 

8 

4 

33 

33,750 

3 

9 

5 

33 

33,750 

4 

| 

9i 

4i 

33 

45,000 

4 

1 

10* 

54 

33 

45,000 

4 

i 

111 

6* 

33 

45,000 

5 

I 

114 

4f 

37 

56,250 

5 

t 

12i 

51 

37 

56,250 

5 

i 

13" 

6* 

37 

75,000 

5 

i 

14 

7f 

37 

75,000 

6 

£ 

134 

5} 

37 

78,750 

6 

1 

144 

61 

37 

78,750 

6 

i 

154 

7i 

37 

90,000 

7 

% 

154 

si 

40 

98,400 

7 

% 

17 

71 

40 

98,400 

8 

i 

17 

5f 

40 

120,000 

8 

i 

18 

61 

40 

120,000 

8 

i 

19 

8 

40 

120,000 

9 

14 

19* 

7 

40 

151,875 

9 

1* 

214 

9 

40 

151,875 

9 

H 

22! 

10 

1PS.  750 

10 

il 

24  1 

105 

200,250 

The  size  of  head  given  is  the  size  of  die.     The  size  of  finis 

led  head  will 

overrun  this  about  *4"  '.     Eye-bars  are  hydraulic  forged  without  the  addi- 

tion of  extraneous  metal  and  without  buckles  or  welds.     The  heads  on 

eye-bars  are  finished  of  the  same  thickness  "T"  as  body  of  bar. 

344 


RESISTANCE  TO  TENSION. 


TABLE    VI.— STANDARD    CLEVIS    NUTS. 
THE  CARNEGIE  STEEL  COMPANY,  LIMITED. 


(Distance  H  can  be  made  to  suit  connections.) 


Diam- 
eter of 
round 
bar. 


A 

Upset 
screw 
end  for 
round 
bar. 


Side  of 
quare 
bar. 


A 

Upset 
screw 
end  for 
square 
bar. 


B 

Diam- 

eter of 

eye. 


L'gth 

of 
fork. 


D 

L'gth 

of 
thread 


E 

Thick- 

ness of 

bar  in 

fork. 


Width 
of  bar 


fork. 


H* 

1% 
If- 

1% 
11 


2% 
2} 


2% 

2* 

2,Ve 

21 

2% 

2} 

2% 

2| 

2% 


If 
If 

2$ 
2 


2| 


2f 

2f 

2f 

2J 

2* 

3 

3J 


3f 
31 
3f 
31 


H/ 
if 


2f 
2| 


2f 


2J- 


21 
2% 


6| 

6i 
64 
6| 

7"' 

7 

7 

7 

8 

8 

8 

8 

8 

8 

S| 

sf 

8i 


2 

21 

21 

21 

21 

2| 

2? 


3* 
31 
31 
31 
31 


4i 
4i 


If 
2i 
2i 


21 
2f 

2f 
21 


3i 
3f 

3f 
3| 

3§ 
3f 
3f 


*  This  clevis  used  for  all  smaller  bars. 


RESISTANCE  TO  TENSION. 
TABLE  VII.— TURNBUCKLES. 


345 


D.  Size  =  diameter  of  screw. 

A.  Length  in  clear  between  heads. 

B.  Length  of  tapped  heads  =  1£D. 

C.  Total  length  of  buckle. 

L.  Total  length  of  buckle  and  stub  ends  when  open. 


Size 

A 

B 

C 

L 

Size 

A 

B 

C 

L 

D 

D 

I 

G 

% 

74 

22 

1} 

6 

2J 

Hi 

28 

% 

6 

2%2 

7« 

22 

H 

6 

2% 

11| 

29 

\ 

6 

1 

74 

22 

2 

6 

3 

12 

29 

% 

f> 

2%2 

7% 

22 

21 

6 

3.% 

12| 

29 

1 

6 

% 

7J 

22 

2| 

6 

3f 

12f 

30 

1 

6 

H 

Si 

23 

21 

6 

3« 

13J 

31 

f 

6 

1% 

8f 

24 

2} 

6 

3| 

Wi 

32 

1 

6 

1} 

9 

25 

2f 

6 

3« 

13| 

32 

I* 

6 

1% 

9f 

25 

2| 

6 

4j 

141- 

33 

u 

6 

if 

91 

26 

2| 

6 

4« 

14f 

33 

it 

6 

*« 

io| 

27 

3 

6 

4* 

15 

34 

H 

6 

2* 

10* 

27 

3f 

6 

4 

15! 

36 

if 

6 

2Ji^ 

loj 

28 

3j 

6 

5i 

16* 

37 

Lengths  given  above,  are  standard  for  bridge,  roof,  and  ordi- 
nary truss  buckles. 

They  have  a  guaranteed  strength  of  60,000  pounds  per  square 
inch  of  section  of  bolt  at  bottom  of  thread.  Stub  bolfc  ends  are 
made  of  good  bridge  iron  having  tensile  strength  of  50,000  pounds 
per  square  inch. 

Open  buckles  of  this  form  can  be  adjusted  with  a  bar,  hook,  or 
wrench,  and  have  the  great  advantage  of  showing  the  ends  of  the 
bolts,  so  that  inspectors  can  see  that  they  have  a  good  hold  of 
thread  and  do  not  butt  together. 


346 


RESISTANCE  TO  TENSION. 


TABLE  VIII.— RIGHT  AND  LEFT  NUTS  OR  SLEEVE- 
NUTS. 


DIMENSIONS    OF    NUTS    FROM    EDGE    MOOR    BRIDGE    WORKS' 
STANDARD. 


B 

Diam. 
of 
screw. 

G 

L'gth 
of 
upset. 

A 

Diameter 
of 
bar. 

A 

Side  of 
square 
bar. 

L 

Length 
of 
nut. 

T 
L'gth 
of 
thr'd. 

W 
Dia. 

of 
hex. 

Weight  of 

One 
nut. 

One  nut 
and  two 
screw- 
ends. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Lbs. 

Lbs. 

ord.  I'ths. 

f 

4* 

f 

% 

6 

1% 

11 

lf 

4i 

1 

» 

%and   f 

!    and% 

6 

IX 

If 

lf 

4i 

H 

45 

% 

f 

6* 

If 

2 

3 

74 

H 

4f 

I     "    % 

% 

6i 

If 

2 

3 

7| 

If 

5 

1         "  IX 

f     "    » 

7 

2f 

4f 

Hf 

li 

5 

H      "IX 

1 

7 

ll 

2f 

4f 

11} 

If 

5i 

H 

i/¥6  "li 

7$ 

2X 

2f 

6f 

16} 

If 

5} 

1%  "ij 

1% 

74 

2X 

2| 

6f 

16} 

li 

54 

1% 

li     "IX 

8 

2X 

3i 

91 

23i 

2 

61 

H    "i% 

if 

8 

2X 

3J 

9i 

23i 

2* 

Pi 

if    "  1% 

1%  "li 

8^ 

24 

34 

124 

3U 

2i 

5J 

U    "i% 

1% 

si 

24 

34 

124 

31* 

2f 

6 

il 

if    "  1% 

9 

2f 

3J 

16f 

41} 

24 

6 

1%    "2 

if 

9 

2^ 

3i 

16f 

41} 

2f 

6* 

2x  «2j 

1%  "li 

94 

2% 

4i 

214 

53} 

2} 

6i 

2?| 

i» 

94 

2% 

4i 

2l| 

53} 

2J 

61 

2}     "2% 

2        "2X 

10 

3X 

41 

264 

66-} 

3 

Bi 

2f 

2J 

10 

3X 

4f 

26* 

66i 

3* 

s* 

2%    "2| 

2« 

104 

3| 

5 

32~ 

81 

34 

7 

2% 

2* 

11 

3f 

5| 

38i 

97} 

3} 

7i 

3 

2% 

114 

3% 

« 

45 

116 

4 

7i 

3} 

2| 

12 

4X 

6i 

53J 

138 

ext.  I'ths. 

H 

4} 

1     "    % 

% 

12 

21 

2 

if 

4i 

% 

f 

Si 

M 

2 

4 

93 

U 

4f 

1     "    % 

% 

8*- 

1  1 

2 

4 

9} 

l| 

5 

1        "IV. 

1     "    % 

9 

1* 

2f 

6i 

15i 

H 

5 

H    "i% 

9 

IJ 

2f 

6i 

i.H 

If 

5} 

li 

IX  "li 

94 

2X 

2J 

81 

21* 

If 

5} 

1%  "i« 

IX 

9A 

2X 

2| 

Sf 

21  J 

li 

54 

1% 

li    "IX 

10 

2X 

3i 

12i 

29| 

2 

5J 

1^    "i9^, 

If 

10 

2% 

3i 

12} 

29  J 

Length  of   u 
inch  shorter  th 


pset  ends  for  use  with  right  and  left 
an  the  dimensions  given  in  column  " 


nuts   may  be  made  one 
G  "  above. 


RESISTANCE  TO  TENSION. 


347 


TABLE  IX.—  SAFE  STRENGTH  OF  FLAT  ROLLED  BARS- 

(Computed  at  10,000  Ibs.  per  square  inch.)  * 


Thickness 
in  inches. 

Width  in  inches. 

1" 

H" 

ii" 

if 

2" 

Ibs. 

Ibs. 

2V' 

2f  ' 

3" 

3i" 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Vl6 

360 

780 

940 

1,090 

1,250 

1,410 

1,560 

1,720 

1,880 

2,030 

* 

1,250 

1,560 

1,880 

2,190 

2,500 

2,810 

3,130 

3,440 

3,750 

4,060 

3/16 

1,880 

2,340 

2,810 

3,280 

3,750 

4,220 

4,690 

5,160 

5,630 

6,090 

i 

2,500 

3,130 

3,750 

4,380 

5,000 

5,630 

6,250 

6,880 

7,500 

8,130 

5/16 

3,130 

3,910 

4,690 

5,470 

6,250 

7,030 

7,810 

8,590 

9,380 

10,200 

I 

3,750 

4,690 

5,630 

6,560 

7,500 

8,440 

9,380 

10,300 

11,300 

12,200 

7/16 

4,380 

5,470 

6,560 

7,660 

8,750 

9,840 

10,900 

13,000 

13,100 

14,200 

1 

5,000 

8,250 

7:500 

8,750 

10,000 

11,300 

12,500 

13,800 

15,000 

16,300 

9/16 

5,630 

7,030 

8,440 

9,840 

11,300 

12,700 

14,100 

15,500 

16,900 

18,300 

1 

6,250 

7,810 

9,380 

10,900 

12,500 

14,100 

15,600 

17,200 

18,800 

20,300 

1^6 

6,880 

8,590 

10,300 

12,000 

13.800 

15,500 

17,200 

18,900 

20,600 

22,300 

I 

7,500 

9,380 

11,300 

13,100 

15,000 

16,900 

18,800 

20,600 

22,500 

24,400 

13/16 
1 
15/16 

8,130 
8,750 
9,380 

10,200 
10,900 
11,700 

12,200  14,200 
13,100,15,300 
14,  100*16,400 

16,300 
17,500 
18,800 

18,300 
19,700 
21,100 

20,300 
21,900 
23,400 

22,300 
24,100 
25,800 

24,400 
26,300 
28,100 

26,400 
28,400 
30,500 

1 

10,000 

12,500 

15,000 

17,500 

20,000 

22,500 

25,000 

27,500 

30,000 

32,500 

lVl6 

10,600 

13,300 

15,900 

18,600 

21,300 

23,900 

26,600 

29,200 

31,900 

34,500 

1* 

11,300 

14,100 

16,900 

19,700 

22,500 

25,300 

28,100 

30,900 

33,800 

36,600 

13/16 

11,900 

14,800 

17,800 

20,800 

23,800 

26,700 

29,700 

32,700 

35,600 

38,600 

H 

12,500 

15,600 

18,800 

21,900 

25,000 

28,100 

31,300 

34,400 

37,500 

40,600 

U 

13,800 

17,200 

20,600 

24,100 

27,500 

30,900 

34,400 

37,800 

41,300 

44,700 

II 

15,000 

18,800 

22,500 

26,300 

30,000 

33,800 

37,500 

41,300 

45,000 

48,800 

U 

16,300 

20,300 

24,400 

28,400 

32,500 

36,600 

40,600 

44,700 

48,800 

52,800 

If- 

17,500 

21,900 

26,300 

30,600 

35,000 

39,400 

43,800 

48,100 

52,500 

56,900 

11 

18,800 

23,400 

28,100 

32,800 

37,500 

42,200 

46,900 

51,600 

56,300 

60,900 

2 

20,000 

25,000 

30,000 

35,000 

40,000 

45,000 

50,000 

55,000 

60,000 

65,000 

*  For  unit  stresses  of  12,000,  12,500,  and  15,000  Ibs.  increase  by  £,  i,  and  \ 
respectively. 
For  working  strength  of  wrougiit  iron  and  steel,  see  pages  324  and  331. 

348 


RESISTANCE  TO  TENSION. 


TABLE  IX. —SAFE  STRENGTH  OF  FLAT  ROLLED  BARS 

(concluded.} 
(Computed  at  10,000  Ibs.  per  square  inch.)  * 


Thickness 
in  inches. 

Width  in  inches. 

31" 

3f" 
Ibs. 

4" 

4i" 

41" 

4f" 

5" 

51" 

6" 

61" 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

ft* 

2,190 

2,340 

2,500 

2,660 

2,810 

2,970 

3,130 

3,440 

3,750 

4,060 

i 

4,380 

4,690 

5,000 

5,310 

5,630 

5,940 

6,250 

6,880 

7,500 

8,130 

8/io 

6,560 

7,030 

7,500 

7,970 

8,440 

8,910 

9,380 

10,300 

11,300 

12,200 

i 

8,750 

9,380 

10,000 

10,600 

11,300 

11,900 

12,500 

13,800 

15,000 

16,300 

%8 

10,900 

11,700 

12,500 

13,300 

14,100 

14,800 

15,600 

17,200 

18,800 

20,300 

i 

13,100 

14,100 

15,000 

15,900 

16,900 

17,800 

18,800 

20,600 

22,500 

24,400 

%6 

15,300 

16,400 

17,500 

18,600 

19,700 

20,800 

21,900 

24,100 

26,300 

28,400 

* 

17,500 

18,800 

20,000 

21,300 

22,500 

23,800 

25,000 

27,500 

30,000 

32,500 

He 

19,700 

21,100 

22,500 

23,900 

25,300 

26,700 

28,100 

30,900 

33,800 

36,600 

1 

21,900 

23,400 

25,000 

26,600 

28,100 

29,700 

31,300 

34,400 

37,500 

40,600 

Hie 

24,100 

25,800 

27,500 

29,200 

30,900 

32,700 

34,400 

37,800 

41,300 

44,700 

1 

26,300 

28,100 

30,000 

31,900 

33,800 

35,600 

37,500 

41,300 

45,000 

48,800 

18A6 

28,400 

30,500 

32,500 

34,500 

36,600 

38,600 

40,600 

44,700 

48,800 

52,800 

i 

30,600 

32,800 

35,000 

37,200 

39,400 

41,600 

43,800 

48,100 

52,500 

56,900 

15/le 

32,800 

35,200 

37,500 

39,800 

42,200 

44,500 

46,900 

51,600 

56,300 

60,900 

1 

35,000 

37,500 

40,000 

42,500 

45,000 

47,500 

50,000 

55,000 

60,000 

65,000 

1%6 

37,200 

39,800 

42,500 

45,200 

47,800 

50,500 

53,100 

58,400 

63,800 

69,100 

If 

39,400 

42,200 

45,000 

47,800 

50,600 

53,400 

56,300 

61,900 

67,500 

73,100 

1%6 

41,600 

44,500 

47,500 

50,500 

53,400 

56,400 

59,400 

65,300 

71,300 

77,200 

1* 

43,800 

46,900 

50,000 

53,100 

56,300 

59,400 

62,500 

68,800 

75,000 

81,300 

If 

48,100 

51,600 

55,000 

58,400 

61,900 

65,300 

68,800 

75,600 

82,500 

89,40C 

H 

52,500 

56,300 

60,000 

63,800 

67,500 

71,300 

75,000 

82,500 

90,000 

97,500 

H 

56,900 

60,900 

65,000 

69,100 

73,100 

77,200 

81,300 

89,400 

97,500 

105,600 

If 

61,300 

65,600 

70,000 

74,400 

78,800 

83,100 

87,500 

96,300 

105,000 

113,800 

11 

65,600 

70,300 

75,000 

79,700 

84,400 

89,100 

93,800 

103,100 

112,500 

121,900 

2 

70,000 

75,000 

80,000 

85,000 

90,000 

95,000 

100,000 

110,000 

120,000 

130,000 

*  See  foot-note,  preceding  page. 


RESISTANCE  TO  TENSION. 


349 


TABLE  X.—  SAFE  TENSILE   STRENGTH,  IN   TONS,  OF 
COMMON    SIZES    OF    STEEL    ANGLES   WITH    ONE 
J-INCH  HOLE  FOR  f-INCH  RIVET  DEDUCTED. 
(Based  on  a  working  stress  of  15,000  Ibs.  per  square  inch.) 


Size  of  Angle. 

Tons. 

Size  of  Angle. 

Tons. 

Size  of  Angle. 

Tons. 

6X4   X} 

47.10 

3JX3JXJ 

30.21 

3   X2JXi 

15.45 

f 

39.82 

I 

25.72 

| 

11.92 

.  J 

32.22 

i 

21.07 

ft 

10.12 

* 

16.12 

i 

4 

8.17 

5X3JXf 

38.62 

I 

32.77 

3*X3   Xf 

23.40 

3   X2   XX 

12.15 

i 

26.70 

i 

19.20 

J 

10.50 

| 

14.77 

% 

9.00 

5X3   X| 

35.85 

i 

7.27 

I 

30.45 

3iX2iX| 

21.07 

£ 

24.82 

% 

19.27 

2JX2iX% 

12.15 

f 

18.97 

| 

17.22 

| 

10.50 

13.35 

% 

9.00 

4X4   XJ 

35.85 

J 

9.15 

i 

7.27 

| 

21.22 

3   X3   X| 

21.07 

2JX2  X% 

10.50 

4X3iX| 

28.12 

4 

17.32 

2 

8 

9.15 

t 

17.55 

I 

13.35 

% 

7.80 

i 

9.15 

J 

6.30 

4X3   Xfi 

25.72 

i 

21.07 

1 

16.12 

EESISTANCE  TO  TENSION. 


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RESISTANCE  TO  TENSION. 


351 


IRON  WIRE. 

TABLE  XII.— SHOWING  SIZE,  WEIGHT,  AND  STRENGTH 
OF  CHARCOAL-IRON  WIRE. 

(Trenton  Iron  Co.'s  List.) 


No.  by 
wire 
gauge. 

Diameter 
in  deci- 
mals of 
1  inch. 

Feet  to 
the 
pound. 

Weight  of 
1  mile, 
in  Ibs. 

Area  of 
section, 
in  deci- 
mals of 
1  square 
inch. 

Actual 
breaking 
weight  of 
bright  mar- 
ket wire, 
in  Ibs. 

Tensile 
strength  of 
bright  mar- 
ket wire 
per  sq.  in. 
of  section, 
in  Ibs.- 

00000 

.450 

1.863 

2833  .  248 

.  15904 

12,598 

79,217 

0000 

.400 

2.358 

2238  .  878 

.  12566 

9,955 

79,220 

000 

.360 

2.911 

1813.574 

.10179 

8,124 

79,811 

00 

.330 

3.465 

1523.861 

.08553 

6,880 

80,437 

0 

.305 

4.057 

1301.678 

.07306 

5,926 

81,110 

1 

.285 

4.645 

1136.678 

.06379 

5,226 

81,925 

2 

.265 

5.374 

982  .  555 

.05515 

4,570 

82,873 

3 

.245 

6.286 

839.942 

.04714 

3,948 

83,756 

4 

.225 

7.454 

708.365 

.  03976 

3,374 

84,862 

5 

.205 

8.976 

588.139 

.03301 

2,839 

86,000 

6 

.190 

10.453 

505.084 

.02835 

2,476 

87,349 

7 

.175 

12.322 

428.472 

.  02405 

2,136 

88,802 

8 

.160 

14.736 

358.3008 

.02011 

1,813 

90,153 

9 

.145 

17.950 

294.1488 

.01651 

1,507 

91,276 

10 

.130 

22  .  333 

236  .  4384 

.01327 

1,233 

92,916 

11 

.1175 

27  .  340 

193.1424 

.01084 

1,010 

93,170 

12 

.105 

34.219 

154.2816 

.00866 

810 

93,530 

13 

.0925 

44.092 

119.7504 

.00672 

631 

93,900 

14 

.080 

58.916 

89.6016 

.00503 

474 

94,234 

15 

.070 

76.984 

68.5872 

.00385 

372 

96,701 

16 

.061 

101.488 

52  .  008 

.  00292 

292 

100,000 

17 

.0525 

137.174 

38.4912 

.00216 

222 

102,777 

18 

.045 

186.335 

28.3378 

.00159 

169 

106,289 

19 

.040 

235.084 

22.3872 

.0012566 

137 

109,024 

20 

.035 

308.079 

17.1389 

.0009621 

107 

111,215 

The  gauge  given  is  that  adopted  by  the  Trenton  Iron  Company. 

The  strengths  given  in  the  last  column  of  the  above  table  are 
based  upon  tests  made  with  bright  (not  annealed)  charcoal- 
iron  wire.  The  strength  of  Swedish  iron  is  about  10  per  cent, 
less,  and  that  of  mild  bessemer  and  ordinary  crucible  cast  steel 
about  10  and  25  per  cent.,  respectively,  greater,  than  that  of 
charcoal  iron.  Special  grades  of  crucible  cast  steel  vary 
between  30  and  100  per  cent,  over  charcoal  iron. 

Annealing  renders  wire  more  pliable  but  less  elastic,  and  reduces 
its  strength  about  20  or  25  per  cent.  Galvanizing  reduces  the 
tensile  strength  about  10  per  cent.,  while  tinning  and  coppering 
exert  no  apparent  influence  upon  the  metal.  Unannealed  or  hard 
brass  wire  has  about  three-fourths  the  strength  of  the  above  table, 
and  about  one-ninth  more  weight. 


352  RESISTANCE    TO   TENSION. 

Hard  copper  wire  may  be  taken  at  two-thirds  of  the  tabular 
strengths,  and  full  one-seventh  more  in  weight. 

WIRE  HOPES. 

Two  kinds  of  wire  rope  are  manufactured.  The  most  pliable 
variety  is  made  of  six  strands  of  nineteen  wires  each,  laid  around 
a  hemp  heart,  and  is  generally  used  for  hoisting  and  running  rope. 
It  will  wind  on  moderate-sized  drums  and  pass  over  small 
sheaves. 

"For  standing  rope,  guys  and  rigging,  ropes  made  of  six  strands 
of  twelve  or  seven  wires  each  are  better  adapted,  as  they  are 
much  stiffer  than  rope  with  19  wires  to  the  strand.  From  f-inch 
diameter  down  to  the  smaller  sizes  this  rope  gives  excellent 
service  for  transmitting  power. 

Steel  ropes  are  in  many  places  superseding  iron  ropes. 

In  substituting  steel  rope  for  iron  rope,  however,  the  object 
in  view  should  be  to  gain  an  increased  wear  for  the  rope,  rather 
than  to  reduce  the  size. 

To  be  serviceable,  a  steel  rope  should  be  of  the  best  obtainable 
quality,  as  ropes  made  from  low  grades  of  steel  are  inferior  to 
good  iron  ropes.  The  constant  bending  and  vibration  to  which 
they  are  subjected  soon  causes  the  poor  steel  to  become  brittle 
and  unsafe. 

Ropes  are  made  up  to  three  inches  in  diameter,  both  of  iron 
arid  steel,  upon  special  application. 

For  safe  working  load,  allow  one-fifth  to  one-seventh  of  the 
ultimate  strength,  according  to  speed,  so  as  to  get  good  wear  from 
the  rope.  When  substituting  wire  rope  for  hemp  rope,  it  is  good 
economy  to  allow  for  the  former  the  same  weight  per  foot  which 
experience  has  approved  for  the  latter. 

Wire  rope  is  as  pliable  as  new  hemp  rope  of  the  same  strength  ; 
the  former  will  therefore  run  over  the  same  sized  sheaves  and 
pulleys  as  the  latter.  But  the  greater  the  diameter  of  the 
sheaves,  pulleys  or  drums,  the  longer  wire  rope  will  last.  In  the 
construction  of  machinery  for  wire  rope  it  will  be  found  good 
economy  to  make  the  drums  and  sheaves  as  large  as  possible. 
The  minimum  size  of  drum  is  given  in  a  column  in  Table  XIII. 

Experience  has  demonstrated  that  the  wear  increases  with  the 
speed.  It  is,  therefore,  better  to  increase  the  load  than  the  speed. 

Wire  rope  is  manufactured  either  with  a  wire  or  a  hemp  centre, 
and  the  kind  of  centre  wanted  should  be  specified  when  placing 


RESISTANCE  TO  TENSION.  353 

an  order.  The  latter  is  more  pliable  than  the  former,  and  will 
wear  better  where  there  is  short  bending. 

Wire  rope  must  not  be  coiled  or  uncoiled  like  hemp  rope.  When 
mounted  on  a  reel,  the  latter  should  be  mounted  on  a  spindle  or 
flat  turn-table  to  pay  off  the  rope.  When  forwarded  in  a  small 
coil,  without  reel,  it  should  be  rolled  over  the  ground  like  a  wheel, 
and  the  rope  run  off  in  that  way.  All  untwisting  or  kinking 
must  be  avoided. 

To  preserve  wire  rope,  apply  raw  linseed  oil  with  a  piece  of 
sheep-skin,  wool  inside,  or  mix  the  oil  with  equal  parts  of  Spanish 
brown  or  lamp-black. 

To  preserve  wire  rope  under  water  or  under  ground,  take 
mineral  or  vegetable  tar,  and  add  one  bushel  of  fresh-slacked 
lime  to  one  barrel  of  tar,  which  will  neutralize  the  acid.  Boil  it 
well,  and  saturate  the  rope  with  the  hot  tar.  To  give  the  mixture 
body,  add  some  sawdust. 

In  no  case  should  galvanized  rope  be  used  for  running  rope. 
One  day's  use  scrapes  off  the  coating  of  zinc,  and  rusting  pro- 
ceeds with  twice  the  rapidity. 

The  grooves  of  cast-iron  pulleys  and  sheaves  should  be  filled 
with  well-seasoned  blocks  of  hard  wood,  set  on  end,  to  be  renewed 
when  worn  out.  This  end  wood  will  save  wear  and  increase 
adhesion.  The  smaller  pulleys  or  rollers  which  support  the  ropes 
on  inclined  planes  should  be  constructed  on  the  same  plan. 
When  large  sheaves  run  with  very  great  velocity,  the  grooves 
should  be  lined  with  leather,  set  on  end,  or  with  India  rubber. 
This  is  done  in  the  case  of  all  sheaves  used  in  the  transmission 
of  power  between  distant  points  by  means  of  rope,  which  fre- 
quently run  at  the  rate  of  4,000  feet  per  minute. 

The  wire  ropes  described  above  are  sold  by  the  foot. 

Ropes,  Hawsers,  and  Cables. 

(HAS  WELL.) 

Ropes  of  hemp  fibres  are  laid  with  three  or  four  strands  of 
twisted  fibres  and  run  up  to  a  circumference  of  twelve  inches. 

Hawsers  are  laid  with  three  strands  of  rope,  or  with  four  rope 
strands. 

Cables  are  laid  with  three  strands  of  rope  only. 

Tarred  ropes,  hawsers,  etc.,  have  twenty-five  per  cent,  less 
strength  than  white  ropes;  this  is  in  consequence  of  the  injury 
the  fibres  receive  from  the  high  temperature  of  the  tar — 290°. 


354 


RESISTANCE  TO  TENSION. 


GALVANIZED  STEEL  WIRE  STRAND,  COMPOSED 
OF  7  WIRES,  TWISTED  TOGETHER  INTO  A 
SINGLE  STRAND. 

FOR  SMOKESTACK  GUYS,  SIGNAL  STRAND,  TROLLEY  LINE  SPAN 
WIRE  AND  SIMILAR  PURPOSES. 


Diameter. 

Weight  per 
100  feet. 

Estimated 
breaking 
strength. 

Price  per 
100  feet. 

Inch. 

Pounds. 

Pounds. 

J 

51 

8,320 

$2.25 

15/32 

48 

7,500 

2.05 

¥* 

37 

6,000 

1.65 

30 

4,700 

1.40 

k 

21 

3,300 

1.05 

%2 

18 

2,600 

.90 

17/64 

15 

2,250 

.75 

1 

Hi 

1,750 

.60 

%2 

8| 

1,300 

.50 

% 

6i 

1,000 

.45 

%2 

4 

700 

.35 

%4 

3i 

525 

.28 

t 

2J 

375 

.22 

%2 

2 

320 

.20 

Tarred  hemp  and  manila  ropes  are  of  about  equal  strength. 
Manila  ropes  have  from  twenty-five  to  thirty  per  cent,  less 
strength  than  white  ropes.  Hawsers  and  cables,  from  having 
a  less  proportionate  number  of  fibres,  and  from  the  increased 
irregularity  of  the  resistance  of  the  fibres,  have  less  strength  than 
ropes;  the  difference,  varying  from  thirty-five  to  forty-five  per 
cent.,  being  greatest  with  the  least  circumference. 

Ropes  of  four  strands,  up  to  eight  inches,  are  fully  sixteen 
per  cent,  stronger  than  those  having  but  three  strands. 

Hawsers  and  cables  of  three  strands,  up  to  twelve  inches,  are 
fully  ten  per  cent,  stronger  than  those  having  four  strands. 

The  absorption  of  tar  in  weight  by  the  several  ropes  is  as  fol- 
lows :  i 


Bolt-rope 18  per  cent. 

Shrouding.  .15  to  18  per  cent. 


Cables 21  per  cent. 

Spun-yarn.  .25  to  30  per  cent. 


White  ropes  are  more  durable  than  tarred. 

The  greater  the  degree  of  twisting  given  to  the  fibres  of  a  rope, 
etc.,  the  less  its  strength,  as  the  exterior  alone  resists  the  greater 
portion  of  the  strain. 


RESISTANCE  TO  TENSION. 


355 


TABLE    XIII.— STRENGTH     OF    IRON-    AND    STEEL- 
WIRE  ROPES. 

MANUFACTURED    BY    THE    JOHN    A.    ROEBLING'S    SONS    Co., 
NEW  YORK. 


Trade 
No. 

Diam. 
in 
inches. 

Weight 
per  foot 
in  Ibs.  of 
rope  with 
hemp 
centre. 

Iron. 

Cast  Steel. 

Min.   size  of 
drum    or 
sheave  in  feet. 

Break- 
ing 
strain 
in  tons. 

Proper 
working 
load 
in  tons. 

Break- 
ing 
strain 
in  tons. 

Proper 
working 
load 
in  tons. 

Iron. 

Cast 

steel. 

HOISTING  ROPE. 

WITH    NINETEEN    WIRES    TO    THE    STRAND. 

1 

2*4 

8.00 

74.00 

15.00 

155 

31 

13 

8.50 

2 

2 

6.30 

65.00 

13.00 

125 

25 

12 

8 

3 

1% 

5.25 

54.00 

11.00 

106 

21 

10 

7.25 

4 

1% 

4.10 

44.00 

9.00 

86 

17 

8 

6.25 

5 

1% 

3.65 

39.00 

8.00 

77 

15 

7 

5.75 

1% 

3.00 

33.00 

6.50 

63 

12 

7 

5.50 

6 

1*4 

2.50 

27.00 

5.50 

52 

10 

6 

5 

7 

1*6 

2.00 

20.00 

4.00 

42 

8 

6 

4.50 

8 

1 

1.58 

16.00 

3.00 

33 

6 

5.25 

4 

9 

1.20 

11.50 

2.50 

25 

5 

4 

3.50 

10 

% 

0.88 

8.64 

1.75 

18 

3.5 

4 

3 

1014 

% 

0.60 

5.13 

1.25 

12 

2.5 

3 

2.25 

ioy2 

QA& 

0.48 

4.27 

0.75 

9 

1.5 

2.75 

1.75 

0.39 

3.48 

0.50 

7 

1 

2.25 

1.50 

10a 

"vie 

0.29 

3.00 

0.37 

5.5 

0.75 

2 

1.25 

10% 

% 

0.23 

2.50 

0.25 

4.5 

0.5 

1.50 

1 

STANDING     ROPE    FOR    GUYS    AND    RIGGING. 

WITH    SEVEN    WIRES    TO    THE    STRAND. 

11 

1W 

3.37 

36.00 

9.00 

62 

13 

13 

8.50 

12 

1^6 

2.77 

30.00 

7.50 

52 

10 

12 

8 

13 

1*4 

2.28 

25.00 

6.25 

44 

9 

10.75 

7.25 

14 

1*6 

1.82 

20.00 

5.00 

36 

7.50 

9.50 

6.25 

15 

1 

1.50 

16.00 

4.00 

30 

6 

8.50 

5.75 

16 

T6 

1.12 

12.30 

3.00 

22 

4.50 

7.50 

5 

17 

% 

0.92 

8.80 

2.25 

17 

3.50 

6.75 

4.50 

18 

ii/ie 

0.70 

7.60 

2.00 

14 

3 

6 

4 

19 

% 

0.57 

5.80 

1.50 

11 

2.25 

5.25 

3.50 

20 

9/4e 

0.41 

4.10 

1.00 

8 

1.75 

4.50 

3 

21 

0.31 

2.83 

0.75 

6 

1.50 

4 

2.50 

22 

%o 

0.23 

2.13 

0.50 

4.50 

1.25 

3.50 

2.25 

23 

0  21 

1  65 

4 

2  75 

24 

K/ 

0  16 

1  '38 

3 

0  75 

2crv 

25 

v!6 
%2 

O!l25 

i!o3 



2 

o!so 

.  OU 

2.25 

1  .  75 
1.50 

NOTE. — A  valuable  pamphlet  on  wire  rope  for  the  transmission  of  power 
may  be  obtained  from  the  Trenton  Iron  Co.,  of  Trenton,  N,  J. 


356 


RESISTANCE  TO  TENSION. 


To  compute  the  Strain  that  can  he  home  with 
Safety  hy  New  Ropes,  Hawsers,  and  Cahles, 
Deduced  from  the  Experiments  of  the  Russian 
Government  upon  the  Relative  Strength  of 
Different  Circumferences  of  Ropes,  Hawsers, 
etc. 

The  United  States  Navy  test  is  4,200  pounds  for  a  white  rope,  of 
three  strands  of  best  Riga  hemp,  of  one  and  three-fourths  inches  in 
circumference  (i.e.,  17,000  pounds  per  square  inch);  but  in  the  fol- 
lowing table  14,000  pounds  is  taken  as  the  unit  of  strain  that  can 
be  borne  ivith  safety. 

RULE. — Square  the  circumference  of  the  rope,  hawser,  etc.,  and 
multiply  it  by  the  following  units  for  ordinary  ropes,  etc. 


TABLE  XIV.— -SHOWING  THE  UNITS  FOR  COM- 
PITTING  THE  SAFE  STRAIN  THAT  MAY  BE 
BORNE  BY  ROPES,  HAWSERS,  AND  CABLES. 


Ropes. 

Hawsers. 

Cables. 

White. 

Tarred. 

4 

cc 

4 

•v 

Description. 

*SH 

§ 

TJ 

d 

D 

1 

-3 

02 
Tj 

02 

CO 

CO 

18 

CO 

CO 

1 

1 

I 

i 

£ 

33 

9 

IP 

CO 

GQ 

« 

CO 

•g 

1 

E§ 

i 

"V. 

Circumference  in  inches.  .  . 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

White  rope,  2.5  to  6  ins.  . 

1,140 

1,330 

— 

— 

600 

— 

— 



White  rope,  6  to  8  ins   . 

1,090 

1,260 

— 

— 

570 

— 

510 

— 

White  rope,  8  to  12  ins. 

1,045 

880 

— 

— 

530 

— 

530 



White  rope,  12  to  18  ins 

— 

•  — 

— 

— 

550 

— 

550 

— 

White  rope,  18  to  26  ins 

— 

— 

— 

— 

— 

— 

560 



Tarred  rope,  2.5  to  5  ins 

— 

— 

855 

1,005 

— 

460 

— 

— 

Tarred  rope,  5  to  8  ins.  .  . 

— 

— 

825 

940 

— 

48u 





Tarred  rope,  8  to  12  ins.   . 

— 

— 

780 

820 

— 

50o 

— 

505 

Tarred  rope,  12  to  18  ins 

— 

— 

— 

— 

— 

— 

— 

525 

Tarred  rope,  18  to  26  ins. 

— 

— 

-  — 

— 

— 

— 



550 

Manila  rope,  2.5  to  6  ins.  . 

810 

950 

— 

— 

440 

— 

— 

Manila  rope,  6  to  12  ins.  . 

760 

835 

— 

— 

465 



510 



Manila  rope,  12  to  18  ins. 

— 

— 

— 

— 

— 

— 

535 



Manila  rope,  18  to  26  ins. 

— 

— 

~"~ 

— 

— 

— 

560 

— 

When  it  is  required  to  ascertain  the  weight  or  strain  that  can 
be  borne  by  ropes,  etc.,  in  general  use,  the  above  units  should  be 
reduced  one-third,  in  order  to  meet  the  reduction  of  their  strength 
by  chafing  and  exposure  to  the  weather. 


RESISTANCE  TO  TENSION. 


357 


TABLE   XV.— STRENGTH   AND   WEIGHT   OF   MANILA 
ROPE. 


•^ 

•+3 

8 

§ 

8 

1 

a 

1 

Breaking 
load. 

imeter. 

1 

I 

i 

Breaking 
load. 

Q 

1 

1 

a 

1 

4) 

ins. 

ins. 

Ibs. 

Ibs. 

tons. 

ins. 

ins. 

Ibs. 

Ibs. 

tons. 

0.239 

H 

.019 

560 

0.280 

1.92 

6 

1.19 

25,536 

12.77 

0.318 

1 

.033 

784 

0.39 

2.07 

6^41 

1.39 

29,120 

14.56 

0.477 

.074 

1,568 

0.78 

2.23 

7  / 

1.62 

32,704 

16.35 

0.636 

2  2 

.132 

2,733 

1.36 

2.39 

1.86 

36,288 

18.14 

0.795 

2-V& 

.206 

4,278 

2.14 

2.55 

8  2 

2.11 

39,872 

19.93 

0.955 

3 

.297 

6,115 

3.06 

2.86 

9 

2.67 

47,040 

23.52 

1.11 

3^5 

.404 

8,534 

4.27 

3.18 

10 

3.30 

54,208 

27.10 

1.27 

4 

.528 

11,558 

5.78 

3.50 

11 

3.99 

61,376 

30.69 

1.43 

4V& 

.668 

14,784 

7.39 

3.82 

12 

4.75 

68,544 

34.27 

1  59 

5 

.825 

18,368 

9.18 

4.14 

13 

5.58 

75,712 

37.86 

1.75 

5V2 

.998 

21,952 

10.97 

4.45 

14 

6.47 

82,880 

41.44 

Working  Loads. — For  manila  ropes  from  1  to  If  ins. 
diam.,  running  at  different  speeds  over  sheaves  of  the  diams. 
stated,  Mr.  C.  W.  Hunt  (Trans.  Am.  Soc.  Mechl.  Engrs.,  Vol. 
XXIII,  1901)  gives  a  table  embodying  approximately  the 
following  results  of  experience.  Working  load  =  C  X  ultimate 
strength  of  new  rope,  as  given  in  above  table.  D  =  minimum 
diam.  of  sheave  in  ins. 

r'rope  l%"rope 

Speed       ft.  per  min.         as  for  work  on  ODD 

Slow          50  to  100  derrick,  crane,  quarry  0.140      8          14 
Medium  150  to  300  wharf,  cargo  0.056     12  18 

Rapid      400  to  800  0.028    40          70 

Such  ropes  wear  out  rapidly.  A  rope  1|  ins.  diam.  wears  out 
in  lifting  from  7,000  to  10,000  tons  of  coal.  On  the  other  hand, 
1J  inch  transmission  ropes,  running  5000  ft.  per  min.  and  carry- 
ing 1000  H.  P.  over  sheaves  5  ft.  and  17  ft.  in  diam.  last  for 

years. 


358 


RESISTANCE  TO  TENSION. 


TABLE   XVL-— WEIGHT   AND   PROOF   STRENGTH   OP 
CHAIN. 

MANUFACTURED  BY  THE  NEW  JERSEY  STEEL  AND  IRON  COMPANY, 


X.B. 

Stud  chain. 

Short-link  chain. 

crane 

chain. 

Average 

Average 

Size. 

weight 

Proof. 

Size. 

weight 

Proof. 

Proof. 

per 

per 

fathom. 

fathom. 

inches. 

Ibs. 

tons. 

inches. 

Ibs. 

tons. 

tons. 

| 

33 

10 

% 

2f 

i 

.  — 

% 

38 

12 

i 

5 

4 

.  — 

I 

43 

14 

% 

7 

1 

— 

% 

50 

16 

91 

2 

3 

i 

58 

18 

% 

12 

2* 

4 

1*S 

65 

20 

15 

4 

44 

H 

72 

23 

% 

19 

4-1 

Bf 

1& 

80 

26 

I 

25 

5^ 

7 

H 

88 

28 

% 

30 

7^ 

8| 

1% 

98 

31 

f 

35 

8 

10 

if 

110 

34 

% 

40 

9J 

Hi 

1« 

114 

37 

I 

47 

11 

13 

1* 

127 

41 

% 

54 

12* 

14J 

1% 

138 

44 

61 

14" 

16 

If 

150 

48 

V4 

69 

16 

19 

1% 

157 

52 

\\ 

76 

18 

21 

if 

170 

56 

1% 

85 

20 

23 

1% 

184 

60 

H 

95 

22 

25 

U 

200 

64 

l« 

103 

24 

27 

1% 

214 

68 

If 

113 

26 

29 

2 

230 

72 

1% 

123 

28 

31 

2J 

250 

80 

H 

133 

30 

33 

21 

290 

88 

RESISTANCE  TO  TENSION. 


359 


Strength  of  Old  Iron. — A  square  link  12  inches  broad,  1 
inch  thick,  and  about  12  feet  long  was  taken  from  the  Kief? 
Bridge,  then  40  years  old,  and  tested  in  comparison  with  a  similar 
link  which  had  been  preserved  in  the  stock-house  since  the  bridge 
was  built.  The  following  is  a  record  of  a  mean  of  four  longitu- 
dinal test  pieces,  1 X IJXS  inches,  taken  from  each  link. 


Old  link 
from  bridge. 

New  link  from 
storehouse. 

Tensile  strength  per  square  inch,  tons.  .  . 
Elastic  limit  per  square  inch,  tons.  

21.8 
11.1 
14  05 

22.2 
11.9 

18.42 

17.35 

18.75 

dike  Mechanical  World,  London.) 


360 


RESISTANCE  TO  SHEARING. 


CHAPTER 


RESISTANCE  TO  SHEARING.—  RIVETED 
JOINTS. 

STRENGTH  OF  PINS  IN  IRON  AND  STEEL  TRUSSES.— 
STRENGTH  OF  BOLTS  IN  WOODEN  TRUSSES  AND 
GIRDERS. 

BY  shearing  is  meant  the  pushing  of  one  part  of  a  piece  by 
the  other.  Thus  in  Fig.  1,  let  abed  be  a  beam  resting  upon  the 
supports  SS,  which  are  very  near  together.  If  a  sufficiently 


Fig.  I 

heavy  load  were  placed  upon  the  beam,  it  would  cause  the  beam 
to  break,  not  by  bending,  but  by  pushing  the  whole  central  part 
of  the  beam  through  between  the  ends,  as  represented  in  the 
figure.  This  mode  of  fracture  is  called  "shearing." 

Shearing  stresses  exist  whenever  two  forces  acting  like  a  pair 
of  shears  tend  to  cut  a  body  between  them. 

When  two  bars  of  steel  or  iron  are  connected  together  by  a 
rivet,  as  in  Fig.  2,  the  stresses  in  the  bars  acting  as  indicated  by 
the  arrow-heads,  the  tendency  is  to  shear  the  rivet  at  the  joint 
between  the  two  bars,  as  though  it  were  cut  by  a  pair  of  shears. 
When  the  shearing  stresses  tend  to  shear  the  piece  only  at  one 
place,  as  in  Fig.  2,  the  piece  is  said  to  be  in  single  shear;  when 
the  stresses  tend  to  shear  the  piece  at  two  sections,  as  in  Fig.  1, 
the  piece  is  in  "double  shear." 


RESISTANCE  TO  SHEARING. 


361 


The  resistance  of  a  body  to  shearing  is,  like  its  resistance  to 
tension,  directly  proportional  to  the  area  to  be  sheared.  Hence, 
if  we  denote  the  safe  resistance  of  one  square  inch  of  the  mate- 


Fig.  2 

rial  to  shearing  by  F,  we  shall  have  as  the  safe  resistance  to 
shearing, 

Safe  shearing  strength  =  area  to  be  sheared  X  F,          (1) 

A  piece  of  timber  may  be  sheared  either  longitudinally  or 
transversely;  and,  as  the  resistance  is  not  the  same  in  both  cases, 
the  value  of  F  will  be  different  in  the  two  cases.  Hence,  in 
substituting  values  for  F,  we  must  distinguish  whether  the  force 
tends  to  shear  the  piece  longitudinally  (lengthwise)  or  trans- 
versely (across). 

Table  I.  gives  the  average  working  values  of  F  in  building  con- 
struction as  recommended  by  the  best  authorities,  and  as  used 
by  structural  engineers. 

TABLE  I.— SAFE  RESISTANCE  TO  SHEARING,  IN  LBS. 
PER  SQUARE  INCH,  FOR  IRON,  STEEL,  AND  WOOD. 


Materials. 

Values  for  F. 

Cast  iron   .                

6,000 
Rolled  steel. 

7,  000  to  10,  000 
7,500* 
7,  500  to  10,  000 
7,  500  to    9,000 

•  Across  grain 
400 
400 
600 
1,000 
1,200 
900 
750 
500 
500 
750 

Webs  of  rolled  beams    and  riveted 
girders.                               .      

Wrought  iron. 
6,000  to  9,000 
6,000 
7,500 
7,500 

With  grain. 

Bolts  and  field-driven  rivets  
Rivets  shop-driven 

Pins 

Woods. 
Cedar.  ...                 

Chestnut 

125 
80 
150 
125 
125 
90 
80 
70 
90 
60. 

Hemlock.  .                     

Oak,  white 

Pine,  Georgia  yellow... 

Pine  Oregon 

Pine,  Norway  

Pine,  white.  . 

Redwood  (Califorina)    .... 

Spruce. 

Whitewood. 

*  For  bolts  in  the  connection-angles  of  beams,  a  shearing  stress  of  10,000 
Ibs.  is  usually  allowed,  and  the  author  believes  that  the  same  unit  stress 
may  be  used  for  bolts  in  the  joints  of  wooden  trusses. 


362 


RESISTANCE  TO  SHEARING. 


There  are  but  few  cases  of  architectural  construction  in  which 
the  resistance  of  wood  to  shearing  has  to  be  provided  for.  The 
one  most  frequently  met  with  is  at  the  end  of  the  tie-beam  in 
wooden  trusses. 


Fig.  3 

Fig.  3  shows  the  shearing  of  the  end  of  the  tie-beams  due  to 
the  thrust  of  the  rafter,  the  drawing  being  made  from  a  photo- 
graph of  an  actual  instance. 

There  is  always  a  tendency  for  beams  to  shear  vertically  at 
the  points  of  support,  as  in  Fig.  1,  but  it  is  very  rare  that  wooden 
beams  are  subject  to  dangerous  stresses  from  shearing.  It- 
could  only  happen  in  the  case  of  a  very  short  beam  very  heavily 
loaded.  The  .vertical  shearing  stresses  in  a  beam  are  explained 
in  Chapter  XX. 

A  very  long  beam  might  also  possibly  fail  by  shearing  longi- 
tudinally, but  such  failure  is  not  likely  to  occur  under  the  safe 
load  given  by  either  the  formula  for  strength  or  the  formula 
for  stiffness.  Other  common  instances  in  which  failure  by  shear- 


Fig.  4 

ing  may  take  place,  are  in  the  case  of  rivets,  pins,  and  bolte3 
which  are  hereinafter  more  fully  explained. 


RIVETED  JOINTS.  363 

Example  of  Shear  at  End  of  Tie-beam. — In  the  case  of  the 
truss  joint,  Fig.  4,  the  rafter  exerts  a  thrust  which  tends  to 
push  or  shear  off  the  piece  A  BCD,  and  the  area  of  the  section 
along  CD  should  offer  enough  resistance  to  keep  the  rafter  in 
place.  This  area  is  equal  to  CD  times  the  breadth  of  the  tie- 
beam;  and,  as  the  breadth  is  fixed,  we  have  to  determine  the 
length,  CD.  If  we  let  H  denote  the  horizontal  thrust  of  the 
rafter,  or  the  tension  in  the  tie-beam,  by  a  simple  deduction 
from  formula  (1),  we  have  the  rule, 

TT 

Length  of  CD  in  inches  = : rn — FJ FT»  (2) 

breadth  of  beam  X  ^ 

Fj  in  this  case,  being  the  resistance  to  shearing  longitudinally. 

EXAMPLE  I. — The  horizontal  thrust  of  a  rafter  is  20,000 
pounds,  the  tie-beam  is  of  Oregon  pine,  and  is  ten  inches  wide: 
how  far  should  the  beam  extend  beyond  the  point  Z)? 

Ans.  In  this  case  H  =  20,000  pounds,  and  from  Table  I.  we 
find  that  ^=125.  Then 

20,000 
CD==  10X125'  °r  16mches' 

Practically  a  large  part  of  the  thrust  is  generally  taken  up 
by  an  iron  bolt  or  strap  passed  through  or  over  the  foot  of  the 
rafter  and  tie-beam,  in  order  to  keep  the  rafter  in  place.  As 
the  bolt  and  shoulder  seldom  act  together,  the  length  of  the 
tie-beam  at  CD  should  either  be  made  long  enough  to  resist 
the  entire  thrust  without  help  from  the  bolt,  or  else  the  bolt  or 
strap  should  be  strong  enough  to  resist  the  entire  thrust.  The 
designing  of  such  joints  is  more  fully  considered  on  pages  382 
to  397. 

RIVETED  JOINTS. 

The  most  common  method  of  uniting  pieces  of  wrought  iron 
or  steel  in  framed  structures  is  by  means  of  rivets5  and  that 
the  structures  shall  be  equally  strong  in  all  its  parts  it  is  essential 
that  the  joints  shall  be  carefully  designed. 

A  rivet  is  a  piece  of  metal  with  a  solid  head  at  one  end,  and  a 
long  circular  shank. 

Riveting  consists  of  heating  the  rivet,  passing  it  through  the 
holes  in  the  plates  to  be  united  while  hot,  and  then  forging 
another  solid  head  out  of  the  projecting  end  of  the  shank. 


364 


RIVETED  JOINTS. 


The  hammering  causes  the  heated  shank  to  fill  all  parts  of  the 
holes,  and  the  contraction  of  the  metal,  as  it  cools,  draws  the 
heads  together,  thus  firmly  forcing  and  holding  the  pieces 
together. 

Rivets  are  generally  made  either  of  mild  steel  or  the  best 
wrought  iron,  the  latter  being  the  most  reliable.  The  rivet- 
heads  are  made  in  four  ways,  as  shown  in  Fig.  5. 


Fig.  5. 

The  first  shape  is  the  one  generally  used.  The  second  and 
third  are  used  only  for  their  appearance;  and  the  fourth,  or 
counter-sunk  head,  is  only  used  when  a  smooth  surface  is  desir- 
able, as  over  a  bearing  plate. 

The  exact  sizes  of  heads,  shapes;  etc.,  of  rivets  vary  in  differ- 
ent mills. 

When  the  size  of  rivet  is  specified  the  hole  is  always  made  ^ 
inch  larger;  but  the  rivet  is  generally  designated  by  the  size  of 
the  hole. 

Pitch. — The  distance  between  the  centres  of  the  rivets,  in 
the  line  of  riveting,  is  called  the  pitch.  This  (for  practical 
reasons)  should  never  be  less  than  2}  diameters ;  nor  should  the 
centre  of  the  hole  (if  possible)  be  nearer  to  any  edge  than  1J 
diameters.  In  angle  work,  however,  it  is  often  necessary  to 
make  the  distance  from  the  edge  less  than  the  above,  but  in  thick 
plates  it  should  always  be  more.  In  drilled  work  the  pitch 
might  be  reduced  to  2  diameters.  If  rivet-heads  are  counter- 
sunk the  pitch  should  be  increased  according  to  the  amount  of 
metal  cut  away,  to  make  room  for  the  rivet-head. 

Rivet-holes  are  generally  made  by  punching,  by  a  powerful 
steam-punch,  as  this  is  much  the  cheapest  method,  The  best 


RIVETED  JOINTS.  365 

way  to  make  the  holes  is  to  drill  them  after  the  pieces  are  bolted 
or  clamped  together. 

Punching  makes  a  ragged  and  irregular  hole,  and  injures  the 
metal  about  the  hole,  causing  a  loss  of  strength  to  the  remaining 
portion  of  the  metal  of  15  per  cent,  in  wrought-iron,  and  often  35 
per  cent,  in  steel. 

Besides  this,  in  punching  there  is  liability  of  cracking  the  plate, 
and  of  not  having  the  holes  in  the  two  plates  that  are  to  be  united 
come  exactly  opposite  each  other. 

The  hardening  of  the  metal  by  punching  also  decreases  the  duc- 
tility of  the  pieces. 

The  injury  done  by  punching  in  steel  plates  may  be  almost  en- 
tirely removed,  however,  by  annealing,  and  in  first-class  work 
this  should  always  be  done. 

In  drilled  work  there  is  no  loss,  and  the  holes  are  not  only 
accurately  located,  but  accurately  cut,  and  the  strength  of  the 
remaining  fibres  is  even  increased  from  12  to  25  per  cent. 

The  cost  of  drilling,  however,  is  very  great,  so  that  it  is  not 
likely  to  be  employed,  except  in  making  the  joints  in  trusses  and 
connecting  tie-bars,  where  the  number  of  rivets  is  not  great. 

A  medium  course  between  punching  and  drilling  is  to  punch 
the  holes  a  size  smaller  than  desired,  and  then  drill  or  ream  them 
to  actual  size,  when  partially  secured  together.  The  loss  of 
strength  by  this  method  will  be  very  slight. 

In  most  cases,  however,  the  architect  will  have  to  be  satisfied 
with  punched  holes,  and  must,  therefore,  allow  sufficient  metal  to 
make  good  any  damage  done,  or  for  any  inaccuracies. 

In  driving  and  heading  the  rivet,  however,  machine  riveting  is 
much  better  than  hand  riveting,  as  a  greater  pressure  is  used, 
and  the  metal  more  completely  fills  the  hole. 

In  designing  riveted  work,  whether  to  be  hand  or  machine" 
riveted,  the  architect  must  bear  in  mind  the  necessity  of  placing 
the  rivets  so  that  they  can  be  inserted  in  the  holes  from  one  side 
and  hammered  from  the  other;  and  for  machine  work,  that  the 
machine  can  reach  them.  Thus,  the  minimum  distance  from  the 
inside  face  of  one  leg  of  an  angle  iron  to  centre  of  nearest  rivet- 
hole  in  other  leg  should  be  at  least  li  inch  for  f-inch  rivets,  1  inch 
for  f-inch  rivets,  J  inch  for  f-inch  rivets,  %  inch  for  J-inch  rivets; 
and,  if  possible,  these  distances  should  be  increased. 

Failure  of  Riveted  Joints.  —  Riveted  joints  may  yield  in  any 
one  of  five  ways : 

1st.  By  the  crushing  of  the  plate  in  front  of  the  rivets  (Fig.  6). 


366 


RIVETED   JOINTS. 


2d.   By  the  shearing  of  the  rivets  (Fig,  7). 

3d.   By  the  tearing  of  the  plate  between  the  rivet-holes  (Fig.  8). 

4th.   By  the  rivet  breaking  through  the  plate  (Fig.  9). 

5th.  By  the  rivet  shearing  out  the  plate  in  front  of  it. 


Fig.  6 


Fig.  7 


Fig.  8 


Fig.  9 


The  two  latter  cases  are  likely  to  occur  only  in  the  case  of  a 
single  riveted  lap-joint. 

To  design  a  riveted  joint  so  that  it  will  not  break  in  either  of 
these  ways,  it  is,  therefore,  necessary  to  calculate  for  the  shearing 
strength  of  the  rivets,  for  the  crushing  strength  of  the  plates  joined, 
and  to  space  the  rivets  far  enough  apart  that  the  metal  will  not 
tear  between  the  rivets. 

The  process  of  designing  a  riveted  joint  practically  consists  in 
first  assuming  the  size  of  rivet  to  bo  used,  and  then  catenating  the 
number  required  to  resist  shearing  and  to  prevent  the  crushing 
of  the  plates  joined,  and  then  using  the  larger  number.  They 
are  then  spaced  by  the  rule  that  the  pitch  shall  not  be  less  than 
2J  diameters,  nor  more  than  16  times  the  thickness  of  the  thin- 
nest plate  at  the  joint,  and  the  distance  from  the  centre  of  the 
rivet  to  end  of  the  plate  should  not  be  less  than  1J  diameters. 
The  following  table  gives  the  sizes  of  rivets  to  be  preferred  for 
different  thicknesses  of  plates: 
For  plates  from  J  inch  to  %  inch  thick,  use  rivet-holes  f  inch  in 

diameter. 
For  plates  from  \  inch  to  f  inch  thick,  use  rivet-holes  f  inch  in 

diameter.* 
For  plates  from  %  inch  to  %  inch  thick  use  rivet-holes  J  inch  in 

diameter. 


*  In  truss  work  f"  rivets  are  generally  used  for  thicknesses  of  plates  and 
angles  from  %o-inch  to  i^lo-inch. 


RIVETED  JOINTS,  367 

For  plates  from  J  inch  to  1  inch  thick,  use  rivet-holes  1  inch  in 
diameter. 

The  number  of  rivets  required  to  resist  shearing  can  be  easily 
determined  by  dividing  the  total  amount  of  strain  by  the  number 
opposite  the  size  of  the  rivet,  in  the  fourth  column  of  Tables  II. 
and  III.,  pages  371  and  372,  if  the  rivet  is  in  single  shear;  and  if  in 
double  shear,  take  one-half  the  number  of  rivets. 

To  find  the  number  of  rivets  required  to  prevent  crushing, 
divide  the  total  amount  of  strain  by  the  bearing  value  of  the  rivet 
given  in  these  tables. 

Note. — Table  III.  should  only  be  used  for  the  connections  of  steel 
floor  beams  and  roof  trusses  where  the  usual  loads  are  to  be  sup- 
ported ;  for  riveted  girders  and  live  loads,  or  where  only  actual 
loads  have  been  provided  for,  Table  II.  should  be  used.  The 
heavy  zigzag  line  in  the  tables  indicates  the  limit  at  which  the 
bearing  value  exceeds  single  shear.  All  values  above  these  lines 
are  in  excess  of  single  shear;  all  values  below  are  less  than  single 
shear. 

The  principal  cases  in  which  riveted  joints  occur  in  build- 
ing construction  are:  1.  In  the  joints  of  wrought-iron  trusses. 
2.  Splicing  of  tie-bars.  3.  In  the  connecting  angles  of  floor 
beams.  4,  In  riveted  girders. 

Splicing  of  Tie-bars. 

Tie-bars  may  be  spliced  in  three  ways. 
1st.  By  a  lap-joint,  as  shown  in  Fig.  10. 


L 


H 


Fig.  10 
2d.  By  a  single  cover  plate,  as  shown  in  Fig.  11. 


Fig.  II 


368  RIVETED  JOINTS. 

3d.  By  two  cover  plates,  as  in  Fig.  12. 


Fig.  12 

In  Figs.  10  and  11  the  rivets  are  in  single  shear;  in  Fig.  12  they 
are  in  double  shear.  The  last  method  is  much  the  best,  although 
it  is  also  the  most  expensive.  The  cover  plates  should  always  be 
the  full  width  of  the  bars  connected,  and  ^  inch  more  in  thickness 
for  the  two  plates,  or  for  one  single  plate. 

For  lapped  joints,  which  is  the  most  common  joint  used,  the 
rivets  should  be  arranged  as  in  Fig.  13,  in  which  case  the  plates 


D  c  B  A 


Fig.  13 

are "  only  weakened  by  the  width  of  one  rivet-hole,  at  A.  At  B7 
two  rivet-holes  are  lost,  but  the  strain  has  been  reduced  by  an 
amount  equal  to  the  value  of  one  rivet-hole  and  so  on. 

If  the  plates  are  narrow  and  thick,  the  rivets  may  be  arranged 
as  in  Figs.  14  or  15. 


Fig.  14 

Where  cover  plates  are  used,  Fig.  15  is  the  best  arrangement, 
for  by  it  the  cover  plates  are  weakened  by  only  two  rivet-holes 
(the  ones  nearest  the  joint) ;  while  in  Fig.  14  the  cover  plates 


RIVETED  JOINTS.  369 

are  weakened  by  three  holes  nearest  the  joint,  and,  consequently, 
must  be  made  thicker. 


o  o     i     o  o 

O  OjO  o 

O  O     6  O     O  O 

o'  o  o 

o    o      I      o    o 


Fig.  15 

When  rivets  are  arranged  in  rows,  it  is  called  chain  riveting; 
when  rivets  are  arranged  to  come  opposite  the  space  between  the 
preceding  rivets,  they  are  said  to  be  staggered,  as  in  Figs.  13 
and  14. 

In  designing  riveted  joints  care  must  be  exercised  not  to 
weaken  the  plates  any  more  than  is  absolutely  necessary. 

EXAMPLE  2. — A  12"  X  V  tie-bar  is  so  long  that  it  has  to  be 
made  in  two  pieces  with  a  splice;  the  strain  on  the  piece  is  65,000 
Ibs.  How  many  rivets  will  be  required  ? 

Ans.  We  will  assume  that  the  joint  is  to  be  a  lapped  joint,  as  in 
Fig.  13,  and  that  we  will  use  f-inch  rivets. 

From  Table  IT.  we  find  that  the  resistance  of  a  J-inch  rivet  to 
single  she^r  is  3,310  Ibs.  and  the  bearing  value  for  a  half-inch 
plate  5,630  Ibs.  Dividing  the  strain,  65,000  Ibs.,  by  the  smaller 
of  these  two  quantities,  3,310,  we  find  we  shall  require  20  rivets; 
but  as  20  rivets  will  not  give  us  the  arrangement  we  wish,  we  will 
use  25,  as  in  Fig.  13.  The  distance,  P,  between  the  centres  of 
rivets  measured  on  the  slant  should  be  at  least  2J  diameters,  or 
2J  X  i  inch  =  1J  inches,  or,  we  will  say,  2  inches. 

Beam  Connections. 

EXAMPLE  3. — A  10-inch,  30-lb.  standard  steel  beam  having  a 
span  of  3J  feet  supports  a  load  at  the  centre  of  40,000  Ibs.  and  is 
'framed  at  one  end  to  a  15-inch  50-lb.  steel  beam;  how  many  \-inch 
rivets  will  be  required  in  the  connection  ? 

Ans.  From' the  table  giving  the  properties  of  standard  steel 
I-beams,  we  find  the  web  thickness  of  the  10-inch  beam  to  be 
0.455C%)  inch,  and  of  the  15-inch  beam  to  be  0.558  inch.  The 
standard  connection  angle  for  a  10-inch  beam  (see  Chap.  XV.)  is 
6  X  4  X  i".  The  number  of  rivets  required  in  the  10-inch  beam 


370  .         RIVETED   JOINTS. 

will  therefore  be  determined  either  by  the  bearing  resistance  of 
the  web  of  the  10-inch  beam,  or  by  the  resistance  to  shearing. 
From  Table  III.  we  find  the  bearing  value  of  a  f-inch  rivet  on  a 
%-inch  plate  to  be  5,890  Ibs.  and  the  resistance  to  single  shear 
to  be  4,420  Ibs.  Dividing  one  half  the  load,  or  20,000  Ibs.,  by 
5,890,  we  find  that  4  rivets  will  be  required  to  sustain  the  load 
without  crushing  the  web. 

As  the  rivets  will  be  in  double  shear  the  resistance  of  each 
rivet  will  be  8,836  Ibs.,  and  of  the  4  rivets  35,344  Ibs.,  which  is 
,  in  excess  of  the  load ;  hence  4  rivets  will  be  required  in  the  10-inch 
beam.  In  the  15-inch  beam  the  number  of  rivets  will  be  deter- 
mined by  the  shearing  value,  as  here  the  rivets  are  in  single  shear. 
20,000  Ibs.  divided  by  4,418  requires  5  rivets,  or  say  3  in  each 
angle.  To  accommodate  the  4  rivets  in  the  10-inch  beam,  the 
connection  angle  should  be  6|  inches  long. 

The  standard  connection  for  10-inch  beams  shows  3  rivets 
in  each  flange,  but  the  load  which  we  have  assumed  is  greatly 
in  excess  of  that  for  which  the  standard  connection  is  designed. 
The  maximum  safe  distributed  load  for  this  beam  for  a  10-ft. 
span  is  28,630  Ibs.,  or  14,315  Ibs.  at  each  end,  for  which  3  rivets 
are  ample. 

EXAMPLE  4. — One  end  of  a  10  X  12  wooden  beam  is  supported 
on  a  4  X  4  X  %-inch  angle  bracket,  riveted  to  the  web  of  an  18-inch 
60-/6.  steel  beam;  the  load  on  the  wooden  beam  is  18,000  Ibs.;  how 
many  \-inch  rivets  will  be  required  in  the  bracket  f 

Ans.  As  the  rivets  are  in  single  shear,  and  the  web  and  angle 
are  each  J-inch  thick,  the  number  of  rivets  will  be  determined  by 
the  resistance  to  shearing,  that  being  less  than  the  bearing  value. 
The  load  to  be  supported  by  the  bracket  will  be  one-half  the  load 
on  the  beam,  or  9,000  Ibs.  Dividing  this  by  4,420,  we  find  that 
two  f-inch  rivets  are  not  quite  sufficient,  and  we  must  therefore 
use  either  three  f-inch  rivets,  or  two  f-inch  rivets.  The  f-inch 
rivets  should  be  placed  4  inches  on  centres,  and  the  }-inch  rivets 
6  inches. 

Rivets  in  Plate  Girders. — The  methods  for  proportion- 
ing the  rivets  to  resist  the  various  strains  in  plate  girders  are 
explained  in  detail  in  Chapter  XX. 

Bending  Moment  in  Rivets. — While  pins  should  always 
be  computed  for  resistance  to  cross  breaking,  it  is  not  the  custom 
to  consider  the  bending  moment  in  rivets;  as  in  a  well-riveted 
joint  it  is  practically  impossible  to  produce  any  bending  of  the 
rivet,  neither  do  the  tests  on  riveted  joints  show  any  signs  of  the 


SHEARING  AND  BEARING  VALUES  OF  RIVETS.  371 


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i-l 

rH  rH 

372  SHEARING  AND  BEARING  VALUES  OF  RIVETS. 


HDO 

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RIVET  SIGNS  AND  PROPORTIONS. 


373 


—  t  ^ 

f  - 

J~ 

r  ' 

N 

\::. 

*j 

—  | 

>v 

11 

I 

! 

374 


LENGTHS  OF  RIVETS. 


TABLE      IV.— LENGTHS      OF      RIVETS— LENGTH 
RIVET   SHANK   REQUIRED    TO   FORM   HEAD. 


PLAIN   RIVETS. 


—  GRIP-  — 


NGTH---—--->! 


COUNTERSUNK  RIVETS. 


i<-  -----  GRIP-  .....  > 


0 


K  -----  LENGTH-—  —  >j 


Diameter  in  inches. 


1/2  |  5/8  I  3/4  |  7/8  |     1 


Grip. 


Length  in  inches. 


3% 
4  8 


4% 
4% 
5 

5 '4 
5% 


ey2 

6-l| 

7 
73/8 

7y2 


23/8 

2y2 


3% 
4 


4% 

5 


5% 


6% 

73/8 


2-M 

f 


3M 

4 

4% 

4y2 
s'8 


6% 
6-M 
6% 

7 

7M 
734 


7% 

8 


l3/8 

iy2 
1% 
m 


28 


3V2 

3% 
4 

494 


sy2 

5% 
5% 


Diameter  in  inches. 


1/2      5/8      3/4      7/8 


Length  in  inches. 


1% 

2  8 

2i| 

23/8 


f8 
% 


334 
3% 
4 


1% 


334 

3% 


4% 
4% 


4% 
5 


1*4 

1% 


2% 
2% 

2% 
f8 


aK 

f/8 
4fc 


134 

iK 


334 

4 


4% 
5 

5H 


6 

614 

63/8 

6y2 

6% 


For  weight  of  rivets  see  Index. 


STRENGTH  OF  PINS.  375 

rivets  breaking  in  that  way.  Mr.  C.  W.  Bryan,  engineer  for  the 
Edge  Moor  Bridge  Works,  says:  "Rivets  will  fail  by  flexure 
only  in  those  cases  of  bad  designing  where  the  rivets  are  long  and 
it  is  impossible  to  drive  them  tight  enough  to  have  them  upset 
and  completely  fill  the  holes."  He  also  adds:  "Rivets  are 
never  proportioned  for  flexure."  *  The  only  person  that  considers 
the  bending  moment  on  rivets,  so  far  as  the  author  has  been  able 
to  learn,  is  Mr.  Louis  DeCoppet  Berg,  who  has  taken  up  the 
subject  of  riveted  joints  most  elaborately  in  Chapter  IX.  of  Part 
II.  of  his  "Safe  Building." 

Strength  of  Pins  in  Steel  Bridge  and  Roof 
Trusses. — Iron  and  steel  trusses  are  now  so  generally  used  that 
it  is  necessar}^  for  the  architect  who  is  at  all  advanced  in  his  pro- 
fession to  know  how  to  determine  the  strength  of  the  joints  and 
especially  of  pin  joints;  and  to  facilitate  the  calculation  of  the 
necessary  size  of  pins,  we  give  Table  V.,  which  shows  the  single 
shearing  strength  and  bearing  value  of  pins,  and  Table  VI.,  show- 
ing the  maximum  bending  moment  allowed  in  pins. 

Pins  must  be  calculated  for  shearing,  bending,  and  bearing 
strains,  but  one  of  the  latter  two  only  (in  almost  every  case)  deter- 
mines the  size  to  be  used. 

By  bearing  strain  is  meant  the  force  required  to  crush  the  edges 
of  the  iron  plates  against  which  the  pin  bears. 

The  several  strains  per  square  inch  usually  allowed  on  pin  con- 
nections in  bridges  are:  shearing,  7,500  pounds;  crushing,  12,000 
pounds;  and  bending,  15,000  pounds  for  iron,  and  20,000  pounds 
for  steel.  In  roof  trusses,  22,500  Ibs.  fibre  stress  is  commonly 
allowed. 

The  shearing  strain  is  measured  on  the  area  of  cross-section ;  the 
crushing  strain,  on  the  area  measured  by  the  product  of  the  diam- 
eter of  the  pin  by  the  thickness  of  the  plate  or  web  on  which  it 
bears. 

The  bending  moment  is  determined  by  the  same  rules  as  given 
for  determining  the  bending  moment  of  beams. 

When  groups  of  bars  are  connected  to  the  same  pin,  as  in  the 
lower  chords  of  trusses,  the  sizes  of  bars  must  be  so  chosen,  and 
the  bars  so  placed,  that  at  no  point  on  the  pin  will  there  be  an 
excessive  bending  strain,  on  the  presumption  that  all  the  bars  are 
strained  equally  per  square  inch. 

"'Modern  Framed  Structures,  p.  261. 


376      SHEARING  AND  BEARING  VALUES  OF  PINS, 


g 

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s^ 


BENDING  MOMENT  IN  PINS. 


377 


TABLE  VI.— MAXIMUM  BENDING  MOMENTS  IN  INCH 
POUNDS  TO  BE  ALLOWED  ON  PINS  FOR  MAXI- 
MUM FIBRE  STRAINS  OF  15,000,  20,000,  AND  22,500 
POUNDS  PER  SQUARE  INCH.* 


Diam- 
eter of 
pin. 

Moment 
15r,6oO. 

Moment 
20,000. 

Moment 
22,500. 

Diam- 
eter of 
pin. 

Moment 
15,000. 

Moment 
20,000. 

Moment 
22,500. 

In. 

Lbs.  in. 

Lbs.  in. 

Lbs.  in. 

Inches 

Lbs.  in. 

Lbs.  in. 

Lbs.  in. 

1 

1,470 

1,960 

2,210 

4 

94,200 

125,700 

141,400 

1/^i 

2,100 

2,800 

3,140 

4M 

103,400 

137,800 

155,000 

1^4 

2,880 

3,830 

4,310 

4*4 

113,000 

150,700 

169,600 

Ws 

3,830 

5,100 

5,740 

m 

123,300 

164,400 

185,000 

1^ 

4,970 

6,630 

7,460 

4^ 

134,200 

178,900 

201,300 

1^6 

6,320 

8,430 

9,480 

4% 

145,700 

194,300 

218,500 

I'M 

7,890 

10,500 

11,800 

4% 

157,800 

210,400 

236,700 

l% 

9,710 

12,900 

14,600 

4% 

170,600 

227,500 

255,900 

2 

11,800 

15,700 

17,700 

5 

184,100 

245,400 

276,100 

2^ 

14,100 

18,800 

21,200 

5^ 

198,200 

264,300 

297,300 

16,800 

22,400 

25,200 

5!>4 

213,100 

284,100 

319,600 

2% 

19,700 

26,300 

29,600 

5% 

228,700 

304,900 

343,000 

2V£ 

23,000 

30,700 

34,500 

%y* 

245,000 

326,700 

367,500 

2*1 

26,600 

35,500 

40,000 

5% 

262,100 

349,500 

393,100 

2M 

30,600 

40,800 

45,900 

5% 

280,000 

373,300 

419,900 

2% 

35,000 

46,700 

52,500 

5% 

298,600 

398,200 

447,900 

3 

39,800 

53,000 

59,600 

6 

318,100 

424,100 

477,100 

3V6 

44,900 

59,900 

67,400 

6J^ 

338,400 

451,200 

507,600 

3*4 

50,600 

67,400 

75,800 

6/4 

359,500 

479,400 

539,300 

3% 

56,600 

75,500 

84,900 

6% 

381,500 

508,700 

572,300 

31^ 

63,100 

84,200 

94,700 

6V£ 

404,400 

539,200 

606,600 

3% 

70,100 

93,500 

105,200 

6% 

428,200 

570,900 

642,300 

3?4 

77,700 

103,500 

116,500 

6'K 

452,900 

603,900 

679  ,400 

3% 

8570C 

114,200 

128,500 

&A 

478,500 

638,000 

717,800 

REMARKS. — The  following  is  the  formula  for  flexure  applied  to  pins: 


32 


SAd 
or    -_. 


M  =  moment  of  forces  for  any  section  through  pin. 

S  =  strain  per  sq.  in.  in  extreme  fibres  of  pin  at  that  section. 

A  =area  of  section. 

d  =  diameter. 

TT  =3.14159. 

The  forces  are  assumed  to  act  in  a  plane  passing  through  the  axis  of  the  pin. 

The  above  table  gives  the  values  of  M  for  different  diameters  of  pin,  and 
for  three  values  of  $. 

If  M  max.  is  known,  an  inspection  of  the  table  will  therefore  show  what 
diameter  of  pin  must  be  used  in  order  that  S  may  not  exceed  15,000,  20,000, 
or  22,500  Ibs.,  as  the  requirements  of  the  case  may  be. 

For  railroad  bridges  proportioned  to  a  factor  of  safety  of  5,  it  is  custom- 
ary to  make  S  max.  =  15,000  Ibs.  in  iron  and  =20,000  Ibs.  in  steel. 

*  Carnegie  Steel  Company's   Handbook. 


378  BENDING  MOMENT  IN   PINS. 

The  following  example  will  show  the  method  of  determining 
the  size  of  pin  in  a  simple  joint. 

EXAMPLE  5. — Determine  the  size  of  pin  for  the  joint  shown  by 
Fig.  16,  which  is  in  the  lower  chord  of  a  steel  truss,  the  middle  bar 
being  a  vertical  suspension  rod  merely  to  hold  the  chord  in  place. 


40,000         1  X  4 


40,000         1X4'' 


I 

— I— 

Fig.  16 

Arts.  The  shearing  and  crushing  strain  in  this  case  is  40,000 
pounds.  The  bending  moment  will  be  the  stress  multiplied  by 
the  distance  between  the  centres  of  the  two  outer  bars  or  40,000 
X 1"=  40,000  inch  pounds.  From  Table  VI.,  we  find  that  to 
sustain  a  bending  moment  of  40,000  pounds,  with  a  fibre  strain 
of  20,000  pounds,  will  require  a  2f "  pin.  From  Table  V.  we  find 
that  the  bearing  value  of  a  2f  "  pin  is  but  33,000  pounds,  and  that 
we  must  increase  the  size  of  the  pin  to  3f  inches.  The  shearing 
strength  of  a  3|"  pin  is,  from  Table  V.,  67,000  pounds,  so  that  the 
size  of  pin  we  must  use  in  this  case  is  determined  by  the  bearing 
strain.  To  be  sure  of  the  correct  size  of  the  pin,  one  must 
make  the  calculation  for  all  three  of  the  strains. 

Bending  Moment  in  Pins. 

The  only  difficult  part  of  the  process  of  calculating  the  sizes  of 
pins  will  generally  be  found  in  determining  the  bending  moment. 
In  cases  where  the  strains  all  act  in  the  same  plane,  the  bending 
moment  can  generally  be  determined  by  multiplying  the  outside 
force  by  the  distance  from  its  centre  to  the  centre  of  the  next  bar, 
as  in  the  foregoing  example.  When,  however,  the  forces  act  in 
several  planes,  as  is  generally  the  case,  the  process  of  determining 
the  bending  moment  is  more  difficult,  and  can  be  best  determined 
by  a  graphic  process,  first  published  by  Prof.  Chas.  Green,  and 
included  in  his  lectures  to  the  students  in  engineering  at  the 
University  of  Michigan. 

EXAMPLE  6. — As  the  pieces  acting  on  any  well-designed  joint 
are  symmetrically  arranged,  it  is  unnecessary  to  consider  more 
than  one-half  of  their  number.  Fig.  17  shows  a  sketch  of  one- 
half  the  members  of  a  joint  in  the  lower  chord  of  a  Howe  truss. 


BENDING  MOMENT  IN  PINS.  379 

The  pieces  are  parallel  to  the  plane  of  the  paper,  and  the  pin  is 
perpendicular  to  the  same,  but  drawn  in  cabinet  perspective,  at 
an  angle  of  45°  with  a  horizontal. 

The  bars  are  assumed  to  be  each  one  inch  thick  and  the  channel 
to  have  one-half-inch  web.  The  centre  of  the  hanger  is  f "  from 
the  centre  of  the  channel. 

The  method  of  obtaining  the  bending  moment  is  as  follows : 

Draw  the  line  A  B  (Fig.  18)  at  an  angle  of  45°  with  a  horizontal, 
and,  commencing  with  c,  lay  off  the  distances  between  the  centres 
of  the  bars  to  a  scale  (1 J"  or  3"  to  the  foot  will  be  found  most  con- 
venient) ;  then  draw  the  lines  1-2,  2-3,  etc.,  parallel  to  the  pieces 
which  they  represent  in  the  truss,  to  a  scale  of  pounds.  Resolve 
the  oblique  forces  into  their  horizontal  and  vertical  components 
(in  this  example  there  is  but  one  oblique  force). 

Next  draw  the  stress  diagram  (Fig.  19)  as  follows:  On  a  hori- 
zontal line  lay  off  1-2,  equal  to  the  first  or  outer  force ;  2-3,  equal 
to  the  next,  then  3-4 ;  and  4-1,  being  the  horizontal  component  of 
the  brace,  closes  the  figure.  In  the  same  way,  lay  off  the  vertical 
forces  1-5,  5-6  and  6-1.  If  the  forces  are  correct,  the  sum  of  the 
forces  acting  in  one  direction  will  always  equal  those  acting  in 
the  opposite  direction.  From  1  draw  the  line  1-0  at  45°,  equal  to, 
say,  20,000  pounds,  or  any  other  convenient  number  at  the  same 
scale.  Draw  0  2,  0  3,  0  4,  etc.  Then,  in  Fig.  18,  starting  at  the 
first  horizontal  force,  draw  c  d  parallel  to  0  2,  d  e  parallel  to 
0  3,  e  f  parallel  to  0  4,  and  /  k  parallel  to  0  1. 

In  the  same  way,  starting  at  the  first  vertical  force,  draw  r  s 
parallel  to  0  5,  s  t  parallel  to  0  6,  and  t  v  parallel  to  0  1.  Then  the 
line  c  d  e  f  k  will  represent  the  boundary  of  the  horizontal  ordi- 
nates,  and  r  s  t  v  the  boundary  of  the  vertical  ordinates.  And  to 
find  the  resultant  of  these  ordinates  at  any  point  on  the  pin  it  is 
only  necessary  to  draw  the  diagonal  from  the  ends  of  the  ordinates 
at  that  point.  Thus,  the  resultant  at  X,  Fig.  18,  will  be  m-n,  and 
it  is  evident  that  this  is  the  longest  hypothenuse  which  can  be 
drawn ;  and  this  hypothenuse,  multiplied  by  0-1  (20,000  pounds) 
gives  52,500  pounds  as  the  maximum  bending  moment  on  the 
pin. 

To  obtain  the  maximum  bending  moment  it  is  necessary  to 
take  the  longest  hypothenuse  that  can  be  drawn,  no  matter  at 
what  place  it  occurs. 

If  one  desires  to  try  the  effect  of  changing  the  order  of  the  bars 
on  the  pin,  it  can  readily  be  done.  Suppose  the  diagonal  tie  to 
change  places  with  the  next  chord  bar.  The  horizontal  stress 


380 


.BENDING  MOMENT  IN   PINS. 


diagram  then  becomes  1-2,  2-3,  3-4',  4'-l.     The  equilibrium 
polygons  will  now  be  (Fig.  20)  c  d  e  /'  kf  and  rf  s'  V  w  and  the 


longest  hypothenuse,  w  x,  or  3f",  which  makes  the  bending 
moment  75,000  pounds,  showing  that  the  arrangement  in  Fig.  17 
is  the  best. 


BENDING  MOMENT  IN    PINS. 


381 


As  a  rule,  in  arranging  the  bars  on  a  pin,  thoss  forces  which 
counteract  each  other  should  be  close  together. 

EXAMPLE  7. — To  further  illustrate  this  method  of  determining 
the  bending  moment  on  pins,  we  will  determine  the  bending 


FIG.  24 


moment  for  the  pin  at  the  point  A,  Fig.  21.  This  is  the  same 
truss  as  worked  out  in  Example  10,  Chapter  XXVI.,  the  strains 
given  in  Fig.  21  being  J  of  the  strains  at  the  joint,  as  all  the  pieces 
are  doubled.  Fig.  22  shows  the  size  and  arrangement  of  the  ties 
and  strut.  It  is  assumed  that  the  web  of  the  channel  is  re- 
inforced to  make  it  f"  thick.  Drawing  th  .ne  AB,  Fig.  24 ,  we 
lay  off  the  outer  force  at  a;  then  measuring  off  an  inch,  the  dis- 
tance between  centres  of  the  two  outer  bars,  we  lay  off  the  next 
force  parallel  to  the  direction  in  which  it  acts ;  and  in  the  same 
way,  the  other  two  forces.  The  three  inclined  forces  must  be  re- 
solved into  their  horizontal  and  vertical  components.  We  next 
draw  the  stress  diagram  (Fig.  23)  to  the  same  scale  of  pounds, 
making  1  0  equal  to  20;000  pounds.  The  lines  0  4  and  0  6  happen, 
in  this  case,  to  coincide.  Then,  in  Fig.  24,  we  draw  a  b  parallel 
to  0  2,  b  c  parallel  to  0  3,  c  d=04,  and  d  e  parallel  to  0  1.  In, 


382  STRENGTH  OF  BOLTS. 

the  same  way,  we  obtain  the  line  TijkB.  In  this  case,  it  will  be 
seen  that  the  longest  horizontal  ordinate  is  h  b,  while  at  that 
point  there  is  no  vertical  ordinate;  also,  that  no  hypothenuse 
can  be  drawn  which  will  be  as  long  as  h  b,  so  that  we  must  take 
h  b  as  the  greatest  resultant;  and  this,  multiplied  by  20,000 
pounds,  gives  31,800  pounds  as  the  maximum  bending  moment 
on  the  pin.  It  will  be  seen  that  this  is  just  the  product  of  the 
outer  force  by  its  arm  to  the  centre  of  the  next  bar,  so  that  the 
greatest  bending  moment  is  at  that  point. 

To  determine  the  size  of  the  pin,  we  find,  from  Table  VI.,  that 
for  a  steel  pin  to  sustain  this  moment,  allowing  a  fibre  strain  of 
20,000  pounds,  we  shall  need  a  2|- "  pin.  This  pin  has  a  bearing 
value  of  31,500  pounds  for  a  bar  an  inch  thick.  The  outer  bar  in 
this  case  is  J"  thick,  and  has  a  strain  of  31,800  pounds,  equivalent 
to  42,400  pounds  for  a  1"  bar.  And  we  see,  from  Table  V.,  that 
we  shall  need  to  use  a  3J"  pin  to  meet  this  strain.  The  shearing 
strength  of  a  3J"  pin  is  36  tons,  or  more  than  double  the  strain. 
Hence  we  must  use  a  3J"  pin,  or,  by  increasing  the  thickness  of 
the  bars,  we  might  reduce  the  pin  to  3  inches. 

Strength  of  Bolts  in  Wooden  Trusses  and  Girders. 

The  strength  of  bolts  in  the  joints  of  wooden  structures  is 
something  that  has  been  given  very  little  attention  by  writers  and 
engineers.  The  author  knows  of  but  one  book  which  gives  any 
explanation  of  the  way  in  which  the  size  and  number  of  the  bolts 
should  be  computed,  or  how  to  determine  the  stresses  in  them.* 
The  only  actual  knowledge  that  we  have  of  the  strength  of  bolt 
joints  in  timber  trusses  is  that  derived  from  a  series  of  tests 
made  at  the  Massachusetts  Institute  of  Technology  and  described 
in  the  Technology  Quarterly  for  September,  1897.  The  results 
of  these  tests  were  discussed  by  the  author  in  the  Engineering 
Record  of  November  17,  1900. 

The  following  rules  and  tables  are  entirely  original  with  the 
author;  they  are  based  upon  the  general  principles  of  stresses, 
upon  the  tests  above  referred  to,  and  upon  a  very  extended 
experience  with  wooden  trusses.  The  author  believes  that  when 
correctly  used  they  will  give  perfectly  safe  results  without  an 
undue  excess  of  strength. 

*The  Design  of  Simple  Roof  Trusses  in  Wood  and  Steel  by  M.  A.  Howe, 
C.E. — John  Wiley  &  Sons,  Publishers. 


STRENGTH  OF   BOLTS. 


383 


TABLE  VIT.— PERMISSIBLE  BEARING  VALUE  (END 
COMPRESSION)  OF  BOLTS  IN  TIMBER,  PER  INCH 
OF  LENGTH,  AND  DISTANCE  CENTRE  OF  BOLT 
MUST  BE  FROM  END  OF  TIMBER  OR  FROM  THE 
NEXT  BOLT.* 


Dia- 
meter 
of 

Yellow  pine. 

Oregon  pine 
or  oak. 

Spruce. 

White  or 
soft  pine. 

bolt 
in 

Bear- 

Dis- 

Bear- 

Dis- 

Bear- 

Dis- 

Bear- 

Dis- 

ins. 

ing, 

tance, 

ing, 

tance, 

ing, 

tance, 

ing, 

tance, 

Ibs. 

ins. 

Ibs. 

ins. 

Ibs. 

ins. 

Ibs. 

ins. 

a 

1125 

5 

1012 

44 

900 

5 

750 

5 

1310 

6 

1183 

5 

1050 

54 

880 

54 

1 

1500 

6 

1350 

54 

1200 

6| 

1000 

6 

14 

1690 

7 

1520 

6 

1350 

7 

1125 

7 

H 

1870 

74 

1690 

6f 

1500 

74 

1250 

8 

if 

2060 

8 

1860 

7* 

1650 

8 

1375 

9 

i* 

2250 

9 

2025 

8" 

1800 

9 

1500 

10 

if: 

2625 

10 

2360 

9 

2100 

10 

1750 

11 

2 

3000 

11 

2700 

10 

2400 

12 

2000 

12 

2J 

3375 

12 

3040 

11 

2700 

134 

2250 

13* 

24 

3750 

13 

3375 

12 

3000 

15 

2500 

15 

2j 

4125 

14 

3710 

13 

3300 

16* 

2750 

16J 

3 

4500 

15 

4050 

14 

3600 

18 

3000 

18 

*  Based  on  a  bearing  resistance  of  1500  Ibs.  per  sq.  in.  for  Southern  yellow 
pine,  1350  Ibs.  for  oak  and  Oregon  pine,  1200  Ibs.  for  spruce,  and  1000  Ibs. 
for  white  pine. 

TABLE  VIII.— PERMISSIBLE  BEARING  VALUE  (ACROSS 
THE  GRAIN)  OF  BOLTS  IN  TIMBER,  PER  INCH 
OF  LENGTH.* 


Diameter 
of  bolt 
in  ins. 

Yellow 
pine. 

Oregon 
pine. 

Spruce. 

White 
pine. 

Oak. 

| 

375 

300 

225 

187 

450 

•J 

437 

350 

262 

220 

525 

1 

500 

400 

300 

250 

600 

If 

562 

450 

337 

280 

675 

14 

625 

500 

375 

310 

750 

if 

687 

550 

412 

345 

825 

14 

750 

600 

450 

375 

900 

if 

875 

700 

490 

437 

1000 

2 

1000 

800 

600 

500 

1200 

*  Based  on  unit  stresses  of  600  Ibs.  per  sq.  in.  for  oak,  5.00  for  Southern, 
yellow  pine,  400  for  Oregoii  pine,  300  f.or  spruce,  and  250  far  white  Dine* 


384 


STRENGTH   OF   BOLTS. 


TABLE  IX.— MAXIMUM  PERMISSIBLE  TENSION, 
SHEAR,  AND  BENDING  MOMENT  (IN  INCH- 
POUNDS)  FOR  WROUGHT-IRON  BOLTS  IN 
TIMBER. 


Diam. 

Diam. 

of 

Ten- 

Single 

Bending 

of 

Ten- 

Single 

Bending 

bplt 

sion, 

shear, 

moment, 

bolt 

sion, 

shear, 

moment, 

in 

Ibs.* 

Ibs. 

inch-lbs. 

in 

Ibs.* 

Ibs. 

inch-lbs. 

ins. 

ins. 

| 

6,000 

4,420 

931 

If 

35,000 

24,050 

11,800 

8" 

8,400 

6,010 

1,479 

2 

45,000 

31,416 

17,700 

1 

10,860 

7,850 

2,210 

2f 

60,000 

39,760 

25,200 

H 

13,720 

9,940 

3,140 

2| 

74,000 

49,080 

34,500 

H 

17,700 

12,270 

4,310 

2f 

92,000 

59,400 

45,900 

if 

21,400 

14,480 

5,740 

3 

108,000 

70,700 

59,600 

fi 

25,740 

17,670 

7,460 

3} 

130,000 

82,950 

75,800 

Unit  stresses:  Tension,  20,000  Ibs.,  shear,  10,000  Ibs.,  bending  22,500  Ibs. 
*  To  be  used  only  in  truss  joints.     Not  safe  for  rods. 

General  Principles. — As  a  rule,  bolts  as  used  in  wooden  trusses 
and  girders  are  subject  to  the  same  kind  of  stresses  as  pins  or 
rivets  in  steel  structures,  although  occasionally  they  are  subject 
only  to  direct  tension.  When  the  pieces  joined  are  not  more  than 
two  inches  thick,  so  that  they  can  be  drawn  tightly  together, 
thereby  producing  a  good  deal  of  resistance  from  friction,  the 
bolts  may  be  considered  as  rivets  and  proportioned  for  shearing 
and  bearing  only,  the  bending  moment  being  neglected. 

When  the  pieces  of  wood  joined  are  more  than  two  inches  thick, 
the  bolts  should  be  proportioned  for  shearing,  bearing,  and 
flexure. 

Tables. — To  facilitate  computing  the  number  and  size  of  the 
bolts,  the  author  has  prepared  Tables  VII.,  VIII.,  and  IX.,  giving 
the  safe  resistance  of  bolts  of  different  sizes  to  each  kind  of  stress, 
and  also  the  length  of  wood  required  beyond  or  between  the  bolts 
to  prevent  shearing  of  the  wood. 

The  bearing  resistance  is  determined  by  the  resistance  of  the 
wood  to  crushing,  and  not  by  the  resistance  of  the  bolt,  but  for 
convenience  it  is  considered  as  a  property  of  the  bolt.  The 
resistance  of  wood  to  crushing  across  the  grain  being  very  much 
less  than  against  end  wood,  the  bearing  resistance  both  ways  is 
given.  With  these  tables  it  is  only  necessary  to  compute  the 
stress  of  each  kind,  and  to  select  the  bolt  or  number  of  bolts  that 
will  resist  all  of  the  stresses. 


STRENGTH  OF  BOLTS.  385 

The  unit  stresses  allowed  in  computing  the  tables  are  some- 
what larger  than  are  recommended  for  struts  or  rods,  but  for  the 
conditions  under  which  bolts  are  generally  used  the  author 
believes  the  tables  may  be  used  with  perfect  confidence.  The 
safe  tension  given  in  Table  IX.,  however,  should  only  be  used 
when  the  stress  is  computed  as  directed  in  Case  V. 

Special  Cases. — The  various  ways  in  which  bolts  are  used  in 
wooden  structures  to  transmit  a  load  or  stress  from  one  piece  to 
another  are  illustrated  by  Figs.  25  to  35,  which  may  be  divided 
into  five  cases,  each  of  w7hich,  to  make  the  explanation  more 
readily  understood,  is  treated  separately. 

Case  1.  Bolts  in  Built-up  Tie-beams. — Figs.  25  and  26.  Tie- 
beams  of  wooden  trusses,  when  more  than  30  feet  long,  must 
usually  be  built  up  of  several  pieces  on  account  of  the  expense 
of  a  single  stick  of  timber  of  the  full  length.  Such  tie-beams 
can  generally  be  built  to  the  best  advantage  of  2-inch  plank, 
breaking  joint  and  bolted  together  side  by  side. 

As  the  tensile  stress  in  a  tie-beam  is  often  very  considerable, 
the  placing  of  the  joints  and  the  size  and  number  of  the  bolts 
must  be  determined  with  much  care,  otherwise  the  beam  may 
be  pulled  apart  longitudinally  so  as  to  permit  the  truss  to  sag, 
or  possibly  to  collapse. 

EXAMPLE  8. — Fig.  25  is  given  as  a  typical  example  of  a  built 
tie-beam.  It  represents  the  tie-beam  of  a  six-panel  Howe  Truss 
of  50  feet  span  carrying  two  floors  and  a  roof,  the  direct  tension 
in  the  different  panels  being  as  indicated  on  the  lower  line.  The 
thickness  of  the  planks  are  drawn  out  of  proportion  to  the 
length  in  order  to  more  clearly  show  the  end-joints.  The  black 
circles  in  the  centre  plank  represent  the  vertical  rods.  The  wTood 
is  to  be  Oregon  pine. 

It  will  be  seen  that  the  rods  practically  cut  the  centre  plank 
in  two,  and  for  this  reason  it  is  better  to  build  the  tie-beam  of  an 
uneven  number  of  planks  rather  than  of  an  even  number,  and  the 
centre  course  of  planks  should  be  jointed  at  the  rods. 

No  dependence  is  placed  upon  the  centre  course  of  planks  for 
resisting  the  tension,  although  they  count  in  resisting  the  trans- 
verse strain. 

The  length  of  the  planks  that  should  be  used  for  the  outer 
courses,  and  the  way  in  which  they  should  break  joint,  is  a 
matter  that  will  vary  for  different  trusses,  and  for  which  no 
definite  rule  can  be  given. 

In  general  the  planks  should  be  of  such  length  and  so  arranged 


386 


STRENGTH  OF  BOLTS. 


that  the  distance  between  the  joints  in  adjacent  courses,  as  at 
X  and  y,  will  be  as  great  as  practicable,  and  so  that  not  more  than 
two  joints  will  come  opposite  each  other. 

For  the  tie-beam  in  question,  the  length  and  arrangement 
shown  is  as  good  as  can  be  devised.  This  gives  a  distance  be- 
tween X  and  y  of  12  feet ;  which  is  about  as  little  as  would  answer. 
At  the  centre,  where  the  stress  is  greatest, 
only  one  joint  occurs  at  any  given  cross 
section. 

In  this  beam,  the  two  outer  planks  A' A 
must  be  capable  of  resisting  the  full  tensile 
strength  in  the  centre  panels  of  the  truss, 
and  the  planks  B  and  C  must  transmit  the 
stress  in  the  second  panel  to  the  end  braces. 
We  must  therefore  place  enough  bolts  be- 
.  tween  the  joints  X-Y  to  transmit  the  stress 
from  the  outer  planks  to  planks  B  and  C. 

The  stress  to  be  transmitted  is  the  stress 
in  the  second  panel,  or  58,000  Ibs.     We  may 
|     assume  that  A'  will   receive   one  half  of 
J     this,  or  29,000  Ibs.,  and  that  if  we  provide 
I     enough  bolts  to  transmit  29,000  Ibs.  from 
[j     A'  to  B,  the  other  side  of  the  tie-beam  will 
carry  a  like  strain. 

These  bolts  must  be  computed  for  shear- 
*  ing  and  bearing.  The  bolts  will  be  in  single 
shear  between  A'  and  B.  We  will  now  see 
how  many  1-inch  bolts  will  be  required  to 
resist  a  shearing  and  bearing  stress  of 
29,000  Ibs. 

From  Table  IX.  we  find  the  resistance 
of  a  1-inch  bolt  to  single  shear  to  be  7,850 
Ibs. ;  hence,  to  resist  a  stress  of  29,000  Ibs. 
will  require  four  bolts. 

The  resistance  of  a  1-inch  bolt  in  Oregon 
pine  (Table  VII.)  is  1,350  Ibs.  per  inch  of 
bearing.  As  the  bearing  in  each  plank  is  2  inches,  we  have 
2,700  Ibs.  as  the  safe  resistance  to  bearing  of  one  bolt,  conse- 
quentlv  it  will  require  eleven  1-inch  bolts  to  avoid  crushing  the 
wood.  As  the  number  is  larger  than  that  required  to  resist 
shearing,  it  is  the  number  of  bolts  required. 


STRENGTH   OF   BOLTS.  387 

These  bolts  must  be  placed  between  the  points  X  and  Y  at 
each  side  of  the  centre.  From  the  distance  column  in  Table  VII. 
we  see  that  the  bolts  should  be  placed  at  least  5J  inches  from 
the  end  of  the  planks.  Calling  it  6  inches  and  putting  two  bolts 
atX  and  two  at  Y,  we  must  divide  the  remaining  space,  11  feet, 
by  the  remaining  7  bolts.  As  there  will  be  8  spaces,  the  bolts  will 
be  16  J  inches  apart,  longitudinally.  They  should  be  staggered, 
as  shown  in  Fig.  26. 


Joint 

Vspike 

* 

//  ' 
<-6^ 

t 

jl/"      ,      ,        xU                       -J  ' 

,M 

i 

rzr 

Fig.  26.—  Elevation  of  Beam  opposite  X. 

These  11  bolts  each  side  of  the  centre  will  be  sufficient  to 
transmit  the  entire  tensile  stress  to  the  supports,  but  bolts 
should  also  be  inserted  between  the  points  Y-Y',  and  between 
X-X'  and  the  ends,  to  bind  the  planks  together.  These  bolts, 
however,  need  not  be  as  large,  nor  as  near  together;  f-inch 
bolts  will  answer,  spaced  about  2  feet  on  centres.  Two  bolts 
should  always  be  placed  at  the  end  of  a  built  tie-beam. 

The  bolts  should  be  of  wrought  iron  or  mild  steel,  driven 
through  holes  of  the  same  size  as  the  bolt,  provided  with  washers, 
and  the  nuts  screwed  up  tight, 

Case  II.  Bolts  in  Girders,  as  in  Figs.  27  and  28.  —  The  construc- 
tion shown  by  Figs.  27  and  28  is  very  commonly  used,  where  a 
girder  cannot  project  its  entire  depth  below  the  floor  joists. 
The  bolts  in  Fig.  27  should  be  computed  for  resistance  to  bearing 
and  shearing,  and  in  Fig.  28  to  bearing,  shearing,  and  flexure. 
In  either  case  the  resistance  to  single  shear  must  equal  S  or  S', 
whichever  is  the  larger. 

Bearing  on  wood  per  inch= 


In  case  Fig.  28,    Bending  moment  =  '-jL  or  ^-~-9  whichever  is 
larger,  B  and  L  being  measured  in  inches. 


388 


STRENGTH   OF   BOLTS. 


EXAMPLE  9. — We  will  suppose  that  we  wish  to  use  the  con- 
struction shown  in  Fig.  27.  The  girder  to  be  S"X14",  with  a 
span  of  14  ft.  The  floor  joists  to  be  3"X  12",  with  a  span  of  20 
ft.,  measured  from  the  centres  of  girders.  Joists  and  girders  to 
be  of  Oregon  pine.  Angles  to  be  4"X3i"Xf".  The  floor  load 
to  be  figured  at  60  Ibs.  per  sq.  ft.,  including  weight  of  floor. 


Fig.  28 


How  many  and  what  size  bolts  should  be  used,  S  and  Sf  being 
equal? 

Ans.  The  floor  area  supported  by  girder=  14  X  20=  280  sq.  ft. 
at  60  Ibs.  persq.  ft.  S  +  S'=  280X60  =16,800  Ibs.  or  S=  8,400 Ibs. 
Try  J"  bolts.  Total  single  shear  =8,400  Ibs.  Resistance  of  one 
f"  bolt  to  single  shear,  (see  Table  IX.)  =  4,420  Ibs.  Hence  two 
bolts  will  resist  the  shearing  stress. 

.     ,      16,800      16,800 
Bearing  stress  per  mch=- 


~ 


8 


-  =  2,100  Ibs. 


Bearing  resistance  of  one  f"  bolt  in  Oregon  pine,  across  the 
grain,  Table  VIII,  =  300  Ibs.  Hence  seven  bolts  will  be  required 
to  prevent  crushing  of  the  wood.  As  the  span  is  14  ft.,  this  will 
require  a  f-inch  bolt  every  2  feet.  The  centre  of  the  bolts  should 
be  at  least  3"  above  the  bottom  of  the  girder. 

EXAMPLE  10. — Construction  as  shown  in  Fig.  28.  Girder 
6"X14",  Oregon  pine,  12  ft.  span.  Joists  2"X12",  18  ft.  span 
to  centre  of  girder,  on  each  side.  Total  floor  load  65  Ibs.  per  sq. 
ft.  Strips  on  sides  of  girder  3"X4";  Z/=3".  How  many  and 
what  size  bolts  should  be  used? 

Ans.  Load  supported  by  girder  =  12'  X  18'  X  65  =  14,040  Ibs. 
£=7^020  Ibs.  =  shearing  stress 

14  040 
Bearing  stress  per  inch= — ^ — -  =  2,340  Ibs. 

Bending  moment  =  — — 9    *  =  10,530  Ibs. 


STRENGTH   OF   BOLTS. 


389 


To  resist  the  shearing  stress  will  require  two  f"  bolts.  To 
resist  the  bearing  stress  (use  Table  VIII.)  will  require  eight  f" 
bolts,  or  seven  J- "  bolts. 

To  resist  the  bending  moment  (use  Table  IX.)  will  require 
eleven  f "  bolts,  or  seven  {"  bolts.  Eleven  J"  bolts  would  give  a 
spacing  of  only  about  13",  allowing  for  one  bolt  at  each  end,  and 
this  would  injure  the  girder,  hence  we  must  use  seven  J"  bolts, 
which  would  be  spaced  about  22"  on  centres.  Practically  the 
strain  on  the  bolts  will  be  somewhat  relieved  by  toe-nailing  the 
joists  to  the  girder,  but  it  is  not  safe  to  put  much  dependence 
upon  the  spikes. 

Caselll.  Pin  Bolts,  as  in  Figs.  29-31. — Whenever  ties  or  struts 


1 


ELEVATION 


B' 

—  *,-- 

*8—  >                | 

* 

Q 

m 

B' 

--•t_ 

V2S—  >                  | 

•b 

t 

- 

J                PLAN 
Fig.  29 

are  joined  by  bolts  in  the  manner  indicated  by  Figs.  29-31,  and 
the  thickness  B  exceeds  2  inches,  the  diameter  of  the  bolt  or 


Fig.  30 


390 


STRENGTH   OF   BOLTS. 


bolts  should  be  computed  for  resistance  to  shearing,  bearing  and 
flexure. 

For  any  one  of  these  joints  the  stresses  will  be  as  follows; 

Single  shear  =  -. 

Zi 

Of 

Bearing  pressure  on  pin  per  inch  of  length  =  -^-.* 


T>    j- 

Bending  moment  j  =  —  9  -  . 

//  there  should  be  more  than  one  bolt,  divide  the  stress  obtained 
by  the  above  formulas  by  the  number  of  bolts,  to  find  the  stress 
in  each  bolt. 


Fig.  31 

In  Fig.  29  S  equals  the  horizontal  component  of  the  thrust  T. 

EXAMPLE  11. — Construction  as  in  Fig.  29.  A  6"  X 10"  raf ter 
is  joined  to  two  3"X  10"  tie-beams  by  a  single  bolt.  The  thrust 
in  the  rafter  is  30,000  Ibs.,  and  the  angle  between  the  rafter  and 
tie-beams  is  30  degrees.  What  should  be  the  diameter  of  the 
bolt,  the  timber  being  spruce? 

Ans.  The  horizontal  component  of  30,000  Ibs.  at  an  angle  of 
30°  is  practically  26,000  Ibs.  Then  S=  26,000,  B=§  inches, 
L=9  inches.  Single  shear  =13,000  Ibs. 

26  000 
Bearing  pressure  per  inch  of  bolt  =— -^ —  =  4,333  Ibs. 


Bending  moment 


=19,500  Ibs. 


*  This  holds  good  only  when  B'  in  Figs.  29  and  30  is  one  half  or  more  of 
B,  and  for  Fig.  31,  when  B'  is  two  thirds  or  more  of  B. 

f  Based  on  the  supposition  that  the  bolt  acts  as  a  beam  fixed  at  both  ends 
and  uniformly  loaded. 


STRENGTH  OF   BOLTS.  391 

From  Table  IX.  we  find  that  to  resist  a  shearing  stress  of  13,000 
Ibs.  will  require  a  1  f  "  bolt,  and  to  resist  a  bending  moment  of 
19,500  Ibs.  will  require  a  21-inch  bolt. 

To  resist  a  bearing  pressure  of  4,333  Ibs.  on  end  wood  in  spruce 
will  require  a  larger  bolt  than  is  given  in  the  table  (Table  VII.). 
If  we  divide  our  stress  of  4,333  Ibs.  by  1,200,  the  allowed  pressure 
per  sq.  inch  for  spruce,  we  obtain  3|  inches  for  the  diameter 
of  the  bolt;  hence  in  this  example  the  diameter  of  the  bolt  is 
determined  by  the  bearing  pressure.  This  is  a  larger  bolt  than  it 
is  desirable  to  use,  and  we  will  see  what  diameter  will  be  required 
if  we  make  the  strut  8"X8",  and  the  tie-beams  4"X8",  as  the 
strength  of  the  timber  would  be  about  the  same. 

Using  these  dimensions,  B=S  ins.  and  L,  12  ins.     This  will 

26  000 
give  us  a  bearing  pressure  of—     — =3,250  Ibs.  and  a  bending 

o 
oc  f\C\(\  V  1  2 

moment  of      '     "          =  26,000  Ibs.     The  shear  will  be  the  same 

\£i 

as  before,  as  it  is  not  affected  by  the  width  of  B. 

To  resist  a  bearing  pressure  of  3,250  Ibs.  will  require  (see 
Table  VII.)  a  2J"  bolt,  and  to  resist  a  bending  moment  of  26,000 
Ibs.,  a  2J"  bolt.  Hence  if  we  make  the  strut  8"XS"  we  should 
use  a  2f"  bolt,  and  D  should  be  16J"  (from  Table  VII,). 

EXAMPLE  12. — Same  construction  as  above,  but  with  three 
bolts,  placed  as  shown  by  dotted  circles,  instead  of  one.  Strut 
to  be  6"  X 10" ;  tie-beams,  3"  X 10",  spruce.  Stress  to  be  the  same 
as  in  the  above  example.  The  shearing,  bearing,  and  bending 
stresses  will  also  be  the  same,  but  as  we  are  using  three  bolts,  each 
stress  should  be  divided  by  three. 

This  will  give  the  stress  on  each  bolt,  and  the  corresponding 
size  of  bolt,  as  follows: 


Shearing  stress     =4,333  Ibs.,  requires  a  f-inch  bolt. 

Bearing  pressure  =1,444  Ibs.,         "         "  11-inch  bolt. 

Bending  moment=  6,500  Ibs.,         "         "  IJ-inch  bolt. 

In  this  case  the  bending  moment  requires  the  largest  bolt,  and 
we  must  use  three  1  J-inch  bolts. 

EXAMPLE  13.— Construction  as  in  Fig.  30.  Centre  beam  to 

be  6"X8",  and  outer  beams  3"X8",  all  of  Oregon  pine. 


392 


STRENGTH  OF  BOLTS. 


Assume  tension  in  centre  beam  to  be  24,000  Ibs.    What  should  be 
the  diameter  of  the  bolt? 

.4ns.  £=24,000;  £=6",  and  L= 9". 

Single  shear=  12,000  Ibs. 
Bearing  pressure  per  inch= — '— — =4,000  Ibs. 

Bending  moment  =  24'°P)? X  9=  18,000  Ibs. 
\2i 

To  resist  the  shear  will  require  a  1J"  bolt,  to  resist  bearing 
pressure  a  3"  bolt,  and  to  resist  the  bending  moment  will  re- 
quire a  2J"  bolt.  For  a  3"  bolt  the  distance  D  should  be  14". 

EXAMPLE  14. — Same  conditions  as  in  Example  13,  except  that 
two  bolts,  one  behind  the  other,  will  be  used.  With  two  bolts, 
each  stress  will  be  one-half  of  that  for  a  single  bolt.  Dividing 
the  stresses  obtained  in  example  13  by  2,  we  have: 

Single  shear  =6,000  Ibs.,  requires  a  f-inch  bolt. 
Bearing  pressure  =2,000  Ibs.,  requires  a  IJ-inch  bolt. 
Bending  rnoment=  9,000  Ibs.,  requires  a  If-inch  bolt. 

Hence  the  size  of  the  bolt  is  determined  by  the  bending 
moment,  and  we  must  use  two  If -inch  bolts.  For  a  If -inch  bolt 
D  should  be  at  least  8J  inches,  and  the  distance  between  the 
bolts  an  inch  or  so  more,  say  10  inches. 

Case  IV.  Strop  and  Bolt  Joint,  as  in  Fig.  32. — The  construc- 
tion indicated  by  Fig.  32  is  sometimes  used  to  secure  the  foot  of 

b 


Fjg.  32 

the  rafter  in  wooden  trusses  to  the  tie-beam.  When  the  dis- 
tance D  is  sufficient  to  resist  the  shearing  stress,  as  explained 
at  the  beginning  of  this  chapter,  the  strap  is  only  of  value  in 


STRENGTH  OF  BOLTS.  393 

holding  the  rafter  in  place,  and  the  bolt  is  not  subject  to  any 
great  stress.  When  it  is  impossible  to  get  the  necessary 
length  for  D,  then  the  strap  and  bolt  should  be  computed  to 
resist  the  full  stress. 

As  the  strap  should  not  usually  be  more  than  J"  to  f  "  thick, 
only  the  shear  and  bearing  pressure  on  the  bolt  need  be  con- 
sidered. These  should  be  computed  as  follows: 

S 
Single  shear  =  — = tension  in  strap. 

A 

S 
Bearing  pressure  per  inch  on  wood=-o  where  B= breadth  of 

tie-beam  in  inches. 

Cf 

Bearing  pressure  per  inch  on  strap =--,  where  t  equals  thickness 

of  strap  in  inches. 

To  find  the  value  of  S,  draw  a  line  T,  representing  the  thrust  in 
the  rafter  to  a  scale  of  pounds  to  the  inch,  and  parallel  with  the 
axis  of  the  rafter.  From  the  end  a  draw  an  indefinite  line  parallel 
to  the  axis  of  the  strap,  and  from  the  end  b  a  line  at  right  angles 
to  the  seat  of  the  rafter.  These  lines  will  intersect  at  (7,  and  ac, 
measured  by  the  scale  used  in  drawing  T,  will  give  the  value  of 
S  in  pounds.  If  the  rafter  in  Fig.  32  rests  on  the  top  of  the  tie- 
beam,  then  be  will  be  vertical,  but  if  the  tie-beam  is  notched  out, 
as  shown  by  the  dotted  lines,  then  the  line  from  b  should  be  drawn 
at  right  angles  to  the  bottom  of  the  notch,  which  will  give  the  point 
cf.  It  will  be  seen  that  notching  the  tie-beam  increases  the  stress 
in  the  strap. 

EXAMPLE  15. — In  a  king  rod  truss  of  36  feet  span  the  com- 
pression in  the  rafter  is  18,000  Ibs.,  and  the  inclination  of  the 
rafter  45°.  The  rafter  is  to  be  6"  X  6"  and  the  tie-beam  6"  X  8", 
both  of  spruce.  What  size  strap  and  pin-bolt  will  be  required  to 
hold  the  foot  of  the  rafter,  without  notching  into  the  tie-beam? 

Ans.  The  first  step  is  to  determine  the  stress  S.  As  the  in- 
clination of  the  rafter  is  45°,  and  the  seat  of  the  rafter  is  hori- 
zontal, the  line  ac  (Fig.  32)  must  equal  ab;  hence  S  will  equal 
T,  or  18,000  Ibs. 

Then  the  single  shear  on  bolt  will  be    9,000  Ibs. 
Tension  in  each  side  of  strap  will  be    9,000  Ibs. 

-lo   AriQ 

Bearing  pressure  per  inch  on  wood=  -1— — =  3,000  Ibs. 

9,000 
Bearing  pressure  per  inch  on  strap,  — — ~. 


394 


STRENGTH   OF   BOLTS. 


That  the  strap  may  not  crush  the  top  of  the  rafter,  it  should 
be  at  least  3  inches  wide.  At  10,000  Ibs.  per  sq.  inch  the  sec- 
tional area  required  in  the  strap  will  be  .9  inch.  If  we  divide  this 
by  the  width  (3)  we  have  .3  inch  for  the  thickness.  We  will 
therefore  make  the  strap  f  inch  thick  and  3  inches  wide.  The 
bearing  pressure  per  inch  on  the  strap  will  then  be 

9,000 


The  bolt  must  therefore  be  able  to  resist  a  single  shear  of 
9,000  Ibs.,  a  bearing  pressure  against  spruce  of  3,000  Ibs.  per 
inch,  and  a  bearing  pressure  '  against  the  strap  of  24,000  Ibs, 
From  Table  IX.  we  find  that  it  will  require  a  l|-inch  bolt  to 
resist  the  shear;  from  Table  VII  we  find  that  it  will  require  a 
2J-inch  bolt  to  reduce  the  pressure  on  the  wood  to  the  proper 
limit,  and  from  Table  V.  of  this  chapter  that  we  should  use  a 
2-inch  pin  for  a  bearing  of  24,000  Ibs.  on  the  strap.  The  largest 
bolt  is  that  required  for  the  bearing  against  the  wood,  or  2J 
inches.  If  the  width  of  the  beam  and  rafter  was  increased  to 


Fig.  33 


Fig.  34 


8  inches,  the  bearing  on  the  wood  per  inch  would  be  reduced  to 
2,250  Ibs.,  which  would  require  only  a  2-inch  bolt;  the  same 
diameter  as  required  for  bearing  on  the  strap.  As  a  rule  this 
form  of  joint  is  not  desirable  for  trusses  having  a  span  of  more 
than  36  feet,  or  where  the  compression  in  the  strut  exceeds 
18,000  Ibs.  It  has  the  advantage  over  the  joint  shown  in  Fig.  33, 
however,  in  that  there  is  no  iron  work  to  project  below  the 
bottom  of  the  tie-beam. 


STRENGTH   OF  BOLTS.  395 

In  the  joint  (Fig.  33)  the  bolt  is  subject  to  direct  tension  only,  the 
stress  in  the  bolt  being  denoted  by  S.  The  value  of  S  is  found 
in  exactly  the  same  way  as  explained  under  Case  IV.  The  rafter 
may  be  let  into  the  tie-beam,  or  it  may  merely  rest  on  top,  the 
stress  in  the  bolt  being  least  in  the  latter  case,  but  it  is  easier  to 
fit  the  members  of  the  truss  together  if  the  rafter  is  let  into  the 
tie-beam  say  1J  or  1J  inches.  If  the  shoulder  is  4  to  6  inches 
long  it  will  hold  the  rafter  while  the  pieces  are  being  fitted 
together,  and  after  they  are  fitted,  the  hole  for  the  bolt  can  be 
bored  in  the  right  position. 

Whenever  S  exceeds  10,000  Ibs.  a  cast  plate,  as  shown  in 
Fig.  34,  made  to  fit  the  inclination  of  the  bolt,  should  be  let  into 
the  bottom  of  the  tie-bearn  for  the  head  of  the  bolt  to  bear 
against.  The  hole  for  the  bolt  should  be  J  inch  larger  than  the 
diameter  of  the  bolt.  The  horizontal  component  of  S  should  be 
determined,  and  the  distances  D  and  D'  made  sufficient  to  resist 
longitudinal  shearing. 

The  horizontal  component  is  found  by  drawing  a  vertical  line 
from  c  and  a  horizontal  line  from  a,  in  the  diagram,  Fig.  33,  in- 
tersecting at  d.  ad,  measured  by  the  scale  of  the  diagram,  will 
give  the  horizontal  component.  The  distance  D  +  D'  should 
equal  the  horizontal  component  divided  by  the  breadth  of  the  tie- 
beam  multiplied  by  the  value  of  F,  Table  I.  of  this  chapter. 

EXAMPLE  16. — Conditions  the  same  as  in  Example  15.  Deter- 
mine the  diameter  of  the  bolt,  and  least  distance  for  D.  In  this 
example  S  will  be  greater  than  in  Example  15,  because  the  seat 
of  the  rafter  is  not  horizontal.  Therefore  draw  T=  18,000  Ibs. 
to  a  scale,  and  parallel  to  the  axis  of  the  rafter.  (See  diagram 
Fig.  33.)  From  the  lower  end  of  T  draw  a  line  parallel  to  the 
bolt,  and  from  b  a  line  at  right  angles  to  the  seat  of  the 
rafter.  These  two  lines  will  meet  at  c,  and  ac  will  give  the 
value  of  8,  which  we  find  to  be  27,000  Ibs.  From  Table  IX.  we 
find  that  it  will  require  a  1  f-inch  bolt  to  resist  a  direct  tension 
of  27,000  Ibs.;  therefore  the  bolt  must  be  If  inches  in  diam- 
eter. On  the  stress  diagram  draw  a  vertical  line  through  c 
and  a  horizontal  line  through  a,  then  ad  represents  the  shearing 
force  to  be  resisted  at  D.  The  line  ad  we  find  measures  19,000 
Ibs.  The  breadth  of  the  tie-beam  is  6  inches,  and  F,  for  spruce, 

Table  I.,  with  the  grain,  is  90  Ibs. ;  then  D  +  D'  must  =  19'000  or  35 

u  xx  yu 

inches,     In  Fig.  33,  D=20  inches,  and  D'  15J  inches;  therefore, 
the  distance  is  sufficient. 


396 


STRENGTH  OF  BOLTS. 


NOTE. — The  author  believes  that  for  computing  the  resistance 
to  longitudinal  shearing,  in  a,  case  like  this,  where  there  is  a  heavy 
compression  on  the  wood  across  the  grain,  it  will  be  perfectly 
safe  to  use  values  for  F  double  those  given  in  Table  I.  This 
opinion  is  based  on  the  tests  made  at  the  Massachusetts  Institute 
of  Technology,  and  mentioned  on  page  382. 

EXAMPLE  17. — To  determine  the  size  of  bolts  for  the  joint 
shown  in  Fig.  35,  the  thrust  in  the  rafter  being  65,500  Ibs.  and 
the  timber  being  yellow  pine. 


Fig.  35 


Ans.  The  first  step  is  to  determine  the  tension  in  the  rods. 
This  is  done  by  drawing  the  diagram,  commencing  with  the  line 
ab,  which  represents  the  thrust  in  the  rafter,  ac  is  drawn 
parallel  to  the  bolts  and  b  c  at  right  angles  to  the  seat  of  the 
rafter.  The  line  ac  scales  96,500  Ibs.,  and  assuming  that  the 
strain  will  be  equal  in  the  two  bolts,  the  tension  in  each  bolt 
will  be  48,250  Ibs.  From  Table  IX.  we  find  that  this  will  require 
a  2-|-inch  bolt.  Therefore  we  must  use  two  bolts  of  2J  inches 
diameter. 

The  horizontal  component  of  ac  is  represented  by  the  line  ad, 
which  scales  68,350  Ibs.  This  will  require  a  shearing  area  in 

hard  pine  of  -  — —  or  547  sq.  inches.     As  the  tie-beam  is  8 


125 


547 


inches  wide  the  length  must  be  ^--  or  68  J  inches.     In  the  draw- 
ee 

ing  we  have  much  more  than  this,  hence  there  will  be  no  danger 
of  the  bottom  plates  shearing  the  wood. 


STRENGTH  OF  BOLTS.  397 

Theoretically,  the  size  of  the  washers  should  be  equal  to  the 
stress  in  one  bolt  divided  by  the  resistance  of  the  wood  to  crushing 

48  250 

across  the  grain,*  or  -~r=—OT$Q  sq.  inches,  but  as  a  slight  crush- 
o(JU 

ing  of  the  fibres  in  this  case  would  do  no  particular  harm,  we 
will  reduce  the  area  to  64  sq.  inches  or  8X  8  inches. 

*  For  resistance  of  woods  to  crushing  across  the  grain,  see  Chapter  XIV. 


398  BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS, 


CHAPTER  XIII. 

PROPORTIONS  OP  CAST-IRON  AND  STEEL 
BEARING  -  PLATES  FOR  COLUMNS, 
BEAMS  AND  GIRDERS,  AND  FOR  BRAC- 
KETS ON  CAST  COLUMNS. 

If  a  heavily  loaded  column  or  girder  should  rest  directly  upon 
a  wall  or  pier  of  masonry,  the  weight  would  be  distributed  over 
such  a  small  area  that  in  most  cases  there  would  be  danger  of 
crushing  the  masonry,  particularly  if  it  were  of  brick  or  rubble 
work.  To  prevent  this  a  bearing-plate  should  be  placed  between 


y/\      \//w/w/y///y////'//'. 

SECTION  y 


Fig.  2 


Fig.  3 

the  end  of  the  beam  or  column  and  the  masonry,  the  size  of  the 
plate  being  such  that  the  load  from  the  column  or  girder  divided 
bv  the  area  of  the  plate  shall  not  exceed  the  safe  crushing  strength 
of  the  masonry  per  unit  of  measurement, 


BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS-  399 

TABLE  I.— MAXIMUM  LOAD  PER  SQUARE  INCH  ON 
DIFFERENT  KINDS  OF  MASONRY  FROM  BEAR- 
ING PLATES. 

For  granite 1,000  Ibs.  per  sq.  in. 

"     best  grades  of  sandstone 700    "      "     "     " 

"     soft  sandstone. 400    "      "     "     " 

"     hard  stone  rubble 150  to  250    "      "     "     " 

"     extra-hard  brickwork  in  cement  mor- 
tar  150  to  200    "      "     "     " 

"     good  hard  Eastern  brickwork  in  lime 

mortar -.  .  .  . 120    "      "     "     " 

"     common  brickwork 100    "      "     "     " 

"     good  Portland  cement  concrete. 200    "      "    /'     " 

"     sand  or  gravel GO    "      ".    "     " 

EXAMPLE  1. — The  basement  columns  of  a  six-story  warehouse 
support  a  possible  load  of  212,000  pounds  each;  under  the  column 
is  a  base-plate  of  cast  iron  resting  on  a  bed  of  Portland-cement 
concrete  two  feet  thick.  What  should  be  the  dimensions  of 
the  base-plate? 

Answer. — As  the  plate  rests  on  concrete,  the  bottom  of  the 
plate  should  have  an  area  equal  to  212,000-^200=1060  square 
inches,  or  33  inches  square.  The  column  should  be  about  10 
inches  in  diameter  and  1  inch  thick.  The  shape  of  the  base-plate 
should  be  as  shown  in  Fig.  1. 

Shape  of  Column  Base-Plates. — For  small  columns  and  wooden 
posts  with  light  loads,  plain  flat  plates  of  cast  iron  are  generally 
used.  They  may  have  a  raised  ring  or  cross  to  fit  inside  the  base 
of  a  hollow  column,  or  for  a  wooden  post  a  raised  dowel,  1 J  inches 
or  2  inches  in  diameter.  If  the  plate  is  very  thick,  a  saving  in 
the  weight  of  the  plate  may  be  made  by  bevelling  the  edge,  as 
shown  in  Fig.  2,  without  loss  of  strength.  The  outer  edge,  how- 
ever, should  not  be  less  than  J-  inch  thick. 

When  the  bearing-plate  is  so  large  that  the  projection  beyond 
the  column  is  more  than  six  inches,  a  ribbed  plate  should  be 
used  similar  to  that  shown  in  Fig.  1 ,  which  is  drawn  for  a  round 
column.  Fig.  9,  Chapter  XIV.,  shows  a  similar  base-plate  for 
an  H-shaped  column.  With  such  plates  no  transverse  strain 
is  developed,  and  if  the  column  is  bolted  to  the  plate,  it  adds 
greatly  to  the  stability  o  f  the  column. 

For  base-plates  similar  to  Fig.  1  the  height  H  should  be  equal 
to  the  projection  P  and  D  should  be  equal  to  the  diameter  of 


400  BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS. 

the  column.  The  thickness  of  all  portions  of  the  plate  should 
be  equal,  or  nearly  so,  to  that  of  the  column  above  the  base, 
This  is  not  so  much  required  for  strength  as  to  get  a  perfect 
casting,  as  such  castings  are  liable  to  crack  by  unequal  cooling 
when  the  parts  are  of  different  thickness.  The  projection  of 
the  flange  C  should  be  at  least  3  inches,  to  permit  of  bolting  the 
column  to  the  plate. 

For  steel  columns,  base-plates  of  steel,  such  as  are  shown  in 
connection  with  the  details  of  Z-bar  and  channel  columns, 
Chapter  XIV,  are  commonly  used,  although  for  very  heavy  steel 
columns  cast-iron  base-plates  are  also  used,  and  where  the  cast 
iron  is  entirely  in  compression,  they  are  to  be  preferred  to  steel 
bearing-plates. 

Calculations  for  Bearing  -Plates.  —  For  ribbed  or  bracketed 
plates,  such  as  Fig.  1,  proportioned  as  above  described,  no  other 
calculation  is  necessary  than  that  of  finding  the  area  of  the  base, 
as  illustrated  by  Example  1.  With  flat  plates,  however,  a  trans- 
verse strain  is  developed  in  the  metal,  and  it  is  necessary  to 
compute  the  thickness  of  the  plate  as  well  as  its  size.  To  find  the 
size  and  thickness  of  flat  plates  under  columns  and  posts  — 

First  determine  the  size  of  the  plate  by  dividing  the  load  on 
the  column  in  pounds  by  the  safe  resistance  of  the  material  on 
which  the  plate  rests,  as  explained  in  Example  1. 

Second.  —  Knowing  the  size  of  the  plate  and  the  size  of  the 
column,  determine  the  projection  of  the  plate  beyond  the  column. 

Let  w  =  pressure  under  the  plate  in  Ibs.  per  sq.  in. 
TF=Load  on  column  in  pounds; 
A  =  Area  of  plate  in  sq.  ins.  ; 
jB=one  side  of  square  plate  in  inches; 
Z)=  diameter  of  round  column  or  side  of  square  post  in 

inches: 
A  '=  difference  between  area  of  plate  and  sectional  area 

of  column; 

P—  projection  of  edge  of  plate  beyond  column  in  inches; 
t*=  thickness  of  plate  in  inches; 
then 


-,  B^VJ,    and 

w' 


For  cast-iron  plates, 


t=       w--'  divided  by  80.  (1) 


BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS.  401 
For  steel  plates, 


t=  A/  -:£-i^_  divided  by  220. 

EXAMPLE  2. — A  yellow-pine  post  12  ins.  square  supports  a 
probable  load  of  115,200  Ibs.  The  post  will  rest  on  a  cast-iron 
plate  bedded  on  first-class  brick  work  in  cement  mortar.  What 
should  be  the  size  and  thickness  of  the  plate? 

Ans.     1^=115,200.     w  =  200.    A  =  115, 200 ^200=  576  sq.  ins. 

£:=\/576=24  ins.     A'=  576 -144=  432  sq.  ins. 

24-12 
p= — - — =6  ins. 


Then  ^ 

\-£  oU 

208 
For  a  steel  plate  t=  -^-  or  1  inch. 

The  cast-iron  plate  may  be  made  2.6  ins.  thick  under  the  post 
and  bevelled  to  1J  ins.  at  the  edges. 

For  a  rectangular  post  the  plate  should  be  proportioned  so  that 
the  projection  will  be  the  same  on  each  side  of  the  post. 

When  computing  the  area  of  bearing-plates  under  columns 
the  probable  load  on  the  column  rather  than  the  possible  load 
should  be  taken. 


Bearing-plates  Under  Beams  or  Girders. 

The  ends  of  heavily  loaded  beams  or  girders  should  rest  on 
bearing-plates,  either  of  iron,  steel,  or  strong  smooth  stone. 

The  area  of  these  bearing-plates  should  be  computed  in  the 
same  way  as  the  area  of  bearing-plates  under  columns. 

The  thickness  of  cast-iron  plates  may  be  computed  by  the  fol- 
lowing formula: 

t=.0 
For  steel  plates 

£=.0137 

in  which  w  =  the  safe  bearing  resistance  of  the  masonry  per  sq. 
inch,  and  P  equals  the  projection  of  the  plate  beyond  the  beam, 
(Fig.  3). 


402  BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS. 

EXAMPLE  3. — A  wooden  beam  10  ins.  wide  supports  a  uniform 
load  of  24,000  Ibs.  What  size  bearing-plate  of  cast  iron  should 
be  used  on  common  brickwork? 

Ans.  Load  on  bearing  plate  =  24,000 -f-2=  12,000  Ibs. 

Area  of  plate  =  12,000 -s- 100=  120  sq.  ins. 

IK 1  n 

Size  of  plate,  8"  X  15".     P=  -       -  =  2$". 

2t 

t=  .024  X  2JV/106=  .024  X  2J  X  10=  .6  ins. 

When  the  theoretical  thickness  is  less  than  an  inch,  the  plate 
had  better  be  made  1  inch  thick. 

EXAMPLE  4. — A  24-inch  80-lb.  steel  beam  supports  a  distributed 
load  of  60,000  Ibs.     What  size  of  bearing-plate  should  be  used 
on  brickwork  capable  of  sustaining  150  Ibs.  per  square  inch? 
Ans.     Load  on  plate=  60,000 ^2=  30,000  Ibs. 
Area  of  plate  =30, 000  -=-150  =200. 
Make  size  of  plate  12X17  ins.     Width  of  beam  flange 
is  7  ins. 

17-7 
Hence  P=  — - — =5  ins. 

For  cast  iron  t=    .024x5N/l5~0=  1.47  ins. 

For  steel         ^=.0137X5V/150=0.84  ins.  or  £  inch. 

The  load  on  the  plate  equals  the  end  reaction  of  beam,  which 
is  one-half  of  a  distributed  or  centre  load.  When  the  load  is 
irregularly  applied  the  reaction  may  be  computed  as  explained 
under  supporting  forces,  Chapter  IX. 

The  following  table  gives  the  standard  sizes  for  steel  bearing- 
plates  under  I-beams  and  channels  as  recommended  by  the 
Carnegie  Steel  Co.  and  Jones  &  Laughlins,  and  the  bearing 
values  for  three  grades  of  masonry.  When  the  reaction  of  the 
beam  exceeds  the  safe  bearing  value  given  in  the  table,  the  size 
and  thickness  of  the  plate  should  be  determined  by  the  foregoing 
rule.  If  the  reaction  is  less  than  the  bearing  value,  the  size  of 
the  plate  can  be  reduced. 

As  the  reactions  vary  with  the  span  of  the  beam,  such  a  table 
as  the  following  should  be  used  with  caution,  and  the  reaction 
always  compared  with  the  bearing  value  of  the  plate ; 


BEARING-PLATES  FOR  GIRDERS  AND  COLUMNS.  403 
TABLE  II.— STANDARD  STEEL  WALL  BEARING-PLATES. 


Depth  of  beam 
or  channel. 

Bearing  on  wall. 

Plates. 

Safe  bearing 
values  in  tons 
for  plates  rest- 
ing on 

CO 

p 

! 

,a 
.£f 

Size. 

1 
.1 

Its 

%•* 

oa^ 

3"  4"  5"  and  6"   ... 

6" 
6" 

6"X   6" 
6"X    6" 

* 

1.8 
1.8 
3.2 
3.2 

4.8 
4.8 
7.2 
7.2 
9.6 
9.6 
10.8 
10.8 
12.8 

2.7 
2.7 
4.8 
4.8 
7.2 
7.2 
10.8 
10.8 
14.4 
14.4 
16.2 
16.2 
19.2 

4.5 
4.5 
8.0 
8.0 
12.0 
12.0 
18.0 
18.0 
24.0 
24.0 
27.0 
27.0 
32.0 

4 
5 
9 
14 
14 
20 
20 
31 
41 
54 
46 
61 
73 

3",  4",  5",  and  6"  

7"  and  8"  ! 

7"  and  8" 

8" 
8" 
8" 
8" 
12" 
12" 
12" 
12" 
12" 
12" 
16" 

8"  X   8" 
8"X    8" 
8"  X  12" 
8"X12" 
12"X12" 
12"X12" 
12"  XI  6" 
12"X16" 
12"  XI  8" 
12"  XI  8" 
16"X16" 

1  4'f 

1    ' 
1    ' 

9"  and  10"  

9"  and  10" 

12"  I  31.5  Ibs  

12"!  31.5  Ibs  
12"  I  40  Ibs.,  15"  I  42  Ibs  . 
12"!  40  Ibs.,  15"  I  42  Ibs.. 
15"  I  60  and  80  Ibs. 

15"  I  60  and  80  Ibs  

18"   20",  and  24" 

*  Use  the  thicker  plate  for  bearing  values  exceeding  those  given  under 
common  brickwork. 

Bearing-plates  on  brickwork  may  be  considerably  reduced  in 
size  by  placing  a  strong  flat  stone  under  them.  The  area  of  the 
stone  should  be  proportioned  by  the  above  rule,  and  the  thick- 
ness of  the  stone  should  be  at  least  equal  to  its  projection  beyond 
the  iron  plate. 

BEDDING. 

Base-plates  should  be  bedded  or  grouted  in  cement  from  one- 
half  to  three-quarters  of  an  inch  thick,  the  plate  to  be  rammed 
down  solid,  true  and  level .  Web-plates  should  have  holes  in  the 
bottom,  as  shown  in  Fig.  1,  to  show  if  the  cement  is  distributed 
evenly  under  the  plate. 

Bearing-Brackets  on  Cast-iron  Columns. 

Fig.  4  shows  the  usual  method  of  connecting  iron  floor-beams 
and  girders  with  cast-iron  columns.  The  ends  of  the  beam  and 
girder  rest  on  plates  P  cast  on  the  columns,  and  the  plates  are  sup- 
ported by  cast  brackets  C,  so  that  no  transverse  strain  can  come 
upon  the  plate.  For  single  beams  one  bracket  is  sufficient ;  for 
double  beams,  or  for  wide  beams  or  riveted  girders,  two  brackets 
should  be  used.  The  ends  of  the  beams  and  girders  are  fastened 


404  BEARING-BRACKETS  ON  CAST-IRON  COLUMNS. 

to  the  column  by  bolting  to  the  lugs  L,  which  are  also  cast  on  the 
column.     (See  also  Fig.  8,  Chapter  XIV.) 

As  the  plates  can  resist  but  little  transverse  strain,  it  is  evident 
that  the  strength  of  the  support  consists  in  the  resistance  of  the 
brackets  and  plate  to  being  sheared  or  sliding  down  on  the  col- 
umn, and  also  on  the  resistance  of  the  bracket  to  crushing.  The 


TfffF 


Fig.  4. 

thickness  of  the  plate  and  brackets  should  not  be  less  than  the 
thickness  of  the  body  of  the  column,  and  this  simple  rule  will 
generally  insure  sufficient  strength  for  supporting  the  beams  or 
.girders.  In  case  of  very  heavily  loaded  beams  or  girders,  it 
would  be  well,  however,  to  calculate  the  resistance  of  the  support 
both  to  shearing  and  crushing. 

Both  the  plate  and  bracket  would  offer  resistance  to  shearing, 
but  the  author  advocates  considering  only  the  resistance  of  the 
bracket.  The  resistance  of  a  single  bracket  to  shearing  is  equal 
to  the  height  D  multiplied  by  the  thickness  of  the  plate,  and 
the  product  by  7,000  pounds.  Thus  if  the  length  D  is  six  inches 
(which  should  be  about  the  minimum  length),  and  the  thickness 
of  the  bracket  one  inch,  the  shearing  area  would  be  six  inches, 


BEARING-BRACKETS  ON  CAST-IRON  COLUMNS.  405 


which,  multiplied  by  7,000,  gives  42,000  pounds  as  the  safe 
strength  of  one  bracket. 

The  resistance  to  crushing  may  be  found  by  multiplying  the 
distance  X  by  the  thickness  of  the  bracket  and  the  product  by 
13,000.  Thus,  if  X  is  four  inches  and  the  thickness  one  inch,  the 
resistance  to  crushing  would  be  52,000  pounds.  Such  a  bracket 
would  support  the  end  of  a  20-inch  light  steel  beam  of  16  feet 
span  under  its  full  load ;  for  heavier  beams  the  thickness  of  the 
bracket  and  also  the  length  D  should  be  increased. 

Bevel  of  Brackets. — If  the  plate  P,  on  which  the  beam  rests,  is 
cast  square  to  the  column,  then,  when  the  beam  deflects,  the  load 
will  be  brought  on  the  extreme  outer  edge  of  the  column.  To 
avoid  this  the  shelf  should  be  sloped  downward,  away  from  the 
column,  with  a  bevel  of  ^-inch  per  foot. 

TABLE  III.— STANDARD  CONNECTIONS  TO  CAST-IRON 

COLUMNS. 

The  following  table,  published  by  the  Passaic  Rolling  Mill  Co,, 
will  be  found  useful,  when  detailing  cast-iron  columns* 
ALL  DIMENSIONS  ARE  IN  INCHES. 


Jl 

A 

B 

C 

D 

E 

F 

G 

H 

K 

|| 

ft'0 

g"8 

Holes 

cored 

20 
18 

5 

4 

5 
5 

6 
6 

104 
104 

HeM<N 
i-H  T-H 

H 

14 

2 

2 

14 

14 

2 
2 

1 
1 

for 
bolts. 

15 

4 

34 

54 

94 

14 

2 

14 

If 

1 

12 

3 

o 

44 

H 

1! 

2 

14 

14 

1 

406  BEARlNti-BRACKETS  ON  CAST-IRON  COLUMNS. 


Js 

A 

B 

C 

D 

E 

F 

G 

H 

K 

_M  J3 

jj 

XJ  O 

Holes 

cored 

10 
9 

3i 
3 

34 

3 

4 

4 

7 
7 

I 

1 
1 

2 
2 

it 

If 

1 
1 

for 
bolts. 

8 

2i 

3 

4 

7 

1 

1 

2 

H 

if 

| 

7 

2i 

2i 

4 

7  ' 

1 

1 

2 

li 

i 

STRENGTH  OF  POSTS,  STRUTS,  AND  COLUMNS.  407 


CHAPTER  XIV. 


STRENGTH  OP  POSTS,  STRUTS,  AND  COLUMNS. 

DETAILS  OF  CONNECTIONS  AND  BASE-PLATES. 

As  the  strength  of  a  post,  strut,  or  column,  depends  primarily 
upon  the  resistance  of  the  given  material  to  crushing,  we  must 
first  determine  the  ultimate  crushing  strength  of  all  materials 
used  for  this  purpose. 

The  following  table  gives  the  strength  for  all  materials  used 
in  building,  excepting  brick,  stone,  and  masonry,  which  will  be 
found  in  Chapter  V. 

TABLE  I.— AVERAGE  ULTIMATE  CRUSHING  LOADS, 
IN  POUNDS  PER  SQUARE  INCH,  FOR  BUILDING- 
MATERIALS. 


Material. 

Crushing 
weight,  in 
Ibs/per 
sq.  inch. 

Material. 

Crushing 
weight,  in 
Ibs.  per 
sq.  inch. 

For  STONE,  BRICK,  and 
MASONRY    see  Chap. 

C. 

WOODS  (continued). 
Cypress  

C. 
3,375 

Hemlock  

3,000 

Oak,  white 

4,000 

METALS. 
Cast  iron.  . 

80,000 

Pine,  Georgia  yellow.  ..  . 
Pine,  Oregon   . 

5,000 
4  500 

Wrought  iron  

36,000 

Pine,  Norway..        .... 

3,800 

Steel  (rolled  shapes)  .... 

48,000 

Pine,  white  

3,500 

Pine  (Colorado)  

3,150 

WOODS  (Endways).* 
Cedar  

3,500 

Redwood  (California).  .  . 

3,000 
4,000 

Chestnut  

4,000 

Whitewood. 

3,000 

*  For  crushing  resistance  of  timbers  perpendicular  to  the  grain  see 
Table  VI. 

The  values  for  cast  iron,  wrought  iron,  and  steel  are  tho^e  gen- 
erally used,  although  a  great  deal  of  iron  is  stronger  than  this. 
The  values  for  woods  are  those  recommended  by  leading  engineers, 
and  may  be  considered  as  a  fair  average  of  the  results  obtained  by 
experiment  on  full-size  pieces  of  merchantable  lumber.  The 
values  for  yellow  pine,  white  pine,  white  oak,  and  cypress  were 


408  STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS. 

obtained  from  results  of  the  tests  conducted  since  1890  by  the 
U.  S.  Forestry  Division.  The  values  for  the  other  woods  were 
compiled  from  the  best  test  data  available,  and  are  believed  to 
be  as  near  the  actual  strength  of  ordinary  full-size  timbers  as  can 
be  determined. 

The  values  for  wood  are  for  dry  timber.  Wet  timber  is  only 
about  one-half  as  strong  to  resist  compression  as  dry  timber,  and 
this  fact  should  be  taken  into  account  when  using  green  timber. 

The  strength  of  a  column,  post,  or  strut,  depends,  in  a  large 
measure,  upon  the  proportion  of  the  length  to  the  diameter  of 
least  thickness.  Up  to  a  certain  length,  failure  occurs  simply 
by  compression,  and  above  that  length  by  first  bending  and 
then  breaking. 

Wooden  Columns. 

For  wrooden  columns,  where  the  length  is  not  more  than  twelve 
times  the  least  thickness,  the  strength  of  the  column  or  strut  may 
be  computed  by  the  rule, 

&  f    ,      ,      area  of  cross-section  X  C 

Safe  load  = r —     — > — j—  (1) 

factor  of  safety 

where  C  denotes  the  strength  of  the  given  material  as  given  in 
Table  I. 

The  factor  of  safety  to  be  used  depends  upon  the  place  where 
the  column  or  strut  is  used,  the  load  which  comes  upon  it,  the 
quality  of  the  material,  and,  in  a  large  measure,  upon  the  value 
taken  for  C. 

For  lumber  of  ordinary  quality,  and  containing  no  very  bad 
knots,  the  author  would  recommend  that  a  factor  of  safety  of 
five  be  used ;  or,  in  other  words,  that  the  safe  stress  per  square 
inch  of  section  area  be  made  one-fifth  of  the  values  given  in 
Table  I. 

If  the  post  is  badly  season-checked,  cross-grained,  or  contains 
bad  knots,  a  larger  factor,  say  six  or  seven,  should  be  used.  The 
character  of  the  load  should  also  be  taken  into  consideration  in 
determining  the  factor  of  safety.  Thus  the  author  would  use  a 
larger  factor  for  a  post  supporting  a  brick  wall  than  for  one 
supporting  a  floor,  as  in  the  former  case  the  full  load  is  at  all 
times  on  the  post,  and  the  least  reduction  of  its  sectional  area  in 
case  of  fire  might  cause  it  to  give  way.  Columns  supporting 


STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS-  409 

machinery,  or  struts  in  railway  bridges,  should  have  a  factor  of 
safety  of  from  6  to  8,  if  the  values  of  C,  given  in  Table  I.,  are  used. 

EXAMPLE  1. — What  is  the  safe  load  for  a  hard-pine  post  10  X 10 
inches,  12  feet  long,  using  a  factor  of  safety  of  5? 

Ans. — Area  of  cross-section  =  100  sq.  ins.;  safe  load  per  sq.  in. 

cnrjO 

-  ^-  =1000;  1000X100=  100,000  Ibs. 

EXAMPLE  2. — It  is  required  to  support  a  brick  wall  weighing 
80,000  Ibs.  by  an  Oregon  pine  post  11  feet  long.  What  should  be 
the  size  of  the  post? 

Ans. — We  would  recommend  a  factor  of  safety  of  6.     Then  safe 

4500  80  000 

resistance  per  sq.  in.  of  section  area=  — - —  =  750 ;  -•   '       =106  sq. 

o  7o(J 

ins.  required  in  section  of  post,  or  say  a  10  X 11  or  9  X 12  post. 


Strength  of  Wooden  Posts  over  Twelve  Diameters 
in  Length. 

When  the  length  of  a  post  exceeds  twelve  times  its  least  thickness 
or  diameter,  the  post  is  liable  to  bend  under  the  load,  and  hence 
to  break  under  a  less  load  than  would  a  shorter  column  of  the 
same  cross-section. 

To  deduce  a  formula  which  would  make  the  proper  allowance 
for  the  length  of  a  column  has  been  the  aim  of  many  engineers, 
but  their  formulae  have  not  been  verified  by  actual  results. 

Until  within  two  or  three  years  the  formula)  of  Mr.  Lewis 
Gordon  and  Mr.  C.  Shaler  Smith  have  been  generally  used  by 
engineers,  but  the  extensive  series  of  tests  made  on  the  Govern- 
ment testing  machine  at  Watertown,  Mass.,  on  full-sized  col- 
umns, show  that  these  formulae  do  not  agree  with  the  results 
there  obtained. 

Mr.  James  H.  Stanwood,  Instructor  in  Civil  Engineering,  Mass. 
Institute  of  Technology,  in  the  year  1891  platted  the  values  of  all 
the  tests  made  at  the  Watertown  Arsenal  up  to  that  time  on  full- 
size  posts.  From  the  drawing  thus  obtained  he  deduced  the  fol- 
lowing formula  for  yellow-  pine  posts  : 


Safe  load  per  square  inch=  1000-  10  X?.        (2) 

breadth  in  inches 

The  author  has  carefully  compared  this  formula  with  the  results 
of  actual  tests,  and  with  other  formula,  and  believes  that  it  meets 
the  actual  conditions  more  nearly  than  any  other  formula,  and 


410    STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS. 

he  has  therefore  discarded  the  tables  of  wooden  posts  given  in  the 
earlier  editions  of  this  work  and  prepared  the  following  tables 
for  the  strength  of  round  and  square  posts  of  sizes  coming  within 
the  range  of  actual  practice. 

For  other  sizes  the  loads  can  easily  be  computed  by-  the 
formula. 

The  loads  for  Texas  pine,  oak  and  white  pine  posts  were  com- 
puted by  the  following  formulae: 
For  Texas  (yellow)  pine : 


Safe  load  per  square  inch=  850- 8.5  Xr^       i.  -.       (3) 

breadth  in  ins. 

For  oak  and  Norway  pine: 

Safe  load  per  square  inch  =  750 — 7. 5  X  r~          m  mS*  .     (4) 

breadth  in  ins. 

For  white  pine  and  spruce  posts : 

Safe  load  per  sqnare  inch=  625 - 6  X    leng*h  m  ms'  . ,        (5) 

breadth  in  ins.  ' 

in  which  the  breadth  is  the  least  side  of  a  rectangular  strut,  or  the 
diameter  of  a  round  post.  The  round  posts  were  computed  for 
the  half-inch,  to  allow  for  being  turned  out  of  a  square  post,  of 
the  size  next  larger. 

The  formula?  were  only  used  for  posts  exceeding  12  diameters 
for  yellow  pine,  and  ten  diameters  for  other  woods. 

For  posts  having  bad  knots,  or  other  defects,  or  which  are 
known  to  be  eccentrically  loaded,  a  deduction  of  from  10  to  25 
per  cent,  should  be  made  from  the  values  given  in  the  tables. 


STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS.  411 


TABLE  II.— SAFE  LOAD  IN  POUNDS  FOR  YELLOW  PINE 
AND  OREGON  PINE  POSTS  (ROUND  AND  SQUARE.)* 


Size  of 
Post 
in  inches. 

Length  of  Post  in  feet. 

8 

10 

12 

11 

15 

16 

18 

20 

24 

4X6 

18,200 
19,590 
^-30,200 
40,300 
50,400 
38,540 
64,000 
80,000 
96,000 
70,900 
100,000 
120,000 
140,000 
103,900 
144,000 
168,000 
192,000 
196,000 
256,000 
324,000 
400,000 

16,800 
18,760 
28,800 
38,400 
48,000 
37,130 
54,400 
68,000 
81,600 
61,970 
100,000 
120,000 
140,000 
103,900 
144,000 
168,000 
192,000 
196,000 
256,000 
324,000 
400,000 

15,360 
17,550 
.  27,400 
36,500 
45,600 
35,710 
52,500 
65,600 
78,700 
60,190 
85,600 
102,700 
119,800 
90,912 
144,000 
168,000 
192,000 
196,000 
256,000 
324,000 
400,000 

16,500 
25,900 
34,000 
43,200 
34,300 
50,600 
63,200 
76,800 
58,350 
83,200 
99,800 
116,500 
88,730 
123,800 
144,500 
165,100 
196,000 
256,000 
324,000 
400,000 

25,200 
33,600 
42,000 
33,590 
49,600 
62,000 
74,400 
57,429 
82,000 
98,400 
114,800 
87,690 
122,400 
142,800 
163,200 
170,900 
229,100 
324,000 
400,000 

24,500 
32,600 
40,800 
32,890 
48,600 
60,800 
73,000 
56,580 
80,800 
97,000 
113,100 
86,550 
121,  COO 
141,100 
161,300 
169,100 
225,300 
289,400 
400,000 

46,700 
53,400 
70,100 
54,800 
78,400 
94,100 
109,800 
84,160 
118,100 
137,800 
157,400 
165,800 
221,400 
285,100 
356,800 

76,000 
91,200 
100,400 
82,290 
115,200 
134,400 
153,600 
162,400 
217,600 
280,800 
352,000 

109,440 
127,680 
145,920 
155,800 
209,900 
272,160 
342,400 

5£  round.  . 

6X6   .  .  o  " 

6X8  

6X10  
7^  round.  . 

8X8 

8X10  
8X12  

9i  round.  . 
10  X  10  
10X12  
10X14  
lli  round 
12X12  
12X14  
12  X  16  
14X14  
16X16  
18X18  
20X20  

*  These  two  woods  appear  to  be  of  about  equal  strength  for  posts  ex- 
ceeding 12  diameters  in  height. 

TABLE  III.— SAFE  LOAD  FOR  TEXAS  (YELLOW)  PINE 
POSTS  (ROUND  AND  SQUARE). 


Size  of 
post  in 
inches. 

Length  of  post  in  feet. 

8 

10 

12 

14 

15 

16 

18 

20 

24 

4X6  

15  500 

14  280 

13050 

5£  round.. 

16,650 

15,790 

14,900 

14,030 

6X6....  . 

25,704 

24,480 

23,256 

22,032 

21,420 

20,808 

6X8  

34,272 

32  640 

31,008 

29  376 

28,560 

27,744 

6X10  

42,840 

40,800 

37,760 

36,720 

35,700 

34,680 

7^  round.  . 

32,740 

31,540 

30,340 

29,140 

28,540 

27,940 

26,740 

8X8  

47  870 

46,240 

44,600 

42,970 

42,160 

41,340 

39,710 

8X10  

59,840 

57,800 

55,760 

53,720 

52,700 

51,680 

49,640 

8X12...    . 

71,808 

69,360 

66,910 

64,460 

63,240 

62,000 

59,560 

9^  round  . 

54.150 

52,650 

51,150 

49,580 

48,820 

48,070 

46,570 

10X10..     . 

85,000 

78,800 

72,760 

70,720 

69,700 

68,680 

66,640 

64,600 

10  X  12.  .    . 

102,000 

89,760 

87,300 

84,860 

83,640 

82,400 

80,000 

77,500 

10X14..     . 

119,000 

104,700 

101,860 

99,000 

97.5PO 

96,150 

93,300 

90,400 

11-J-  round 

88,290 

79,100 

77,250 

75,400 

74,470 

73,550 

71,700 

69,850 

66,160 

12X12  

122,400 

110,160 

107,700 

105,260 

104,040 

102,800 

100,360 

97,920 

93,000 

12X14  

142,800 

128,520 

125,660 

122,800 

121,380 

119,950 

117,100 

114,240 

108,520 

12X16  

163,200 

146,880 

143,600 

140,350 

138,720 

137,080 

133,800 

130,560 

124,030 

14X14  

166,600 

166,600 

149,450 

146,600 

145,180 

143,760 

140,900 

138,080 

132,400 

14X16.  .  .  . 

190,400 

190,400 

170,800 

167,500 

165,900 

164,300 

161,000 

157,800 

151,300 

16X16  

217,600 

217,600 

217,600 

194,700 

193,000 

191,400 

188,200 

184,900 

178,400 

412  STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS. 


TABLE   IV.— SAFE  LOAD   IN  POUNDS  FOR  OAK  AND 
NORWAY  PINE  POSTS  (ROUND  AND  SQUARED 


Size  of 

Length  of  post  in  feet. 

post  in 
inches. 

8 

10 

13 

14 

15 

16 

18 

20 

34 

4X6  

13,680 

12,600 

11,520 

5£  round.  . 

14,700 

13,900 

13,160 

12,370 

6X6  . 

22,680 

21,600 

20,520 

19,440 

18,900 

18,360 

6X8  

30,240 

28,800 

27,360 

25,920 

25,200 

24,480 

6X10... 

37,800 

36,000 

34,200 

32,400 

31,500 

30,600 

7£  round 

28,900 

27,850 

26,780 

25,720 

25,190 

24,660 

8X8.  .  .  . 

42,240 

40,768 

39,360 

37,880 

37,120 

36,480 

35000 

8X10... 

52,800 

50,960 

49,200 

47,360 

46,400 

44,600 

43,760 

8X12... 

63,360 

61,152 

59,040 

56,830 

55,680 

54,720 

52,500 

9£  round 

47,960 

46,440 

45,160 

43,740 

43,100 

42,400 

41,120 

10X10.. 

75,000 

66,000 

64,200 

62,400 

61,500 

60,600 

58,800 

57,000 

10X12.. 

90,000 

79,200 

77,040 

74,880 

73,800 

72,720 

70,560 

68,400 

10X14.. 

105,000 

92,400 

89,880 

87,360 

86,100 

84,840 

82,320 

79,800 

•H  round 

77,925 

69,820 

68,160 

66,490 

65,770 

64,833 

63,170 

61,600 

12X12. 

108,000 

108,000 

95,040 

92,880 

91,700 

90,700 

88,560 

86,400 

82,080 

12X14. 

126,000 

126,000 

110,800 

108,300 

107,000 

105,840 

103,300 

100,802 

95,760 

12X16. 

144,000 

144,000 

126,700 

123,800 

122,300 

120,900 

118,000 

115,200 

109,400 

14X14. 
16X16. 

147,000 
192,000 

147,000 
192,000 

147,000 
192,000 

129,300 
192,000 

128,100 
170,500 

127,000 
168,900 

124,400 
166,100 

121,900 
163,000 

116,800 
157,400 

18X18.  . 

243,000 

243,000 

243,000 

243,000 

243,000 

217,000 

213,800 

210,600 

204,100 

20X20.. 

300,000 

300,000 

300,000 

300,000 

300,000 

300,000 

267,600 

264,000 

256,000 

TABLE  V.— SAFE  LOAD  IN  POUNDS  FOR  WHITE  PINE 
AND  SPRUCE  POSTS  (ROUND  AND  SQUARE). 


Size  of 

Length  of  post  in  feet. 

inches. 

8 

10 

13 

14 

15 

16 

18 

30 

34 

4X6  . 

11,520 

10,550 

9,800 

8,700 

5£  round.  . 

12,350 

11,730 

11,180 

10,490 

6X6.  .... 

19,080 

18,216 

17,352 

16,490 

16,050 

15,620 

6X8  .  .  . 

25,440 

24,290 

23,140 

21,980 

?1,400 

20,830 

6X10  

31,800 

30,360 

28,920 

27,480 

26,760 

26,040 

7£  round.  . 

24,220 

23,380 

22,540 

21,660 

21,260 

20,820 

8X8. 

35,450 

34,300 

33,150 

32,000 

31,420 

30,850 

29,700 

8X10  

44,320 

42,480 

41,440 

40,000 

39,280 

38,560 

37,120 

8X12  

53,180 

51,450 

49,730 

48,000 

47,140 

46,270 

44,544 

9i-  round.. 

40,000 

39,000 

37,860 

36,800 

36,230 

35,730 

34,670 

10X10  

62,500 

55,400 

53,960 

52,520 

51,800 

51,080 

49,640 

48,200 

10X12  

75,000 

66,480 

64,800 

63,000 

62,160 

61,300 

59,570 

57,840 

10  X  14  

87,500 

77,560 

75,600 

73,500 

72,520 

71,510 

69,500 

67,480 

11£  round. 

64,930 

58,390 

57,140 

55,800 

55,170 

54,550 

53,100 

51,950 

12X12  

90,000 

90,000 

79,780 

78,000 

77,180 

76,320 

74,590 

72,860 

69,400 

12X14  

105,000 

105,000 

93,170 

91,050 

90,050 

89,000 

87,020 

85,000 

80,900 

12X16.     .. 

120000 

120,000 

106,300 

104,000 

102,900 

101,700 

99,400 

97,150 

92,500 

14X14/   .  . 

122,500 

122,500 

110,350 

108,350 

107,400 

106,400 

104,460 

102,300 

98,400 

16X16.     .. 

160,000 

160,000 

1(>0,000 

143,870 

142,500 

141,570 

139,260 

136,960 

32,360 

18X18.     .. 

202,500 

202,500 

202,500 

202,500 

183,0(K) 

181,760 

179,170 

176,580 

171,400 

20X20.    .. 

250,000 

250,000 

250,000 

250,000 

250,000 

250,000 

224,500 

221,200 

215,200 

, 

STRENGTH  OF  WOODEN  POSTS  AND  COLUMNS.  413 


Eccentric  [Loading*. 

When  the  load  on  a  post  is  applied  in  such  a  way  that  it  is  not 
distributed  uniformly  over  the  end  of  the  post  the  loading  is 
called  eccentric,  and  the  effect  on  the 
post  is  much  more  injurious  than  if  the 
load  were  uniformly  distributed.  When 
a  post  supports  a  girder  on  one  side 
only,  or  when  the  weight  from  one 
girder  is  much  more  than  from  the 
other,  the  load  becomes  eccentric,  and 
the  sectional  area  of  the  post  should  be 
increased,  to  resist  the  bending  stress 
due  to  the  eccentricity. 

When  the  eccentric  load  is  applied 
as  in  Fig.   1,  the  sectional  area  of  a 
square  or  rectangular  post  should  be 
computed  by  the  following  formula: 
Sectional  area  of  post  in  square  inches 


W  ,  6TF,  X  <?o 

p        PXd    ' 


(6) 


in  which  W=  total  load  on  post  in  Ibs.g 
Wt=  eccentric  load  in  Ibs.  ; 
p=safe  stress  in  Ibs.  per  sq. 

inch. ; 

d0—  distance  from  centre  of 
post  to  centre  of  bearing 
in  ins.; 
c?=side  of  post  parallel  with  girder. 

In  assuming  the  value  of  p,  the  probable  ratio  of  the  side  of  the 
post  to  the  length  should  be  taken  into  account.  Thus  if  it  is 
probable  that  the  length  will  not  exceed  twelve  times  the  side 
(both  being  measured  in  inches)  for  yellow  pine  or  Oregon  pine  . 
posts,  or  10  diameters  for  other  woods,  then  the  value  of  p  for 
short  posts  may  be  taken.  If  the  ratio  will  probably  be  greater 
than  this,  then  the  probable  ratio  should  be  roughly  calculated 
and  p  computed  ior  that  ratio  by  the  formula  given  for  posts 
more  thai).  10  diameters  in  length. 

EXAMPLE  3. — The  post  1\,  Fig.  1,  supports  a  total  load  on  its 
cap-plate  of  00,000  Ibs.,  including  the;  reaction  from  girder  A  of 
12,000  Ibs.  WThat  should  bo  the  size  of  the  post  for  Oregon  pine, 


414  OAST-IRON   COLUMNS  AND  POSTS. 

and  length  of  12  ft.?  Ans.  —  As  it  is  probable  that  the  post  will 
have  to  be  at  least  10  ins.  square,  we  will  assume  1,000  Ibs.  for 
p,  and  10  ins.  for  d.  Wl  will=  12,000  Ibs.  and  d0  7  ins. 


sq.  ins.     Or  the  post  should  be  11  X  11  or  10  X  12  ins. 

From  Table  I.  we  see  that  an  8X10  post,  concentrically 
loaded,  would  support  65,000  Ibs.,  hence  the  eccentric  load  from 
the  girder  increases  the  size  of  the  post  from  8  X  10  to  10  X  12  ins. 

Iron  Caps  and  Bolsters  for  Wooden  Posts. 

Whenever  wooden  posts  are  used  in  tiers,  one  above  another, 
each  post  except  the  top  one  should  have  an  iron  cap-plate,  and 
the  upper  posts  should  set  on  the  cap  of  the  post  below,  and  not 
on  the  girder.  Where  a  wooden  post  supports  only  a  girder  a 
wooden  bolster  may  be  used  in  place  of  the  cap.  Details  of  post 
caps  and  bolsters  are  shown  in  Chapter  XXII. 

Crushing  of  Timber  Perpendicular  to  the  Grain. 

TABLE  VI. 

The  bearing  of  wooden  girders,  the  ends  of  posts  resting  on 
a  girder,  and  washers  on  truss  rods,  should  be  proportioned  so 
that  the  quotient  obtained  by  dividing  the  load  by  the  bearing 
area  will  not  exceed  the  following  safe  unit  strains  : 
White  oak  ..........   600  Ibs.  '  Colorado  pine  .......  200  Ibs. 


Yellow  pine.  0 500 

Oregon  pine 400 

Norway  pine 250 

White  pine 200 


Spruce 250 

Hemlock 200 

Cypress 200 

Redwood.  .  .  175 


Cast-iron  Columns  and  Posts. 

Advantages  and  Disadvantages. — Although  steel  is  being  more 

%  largely  used  every  year  for  the  upright  supports  in  buildings, 

it  will  probably  never  entirely  supplant  the  cast-iron  post,  and,  in 

fact,  it  is  still  a  disputed  question  whether  a  steel  post  is  better 

than  one  of  cast  iron  for  buildings  of  moderate  height. 

For  skeleton  construction,  when*  the  height  of  the  building 
exceeds  twice  its  width,  it  seems  unquestionable  that  the  riveted 
steel  column,  "breaking  joint"  in  alternate  stories,  and  with 
riveted  connections  with  the  beams  and  girders,  is  much  the  best ; 
but  for  the  larger  proportion  of  the  buildings  in  which  iron  posts 


CAST-IRON  COLUMNS  AND  POSTS.  415 

are  used  cast  iron  possesses  advantages  which  the  author  believes 
are  not  exceeded  by  the  riveted  steel  post. 

The  most  important  of  these  advantages  are — low  cost,  quick- 
ness of  production,  adaptability  to  any  desired  shape,  and  ease 
in  making  connections. 

Cast-iron  columns  when  unprotected  will  also  resist  the  action 
of  fire  better  than  unprotected  steel  columns,  as  has  been  quite 
conclusively  demonstrated  by  the  experiments  of  Prof.  Bau- 
schinger,  of  Munich.*  Cast  iron  three  quarters  of  an  inch  or 
more  in  thickness  is  also  practically  uninjured  by  rust,  while  it 
is  claimed  that  wrought  iron  or  steel  may  be  almost  destroyed  by 
it,  unless  kept  constantly  protected  by  some  coating  impervious 
to  moisture. 

For  unprotected  columns  cast  iron  may  be  made  in  more 
attractive  shape  than  steel  columns,  without  additional  cost. 

The  disadvantages  of  cast-iron  columns,  as  found  in  practice, 
are  lack  of  uniformity  in  the  metal,  the  danger  of  shrinkage 
strains,  and  the  difficulty  of  making  rigid  connections. 

There  are  many  contingencies  which  may  arise  in  the  manu- 
facture of  cast-iron  columns  which  preclude  perfect  uniformity 
in  the  product. 

Among  these  are  unevenness  in  the  thickness  of  the  metal, 
which  has  sometimes  been  found  to  be  very  different  on  one  side 
of  a  round  column  from  that  on  the  opposite  side.  The  presence 
of  confined  air,  producing  "blow-holes"  and  "honeycomb,"  and 
the  collection  of  impurities  at  the  bottom  of  the  mould,  are  also 
frequent  sources  of  weakness  in  cast  iron. 

By  careful  inspection  and  by  boring  the  columns  these  defects 
can  be  discovered  and  imperfect  columns  rejected. 

The  most  critical  condition  is  that  due  to  the  unequal  contrac- 
tion of  the  metal  during  the  process  of  cooling,  thereby  giving 
rise  to  initial  strains,  at  times  of  sufficient  force  to  produce  rup- 
ture in  the  column  or  in  its  lugs  on  the  slightest  provocation. 

In  many  cases  the  trouble  is  due  to  faulty  designing  or  careless- 

*  Architect  C.  A.  Ziegler,  of  Philadelphia,  in  commenting  on  the  con- 
flagration at  Paterson,  N,  J.,  in  Feb.,  1902,  says,  in  the  Brickbuilder  for 
March  of  that  year:  "The  manner  in  which  cast-iron  columns  and  girders 
withstood  the  flames  is  most  marvelous.  The  great  majority  that  I  saw 
were  not  only  intact  but  were  as  good  as  new,  although  some  had  appar- 
ently fallen  from  great  heights. 

"The  steel  work ,  on  the  contrary  [in  modern  fireproof  buildings],  wherever 
H  was  reached  by  the  heat,  buckled  and  fell,  heavy  steel  girders  and  posts 
being  twisted  and  knotted  like  whipcords." 


416 


CAST-IRON  COLUMNS  AND    POSTS. 


ness  in  the  execution  of  the  work ;  yet,  even  under  favorable  con- 
ditions, it  is  so  difficult  to  secure  equal  radiation  from  the  moulds 
in  all  directions  that  castings  entirely  exempt  from  inherent 
shrinkage  strains  are  probably  seldom  produced. 

The  most  serious  difficulties  met  with  in  using  cast  columns 
in  tall  buildings  are  the  difficulty  of  making  true  and  rigid  end 
connections  and  the  unreliability  of  the  brackets  which  support 
the  beams  and  girders.  By  skilful  designing  and  careful  work- 
manship  these  difficulties  may  to  a  considerable  extent  be  over- 
come, but  cast  columns  can  never  in  these  respects  be  made  to 
equal  the  best  forms  of  steel  columns. 

The  length  of  cast-iron  columns  in  inches  should  not  exceed 
thirty-six  times  their  diameter,  or  least  dimension. 

Shapes  of  Cast  Columns. — Cast-iron  columns  for  buildings  have 
been  made  in  all  of  the  nine  shapes  shown  in  Fig.  2,  although 
solid  columns  are  seldom  made,  and  only  for  very  small  diameters, 

N°'1  "      "  No.  3  No.  4 


No.  2 


No.  5 


t 

—  *— 

No.  6 


No.  7 


Fig.  2 


For  interior  unprotected  columns  the  hollow  cylindrical  shape 
probably  meets  the  usual  requirements  better  than  any  other. 

For  exterior  columns,  as  in  store  fronts,  the  rectangular  shape, 
No.  5,  is  more  generally  used,  in  order  to  give  a  good  bearing  for 
the  beams  supporting  the  wall  above. 

For  fire-proof  buildings  in  which  cast-iron  columns  are  used 
the  author  believes  that  the  H-shaped  No.  9  is  the  most  desirable, 
because  of  the  following  advantages? 


CAST-IRON   COLUMNS  AND  POSTS. 


417 


Fig.  3 
which  are  often 


1.  Being  entirely  open,  with  both  the  interior  and  exterior  sur- 
faces exposed,  any  inequalities  in  thickness  can  be  readily  dis- 
covered, and  the  thickness  itself  easily  measured,  thus  obviating 
any  necessity  for  boring,  and  rendering  the  inspection  of  the 
columns  much  less  tedious. 

2.  The  entire  surface  of  the  column  can  be  protected  by  paint. 

3.  When  built  in  brick  walls  the  masonry  fills  all  voids,  so  that 
no  open  space  is  left,  and  if  the  column  is 

placed  as  shown  in  Fig.  3,  only  the  edge  of 
the  column  comes  near  the  face  of  the  wall. 

4.  Lugs  and  brackets  can  be  cast  on  such 
columns  better  than  on  circular  columns, 
especially  for  wide  and  heavy  girders. 

5.  The  end  connections  of  the  columns 

do   not   require  projecting   rings,    or  flanges, 
objectionable  in  circular  columns. 

The  cost  of  columns  of  this  shape  should  not  exceed  that  of  cir- 
cular columns  of  the  same  strength. 

The  column  may  be  fire-proofed  in  the  same  way  as  the  Z-bar 
column,  which  it  much  resembles.  The  space  occupied  by  the 
column  slightly  exceeds  that  of  both  the 
cylindrical  and  the  Z-bar  column,  but  not 
enough  to  be  of  any  serious  consequence. 
Pilasters. — Pilasters,  or  columns  with- 
out a  back,  are  often  used  as  a  facing  to 
the  brick  walls  at  the  sides  of  store  fronts. 
If  such  pilasters  are  used  to  support  a 
girder,  the  inner  side,  A,  Fig.  4,  should  be 
wide  enough  to  receive  the  girder,  and  the 
back  should  be  stiffened  by  cast  ribs  about 
every  thirty  inches  in  height.  If  the  load 
on  the  girder  is  very  great  it  will  be  much 
better  construction  to  build  an  H-shaped 
column  in  the  wall,  to  support  the  girder, 
and  put  up  a  false  front  for  appearance, 
as  shown  in  section  by  Fig.  5.  To  com- 
pute the  strength  of  a  pilaster  of  the  sec- 
tion shown  by  Fig.  4,  divide  the  length  in 
inches  by  the  distance  X,  and  from 
Table  VII.  find  the  ultimate  strength  per 
square  inch  of  metal  for  that  ratio.  Then 


PLAN 


ItJoS 


ELEVATION 
OF  BACK 

Fig.  4 


multiply  the  sectional  area  of  the  front  and  two  sides  by  this 


418 


CAST-IRON   COLUMNS  AND  POSTS. 


value,  and  divide  by  10  or  12  for  a  factor  of  safety.  The  pilaster 
should  be  anchored  to  the  brick  wall  by 
long  iron  anchors  hooked  through  a  lug 
cast  on  the  inside  of  the  face.  The  interior 
of  the  pilaster  should  also  be  filled  with 
brickwork. 

Connections   of  Cast-iron   Columns. — The 

bearing  of  cast-iron  columns  should  always 

F'9'  5  be  turned  true  to  the  axis  of  the  column. 

Where  only  two  stories  of  columns  are  used,  and  the  joint  is  at 
a  floor  level,  it  is  not  necessary  to  bolt  the  columns  together. 
For  such  cases  a  joint  made  as  shown  by  Fig.  6 
will  generally  be  found  satisfactory.  If  more 
than  the  two  stories  of  columns  are  used,  or 
the  column  is  not  well  braced  where  the  joint 
occurs,  the  columns  should  be  bolted  together 
by  four  f-inch  bolts  for  columns  10  inches  in 
diameter  or  less,  and  six  bolts  for  12-inch  and 


'aced 


Fig.  6 


Faced 
Joint 


larger  columns.  A  desirable  section  for  such  joints  is  that  shown 
by  Fig.  7.  By  keeping  the  lugs  a  quarter  of 
an  inch  from  the  end,  less  facing  is  required, 
and  a  better  bearing  is  ensured.  Details  of 
end  connections,  brackets  and  base-plate  for 
*£  H-shaped  columns  are  shown  by  Figs.  8  and 
9,  and  for  round  columns  by  Figs.  1,  2  and 
4,  Chap.  XIII.,  also  by  Table  III ,  of  the  same 
chapter.  For  convenience  in  erecting  columns, 
the  joint  is  generally  placed  just  above  the 
beams  or  girder  supported  by  the  column. 
Fig.  7  Projecting  Caps  and  Bases. — Columns  with 

ornamental  caps  and  bases,  should  never  be  cast  as  shown  by 
the  section  Fig.  10,  i.  e.,  if  the  column  is  to  support  a  load.  In 
all  bearing  columns,  the  core  should  extend  in  a  straight  line 
from  end  to  end.  Plain  moulded  caps  and  bases  may  be  cast 
solid  as  in  Fig.  11;  if  more  ornamental  caps  are  desired,  or 
heavy  projecting  bases,  they  should  be  cast  separately  and 
attached  to  the  straight  column  by  screws. 

.    Strength  of  Cast-iron  Columns. 

The  ultimate  resistance  of  cast,  iron  to  crushing  is  generally 
taken  at  80,000  Ibs.  per  square  inch,  and  for  posts,  pintels,  etc., 


CAST-IRON   COLUMNS  AND   POSTS. 


419 


where  the  length  is  not  more  than  six  times  the  diameter,  or 
breadth,  it  will  usually  be  safe  to  figure  the  working  strength  at 


Fig.  10 


Fig.  If 


six  tons  per  square  inch  of  metal.     For  longer  posts,  or  columns, 
the  strength  is  affec^e^  by  tfye  ratio  of  Jength  to  diameter,  but  Uf 


420  CAST-IRON  COLUMNS  AND  POSTS. 

just  what  extent  is  not  definitely  known,  hence  all  formulas  for 
columns  must  be  more  or  less  theoretical.  The  consequence  is 
that  a  great  many  formulas  have  been  published,  and  there  is 
none  that  is  universally  accepted.  The  two  following,  however, 
are  now  more  commonly  adopted  than  any  others,  and  as  they 
appear  to  agree  as  well  as  any  with  actual  tests,  the  author  has 
adopted  them  in  place  of  those  presented  in  the  earlier  editions 
of  this  work. 

Formulas.  * 
For  hollow  round  cast-iron  columns  with  square  ends, 

Yirenglh  LmetalareaxPsO^OQ^l+^^V^ley) 
in  pounds  )  80°  X  S(l-  ot  diam-  J 

80,OOOA 


SOOd2 


For  hollow  rectangular  cast-iron  columns  with  square  ends, 

Ultimate    )  r  sn   of  10-th    in  in<*  T 

strength   \  =  metal  area  X  [80,000-1  +  **'   .Ij  I  (8) 

in  pounds  l,067XSq.ofleastJ 

side  in  inches    J 


80,OOOA 
1  +  l7667d2 


*  The -tables  in  the  handbooks  of  the  Cambria  Iron  Co.,  the  Carnegie  Steel 
Co.,  Jones  &  Laughlins,  and  the  Passaic  Rolling  Mill  Co.  are  based  on 
formulas  (7)  and  (8),  and  they  have  been  adopted  in  the  Boston  building 
laws. 

The  values  obtained  by  these  formulas  will  be  slightly  in  excess  of  those 
given  in  the  Chicago  building  law,  and  considerably  less  than  those  per- 
mitted by  the  building  law  of  Greater  New  York  (  p  =  11 ,300  -  -)  . 

In  1898  Prof.  W.  H.  Burr  made  an  analysis  of  the  results  of  a  number 
of  experiments  on  full-size,  hollow,  round  cast-iron  columns  made  at  the 
Watertowri  Arsenal  and  Phoenixville,  and  by  plotting  the  results  found 

that  a  straight-line  formula  having  the  equation  23  =  30,500  —  160--  repre- 
sents the  average  of  the  plotted  results.     With  a  factor  of  safety  of  four 

this  would  become  p  =  7,625  — 40— . 
a 

According  to  Prof.  Burr's  analysis  the  values  for  p  given  in  the  fourth 


CAST-IRON   COLUMNS  AND  POSTS.  421 

For  solid  cylindrical  cast-iron  columns, 
Ultimate   ) 

\ =metal  areax 

For  the  star,  T  and  II  shape,  use  formula  (7),  taking  d  as 
shown  in  Fig.  2  for  the  diameter. 

The  safe  load  is  generally  taken  at  one  eighth  of  the  ultimate 
strength  or  breaking  load. 

Eccentric  Loading.— Cast-iron  columns  should  not  be 
loaded  with  heavy  eccentric  loads,  i.e.,  a  load  applied  on  one  side 
of  the  column  without  a  corresponding  load  on  the  other  side, 
as  cast  iron  is  unable  to  resist  very  great  bending  strains. 

Tables. 

As  the  allowable  pressure  per  square  inch  of  metal  depends 
upon  the  ratio  of  length  to  diameter,  without  regard  to  actual 
dimensions,  i.e.,  it  would  be  the  same  for  a  column  6  ins.  in 
diameter  and  12  feet  long,  as  for  one  8  ins.  in  diameter  and  16 
feet  long,  it  is  practicable  to  prepare  a  table  which  will  give  the 
value  of  the  portions  of  formulas  (7)  and  (8)  inclosed  in  brackets 
for  all  ratios  of  diameter  to  length,  which  will  very  much  simplify 
the  computation  for  any  particular  column. 

Table  VII.  has  been  computed  by  means  of -the  formulas  for 
ratios  of  length  to  diameter  varying  from  8  to  36,  and  the  same 
result  will  be  obtained  by  using  the  values  given  in  this  table  as 
by  using  the  corresponding  formula. 

To  use  this  table  it  is  only  necessary  to  divide  the  length  of  the 
column  in  inches  by  the  least  thickness  or  diameter  also  in  inches, 
and  opposite  the  number  in  column  1  coming  nearest  to  the 
quotient  find  the  safe  strength  per  square  inch  for  the  column. 
Multiply  this  load  by  the  metal  area  in  the  cross-section  of  the 
column,  and  the  result  will  be  the  safe  load  for  the  column. 

column  of  Table  VII.  represent  a  factor  of  safety  of  a  little  over  four  for 

r-  =  20,  and  nearly  seven  for  --  =  36. 
d  d 

A  series  of  tests  on  full-size  cast-iron  columns  and  brackets  was  made 
under  the  direction  of  Mr.  Stevenson  Constable,  in  December,  1897,  a  report 
of  which  with  illustrations  may  be  found  in  the  Engineering  Record  for 
January  8  and  22,  1898. 


422  CAST-IRON  COLUMNS   AND   POSTS. 

EXAMPLE  4. — What  is  the  safe  load  for  a  10-inch  cylindrical 
cast-iron  column  15  feet  long,  the  shell  being  one  inch  thick? 

Ans.  The  length  of  the  column  divided  by  the  diameter,  both 
in  inches,  is  18,  and  opposite  18  in  Table  VII.  we  find  the  safe  load 
per  square  inch  for  a  round  column  to  be  7,117  pounds.  The 
metal  area  of  the  column  we  find  to  be  28.27  inches;  and  multi- 
plying these  two  numbers  together,  we  have  for  the  safe  load  of 
the  column  201,197  pounds,  or  about  100.5  tons. 

To  still  further  facilitate  computations,  Tables  VIII.,  IX.,  and 
X.  have  been  prepared,  which  give  at  a  glance  the  safe  loads 
(based  on  a  factor  of  safety  of  8)  for  columns  of  the  more  com- 
mon size  and  length.  For  lengths  between  those  given  in  the 
tables  sufficiently  accurate  results  may  be  obtained  by  interpola- 
tion. For  any  other  factor  of  safety  multiply  the  safe  load 
given  in  the  table  by  8,  and  divide  by  the  new  factor  of  safety. 


CAST-IRON   COLUMNS  AND   POSTS. 


423 


TABLE  VII.— STRENGTH  PER  SQUARE  INCH  OF  HOL- 
LOW, ROUND,  AND  RECTANGULAR  CAST-IRON 
COLUMNS. 

(Calculated  by  Formulas  (7)  and  (8).) 


Length  in 
inches  divided 
by  external 
breadth  or 
diameter. 

Breaking  weight  in  pounds 
per  square  inch. 

Safe  load  in  pounds 
per  square  inch. 
Safety  factor  8. 

Round. 

Rectangular. 

Round. 

Rectangular. 

8 

74,074 

75,470 

9,259 

9,433 

9 

72,661 

74,350 

9,082 

9,293 

10 

71,110 

73,126 

8,888 

9,140 

11 

69,505 

71,870 

8,688 

8,983 

12 

67,800 

70,487 

8,475 

8,811 

13 

66,060 

69,084 

8,257 

8,635 

14 

64,257 

67,567 

8,032 

8,446 

15 

62,450 

66,060 

7,806 

8,257 

16 

60,606 

64,516 

7,576 

8,064 

17 

58,780 

62,942 

7,347 

7,867 

IS 

56,940 

61,360 

7,117 

7,670 

19 

55,134 

59,745 

6,892 

7,468 

20 

53,333 

58,180 

6,666 

7,272 

21 

51,580 

56,610 

6,447 

7,076 

22 

49,843 

55,020 

6,230 

6,877 

23 

48,163 

53,470 

6,020 

6,684 

24 

46,512 

51,950 

5,814 

6,494 

25 

44,918 

50,440 

5,614 

6,305 

26 

43,360 

48,960 

5,420 

6,120 

27 

41,862 

47,530 

5,233 

5,940 

28 

40,404 

46,110 

5,050 

5,764 

29 

39,000 

44,742 

4,875 

5,592 

30 

37,647 

43,390 

4,706 

5^424 

31 

36,347 

42,080 

4,543 

5,260 

32 

35,090 

40,816 

4,386 

5,102 

33 

33,884 

39,580 

4,235 

4,947 

34 

32,720 

38,380 

4,090 

4,797 

35 

31,608 

37244 

3,951 

4,655 

36 

30,534 

36,120 

3,817 

4,515 

424 


CAST-IRON   COLUMNS  AND  POSTS. 


TABLE  VIII— SAFE  LOAD  IN  TONS  OF  2,000  POUNDS 
FOR  HOLLOW  ROUND  CAST-IRON  COLUMNS  WITH 
SQUARE  ENDS. 

(Based  on  formula  (7).     Safety  factor  8.) 


Diameter  j 
in  inches,  j 

|  Thickness  1 
j  in  inches,  j 

Length  of  column  in  feet. 

•4-,  a  • 

°£  cu 

Oj  "^ 

«p 

Weight 
per  foot 
of  length. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

5 

SA 

39 

34 

29 

24 

10.0 

31.3 

% 

45 

38 

32 

27 

11.3 

35.3 

5* 

H 

46 

40 

35 

30 

26 

11.2 

35.0 

% 

52 

46 

40 

34 

29 

12.7 

39.7 

6 

% 

52 

47 

41 

36 

31 

27 

24 

12.4 

38  7 

H 

60 

53 

47 

41 

36 

31 

27 

14.1 

44.0 

1 

66 

59 

52 

45 

39 

34 

30 

15.7 

49.0 

7 

65 

60 

54 

48 

43 

38 

34 

14.7 

46.0 

% 

74 

68 

62 

55 

49 

43 

38 

16.8 

52.6 

i 

83 

76 

68 

61 

54 

48 

43 

18.8 

58.9 

8 

% 

78 

72 

67 

61 

55 

50 

45 

40 

36 

33 

17.1 

53.4 

Vs 

89 

83 

76 

70 

63 

57 

51 

46 

41 

37 

19.6 

61.2 

1 

100 

93 

86 

79 

71 

64 

58 

52 

47 

42 

22.0 

68.7 

9 

% 

103 

98 

91 

85 

80 

71 

65 

59 

54 

49 

22.3 

69.8 

1 

117 

110 

103 

95 

90 

80 

73 

67 

61 

55 

25.1 

78.5 

ifc 

129 

122 

114 

105 

99 

89 

81 

74 

67 

61 

27.8 

87.0 

10 

% 

118 

112 

106 

100 

93 

86 

79 

73 

67 

62 

?5.1 

78.4 

1 

133 

127 

120 

112 

105 

97 

89 

82 

76 

69 

28.3 

88.4 

114 

147 

141 

133 

125 

116 

107 

99 

91 

84 

77 

31.4 

98.0 

ifc 

161 

154 

146 

136 

127 

118 

109 

100 

92 

84 

34.4 

107.4 

11 

l 

149 

143 

137 

129 

122 

114 

106 

98 

91 

85 

31.4 

98.2 

ijfi 

165 

159 

152 

144 

135 

126 

118 

109 

101 

94 

34.9 

109.1 

182 

175 

167 

158 

148 

139 

129 

120 

111 

103 

38.3 

119.7 

1% 

197 

190 

181 

171 

161 

151 

140 

130 

121 

112 

41.6 

129.9 

12 

i& 

184 

178 

171 

163 

154 

146 

137 

128 

120 

112 

38.4 

120.1 

202 

195 

188 

179 

170 

160 

150 

141 

132 

123 

42.2 

131.9 

1% 

220 

212 

204 

194 

184 

174 

163 

153 

143 

133 

45.9 

143.4 

1)4 

237 

229 

220 

210 

199 

187 

176 

165 

154 

144 

49.5 

154.6 

13 

1*6 

202 

196 

190 

182 

174 

165 

156 

147 

138 

130 

42.0 

131.2 

1^4 

222 

216 

209 

200 

191 

181 

172 

162 

152 

143 

46.1 

144.2 

1^6 

242 

235 

227 

218 

208 

197 

187 

176 

166 

156 

50.2 

156.9 

1J^ 

261 

254 

245 

235 

224 

213 

201 

190 

179 

168 

54.2 

169.4 

14 

iH 

242 

236 

229 

221 

212 

203 

193 

183 

173 

164 

50.1 

156.5 

1% 

264 

258 

250 

241!  231 

221 

210 

199 

189 

178 

54.5 

170.4 

u| 

2S5 

278 

270 

260 

250 

238 

227 

215 

204 

193 

58.9 

184.1 

i^ 

306 

298 

289 

279 

268 

256 

243 

231 

219 

207 

63.2 

197.4 

15 

1% 

268 

280 

272 

264 

254 

244 

234 

223 

212 

203 

58.9 

183.9 

1^6 

309 

303 

295 

285 

275 

264 

252 

241 

229 

219 

63.6 

203.4 

i 

1% 

332 

325 

316 

306 

295 

283 

271 

259 

246 

235 

68.3 

213.4 

1% 

354 

346 

337 

327 

315 

302 

288 

276 

263 

251 

72.8 

227.6 

16 

1V£ 

333 

327 

319 

310 

300 

290 

278 

267 

255 

243 

68.3 

?13.5 

]^X 

358 

351 

313 

333 

322 

311 

299 

286 

273 

261 

73.4 

229.3 

i:M 

382 

375 

366 

356  344 

332 

319 

306 

292 

279 

78.3 

244.8 

IK 

455 

446  435 

423,  410 

395 

380 

364 

347 

332 

93.2 

291.3 

i 

i 

CAST-IRON  COLUMNS  AND  POSTS. 


425 


TABLE  IX.— SAFE  LOAD  IN  TONS  OF  2,000  POUNDS  FOR 
HOLLOW  SQUARE  AND  RECTANGULAR  CAST-IRON 
COLUMNS  WITH  SQUARE  ENDS. 

(Based  on  Formula  (8).     Safety  factor  8.) 


Size  in 
inches. 

Thick- 
ness in 
inches. 

Length  of  column  in  feet. 

Area  of 
metal 
in 
inches. 

Weight 
per  foot 
of 
length. 

8 

10 

34 
42 
46 
50 
59 

55 
71 
60 
78 
65 
84 
74 
97 

57 
72 
68 
87 
73 
94 

79 
101 
90 
116 
106 
138 

73 
94 
85 
109 
102 
133 

90 
115 
140 
103 
132 
161 

115 

148 
181 

12 

14 

16 

18 

20 

24 

4X  6 
4X  8 
4X  9 
4X10 
4X12 

5X  8 
5X  9 
5X10 
5X12 

6X  6 
6X  8 
6X  9 

6X10 
6X12 
6X15 

7X  7 
7X  9 
7X12 

8X  8 
8X10 

8X12 

N 

« 

i* 

i* 
p 

* 
p 
•« 

i« 
? 

1« 

« 

I* 

ft 

K 

N 

1J4 

1« 

1M 

41 
51 
56 
60 
70 

64 
81 
69 
89 
75 
96 
86 
111 

63 

80 
75 
96 
81 
104 

87 
112 
99 
129 
117 
153 

80 
102 
92 
119 
111 
144 

95 
124 
148 
109 
141 
170 

122 

158 
192 

28 
35 
39 
42 
49 

48 
61 
52 
67 
57 
73 
65 
84 

51 
65 
60 
78 
65 
84 

70 
91 
80 
104 
95 
123 

67 

85 
77 
100 
93 
>21 

83 
107 
129 
95 
122 
148 

106 
138 
167 

12.75 
15.75 
17.25 
18.75 
21.75 

17.25 
22.00 
18.75 
24.00 
20.25 
26.00 
23.25 
30.00 

15.75 
20.00 
18.75 
24.00 
20.25 
26.00 

21.75 
28.00 
24.75 
32.00 
29.25 
38.00 

18.75 
24.00 
21.75 
28.00 
26.25 
34.00 

21.75 
28.00 
33.75 
24.75 
32.00 
38.75 

27.75 
36.00 
43.75 

39.8 
49.2 
53.9 
58.6 
68.0 

53.9 
68.8 
58.6 
75.0 
63.3 
81.3 
72.7 
93.8 

49.2 
62.5 
58.6 
75.0 
63.3 
81.3 

68.0 

87.5 
77.3 
100.0 
91.4 
118.8 

58.6 
75.0 
68.0 
87.5 
82.0 
106.3 

68.0 
87.5 
105  .  5 
77.3 
100.0 
121.1 

86.7 
112.5 
1ZQ.7 

41 
53 
45 
58 
49 
63 
56 
72 

45 
57 
54 
69 

58 
75 

62 
80 
71 
92 
84 
109 

61 

78 
70 
91 
85 
110 

77 
99 
119 
87 
113 
137 

98 
127 
154 

40 
51 
47 
61 
51 
66 

55 
71 
63 
81 
74 
97 

55 
70 
63 
82 
77 
99 

70 
91 
109 
80 
104 
125 

90 
116 
142 

35 

45 
42 
54 
45 

58 

49 
63 
55 

72 
66 
85 

49 
63 
57 
74 
69 
89 

64 
83 
100 
73 
95 
115 

82 
107 
130 



44 
57 
••51 
66 
62 
80 

59 
76 
91 
67 
86 
105 

75 
97 
118 

49 

63 
76 
55 
72 
87 

62 

81 
98 

426 


CAST-IRON  COLUMNS  AND  POSTS. 


TABLE  IX.— SAFE  LOAD  IN  TONS  OF  2,000  POUNDS  FOR 
HOLLOW  SQUARE  AND  RECTANGULAR  CAST-IRON 
COLUMNS  WITH  SQUARE  ENDS  (continued). 

(Based  on  formula  (8).     Safety  factor  8.) 


Size  in 

Thick- 

Length  of  column  in  feet. 

Area  of 
metal 

Weight 
per  foot 

inches. 

inches. 

in 

of 

8 

10 

12 

14 

16 

18 

20 

24 

inches. 

length. 

8X16 

1 

193 

181 

168 

155 

142 

130 

119 

99 

44.00 

137.5 

m 

236 

221 

206 

190 

174 

159 

145 

121 

53.75 

168.0 

9X   9 

H 

111 

106 

99 

93 

86 

80 

74 

63 

24.75 

77.3 

i 

144 

137 

129 

120 

112 

103 

96 

85 

32.00 

100.0 

9X12 

i 

171 

162 

153 

143 

133 

123 

114 

97 

38.00 

118.8 

1*4 

209 

198 

186 

174 

162 

149 

138 

118 

46.25 

144.5 

9X16 

i 

207 

196 

185 

173 

161 

149 

138 

117 

46.00 

143.8 

1^4 

254 

240 

226 

212 

197 

182 

168 

143 

56.25 

175.8 

10X10 

i 

165 

158 

150 

142 

133 

125 

117 

101 

36.00 

112.5 

1*4 

201 

193 

183 

172 

162 

152 

142 

123 

43.75 

136.7 

10X12 

i 

184 

176 

167 

158 

148 

139 

129 

112 

40.00 

125.0 

1J4 

224 

214 

204 

192 

181 

169 

158 

137 

48.75 

152.3 

10X15 

l 

211 

202 

192 

181 

170 

160 

149 

129 

46.00 

143.8 

1*4 

258 

247 

235 

222 

209 

195 

182 

158 

56.25 

175.8 

10X16 

i 

220 

211 

200 

189 

178 

167 

155 

135 

48.00 

150.0 

1J4 

270 

258 

245 

232 

218 

204 

190 

165 

58.75 

183.6 

10X18 

i 

239 

228 

217 

205 

193 

181 

168 

146 

52.00 

162.5 

1*4 

293 

280 

266 

251 

236 

221 

207 

179 

63.75 

199.2 

10X20 

i 

257 

246 

234 

221 

208 

194 

181 

157 

56.00 

175.0 

1*4 

316 

302 

287 

271 

255 

239 

223 

193 

68.75 

214.9 

10X24 

i 

294 

2S1 

257 

252 

237 

222 

207 

180 

64.00 

200.0 

m 

362 

346 

329 

311 

292 

274 

255 

221 

78.75 

246.1 

12X12 

7A 

183 

177 

171 

164 

156 

149 

141 

126 

38.9 

121.7 

i 

207 

201 

193 

185 

177 

168 

159 

142 

44.00 

137.5 

1^4 

253 

245 

236 

223 

216 

206 

195 

174 

53.75 

168.0 

ij^ 

296 

288 

277 

265 

253 

241 

228 

204 

63.00 

196.9 

12X15 

l 

235 

228 

220 

211 

201 

191 

181 

162 

50.00 

156.3 

1*4 

288 

280 

269 

258 

246 

234 

222 

198 

61.25 

191.4 

12X16 

l 

245 

237 

228 

219 

209 

199 

188 

168 

52.00 

162.5 

12X18 

l 

263 

256 

246 

236 

225 

214 

203 

181 

56.00 

175.0 

12X20 

l 

282 

274 

264 

253 

241 

229 

217 

194 

60.00 

187.5 

12X24 

i 

320 

310 

299 

287 

274 

260 

246 

220 

68.00 

212.5 

14X16 

l 

268 

261 

254 

246 

238 

229 

219 

200 

56.00 

175.0 

14X20 

l 

307 

298 

290 

281 

272 

261 

250 

228 

64.00 

200.0 

14X24 

l 

345 

336 

326 

316 

306 

294 

280 

257 

72.00 

225.0 

16X16 

1 

300 

284 

278 

271 

264 

256 

247 

229 

60.00 

187.5 

16X24 

1 

380 

360 

352 

344 

334 

324 

313 

291 

76.00 

237.5 

18X18 

1 

340 

340 

320 

314 

307 

299 

291 

274 

68.00 

212.5 

20X20 

l 

380 

380 

361 

356 

349 

342 

334 

317 

76.00 

237  .  5 

20X24 

l 

420 

420 

399 

393 

386 

378 

369 

351 

84.00 

262.5 

CAST-IRON  COLUMNS  AND  POSTS. 


427 


TABLE  X.—  SAFE  LOAD  IN  TONS  OF  2,000  POUNDS  FOR 
H-SHAPED  CAST-IRON  POSTS.            ^  ^                  ^ 

(Based  on  formula  (7).     Safety  factor  8.)              '    fl 

.._.«.        *,\                                        YS/. 

Size  of  post 
in  inches. 

Area 

i 

Length  of  post  in  feet.          ,    ^^                 ijji 

i    y\                      ty/, 

in 

inches. 

yjji            m 

a.     b.       t. 

10 

12 

13 

14 

K-  -•  -  -   -]j  •,  »  T-  -> 

6X   6X   94 

12% 

41 

36 

33 

31 

I 

16 

53 

46 

43 

40 

1H 

193/6 

1  q1?/ 

64 

A(» 

56 
j.n 

52 

0*7 

48 

rtA 

15 

16 

18 

20 

6  X   8  X   •% 

ld^§ 

18 

4O 

60 

4U 

52 

O/ 

48 

«>4 

45 

INf 

21% 

73 

63 

59 

54 

7X   7X1 

19 

69 

62 

58 

55 

52 

49 

43 

38 

1M 

23% 

84 

75 

71 

67 

63 

59 

53 

46 

7X  9X1 

21 

76 

68 

64 

61 

57 

54 

48 

42 

1M 

25% 

93 

83 

79 

74 

70 

66 

59 

51 

8X  8X  % 

16% 

66 

60 

57 

54 

51 

49 

44 

39 

1 

22 

86 

78 

74 

70 

67 

64 

57 

51 

1*4 

26% 

105 

95 

91 

86 

82 

78 

70 

63 

8X10X1 

24 

93 

85 

81 

77 

73 

69 

62 

56 

1H 

29% 

114 

104 

99 

94 

90 

85 

76 

69 

IK 

34^ 

134 

122 

117 

111 

105 

100 

89 

81 

9X  9X1 

25 

102 

94 

91 

87 

83 

79 

72 

66 

1V4 

30% 

125 

116 

111 

106 

102 

97 

89 

81 

lfc§ 

36 

147 

136 

130 

125 

120 

114 

104 

95 

9X10X1 

26 

106 

98 

94 

90 

86 

83 

75 

69 

iH 

31% 

130 

120 

115 

111 

106 

101 

92 

84 

1H 

37^ 

153 

142 

136 

130 

125 

119 

108 

99 

10X10X1 

28 

118 

111 

107 

103 

99 

95 

88 

81 

1*4 

343^ 

145 

136 

131 

127 

122 

127 

108 

100 

111 

40^ 

171 

160 

155 

149 

144 

138 

128 

117 

1% 

46% 

196 

184 

177 

171 

165 

158 

146 

134 

10X12X1 

30 

127 

119 

115 

111 

106 

102 

94 

87 

1*4 

36% 

156 

146 

141 

136 

131 

126 

116 

107 

1*1 

43^ 

184 

172 

166 

160 

154 

148 

137 

126 

1% 

49% 

211 

198 

191 

184 

177 

170 

157 

144 

2 

56 

236 

222 

214 

207 

199 

191 

176 

162 

12X12X1 

34 

151 

144 

140 

136 

132 

128 

121 

113 

1M 

41% 

186 

177 

172 

167 

163 

158 

149 

139 

m 

49V£ 

220 

209 

203 

198 

193 

187 

177 

165 

if! 

56% 

252 

241 

234 

227 

221 

216 

202 

189 

2 

64 

284 

271 

263 

256 

249 

242 

227 

213 

12X14X1*4 

443x6 

197 

f88 

183 

177 

173 

168 

158 

148 

1V£ 

52  K 

233 

222 

216 

210 

204 

199 

186 

174 

lH 

603/6 

268 

255 

248 

241 

235 

228 

214 

201 

2 

68 

302 

288 

280 

272 

265 

257 

241 

226 

2M 

75% 

335 

319 

310 

301 

292 

285 

268 

251 

428  STEEL  COLUMNS  AND  STRUTS* 


WROUGHT-IRON  AND  STEEL  COLUMNS 
AND  STRUTS. 

Owing  to  the  many  advantages  of  built  steel  columns  over 
cast-iron  columns,  especially  for  tall  buildings,  and  the  great  re- 
duction that  has  taken  place  during  the  past  fifteen  years  in  the 
cost  of  steel  construction,  steel  columns  are  now  very  extensively 
used  in  buildings,  even  of  moderate  height,  and  for  skeleton  con- 
struction, or  buildings  exceeding  six  stories  in  height,  they  are 
certainly  much  to  be  preferred  to  cast  columns. 

Steel  trusses  are  also  much  more  commonly  used  in  buildings 
now  than  in  former  years,  so  that  the  architect  must  have  at  hand 
data  for  designing  the  same  and  computing  the  strength.  In 
the  following  pages  the  author  has  endeavored  to  cover  the 
subject  of  columns  and  struts  quite  completely,  and  to  furnish 
such  data  as  will  enable  one  to  decide  upon  the  shape  of  column 
or  strut  it  is  best  to  use,  and  to  determine  the  size  and  section 
with  the  least  labor. 

Forms  of  Steel  Columns. 

The  forms  of  columns  commonly  used  in  current  American 
building  practice  are  those  shown  by  the  following  sections; 


Larimer  column,  1  row  of  rivets. 
H 


Z-bar  column,  without  'j''  4  angles  and 

covers,  2  rows.  plate,  2  rows. 


v 

4-section  Phcenix  column,  4  rows. 


Nurick  column,  4  rows. 

Channel  column,  with  plates  or  lattice,  4  rows. 
Gray  column,  4  rows. 


STEEL  COLUMNS  AND  STRUTS.  429 

Z-bar  column,  with  single  covers,  6  rows. 
Box  column  of  plates  and  angles,  8  rows. 

8-section  Phoenix  column,  8  rows. 

Z-bar  column,  with  double  covers,  10  rows. 


Each  of  these  shapes  has  its  advocates  among  experienced 
engineers,  and  the  choice  of  a  section  is  generally  governed  by 
some  practical  consideration,  such  as  the  cost,  facility  for  making 
connections,  and  promptness  of  delivery. 

Relative  Advantages  and  Disadvantages. 

The  relative  advantages  and  disadvantages  of  the  various 
sections  are  set  forth  at  considerable  length  by  Mr.  Joseph  K. 
Freitag,  B.S.,  C.E.,  in  his  very  practical  work  on  "Architectural 
Engineering." 

In  general  it  may  be  said  that  the  factors  which  usually  deter- 
mine the  choice  of  a  section  are  one  or  more  of  the  following 
points,  each  of  which  should  be  carefully  considered  when 
designing  an  important  building: 

1.  Cost,  including  shop-work,  availability. 

2.  Ability  to  transfer  loads  to  centre  of  column,  especially  in 
cases  of  heavy  eccentric  loads. 

3.  Convenient  connection  of  floor  system. 

4.  Relation  of  size  of  section  to  small  columns. 

5.  Fireproofing  capabilities  of  the  section.     "Point  1  is  of  the 
greatest  importance  to  the  owner  and  builder,  and  often  governs 
the  selection  of  the  column.     Points  2,  3,  and  4  are  for  the 
engineer's  consideration  ;  while  point  5  is  of  chief  interest  to  the 
architect  and  decorator.'7  * 

Cost,  Availability.  —  These  vary  more  or  less  at  different  times, 
the  cost  depending  principally  upon  the  market  price  of  the 
section  used,  and  upon  the  amount  of  shop-work  required.  In 
general  it  may  be  said  that  those  forms  which  can  be  rolled  or 

*  Freitag. 


430  STEEL   COLUMNS  AND   STRUTS. 

manufactured  by  any  mill  are  likely  to  be  the  cheapest  and  most 
available,  although  there  may  often  be  exceptions  to  this  rule. 

Plates  and  angles  are  generally  the  cheapest  sections  of  rolled 
steel  and  the  most  available,  and  the  Z-bar  is  now  being  rolled  by 
several  mills.  The  Phoenix  column  is  rolled  only  by  the  Phoenix 
Iron  Company,  and  the  Larimer  column  is  manufactured  only  by 
Jones  &  Laughlins,  Limited.  The  number  of  rivets  required  in 
putting  the  sections  together,  which  comes  under  the  head  of 
"  shop-work,"  is  also  an  important  factor  in  the  cost  of  steel 
columns.  The  Larimer  column  possesses  an  advantage  in  this 
respect  over  all  other  shapes,  and  at  the  present  price  of  steel 
beams  this  column  should  be  one  of  the  cheapest  shapes  on  the 
market. 

An  objection  has  been  found  to  the  smaller  sizes  of  this  column, 
particularly  the  6-inch  size,  that  it  is  difficult  to  drive  the  rivets 
which  connect  the  angle  brackets  with  the  I-beam  flanges  without 
interfering. 

Next  to  the  Larimer  column  in  point  of  shop-work  comes  the 
Z-bar  column,  without  cover-plates,  which  has  two  rows  of  rivets. 
For  light  loads  this  shape  appears  to  have  more  advantages  than 
any  other,  as  it  is  an  economical  section,  and  the  connections  for 
floor  beams  and  girders  are  quite  simple,  and  the  shape  also 
permits  of  bringing  the  weight  well  into  the  centre  of  the  column. 

In  tall  buildings,  however,  it  has  almost  invariably  been  found 
necessary  to  add  cover-plates,  and  in  some  instances  no  less  than 
ten  rows  of  rivets  have  been  required,  so  that  for  tall  buildings 
this  section  does  not  appear  to  offer  any  advantage  over  col- 
umns built  of  plates  and  channels,  and  in  point  of  fact  it  is  now 
seldom  used  in  high  or  heavy  buildings.  The  Z-bar  column, 
however,  has  been  more  extensively  used  than  any  other  shape 
in  the  tall  buildings  erected  during  the  past  ten  years  in  Chicago. 
Its  use  in  Eastern  cities  has  been  far  more  limited.  Channel  col- 
umns and  columns  of  plates  and  angles  have  also  been  quite  ex- 
tensively used  both  in  Chicago  and  in  the  East.  Although  some- 
what limited  as  to  section,  channel  columns  afford  a  very  desir- 
able shape,  both  as  regards  economy  of  material  and  facility  for 
making  connections.  Columns  built  up  of  plates  and  angles 
present  a  section  that  can  be  increased  to  any  desired  area,  and 
the  area  of  the  section  can  also  be  considerably  varied  without 
increasing  the  exterior  dimensions. 

With  heavy  eccentric  loads  it  is  sometimes  an  advantage  to  use 


STEEL  COLUMNS   AND   STRUTS. 


431 


a  rectangular  shape,  with  the  long  axis  in  the  direction  of  the 
eccentricity. 

In  practice,  however,  the  choice  of  a  section  is  generally  gov- 
erned more  by  the  considerations  of  cost  and  connection  facilities 
than  by  the  best  theoretical  shape. 

Further  description  of  the  different  columns,  and  also  the 
special  advantages  claimed  for  them,  is  given  in  the  following 
pages. 

A  new  type  of  column  which  has  recently  been  patented  by 
Mr.  John  Lanz,  of  Pittsburg,  is  shown  by  Fig.  12.  The  columns 


Fig.  12 

are  formed  of  rolled  channel  beams,  bent  to  the  necessary  form 
and  riveted  together  into  a  hollow  column  with  projecting 
flanges  of  a  T-shape.  It  is  proposed  to  bend  the  channels  so  as 
to  give  columns  of  circular  cross-section  as  well  as  the  shapes 
illustrated.  Among  the  merits  claimed  for  the  new  column  are 
compactness,  an  unusually  large  radius  of  gyration  for  the 
amount  of  material  used,  and  three  constant  sizes  of  columns  for 
56  different  sectional  areas,  making  it  very  easy  to  get  out  details 
of  the  framing. 


Column  Connections. 

This  feature  in  column  construction  is  a  very  important  one, 
and  often  governs  the  selection  of  the  shape  to  be  used.  Where 
there  are  only  two  or  four  beams  at  the  same  level,  and  these  are 
symmetrically  placed  and  loaded,  satisfactory  connections  can  be 
made  for  almost  any  of  the  sections,  but  when  irregular  placing 
of  beams  is  necessitated,  and  eccentric  loads  must  be  provided 
for,  it  is  important  that  the  character  of  the  column  affords  as 
great  an  opportunity  as  possible  for  the  connection  of  plates  and 


432  STEEL  COLUMNS  AND  STRUTS. 

angles,  and  for  transferring  eccentric  loads  to  the  centre  of  the 
column. 

When  wrought-iron  columns  were  first  used  it  was  customary 
to  use  plates  for  connecting  the  story  lengths,  and  the  beams  or 
girders  often  rested  on  these  plates,  as  shown  in  Figs.  14  and  24. 
In  the  best  practice  at  the  present  time  these  plates  are  often 
omitted,  and  the  ends  of  the  different  lengths  are  closely  fitted 
together  with  milled  ends,  and  splice  plates  are  riveted  to  the 
sides  or  flanges. 

As  it  is  impossible  in  these  pages  to  cover  the  subject  of 
column  connections  in  anything  but  a  general  way,  the  only 
attempt  that  has  been  made  in  this  line  is  to  illustrate  common 
forms  of  connections  that  have  been  used  with  different  forms  of 
columns.  These  will  be  found  in  the  descriptions  of  different 
columns  contained  in  the  following  pages. 

For  a  more  complete  consideration  of  the  subject  the  reader  is 
referred  to  Mr.  Freitag's  ' 'Architectural  Engineering"  and  Mr. 
Birkmire's  "  Skeleton  Construction  in  Buildings." 


Number  and  Spacing  of  Kivets. 

Number  of  Rivets  Required. — No  general  rule  can  be  given  for 
the  number  of  rivets  and  size  of  the  brackets  required  for  col- 
umn connections,  as  the  loads  to  be  supported  vary  in  different 
buildings  and  in  different  portions  of  the  same  building.  The 
number  of  rivets  required  in  each  connection  must  therefore  be 
determined  by  the  rules  given  for  designing  riveted  joints  in 
Chapter  XII.  Connections  for  single  beams,  however,  will  gen- 
erally require  the  same  number  of  rivets  as  are  given  for  beam 
connections,  Chapter  XV.  The  allowable  strains  for  rivets  in 
column  connections  are  generally  taken  at  10,000  Ibs.  per  sq. 
inch  for  single  shear  and  18,000  Ibs.  for  bearing. 

Spacing  of  Rivets. — Steel  and  wrought-iron  columns  fail  either 
by  deflecting  bodily  out  of  a  straight  line  or  by  the  buckling  of 
the  metal  between  rivets  or  other  points  of  support.  Both 
actions  may  take  place  at  the  same  time,  but  if  the  latter  occurs 
alone,  it  may  be  an  indication  that  the  rivet  spacing  or  the  thick- 
ness of  the  metal  is  insufficient. 

The  rule  has  been  deduced  from  actual  experiments  upon 
wrought-iron  columns  that  the  distance  between  centres  of 
rivets  should  not  exceed,  in  the  line  of  strain,  sixteen  times  the 


STEEL  COLUMNS  AND  STRUTS.  433 

thickness  of  metal  of  the  parts  joined,  and  that  the  distance 
between  rivets  or  other  points  of  support,  at  right  angles  to  the 
line  of  strain,  should  not  exceed  thirty-two  times  the  thickness 
of  the  metal. 

Z-Bar  Columns. 

This  column  was  designed  by  Mr.  C.  L.  Strobel,  C.E.,  about  the 
year  1887,  and  for  a  time  the  bars  were  rolled  only  by  the  Carnegie 
Steel  Company.  At  the  present  time  they  are  rolled  by  nearly 
all  of  the  large  mills,  so  that  they  can  be  obtained  as  readily  as 
channels  or  angles.  For  buildings  of  moderate  height  and  load- 
ing, no  more  advantageous  section  can  be  employed,  while  it  is 
probably  as  cheap  as  any.  It  has  also  been  used  quite  exten- 
sively in  tall  buildings,  although  at  the  present  time  columns 
built  of  plates  and  angles  appear  to  be  more  generally  used. 

For  buildings  of  ordinary  height  the  column  is  formed  of  four 
Z-bars  and  one  web  plate,  with  two  rows  of  rivets.  When  un- 
usually heavy  loads  must  be  provided  for,  as  in  the  case  of 
columns  for  the  lower  stories  of  high  buildings,  the  above- 
mentioned  section  may  be  reinforced  to  the  required  strength 
by  using  outside  cover-plates,  as  shown  on  page  478,  or  cover- 
plates  and  angles,  forming  a  closed  or  box  column. 

Connections. — The  usual  form  of  base  plate,  and  the  manner 
of  supporting  single  beams  where  the  column  is  continuous,  are 
shown  by  Fig.  13.  The  beams  should  extend  to  within  |  inch 
of  web  plates,  and  should  be  also  bolted  or  riveted  to  the  sup- 
porting angles. 

The  usual  connection  of  one  column  to  another  is  shown  by 
Fig.  14,  which  represents  a  plan  of  the  cap  plate,  and  vertical  sec- 
tion through  centre  of  column.  The  ends  of  the  two  sections 
should  be  carefully  milled  and  connected  to  the  cap  plate  by  angle 
brackets,  the  whole  construction  being  firmly  riveted  together. 
The  cap  plate  is  usually  made  from  J  to  1  inch  in  thickness,  ac- 
cording to  the  load  to  be  supported.  Where  beams  of  different 
depths  rest  on  the  cap  plate,  they  may  be  brought  to  the  same 
level  by  means  of  cast-iron  bolsters. 

Fig.  15  shows  a  detail  of  one  of  the  columns  used  in  the  Ameri- 
can Surety  Building  in  New  York,  the  connections  shown  being 
those  of  the  sixteenth-  and  seventeenth-story  floor  beams.  It 
will  be  noticed  that  in  this  column  the  end  connections  do  not 
come  at  the  floor  level,  but  at  some  distance  from  it,  and  the 


434 


STEEL  COLUMNS  AND  STRUTS. 


cap  plate  does  not  project  beyond  the  Z-bars,  the  joint  being 
secured  by  means  of  splice  plates.  The  object  in  giving  such  a 
long  bearing  under  the  beams  was  to  obtain  stiffness  to  resist 


Fig.  13 


Fig.  14 


the  horizontal  wind  pressure,  four  rivets  being  placed  in  each 
side  of  the  lower  flange. 

The  connections  shown  in  Fig.  15  are  also  applicable  to  channel 
and  plate  and  angle  columns. 

The  standard  connections  for  double  I-beam  girders  and  single 
floor  beams  to  Z-bar  columns,  detailed  on  page  436,  were  de- 
signed by  the  Carnegie  Steel  Company  to  fairly  cover  the  range 
of  ordinary  practice.  When  the  maximum  loads  in  tons  indi- 
cated for  each  case,  are  exceeded,  the  connections  may  be  corre- 
spondingly strengthened  by  simply  using  longer  vertical  angles 
for  the  brackets  and  increasing  the  number  of  rivets.  In  pro- 
portioning these  connections  the  shearing  strain  on  rivets  was 
assumed  of  a  maximum  intensity  of  10,000  pounds  per  square 
inch. 


STEEL  COLUMNS  AND  STRUTS. 
SECTION  ON  LINE:  as. 


435 


Milled. 


Fig.  15 


436 


STEEL  COLUMNS  AND  STRUTS. 


DETAILS  OF  STAKDABD  CONNECTIONS 
OF  I  BEAMS  TO    Z-BAR  COLUMNS. 

Connections  of  a  single  I  Beam  to  Flanges  of  Z  Bars. 


Fig.  i     j 

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20*1  Beams,          15"  and  12"!  Beams                      tojrf'/to.'y'and  8"     7"and  6" 

44  Tons.                     35  Tons.                                      I  Beams  '         I  Beams 

17.6  Tons.  -     8.8  Tons. 

Connections  of  a  double  Beam  girder  to  Flanges  of  Z  Bars. 

Fig.  5                                         Fig.  6              Fig.  7                Fig.  8 

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2orl  Beams                                  island  12"  10^,'  io,"9"aiidv8ft  7"and  6" 
88  Tons.                                      I  Beams            I  Beams           I  Beams 
53  Tons.            35  Tons.        *7-6  Tons 

The  number  of  tons  indicated,  denote  the  loads  on  single  beams  or 
girders  for  which  the  connections  are  proportioned. 

Rivets  and  Bolts  K  dia  .—-All  Bolts  hai/e  beveled  heads. 


STEEL  COLUMNS  AND  STRUTS.  437 

The  standard  sections  of  Z-bar  columns  as  made  by  the  Carnegie 
Steel  Co.,  together  with  the  safe  loads,  are  given  on  pages  474- 
481.     The  properties  of  Carnegie  Z-bars  are  given  in  Chapter  X. 
Constant  Dimension  Z-bar  Columns. 

On  page  482  is  shown  a  section  of  constant  dimension  Z-bar 
columns  designed  by  the  Carnegie  Steel  Company,  for  the  pur- 
pose of  keeping  the  same  outside  dimensions  throughout  the 
successive  stories  of  the  structure.  The  advantage  of  this  lies 
in  the  quicker  preparation  of  plans  and  subsequent  shop  details; 
the  convenience  to  the  architect  in  dimensioning  walls  and  pillars, 
and  the  simplification  of  the  fireproofing  work. 

For  buildings  of  not  more  than  six  or  eight  stories,  however, 
these  advantages  are  not  sufficient  to  offset  the  disadvantage 
of  the  extra  space  occupied  by  the  column. 

Angle  and  Plate  Columns. 

Four  angles  and  a  plate  riveted  together  as  shown  by  Fig.  1 5a 
are  now  being  quite  extensively  used  in  building  construction, 
particularly  for    columns    having   an   unsupported 
length  of  less  than  90  radii,  also  for  the  outer  posts 
in  steel  mill  buildings,  and  for  light  posts  supporting 
depot  roofs,  etc.   Columns  of  this  section  are  espe-         Fi     ,5a 
cially  convenient  for  making  beam  and  girder  con- 
nections, and  for  splicing,  and  are  also  well  adapted  to  resisting 
eccentric  loads.     The  width  of  the  plate  is  generally  such  that 
the  least  radius  of  gyration  is  in  the  direction  r2,  which  may  be 
obtained  directly  from  the  tables  on  pages  316  and  318. 
Channel  Columns. 

Two  channels,  set  back  to  back,  at  such  a  distance  that  the 
radii  of  gyration  will  be  equal  about  both  axes,  and  connected  by 
lattice  bars,  make  a  very  desirable  column  for  moderate  loads, 
as  in  the  upper  stories,  or  in  buildings  of  three  or  four  stories 
in  height.  For  greater  loads,  cover-plates  may  be  riveted  to  the 
flanges  in  place  of  the  lattice,  as  in  Fig.  18.  Such  columns  are 
very  satisfactory,  especially  for  making  connections,  provided 
that  only  a  single  cover-plate  on  each  side  is  required.  Three 
channels,  riveted  together,  as  in  Fig.  16,  also  make  a  good  column 
for  light  loads;  in  fact  it  was  this  combination  which  suggested 
the  Z-bar  column.  Three  I-beams  riveted  together  in  the  same 
way  have  also  been  used  for  columns,  but  it  is  not  an  advan- 
tageous shape. 


438 


COLUMNS  AND 


Fig.  17  shows  a  light  lattice  column,  with  base-plate,  and 
Fig.  18  a  typical  channel  column  with  single  cover-plates,  and  the 
manner  of  making  splices  and  connections. 


Fig.  I5b 

Type  of  Posts  used  for 
Supporting  the  Bos- 
ton Elevated  Ry. 


H 


Fig.  16 


(P 


Oi 


10|X 


0    0    0    0    0 

-•*& 

A 

a. 

o  o   o  o   o 

Fig.  17 


Fig.  18 

Channel  Column,  with  Cover-plates. 


STEEL  COLUMNS  AND   STRUTS. 


439 


Rule  for  Latticing  of  Channels  and  Angles.  —  When  channels 
are  connected  by  latticework,  as  in  Fig.  19,  that 
there  may  not  be  a  tendency  in  the  channels 
to  bend  between  the  points  of  bracing,  the  dis- 
tance I  should  be  made  to  equal  the  total  length 
of  strut,  multiplied  by  the  least  radius  of  gyra- 
tion of  a  single  channel,  and  the  product  divided 
by  the  least  radius  of  gyration  for  the  whole 

section;    or. 

following  significance: 
1=  length  between  bracing; 
L=  total  length  of  strut; 
r—  least  radius  of  gyration  for  a  single  chan- 

nel; 
R=  least  radius  of  gyration  for  the  whole  sec- 

tion. 

This  same  rule  will  also  apply  for  angles,  though  with  them 
the  latticework  is  generally  doubled,  as  in  Fig.  20. 


-^  where  the  letters  have  the 
H 


Fig.  19 


u 


Total  length  =•  L 


Fig.20 

Generally  it  is  found  desirable  to  make  the  distance  I  less  than 
that  obtained  by  the  above  formula,  or  so  that  the  inclination  of 
lattice-bars  will  be  about  45°  with  the  axis  of  the  column  or  strut. 

The  size  of  the  lacing-bars  should  not  be  less  than  that  given 
in  the  following  table : 


Distance  I,  Fig.  20, 
or  HI,  Fig.  19. 

Size  of  bar, 
in  inches. 

Distance  L  Fig.  20, 
or  H  I,  Fig.  19. 

Size  of  bar, 
in  inches. 

less  than    6" 
6"  or  less  than    7" 
7"  or  less  than    9" 
9"  or  less  than  10" 

ijx.i 

1  3.  V"  §/, 

2V  5/ 
<X>/16 

10"  or  less  than  16" 
16"  or  less  than  20" 
20"  or  less  than  24" 
20"  or  above 

2V  3 
/N  If 

angles 

440 


STEEL  COLUMNS  AND   STRUTS. 


The  proper  distance  for  d  or  7),  Fig.  19,  to  give  a  pair  of  chan- 
nels the  same  radius  of  gyration  in  both  directions  is  given  under 
the  properties  of  channels  in  Chapter  X. 


Plate  and  Angle  Box  Columns. 

"For  high  buildings  or  heavy  loads,  where  the  required  sec- 
tional area  is  greater  than  can  be  obtained  by  using  Z-bar  col- 
umns without  cover-plates,  the  box  column  of  plates  and  angles 
will  be  found  most  satisfactory.  This  'column  form  possesses 
great  advantages  regarding  connections,  in  that  square  surfaces 
are  always  presented.  Box  columns  were  used  in  the  Masonic 
Temple,  the  highest  building  in  Chicago,  and  in  the  Park  Row 
Building,  one  of  the  highest  structures  in  New  York  City."  * 
Fig.  21  shows  a  heavy  column  section,  in  the 
Park  Row  Building,  composed  of  3  web-plates, 
24"X1A6",  4  covers,  48"  X%",  and  8  angles, 
6"X6"X!%",  and  designed  for  a  load  of  1;450 
tons. 

A  column  composed  of  10  web-plates,  4  covers, 
and  12  angles,  and  weighing  46,980  Ibs.,  was 
used  in  the  Waldorf-Astoria  Hotel  to  support 
an  estimated  load  of  2,700  tons. 

g-  21  The  most  common  form  of  box  column  is  that 

shown  by  Fig.  22,   the   thickness  and  number  of  the  web   and 
cover-plates  varying  with  the  load  to  be  sup-       ^  ^^ 

ported. 

Several  examples  of  plate  and  angle  columns 
are  given  in  Chapter  XXVIII. 

Ordinary  connections  for  box  columns  are 
made  as  shown  in  Figs.  15  and  18.  More 
elaborate  connections  are  shown  in  Chapter 
XXVIII. 


Fig.  22 


The  Phoenix  Segmental  Column. 

This  column  has  now  been  on  the  market  for  over  thirty-eight 
years  and  has  been  very  extensively  used  in  buildings,  and  also 
for  posts  in  bridges,  and  for  piles  and  for  wharves  and  piers. 


*  J.  K.  Freitag. 


STEEL  COLUMNS  AND  STRUTS. 


441 


In  the   anthracite  coal   regions  of  Pennsylvania  it  is  very 
extensively  used  as  shafts  for  coal 
screens. 

The  sections  were  first  rolled  of 
wrought  iron,  and  for  a  time  in  both 
steel  and  iron,  but  are  now  made 
only  of  steel. 

The  advantages  claimed  for  this 
column  by  the  manufacturers  are: 
Economy  of  metal,  simplicity  of 
construction,  adaptability  to  the  re- 
quirements of  building  construction, 
and  its  cheapness. 

These  columns  are  made  up  of 
the  rolled  segments  "C,"  Fig.  23, 
which  are  riveted  together  through 
the  flanges  with  rivets  about  6 
inches  apart.  Between  every  two 
segments  an  iron  bar  is  frequently 
inserted,  through  which  the  rivets 
pass.  These  bars,  or  " fillers,"  as 
they  are  called,  increase  the  area 
of  the  cross-section  and  contribute 
much  to  the  strength  of  the  pillar. 
Table  XX.  gives  the  sizes  of  the 
columns  rolled  by  the  Phoenix  Iron 
Company,  as  published  in  their 
book  of  sections,  and  also  the 
radius  of  gyrations  and  safe  loads. 

The  largest  standard  size  of  this 
column  has  a  sectional  area  of  90.9 
square  inches,  capable  of  sustain- 
ing 615  tons  with  an  unsupported 
length  of  36  feet. 

The  column  can  be  made  of  almost  any  length  desired.  In 
the  Schiller  Theatre  Building,  Chicago,  there  are  Phoenix  col- 
umns 92  ft.  10  ins.  long,  while  in  the  Chicago  Board  of  Trade 
12-section  Phoenix  columns,  3'  3"  in  diameter  were  employed 
for  an  unsupported  length  of  90  ft. 

Phoenix  columns  are  in  use  in  several  prominent  high  buildings, 
notably  the  "World,"  "Dun,"  and  "Commercial  Cable"  build- 
ings, New  York;  the  Wainwright  Building,  St.  Louis;  Crocker 


442 


STEEL   COLUMNS  AND   STRUTS. 


Building,  San  Francisco,  and  in  a  great  number  of  buildings  of 
moderate  height.  Owing  to  the  difficulty  of  making  elaborate 
connections,  and  possibly  also  to  the  fact  that  it  is  rolled  only 
by  one  company,  it  has  not  been  much  used  in  the  later  high 
buildings,  although  it  is  still  used  to  a  considerable  extent  in 
other  buildings.  The  sections  of  the  Phoenix  column  afford  a 
convenient  means  of  "jacketing"  cylindrical  cast-iron  columns 
which  need  to  be  strengthened. 

The  interior  surfaces  of  all  Phoenix  columns  are  thoroughly 
painted  before  riveting  the  segments  together.     After  twenty 


Fig.  24 

years  of  service  in  exposed  situations  columns  have  been  cut 
open  and  found  uninjured  by  rust,  and  the  paint  still  in  good 
condition. 


STEEL  COLUMNS  AND  STRUTS. 


443 


Connections. — For  ordinary  floor-beam  connections,  and  for 
joining  the  ends  of  the  columns,  a  connection  similar  to  that  shown 
in  Fig.  24  has  generally  been  used.  The  cap,  which  is  usually  a 
single  plate  J  inch  to  1  inch  in  thickness,  is  made  of  sufficient  size 
to  give  the  requisite  bearing  for  the  beams  or  girders,  and  is  con- 
nected to  the  column  by  means  of  brackets  riveted  to  the  shell 


Fig.  25 


and  plate.  The  cap  is  also  further  supported  by  means  of  gusset- 
plates,  /  and  c,  riveted  either  outside  the  flanges  or  directly  to 
the  shell  of  the  column.  The  upper  column  is  set  after  the  floor 


Fig.  26 

system  is  hi  place,  and  is  secured  to  the  cap-plate  by  angle  brack- 
ets. When  columns  with  fillers  are  used  the  method  shown  in 
Figs.  25  and  26  is  generally  followed.  A  cap-plate  is  used  as  in 


444 


STEEL  COLUMNS  AND  STRUTS. 


the  other  connection,  but  is  supported  by  angles  riveted  to  the 
extended  fillers. 

Fig.  26  shows  a  bracket  formed  beneath  the  cap-plate  in  a 
similar  manner,  a  trapezoidal  plate  being  inserted  between  the 
sections,  in  place  of  the  filler,  to  support  the  bracket-plate.  One 
of  the  plates  passes  through  the  column  and  is  riveted  at  both 
sides ;  the  other  plate  is  riveted  to  the  first  at  the  centre  of  the 
column. 

The  latest  and  most  perfect  type  of  connection  for  this  column, 
especially  where  channel  or  riveted  girders  producing  eccentric 
loads  are  to  be  supported,  is  that  shown  in  Fig.  27.  A  pintle, 


; 

< 

o 
o 

^^ 

O    Q   O   O 

0  0 

G 

( 

o 

O  OjjO    O   O  O 

G/'rder: 

o 

0 
0 

*• 

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o 

0 
°|      ^//e^r 

o 
o 
o 

G 

OS 

- 

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0 

0 
0| 

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6  6 

G 

( 

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Q  O  iiO    O    O  Q 

xt^ 

^ 

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u 

^  faced  JortA 

Fig.  27 

Continuous  Column. 

shown  at  a  reduced  scale,  is  inserted  between  the  flanges,  and  the 
girders  and  beams  are  riveted  directly  to  the  pintle. 

This  connection  is  probably  as  nearly  perfect  as  any  that  could 
be  devised  for  any  column,  as  the  load  is  transmitted  by  the  pintle 
to  all  parts  of  the  column,  and  the  pintle  also  greatly  stiffens  the 
column  at  the  point  of  connection. 


THE  LARIMER  STEEL  COLUMN. 


445 


The  joint  of  the  column  occurs  at  the  centre  of  the  beams  or 
girders,  and  the  column  is  thus  made  continuous  from  cellar  to 
roof,  with  no  brackets  either  above  or  below  the  girder. 


Larimer  Column. 

(Manufactured  by  Jones  &  Laughlins,  Limited,  Pittsburg.) 

This  column  was  patented  June  2,  1891,  its  first  use  in  building 
construction  being  in  the  Newberry  Library  Building  in  Chicago. 


It  is  made  by  bending  two  I-beams  at  right  angles  in  the  middle 
of  the  web  and  riveting  them  together  with  a  small  I-shaped 
filler  between.  The  column  is  very  ]is:ht  and  compact,  and  has 
but  one  row  of  rivets.  Table  XXI.  gives  the  strength  and 
dimensions  of  the  standard  sections. 

The  strength  of  the  larger  columns  may  be  increased  by  rein- 
forcing the  flanges  with  steel  plates,  but  the  expense  of  doing  this 
is  so  great  that  it  will  be  cheaper  to  use  some  other  section.  A 
good  many  tons  of  this  column  are  sold  annually,  but  it  is  not 
very  extensively  used  in  buildings.  It  is  much  used  for  the 


446 


THE   LARIMER  STEEL  COLUMN. 


CONNECTIONS  FOR  LARIMER  COLUMNS. 


THE  LARIMER  STEEL   COLUMN. 


447 


CONNECTIONS,  FOR  LARIMER  COLUMNS 


If  umber  of  rivets  of  supporting  brackets  must  b$ 
determined  in  accordance  to  load  by  using 

&''ftivets  for  all  columns  made  of  7'x  18,  3"lb  I.E.  and  upward 

%n    "        "    "         '- G  ,"  12,  75  lh.  to  7'x  15,  25  Ib,  I..B3, 

^      °      .y    "        *'  "      •"  5  x  16  Ib.  I.  B3.  and  less, 

One  %  rivet,  .may  be  allowed  for  the  bending  of  a%"Cap  Plate,. 


448  THE  NURICK   STEEL  COLUMN. 

support   of    windmills  and  water-tanks,  where  a  light  and  in- 
expensive column  is  desired. 

Connections. — The  usual  connections  for  this  column  are  illus- 
trated on  the  preceding  pages.  Generally  a  cap-plate  is  used  to 
support  the  floor  system  and  to  receive  the  upper  column.  The 
flanges  of  the  columns,  both  above  and  below,  are  secured  to  the 
cap-plate  by  means  of  angle  brackets,  with  two  rivets  in  each  leg 
of  the  brackets.  When  a  more  rigid  connection  is  desired,  a 
welded  ring,  in  the  shape  of  an  angle,  is  made  to  fit  around  the 
top  of  the  column,  the  vertical  flange  being  riveted  to  the  flanges 
of  the  column  and  the  horizontal  flange  to  the  cap-plate,  as  shown 
at  A  A,  page  446.  This  connection  is  desirable  when  the 
column  is  eccentrically  loaded. 

The   Nuriek    Column. 

This  column,  formed  of  four  bent  channels,  riveted  together  as 
in  Fig.  28,  was  introduced  by  Jones  &  Laughlins,  Limited,  in 
1898.  It  is  not  intended  to  be  used  in 
ordinary  skeleton  buildings,  but  only  in 
places  where  a  strong  column  is  desired 
with  the  least  weight  in  the  column  itself. 
It  has  been  used  to  some  extent  in  foundry 
buildings.  Where  the  column  is  exposed 
it  makes  a  better  appearance  than  the 
Z-bar  column. 

Table  XXII  gives  the  dimensions  and 
p.     28  safe   loads   f°r  a    few   sections    of    this 

column.     Details  of  splices  and  connec- 
tions are  given  in  Jones  &  Laughlins'  Manual. 

The  Gray  Column. 

This  column  was  patented  in  December,  1892,  by  Mr.  J.  H. 
Gray,  C.E.,  and  for  a  time  was  quite  extensively  used  in  build- 
ings of  skeleton  construction.* 

The  column  is  made  up  of  angle-bars,  riveted  together  in  pairs 


*  This  column  has  been  used  in  a  number  of  prominent  buildings,  but 
by  many  engineers  it  is  not  now  regarded  with  favor,  owing  to  the  difficulty 
©f  making  satisfactory  connections  for  eccentric  loading. — J.  K.  FREITAG. 


THE  GRAY  STEEL  COLUMNS.  449 

and  braced  about  every  two  feet  in  length  by  tie-plates  usually  8 
or  9  inches  wide,  riveted  to  the  angles  as  shown  by  the  section 
drawings,  Figs.  29-32. 

The  special  advantages  claimed  for  this  column  are : 

1.  A  strong  economical  section.     As  fully  half  of  the  metal  is 
at  the  extreme  outer  edge  of  the  column,  and  practically  none  at 
the  centre,  the  radius  of  gyration  is  very  large  in  proportion  to 
the  weight  of  the  metal.     Moreover,  as  angles  are  the  cheapest 
shape  of  rolled  steel  that  is  manufactured,  and  are  made  by  every 
rolling-mill,  they  can  be  obtained  at  the  lowest  market  price,  and 
the  columns  can  be  built  by  any  bridge  shop  by  paying  a  small 
royalty  to  the  patentee.      (Gray  columns  were  made  by  fourteen 
different  bridge  companies  in  1895.) 

2.  Size  of  column  does  not  vary  when  section  is  increased  or 
diminished.     This  enables  the  architect  to  vary  the  section  of  the 
column  to  suit  differences  in  loading,  without  changing  the  out- 
side  dimensions,    thus   rendering   the   engineering   work   much 
simpler,   and  enabling  the   use   of  uniform  sizes   of  fire-proof 
blocks. 

3.  Does  away  with  "cap-plates"  and  joins  sections  of  columns 
firmly  together,  making  a  continuous  column.     In  the  Reliance 
Building,  Chicago,  there  is  a  Gray  column  290  feet  long,  built  in 
one  piece  at  the  shop. 

4.  By  varying  the  size  or  thickness  of  angles,  and  adding  cover- 
plates,  any  strength  that  may  be  required  can  be  obtained. 

5.  Has  four  flat  sides  for  connections.     The  usual  connections 
for  single  and  double  beams  are  shown  by  Fig.  32. 

The  joint  in  the  column  should  be  made  above  the  floor  system, 
and  the  two  portions  connected  by  splice-plates. 

Where  eccentric  loads  are  to  be  supported  by  this  column  it  is 
essential  that  the  column  be  very  rigidly  bound  together  by  out- 
side plates  or  angles  opposite  or  just  below  the  connection,  as 
otherwise  the  load  will  be  borne  mainly  by  the  pair  of  angles  to 
which  the  girder  is  connected,  and  not  by  the  whole  column. 

6.  Provides    continuous    air-space    from    basement    to    roof. 
Tests  made  in  the  hydraulic  machine  of  the  Keystone  Bridge 
Works  on  14-inch  square   columns,   11  feet  long,  developed  a 
'resistance   to   crushing   of   from   38,000  to   40,000  pounds  per 
square    inch   of   cross-section,  and  a  modulus   of   elasticity  of 
from  24,030,000  to  27,750,000  pounds. 

Table  XXIII.  of  this  chapter  gives  the  safe  loads  in  thousands 
of  pounds,  as  computed  by  Mr.  Gray,  for  the  sizes  of  columns 


450 


STEEL   STRUTS  IN  TRUSSES. 


that  have  been  most  extensively  used.  Experience  has  shown 
that  these  tables  cover  nearly  any  ordinary  steel  skeleton  build- 
ing and  give  all  needed  sections  from  basement  to  top  of  same. 


Fig.  29 


Fig.  32 


Fia.30 


Fig.  31 


Steel  Struts  in  Trusses. 

These  are  generally  made  of  a  pair  of  latticed  channels,  or 
channels  and  plates  for  heavy  trusses  with  pin  connections,  and 
either  of  a  pair  of  light  channels  or  a  pair  of  angles  with  uneven 
legs  for  light  trusses.  For  roof  trusses  having  a  span  not  ex- 
ceeding 80  feet  a  pair  of  4X6XJ  inch  angles  is  generally  suffi- 
cient for  any  of  the  compression  members  unless  subject  to  trans- 
verse strain,  and  the  minor  struts  are  very  often  made  of  a  pair 
of  2X2JXi  inch  angles.  The  angles  are  placed  from  J  to  }  inch 


STRENGTH  OF  STEEL  COLUMNS  AND  STRUTS.  451 

apart,  to  permit  the  filler-plate  used  in  the  joints  to  go  between 
them. 

For  compression  members  subject  to  transverse  strain  a  pair 
of  channels  generally  offer  the  best  section.  If  necessary  the 
channels  can  be  reinforced  by  plates  at  top  and  bottom. 

A  pair  of  angles,  with  a  deep  web-plate  riveted  between,  are 
often  used  for  the  principles  of  Fink  trusses  where  they  are 
subject  to  a  slight  transverse  strain.  See  Chapter  XXV. 

For  very  light  compressive  stresses  and  short  members  a  single 
angle  is  sometimes  used.  If  the  stress  requires  a  greater  section 
than  that  of  one  3  X3  X  \  inch  angle,  it  will  be  cheaper  and  better 
to  use  a  pair  of  smaller  angles. 

Where  angles  are  used  in  pairs  they  should  be  connected  by  a 
rivet  and  small  filler-plate  every  two  feet  in  length,  to  prevent 
the  angles  from  springing  apart. 

Maximum  Length. — It  is  good  practice  not  to  use  a  strut  whose 
unsupported  length  exceeds  150  times  its  least  radius  of  gyration, 
or  50  times  the  least  width  of  the  member.  For  size  of  lattice- 
bars  see  page  439. 


Strength  of  Steel  and  Wr 6 light-iron  Columns 
and  Struts. 

Prof.  Wm.  H.  Burr,  in  his  "Strength  and  Resistance  of  Mate- 
rials," states  that  "The  general  principles  which  govern  the  re- 
sistance of  built  columns  may  be  summed  up  as  follows : 

"The  material  should  be  disposed  as  far  as  possible  from  the 
neutral  axis  of  the  cross-section,  thereby  increasing  the  radius  of 
gyration  (r) ; 

"There  should  be  no  initial  stress; 

"The  individual  portions  of  the  column  should  be  so  firmly 
secured  to  each  other  that  no  relative  motion  can  take  place  in 
order  that  the  column  may  fail  as  a  whole,  thus  maintaining  the 
original  value  of  r." 

The  experiments  quoted  by  Prof.  Burr  would  seem  to  indicate 
that  a  closed  column  is  stronger  than  an  open  one,  this  being 
apparently  due  to  the  fact  that  the  edges  of  the  segments  are 
mutually  supporting  when  held  in  contact  by  a  complete  closure. 
From  a  theoretical  standpoint,  therefore,  the  Phoenix  or  Nurick 
shapes  undoubtedly  present  the  most  favorable  section  for  resist- 
ing compression,  as  they  form  a  closed  column,  and  the  metal  is 


452    FORMULAS  FOR  STEEL  COLUMNS  AND  STRUTS. 

all  at  the  outer  line  and  equally  disposed  around  the  neutral  axis. 
With  the  pintel  connection,  shown  in  Fig.  27,  it  would  seem  that 
these  columns  would  have  a  greater  ultimate  resistance  than  open 
forms,  such  as  the  open  Z-bar,  Gray,  and  Larimer,  although  the 
latter  column  has  developed  a  very  high  ultimate  resistance. 

It  should  also  be  remembered  that  any  form  of  column  having 
a  maximum  and  minimum  radius  of  gyration,  such  as  is  the  case 
with  a  single  I-beam,  channel,  or  angle,  is  not  economical  for  use 
under  a  single  concentric  load,  as  the  minimum  radius  must  be 
used  in  the  calculation,  and  part  of  the  material  is  to  a  certain 
extent  wasted,  when  we  consider  the  ideal  efficiency  of  the 
column. 

Formulas. 

A  great  many  different  formulas  have  been  published  for  the 
strength  of  wrought-iron  and  steel  posts,  and  scarcely  any  two 
leading  structural  engineers  use  precisely  the  same  formula. 
Previous  to  the  year  1888  a  formula  similar  to  formula  (12),  and 
known  as  the  Gordon  formula,  was  generally  used  for  all  forms 
of  columns,  although  with  more  or  less  variation  in  the  constants. 
During  the  year  1888  Mr.  C.  L.  Strobel  deduced  the  following 
formula  for  the  ultimate  strength  of  iron  Z-bar  columns: 

Breaking  loads  in  Ibs.  per  sq.  in.  of  section  area=  46,000  — 125  — . 

This  formula  appeared  to  agree  a  little  more  accurately  than 
the  Gordon  formula  with  the  results  of  tests  that  had  been  made 
on  full-size  columns,  and  as  it  was  easier  of  application  a  modi- 
fication of  it  was  adopted  by  the  Carnegie  Steel  Company  for 
computing  the  strength  of  their  Z-bar  columns. 

This  form  of  formula  is  now  known  as  the  straight-line  formula, 
and  as  it  appears  to  give  a  satisfactory  reduction  of  loads  in  pro- 
portion to  length  of  column,  and  is  comparatively  easy  of  applica- 
tion, some  form  of  the  straight-line  formula  is  now  generally 
used  by  structural  engineers  for  steel  columns  and  struts  in 
preference  to  Gordon's  formula.  For  the  constants  used  in  the 
"  straight-line  formula,"  however,  there  is  no  uniform  practice, 
except  perhaps  in  the  case  of  heavy  columns,  for  which  formula 
(11)  is  quite  generally  used. 

Gordon's  formula  is  still  used  by  many  engineers,  and  as  it  is 
the  standard  used  in  the  Boston  Building  Law  it  is  given  below 
as  formula  (12).  A  comparison  of  formulas  recommended  by 


FORMULAS  FOR  STEEL  COLUMNS  AND  STRU1S.  453 

different  engineers,  and  contained  in  building  laws  will  be  found 
at  the  end  of  this  chapter.  Those  formulas  which,  in  the  opinion 
of  the  author,  most  nearly  represent  the  best  current  practice 
are  given  below. 


Formulas  for  Safe  Loads,  in  Pounds,  on  Steel  and 
Wroug'ht-iroii  Columns  and  Struts. 

Safe  load,  W=pX  sectional  area  (in  sq.  inches)  of  column  or 
strut.  (10) 

For  steel  columns  in  buildings: 

p=17.100-57-r;  (11) 

12,000 
or    p=-      i—  -  -.  (12) 

1-4-——— 

36,000  r2 
For  steel  struts  in  trusses: 

p=  13,500  -50—.  (13) 

For  wr  ought-iron  columns: 

9,000 

—  —  r 


p= 


1+ 


36,000  r2 

in  which  I—  length  of  column  in  inches,  and  r—  least  radius  of 
gyration  (see  Chapter  X.).  The  length  of  the  column  is  measured 
between  the  points  where  it  is  supported  sideways,  and  usually 
between  the  floor  beams. 


Maximum  Safe  Load  for  Columns  and  Struts. 

For  wrought-iron  posts  where  the  length  in  inches  divided  by 
the  least  radius  of  gyration  is  less  than  30,  p  may  be  taken  at 
9,000  Ibs.  to  the  square  inch. 

For  steel  struts,  in  trusses,  where  —  is  less  than  50,  p  should  be 

taken  at  11,000  Ibs.  per  square  inch,  unless  the  section  is  very 
large,  when  12,000  Ibs.  may  be  used. 


454   FORMULAS  FOR  STEEL  COLUMNS  AND  STRUTS. 

For  steel  columns,  such  as  are  used  in  buildings,  it  is  customary 
to  allow  from  12,000  to  14,000  Ibs.  per  square  inch  of  section  when 
the  length  is  less  than  90  radii. 

When  14,000  Ibs.  is  used  for  p,  however,  an  increase  in  area 
should  be  made  for  any  eccentricity  in  the  loads.  (See  formula 
(15).) 

The  tables  for  Carnegie  Z-bar  columns  and  for  the  Larimer 
column  are  computed  at  12,000  Ibs.  per  sqr.r.rc  inch  for  lengths 
of  90  radii  and  under,  and  those  for  the  Phoenix  columns  at  14,000 

Ibs.  for  the  same  ratio  of  — .     The  Chicago  Tinkling  Ordinance 

specifies  13,000  Ibs.  for  lengths  of  60  radii  and  under.  Formula 
(11)  was  used  in  computing  the  strength  given  in  the  tables  for 

the  Gray  columns  for  all  the  values  of  — ,  and  for  Phoenix,  Z-bar, 

Larimer,  and  channel  columns  exceeding  90  radii  in  length. 
This  formula  also  very  nearly  corresponds  with  that  given  in 
the  Chicago  Building  Ordinance. 

Formula  (13)  is  about  an  average  of  the  constants  used  by  lead- 
ing structural  engineers  for  angle  and  channel  struts  in  trusses, 
and  was  used  by  the  Passaic  Rolling  Mill  Company  for  computing 
the  safe  loads  for  angle  struts  and  I-beam  struts  published  in 
their  handbook.  It  is  believed  that  the  stresses  permitted  by 
this  formula  are  such  that  it  may  be  used  for  ordinary  truss  con- 
struction without  allowance  for  rivet-holes.  It  may  be  used  for 
either  pin-  or  rivet-connected  struts. 

According  to  Prof.  Wm.  H.  Burr,  "the  records  of  tests  of 
wrought-iron  channel  columns  with  both  pin  and  flat  ends,  made 
at  the  U.  S.  Arsenal  at  Watertown,  Mass.,  have  shown  conclu- 
sively that  the  ultimate  resistance  of  columns  with  flat  ends  will 
nearly  invariably,  if  not  always,  fall  below  those  of  the  same  col- 
umns with  pin  ends."  This  is  accounted  for  by  the  fact  that 
wTith  a  pin-end  column  the  centre  of  stress  is  practically  at  the 
centre  of  the  section  of  each  end,  and  also  that  the  very  consider- 
able friction  of  the  pin  against  the  pin-hole  exerts  a  considerable 
moment  tending  to  hold  the  ends  of  the  column  in  a  "fixed" 
condition  in  a  plane  normal  to  the  axis  of  the  pin. 

On  the  other  hand,  with  square  ends,  no  matter  how  carefully 
finished,  it  is  almost  impossible  to  apply  the  load  so  that  the 
centre  of  stress  will  coincide  with  the  centre  of  the  column. 

The  old  classification  of  "square,"  "pin  and  square/'  and 
"pin"  has  therefore  been  abandoned. 


FORMULAS  FOR  STEEL  COLUMNS  AND  STRUTS.  455 


Application  of  Formulas. 

EXAMPLE  1. — What  is  the  maximum  load  for  a  steel  column  12 
feet  long,  composed  of  two  6-inch  8-lb.  channels  placed  back  to 
back,  and  secured  by  latticework? 

Ans.  To  obtain  the  maximum  resistance  of  the  section  the 
channels  should  be  placed  3J  ins.  apart  (see  col.  d,  page  299). 
The  least  radius  of  gyration  (r)  will  then  be  the  same  as  for  a 
single  channel  about  axis  AB,  which  is  2.34  (col.  iv.). 

To   find    the  values  of    p,  we  will    use    formula  (11):   then 

7  144 

p=  17,100- 57-=  17,100- 57 X  j^  =  13,595  Ibs.  Substitut- 
ing this  in  formula  (10),  we  have  safe  load  for  column =  13,595 X 
4.76  (area  of  two  channels)  =  64,712  Ibs. 

When  the  value  of  p  obtained  by  formula  (11)  exceeds  12,000 
Ibs.  it  is  recommended  that  12,000  Ibs.  be  used  instead  of  the 
value  obtained  by  the  formula,  unless  the  loads  assumed  are 
much  in  excess  of  the  probable  actual  loads,  or  the  column  has 
a  large  and  closed  section,  when  14,000  Ibs.  may  be  made  the 
maximum.* 

EXAMPLE  2. — What  is  the  safe  load  for  a  column  16  feet  long, 
composed  of  two  12-inch  30-lb.  channels,  with  J-inchx  12-inch 
plates,  riveted  to  channels,  as  shown  in  Fig.  33. 

Ans.  The  first  step  will  be  to  find  the  least  radius  of  gyration, 
by  means  of  the  methods  explained  ,  C  , 

on  page  286. 

From  the  table  of  properties  of 
channels  we  find  that  for  a  single 
channel  I^S.21,  z=.677,  width  of 
flange  =  3. 17,  and  area  =  8. 82. 

The  distance  (d)  between  the  backs 
of  channels  would  then  be  12— (3.17 
X  2)  =  5.86.  As  this  is  less  than  d, 
in  the  table  of  properties,  the  least 
radius  of  gyration  will  be  about  the 

axis  C-D.     The  distance,  I  (Fig.  33)  = 


'  —  -J 

i 

k  Z- 

1         2/ 

i 

.A-- 

i 

I--  i-B 

| 

—  rfd—  * 

I 

/  J 

J 

U>^ 

f_ 

D 

Fig.  33 


5.86 
=  "^" 


.677  =  3.6.     Then 


*  See  last  pages  of  this  chapter. 


456  STRENGTH  OF  STEEL  COLUMNS  AND   STRUTS. 

the  moment  of  inertia  about  CD  will  be  (see  page  286), 

for  the  channels,  2  X  (8.82  X  (3.6)  2  +  5.21)  =  239.03 

2xj-Xl2s 


for  the  plates, 


Total  moment  =383.03. 

Dividing  this  by  the  area  of  the  section,  which  is  29.64,  we  have 
12.92  for  the  square  of  the  radius  of  gyration,  and 


As  this  is  less  than  90,  we  should  not  use  formula  (11),  but  mul- 
tiply the  area  of  the  column  by  the  allowable  strain  per  sq.  inch, 
which  for  such  a  large  section  may  safely  be  taken  at  13,000  Ibs. 
Then  29.64x13,000  =  385,320  Ibs.  =  safe  "load. 

Eccentric  Loads. 

Where  columns  are  used  in  tiers,  one  above  another,  the 
beams  and  girders  which  they  support  must  necessarily  rest  on 
brackets  or  pintle-plates,  beyond  the  centre  of  the  column. 

Such  methods  of  connection  necessarily  produce  a  moment  tend- 
ing to  bend  the  column.  When  the  same  load  is  applied  to  op- 
posite sides  of  the  column,  the  moments  produced  by  the  loads 
will  offset  each  other,  and  the  centre  of  stress  may  be  considered 
as  coinciding  with  the  axis.  Whenever  a  beam,  however,  is 
attached  to  a  column  without  a  corresponding  load  on  the  oppo- 
site side,  the  load  will  be  "eccentric,"  and  the  area  of  the  column 
should  be  correspondingly  increased,  especially  if  strains  as  high 
as  14,000  Ibs.  per  sq.  inch  are  permitted. 

The  following  formula,  known  as  "  Rankine's  formula  for  eccen- 
tric loads,"  is  generally  used  for  computing  the  additional  area 
required  for  eccentric  loading  : 

Additional  area  for  eccentric  load=  —  —  '*  2    °,        (15) 
in  which 

W  =  eccentric  load  in  Ibs.; 

d$=  distance  from  centre  of  column  to  point  of  application; 
d±=  distance  from  centre  of  column  to  extreme  fibre  in  direction 

in  which  column  would  bend  ; 
r2  =  radius  of  gyration  squared,  for  column  used] 

p  =  stress  per  square  inch  for  —  ,  Table  XI. 


STRENGTH  OF  STEEL  COLUMNS  AND  STRUTS.  457 

Note.  —  In  measuring  the  distance  d0  very  much  depends  upon  the  form 
of  the  connection.  Thus  for  single  or  double  beams,  where  angle-brackets 
are  used,  do  should  be  measured  to  the  centre  of  the  bracket.  In  Figs.  13 
and  24  it  should  be  measured  to  the  centre  of  the  rivets  in  the  beam  flanges; 
for  connections,  such  as  shown  in  Figs.  15  and  27,  it  is  generally  considered 
sufficient  to  measure  do  to  the  outside  of  the  column. 

EXAMPLE  1.  —  The  total  load  on  the  top  of  a  second-story 
column  is  194;000  Ibs.,  of  which  30,000  Ibs.  comes  from  the  end  of 
a  girder;  without  a  corresponding  load  on  the  opposite  side  of  the 
column.  It  is  proposed  to  use  a  12-inch  Gray  square  column. 
What  should  be  the  section  of  the  column,  the  distance  to  the  cen- 
tre of  the  bracket  being  2J  in.  and  the  length  of  the  column  10 
feet? 

Ans.  Looking  in  the  table  giving  the  safe  loads  for  a  12-inch 
Gray  column,  we  find  that  the  section  given  in  the  second  line  has 
a  safe  load  of  195,000  Ibs.  for  16  ft.  length,  and  we  will  therefore 
use  that  section  as  a  basis. 

I        192 
For  this  section,  r=3.S  and  —  =  ——  =  50.5;  and  from  col.  I., 

T  o.o 

Table  XL,  we  find  the  value  of  p  for  that  ratio  to  be  14,220. 

Then  TF=30,000;  dQ=S{;  ^=6;  r2=3.82  =  14.44;  and  p= 
14,220. 

Substituting  these  values  in  formula  (15)  we  have  — 


-«-  —  -23  •»  '-• 


The  area  of  the  section  used  is  13.84,  and  adding  to  this  7.23  we 
have  21.07  as  the  required  area,  which  corresponds  with  a  section 
composed  of  eight  3x3§X%"  angles;  therefore  this  latter  sec- 
tion should  be  used. 

EXAMPLE  2. — What  area  would  be  required  for  a  12-inch  Z-bar 
column  under  the  same  conditions  as  given  in  Example  1  ? 

Ans.  From  the  table  on  page  477  we  find  that  the  first  section 
has  a  safe  resistance  of  128.3  tons,  or  considerably  more  than  the 

load  we  wish  to  support,     r  for  this  section  is  3.67  and  — =  52.3. 

The  corresponding  value  for  p  would  then  be  (col.  I,  Table  XL) 
14,120.  We  will  assume  that  the  girder  is  supported  as  in  Fig.  5, 
p.  436,  so  that  dL=B  (page  476)  =6.2  in.,  and  dQ  would  be 
about  8.5  in. 


458  STRENGTH  OF  STEEL  COLUMNS  AND  STRUTS. 

We  would  then  have — - 

30,000X6.2X8.5 
Additional  area  for  eccentric  load  =  —  2   =  9  sq.  in. 

1 4  ,  1  Z\j  X  \«J  •  t)  i  ) 

The  area  required  for  the  total  load,  considered  as  acting  through 
centre  of  column =  —  =  -j  ~^r  =  13.8  sq.  in.  Adding  13.8  and 

P  J-*i, -L^U 

9,  we  have  22.8  as  the  required  area,  which  will  necessitate  using 
the  second  section  given  in  the  table. 

Tables  for  Strength  of  Columns. 

To  lessen  the  labor  of  calculating  the  strength  of  steel  columns 
and  struts,  of  whatever  shape,  the  author  has  computed  Table  XI., 
which  gives  safe  values  of  p  for  lengths  varying  from  30  to  130 

radii.     For  values  of  - —  which  give  a  decimal  remainder  one  can 
r 

readily  interpolate  between  the  values  given.  The  values  in  this 
table  should  correspond  exactly  with  the  results  obtained  by 
using  the  corresponding  formulas. 

Table  XII.  gives  the  safe  loads  for  gas  or  steam  pipe  used  as 
columns.  These  pipes  are  apt  to  vary  somewhat  from  the  thick- 
ness published  by  the  manufacturers,  and  when  using  them  the 
architect  should  see  that  they  have  a  thickness  equal  to  that  given 
in  the  table,  if  the  full  load  is  to  be  allowed.  The  ends  of  the  pipe 
should  be  turned  true  to  the  axis,  and  fitted  with  cast-iron  or 
steel  plates,  having  the  bearing  planed  or  turned  in  a  lath. 

Tables  XIII.,  XIV.,  and  XVI.  give  the  strength  of  standard 
channels  and  angles  used  as  struts.  Only  those  sizes  that  are 
most  commonly  used  are  given. 

In  Table  XIII.  the  safe  loads  for  both  the  minimum  and  the 
maximum  radius  of  gyration  are  given.  If  the  strut  is  used  also  as 
a  beam,  or  is  stayed  so  that  it  cannot  bend  sideways,  the  larger 
value  may  be  used;  but  if  free  to  bend  in  either  direction,  then 
the  smaller  value  should  be  taken.  If  the  struts  are  subjected 
to  a  transverse  strain  they  should  be  computed  as  explained 
under  the  heading  "  Strut  Beams/'  Chapter  XV. 

The  tables  giving  the  safe  loads  for  Z-bar,  Gray,  Larimer,  and 
Nurick  columns  were  not  computed  by  the  author;  they  are, 
however,  believed  to  be  perfectly  safe,  provided  that  an  increase 
in  area  is  made  for  eccentric  loads.  This  is  especially  necessary 
with  the  Gray  columns,  as  the  allowed  value  of  p  in  many  cases 
exceeds  15,000  Ibs. 


STRENGTH  OF  STEEL  COLUMNS  AND  STRUTS.    459 


Application  of  Table  XI. 

This  table  will  be  found  of  most  assistance  in  calculating  the 
strength  of  struts  in  trusses  and  in  making  calculations  for  eccen- 
tric loading,  as  already  illustrated. 

EXAMPLE  1. — What  is  the  safe  resistance  for  a  strut  composed 
of  two  5-inch  9-lb.  standard  steel  channels,  separated  f  inch,  and 
free  to  bend  in  either  direction,  the  distance  between  joints  being 
7'  6"? 

Am.  From  Table  D,  Chapter  -X.,  we  find  the  least  radius  of 

gyration  for  this  section  to  be  1;  — =90;  and  from  column  III., 

Table  XL,  we  find  the  value  of  p  opposite  90  to  be  9,000  Ibs. ; 
then  the  safe  load=area  Xp—5.3  (area  of  two  channels)  X 
9,000=47,700  Ibs. 

EXAMPLE  2. — What  is  the  safe  resistance  of  a  7-inch  15-lb. 
standard  steel  I-beam  used  as  a  strut,  the  length  being  100  inches 
and  the  strut  free  to  bend  in  either  direction? 

Arts.  From  the  table  giving  the  properties  of  I-beams, 
Chapter  X.,  we  find  the  least  radius  of  gyration  for  this  section  to 

be  0.78,  and  the  area  4.42;  — =  —  -  =  128.2;    and  from  column 
r       .75 

III.,  Table  XL,  we  find,  opposite  128,  p=  7,100,  for  128.2  p 
would  be  about  10  Ibs.  less,  or  7,090.  Multiplying  this  by  the 
area  (4.42)  we  have  31,337  Ibs.  as  the  safe  resistance  of  the  strut. 
By  means  of  the  tables  and  rules  given  in  Chapter  X.  the  area 
and  radius  of  gyration  of  any  standard  section  or  any  combina- 
tion of  sections  may  be  found ;  and  once  these  are  obtained  the 
strength  of  a  strut  or  column  may  be  readily  computed,  as  in  the 
above  examples. 


Proportion  of  Floor  Loads  Borne  by  Columns. 

In  tall  buildings  it  is  customary  to  reduce  the  column  loads 
somewhat  from  the  loads  used  in  calculating  the  floor  beams. 
This  is  done  on  the  theory  that  it  is  quite  impossible  for  the  entire 
floor  area  in  every  story  to  be  loaded  to  the  maximum  limit  at  the 
same  time.  For  all  buildings  except  warehouses  it  would  seem 
to  be  good  practice  to  design  the  columns  to  carry  all  the  dead 
load  and  75  per  cent,  of  the  assumed  live  load. 

Thus  if  in  an  office  building  the  dead  load,  or  weight  of  the 


460  COLUMN  LOADS. 

floor  construction,  was  taken  at  80  Ibs.  and  the  live  load  at  80 
Ibs.  per  square  foot,  the  load  on  the  columns  would  be  taken  at 
80  +  60=140  Ibs.  per  square  foot  times  the  floor  area  supported 
by  the  column.  In  some  cases  the  reduction  might  even  be 
greater,  depending  upon  the  live  load  assumed  and  the  position 
of  the  column  in  the  building,  the  reductions  being  greater  in  the 
lower  stories  than  near  the  top. 

The  Building  Law  of  Greater  New  York  specifies  that  for  build- 
ings exceeding  five  stories  in  height  the  column  loads  shall  be 
made  up  as  follows:  "For  the  roof  and  top  floor  the  full  live 
loads  shall  be  used;  for  each  succeeding  lower  floor  it  shall  be 
permissible  to  reduce  the  live  load  by  5  per  cent,  until  50  per 
cent,  of  the  live  load  is  reached,  when  such  reduced  loads  shall  be 
used  for  all  remaining  floors."  Column  loads  and  the  practice 
of  leading  architects  in  regard  to  proportioning  columns  to  the 
loads,  especially  in  high  buildings,  is  discussed  at  considerable 
length  by  Mr.  Freitag  in  his  "Architectural  Engineering." 

Column  Sheets. — In  a  high  building  the  column  loads  vary  to 
such  an  extent,  and  are  made  up  of  so  many  elements,  that  to 
avoid  omissions  and  errors  it  is  necessary  to  make  a  tabulated  list 
of  all  the  loads  transferred  through  the  columns  to  the  footings. 

In  a  building  of  skeleton  construction  the  column  loads  will 
include  floor  and  roof  loads,  wind  loads,  spandrel  and  pier  loads, 
the  weight  of  the  columns  themselves  and  their  fire-proof  cover- 
ing, and  in  some  cases  special  loads,  such  as  tanks,  vaults,  safes, 
and  elevator  loads. 

In  tabulating  the  floor  loads  it  is  a  good  idea  to  separate  the 
dead  and  live  loads  for  convenience  in  proportioning  the  foot- 
ings. See  Chapter  II. 

Formulas  for  computing  the  wind  loads,  on  columns  are  given 
in  Chapter  XXVIII. ;  these  loads  are  also  considered  as  live  loads. 

In  buildings  not  exceeding  100  feet  in  height  wind  loads  are 
generally  disregarded. 

Eccentric  loads  should  always  be  tabulated  separate  from  the 
column  loads. 

On  the  opposite  page  is  shown  a  form  of  column  sheet  which 
combines  all  ordinary  .requirements. 

The  total  load  for  each  story  will  be  the  sum  of  all  of  the  loads 
above. 

The  table  on  page  462,  taken  from  Freitag's  "Architectural 
Engineering,"  shows  a  very  convenient  form  of  schedule  for 
column  lengths  and  column  materials. 


COLUMN  LOADS. 
FORM  OF  COLUMN  SHEET. 


461 


Story 


Column  No.  1. 


Load  on 

column 

concentric 


Load  on 
column 
eccentric 


Column    2. 


Roof  and  ceiling,  dead  load 
live  load  . 

Masonry  piers 

$>  Spandrels,  cornice,  etc.  .  .  . 
«2  Elevators , 

Tanks 

3  Column  and  casing 

Wind 

Total 

Sectional  area  required..  .  . 

From  column  above.* 

Floor,  dead  load 

"       live  load 

Masonry  piers 

Spandrels , 

^       Safes,  vaults,  etc 

Column  and  casing.  ...'... 
Wind 

Total 

Sectional  area  required. .  .  . 

From  column  above.* 

Floor,  dead  load 

live  load 
Masonry  piers, 
Spandrels.  .  .  . 

Sidewalk 

Column  and  casing.  .  .  . 
Wind 
« 

Total 

Sectional  area  required 

Deduct  (^)  live  load 

Total  footing  load 

Area  of  footing  required 


sq.  ins. 


sq.  ins. 


sq.  ft. 


*  In  bringing  down  the  loads  from  the  column  above  the  eccentric  loads 
may  be  added  to  the  concentric  loads  and  their  sum  placed  in  the  first 
column. 


462  COLUMN   LENGTHS. 

SCHEDULE    OF   COLUMN  LENGTHS   AND   MATERIAL. 


Column  No.l 

Column  No.2 

Roof  Line 

Top  of  Columns 

** 

v 

7th  STORY 
7th  Floor  Line 

<< 

V 
V* 

I          ^H**4 

5             "co  t- 

_M_«- 

•^    d 

%Z 

T#     "T* 

I 

6th  STORY 
6th  Floor  Line 

s 

—  H22 

4Ls5x3//x%// 
1  Plate  7  x|%" 

5th  STORY 
5th  Floor  Line 

c? 

c 

^0 

' 

f4" 

1      1 

fC 

1st  Floor  Line 

1'3J4" 

BASEMENT 
Top  of  Stool 

% 

! 

* 

3                          -v       ^VO) 

Grade  15.0 

V 

C 

\ 

D                            T_| 

• 

STRENGTH  OF  COLUMNS  PER  SQ.   INCH.      463 


TABLE  XI.— SAFE  LOADS  PER  SQUARE  INCH  OF 
METAL  AREA  FOR  STEEL  AND  WROUGHT-IRON 
COLUMNS  AND  STRUTS. 


r 

r 

both  in 
inches. 

Steel  columns. 

Steel  struts. 

13,500-50- 
r 

Wrought  iron. 
9,000 

17,100-57- 

12,000 

14-   l" 

1  +  36,000r2 

'^SG.OOOr2 

I. 

II. 

III. 

IV. 

30 

11,706 

12,000 

8,780 

36 

11,581 

11,700 

8,686 

40 

11,488 

11,500 

8,616 

44 

11,388 

11,300 

8*541 

48 

11,277 

11,100 

8,458 

50 

14,250 

11,220 

11,000 

8,415 

52 

14,136 

11,161 

10,900 

8,371 

54 

14,022 

11,100 

10,800 

8,325 

56 

13,908 

11,040 

10,700 

8,280 

58 

13,794 

10,978 

10,600 

8,234 

60 

13,680 

10,908 

10,500 

8,181 

61 

13^23 

10,874 

10,450 

8,156 

62 

13,566 

10,841 

10,400 

8,131 

63 

13,509 

10,808 

10,350 

8,106 

64 

13,452 

10,772 

10,300 

8,079 

65 

13,395 

10,740 

10,250 

8,055 

66 

13,338 

10,704 

10,200 

8,028 

67 

13,281 

10,666 

10,150 

8,000 

68 

13,224 

10,633 

10,100 

7,975 

69 

13,167 

10,597 

10,050 

7,948 

70 

13,110 

10,561 

10,000 

7,921 

71 

13,053 

10,525 

9,950 

7,894 

72 

12,996 

10,489 

9,900 

7,867 

73 

12.939 

10,452 

9,850 

7,839 

74 

12,882 

10,416 

9,800 

7,812 

75 

12,825 

10,380 

9,750 

7,785 

76 

12,768 

10,341 

9,700 

7,756 

77 

12,711 

10,302 

9,650 

7,727 

78 

12,654 

10,264 

9,600 

7,698 

79 

12,597 

10,229 

9,550 

7,672 

80 

12,540 

10,190 

9.500 

7,642 

81 

12,483 

10,152 

9,450 

7,614 

82 

12,426 

10,112 

9,400 

7,584 

83 

12,369 

10,072 

9,350 

7,554 

84 

12,312 

10,033 

9,300 

7,525 

85 

12,255 

9.993 

9,250 

7,495 

86 

12,198 

9,954 

9,200 

7,466 

87 

12,141 

9,916 

9,150 

7,438 

88 

•  12,081 

9,876 

9,100 

7,407 

89 

12,027 

9,836 

9,050 

7,377 

464       STRENGTH  OF  COLUMNS  PER  SQ.   INCH. 
TABLE    XL  (continued). 


I 

r 
both  in 
inches. 

Steel  columns. 

Steel  struts. 
13,500-50^; 

Wrought  iron, 
9,000 

17,100-57- 

12,000 

I2 

1+       l2 

r 

1  +  36,000r2 

36,000r2 

I. 

II. 

III. 

IV. 

90 

11,970 

9,796 

9,000 

7,347 

91 

11,913 

9,756 

8,950 

7,317 

92 

11,856 

9,716 

8,900 

7,287 

93 

11,799 

9,677 

8,850 

7,258 

94 

11,742 

9,638 

8,800 

7,229 

95 

11,685 

9,600 

8,750 

7,200 

96 

11,628 

9,553 

8,700 

7,165 

97 

11,571 

9,516 

8,650 

7,137 

98 

11,514 

9,478 

8,600 

7,109 

99 

11,457 

9,433 

8,550 

7,075 

100 

11,400 

9,389 

8,500 

7,042 

101 

11,343 

9,352 

8,450 

7,014 

102 

11,286 

9,309 

8,400 

6,982 

103 

11,229 

9,273 

8,350 

6,955 

104 

11,162 

9,230 

8,300 

6,923 

105 

11,105 

9,188 

8,250 

6,891 

106 

11,048 

9,146 

8,200 

6,seo 

107 

10,991 

9,104 

8,150 

6,828 

108 

10,934 

9,064 

8,100 

6,798 

109 

10,887 

9,022 

8,050 

6,767 

110 

10,830 

8,981 

8,000 

6,736 

111 

10,773 

8,941 

7,950 

6,706 

112 

10,716 

8,900 

7,900 

6,676 

113 

10,659 

8,860 

7,850 

6,646 

114 

10,602 

8,816 

7,800 

6,612 

115 

10,545 

8,776 

7,750 

6,582 

116 

10,488 

8,734 

7,700 

6,551 

117 

10,431 

8,694 

7,650 

6,521 

118 

10,374 

8,654 

7,600 

6,491 

119 

10,317 

8,613 

7,550 

6,460 

120 

10,260 

8,572 

7,500 

6,429 

121 

10,203 

8,532 

7,450 

6,401 

122 

10,146 

8,492 

7,400 

6,369 

123 

10,089 

8,451 

7,350 

6,338 

124 

10,032 

8,410 

7,300 

6,307 

125 

9,975 

8,368 

7,250 

6,276 

126 

9,918 

8,326 

7,200 

6,245 

127 

9,861 

8,286 

7,150 

6,215 

128 

9,804 

8,246 

7,100 

6,185 

129 

9,747 

8,206 

7,050 

6,155 

130 

9,690 

8,162 

7,000 

.    6,122 

STRENGTH   OF  PIPE  COLUMNS. 


465 


TABLE   XII. —SAFE    LOADS    IN    TONS    FOR    GAS-  OR 
STEAM-PIPE  COLUMNS. 

Computed  by  formula :  p  =  1 1 ,000  -  35  —• 


1 

d 

^"5 

i 

|| 

*o  fl 

08.2 

w  O 

Length  in  feet. 

1 

.2 

V  Q 

3 

QJ  -»-> 

^  o3 

o 
fc 

wl 

§ 

*l 

3S 

&& 

8 

9 

10 

12 

14 

inches. 

inches. 

inches. 

Ibs. 

'2* 

2.875 

.204 

5.74 

1.59 

.94 

5.90 

5.51 

5.21 

_. 

3 

3.5 

.217 

7.54 

2.26 

.16 

9.14 

8.75 

8.35 

7.52 

3* 

4.0 

.226 

9.00 

2.59 

.35 

11.02 

10.66 

10.25 

9.39 

8.62 

4 

4.5 

.237 

10.66 

3.33 

.50 

14.45 

14.11 

13.65 

12.72 

11.78 

4* 

5.0 

.247 

12.34 

3.73 

.68 

16.78 

16.33 

15.88 

14.90 

13.98 

"5 

5 

5.563 

.259 

14.50 

4.17 

.88 

18.76 

18.76 

18.26 

17.31 

16.26 

6 

6.625 

.280 

18.76 

5.57 

2.25 

25.06 

25.06 

25.06 

24.39 

23.32 

3 

7 

7.625 

.301 

23.37 

7.18 

2.59 

32.31 

32.31 

32.31 

32.31 

31.32 

M  is 

8.6^ 

.322 

28.18 

8.14 

2.94 

36.63 

36.63 

36.63 

36.63 

36.63 

u 

'2£ 

2.875 

.56 

13.68 

4.09 

0.82 

14.10 

13.04 

11.86 

c 

3 

3.5 

.608 

18.56 

5.52 

1.02 

21.25 

20.12 

19.04 

16.56 

!_ 

3* 

4.0 

.642 

22.75 

6.63 

1.20 

27.18 

26.02 

24.86 

22.54 

19.89 

02  ^ 

4 

4.50 

.682 

27.48 

8.33 

1.35 

35.31 

34.15 

32.84 

30.19 

27.57 

M 

5 

5.563 

.75 

38.12 

11.73 

1.70 

52.78 

51.37 

49.94 

47.06 

44.16 

_ 

16 

6.625 

.875 

53.11 

15.80 

2.04 

71.10 

71.10 

70.58 

66.99 

64.22 

466 


STRENGTH  OF  CHANNEL   COLUMNS. 


TABLE    XIII.— SAFE    LOADS    IN    TONS    FOR    STRUTS 
FORMED   OF   A   PAIR   OF   CHANNELS. 

Distance  between  webs,  ^  inch. 
If  strut  is  free  to  bend  in  either  direction  use  smaller  value. 

Strains  per  square  inch: 

12,000  Ibs.  for  lengths  of  30  radii  and  under"; 
13,500-50—  for  lengths  over  30  radii. 


D—  >    J.L 

Weight 

Area 

Length  in  feet. 

per 

1  nick- 

of  two 

7*2 

in 

t    \ 

riess 

ins. 

IKo  * 

of  web. 

ro 

8 

9 

10 

11 

12 

14 

33 

0.40 

19.80  -J 

1.48 
5.62 

101.57 
118.80 

97.56 
118.80 

93.55 
18.80 

89.* 
118.80 

85.48 
118.80 

77.44 
118.80 

35 

0.43 

20.58  -j 

1.47 

5.58 

105.32 
123.48 

101.13 
123.48 

96.93 
123.48 

92.73 
123.48 

88.54 
123.48 

80.09 
123.00 

40 

0.52 

23.52  j 

1.46 
5.43 

120.13 
141.12 

115.30 
141.12 

110.48 
141.12 

103.66 
141.12 

100.78 
141.12 

91.14 
140.41 

15 

45 

0.62 

26.48  ] 

1.45 
5.32 

134.91 

158.88 

129.48 

158.88 

123.99 

158.88 

118.50 

158.88 

113.00 

158.88 

102.08 
157.82 

50 

0.72 

29.42  { 

1.46 
5.23 

150.36 
176.52 

144.23 
176.52 

138.20 
176.52 

132.17 
176.52 

126.06 
176.52 

114.00 
174.75 

55 

0.82 

32.36  j 

1.47 
5.16 

165.60 
194.16 

159.00 
194.16 

152.40 
194.16 

145.78 
194.16 

139.22 
194.16 

126.10 
192.00 

20^ 

0.28 

12.06  -j 

1.34 
4.61 

59.81 
72.36 

57.10 
72.36 

54.40 

72.36 

51.70 

72.36 

49.02 
71.99 

43.62 
70.43 

25 

0.39 

14.70  | 

1.31 
4.43 

72.32 

88.20 

68.95 
88.20 

65.60 
88.20 

62.21 
88.20 

58.83 
87.28 

52.03 

85.26 

12 

30 

0.51 

17.64  -j 

1.30 

4.28 

86.52 
105.84 

82.46 
105.84 

78.36 
105.84 

74.30 
105.48 

70.25 
104.25 

62.09 
101.78 

35 

0.64 

20.58  ] 

1.31 
4.17 

101.25 
123.48 

96.52 
123.48 

91.78 
123.48 

87.10 
122.65 

82.37 
121.16 

72.90 
118.33 

40 

0.76 

23.52  { 

1.32 
4.09 

116.01 
141.12 

110.66 
141.12 

105.31 
141.12 

99.96 
139.82 

94.66 
138.06 

83.96 
134.65 

15 

0.24 

8.92  ] 

1.24 

3.87 

42.94 
53.52 

40.78 
53.52 

38.64 
53.29 

36.48 
52.62 

34.32 
51.91 

30.01 
50.43 

20 

0.38 

11.76  | 

1.20 
3.66 

55.86 
70.56 

52.92 
70.56 

49.98 
69.73 

47.04 
68,79 

44.10 

67.82 

38.22 
65.85 

10 

25 

0.53 

14.70  -j 

1.20 
3.52 

69.82 
88.20 

66.15 
87.94 

62.47 
86.69 

58.80 
85.44 

55.12 
84.19 

47.77 
81.69 

30 

0.68 

17.64  -j 

1.22 
3.42 

84.40 
105.84 

80.04 
105.13 

75.71 
103.63 

71.35 
102.04 

67.03 
100.20 

58.34 
97.41 

35 

0.82 

20.58  -j 

1.26 
3.35 

99.76 
123.48 

94.82 
122.34 

89.93 
120.49 

85.04 
118.64 

80.16 
116.79 

70.33 
113.13 

13* 

0.23 

7.78  | 

1.19 
3.49 

36.83 
46.68 

34.87 
46.48 

32.91 

45.82 

30.94 

45.16 

28.98 
44.50 

25.07 
43.15 

15 

0.29 

8.82] 

1.17 
3.40 

41.45 
52.92 

39.18 
52.52 

36.93 
51.81 

34.66 
50.98 

32.41 
50.10 

27.89 
48.64 

9 

20 

0.45 

11.76  -j 

1.15 
3.21 

54.85 
70.56 

51.77 
69.50 

48.71 
68.38 

45.65 
67.29 

42.57 
66.20 

36.42 
64.00 

25 

0.62 

14.70  | 

1.17 
3.10 

69.09 
87.83 

65.31 
86.43 

61.55 
85.00 

57.77 
83.56 

54.00 

82.17 

46.48 
79.30 

*  Of  single  channel. 


STRENGTH  OF  CHANNEL  COLUMNS. 


467 


TABLE    XIII.— SAFE    LOADS    IN    TONS    FOR    STRUTS 
FORMED    OF    A    PAIR    OF    CHANNELS       «~4^~* 

(continued). 

Distance  between  webs,  %  inch. 
If  strut  is  free  to  bend  in  either  direction  use  smaller  value. 

Strains  per  square  inch: 

11,000  Ibs.  for  lengths  of  50  radii  and  under; 
13,500-50-  for  lengths  over  50  radii. 


Weight 

^hick- 

Area 

Length  in  feet. 

D'pth 

ness 

of  two 

rl 

ins. 

foot, 
Ibs.* 

f  web. 

chan- 
nels. 

r° 

6 

7 

8 

9 

10 

11 

11.25 

0.22 

6.70  -j 

1.04 
3.11 

33.63 
36.85 

31.70 
36.85 

29.76 
36.85 

27.83 
36.85 

25.91 
36.85 

23.96 
36.85 

13.75 

0.31 

8.08  | 

1.04 

2.98 

40.56 
44.44 

38.23 
44.44 

35.89 
44.44 

33.57 
44.44 

31.24 
44.44 

28.90 
44.44 

8 

16.25 

0.40 

9.56  \ 

1.03 

2.89 

47.82 
52.58 

45.05 

52.58 

42.25 

52.58 

39.48 
52.58 

36.68 
52.58 

33.91 
52.58 

18.75 

0.49 

1.02  j 

1.03 

2.82 

55.12 
60.61 

51.93 
60.61 

48.70 
60.61 

45.51 
60.61 

42.29 
60.61 

39.09 
60.61 

21.25 

0.58 

2.50  | 

1.03 

2.77 

62.53 

68.75 

58.90 
68.75 

55.25 

68.75 

51.62 
68.75 

47.96 

68.75 

44.34 

68.75 

9.75 

0.21 

5.70  | 

0.99 

2.72 

28.11 
31.35 

26.39 
31.35 

24.66 
31.35 

22.94 
31.35 

21.20 
31.35 

19.47 
31.35 

12.25 

0.32 

7.20  ] 

0.99 
2.59 

35.51 
39.60 

33.33 
39.60 

31.15 
39.60 

28.98 
39.60 

26.78 
39.60 

24.60 
39.42 

7 

14.75 

0.42 

8.68  J 

0.99 
2.50 

42.71 
47.74 

40.18 
47.74 

37.56 

47.74 

34.93 

47.74 

32.28 
47.74 

29.66 
47.13 

17.25 

0.53 

0.14  j 

1.00 
2.44 

50.19 
55.77 

47.15 
55.77 

44.10 
55.77 

41.06 
55.77 

38.02 
55.77 

34.98 
54.73 

19.75 

0.63 

1.62  j 

1.00 
2.39 

57.52 
63.91 

54.03 
63.91 

50.54 
63.91 

47.06 
63.91 

43.57 
63.91 

40.08 
62.39 

8.00 

0.20 

4.76-| 

0.94 
2.34 

23.02 

26.18 

21.50 

26.18 

19.98 

26.18 

18.46 
26.18 

16.94 
26.02 

15.42 
25.41 

6 

10.50 

0.32 

6.18  -S 

0.94 

2  21 

29.89 
33.99 

27.91 
33.99 

25.94 
33.99 

23.97 
33.99 

22.00 
33.32 

20.02 
32.48 

13.00 

0.44 

7.64  -j 

0.95 
2.13 

37.11 
42.02 

34.68 
42.02 

32.27 
42.02 

29.87 
41.88 

27.44 
40.81 

25.04 
39.72 

15.50 

0.56 

9.12  | 

0.95 
2.07 

44.30 
50.16 

41.40 
50.16 

38.53 
50.16 

35.66 
49.68 

32.78 
48.33 

29.89 
47.03 

6.50 

0.19 

3.90  -j 

0.89 
1.95 

18.43 
21.45 

17.13 
21.45 

15.81 
21.45 

14.49 
20.92 

13.18 
20.32 

11.86 
19.72 

5 

9.00 

0.33 

5.30  • 

0.90 
1.83 

25.17 
29.15 

23.41 
29.15 

21.65 

28.83 

19.87 
27.97 

18.11 
27.10 

16.35 
26.22 

11.50 

0.48 

6.76  • 

0.91 
1.75 

32.26 

37.18 

30.03 
37.18 

27.81 
36.36 

25.58 
35.20 

23.35 
34.03 

21.12 

32.88 

5.25 

0.18 

3.10  -j 

0.84 
1.56 

14.28 
170. 

13.17 
16.75 

12.07 
16.15 

10.96 
15.55 

9.85 
14.96 

14.36 

4 

6.25 

0.25 

3.68  -j 

0.84 
1.51 

16.95 
20.2 

15.64 
19.72 

14.33 
18.99 

13.02 

18.26 

11.70 
17.53 

16.80 

7.25 

0.32 

4.26 

0.84 
1.46 

19.6 
23.4 

18.  1C 
22.63 

16.59 
21.75 

15.07 
20.87 

13.54 
19.98 

19.12 

*Of  single  channel. 


468 


STRENGTH  OF  ANGLE  STRUTS. 


TABLE    XIV.— SAFE    LOADS    IN    TONS    FOR    SINGLE 

ANGLE    STRUTS      (STEEL). 
A.  ANGLES  WITH  UNEQUAL  LEGS. 

Strains  per  square  inch: 
11,000  Ibs.  for  lengths  of  50  radii  and  under; 

501 
13,500 for  lengths  over  50  radii. 


Size. 

Thick- 
ness. 

r 
Axis. 
EF* 

Area. 

Length  in  feet. 

4 

5 

6 

7 

8 

9 

10 

6     X4 
5     X3^ 

3/8 
7/8 

0.88 
0.86 

0.76 
0.75 

3.61 
7.99 

42.78 

40.00 

37.21 

34.44 

31  64 

28.86 

26.07 

3/8 
3/4 

3.05 
5.81 

2.40 
5.44 

2.25 
5.06 

2.25 
5.06 

5     X3 

4^X3 

5/16 

3/4 

5/16 
3/4 

5/16 
3/4 

0.66 
0.64 

0.66 
0.64 

0.73 
0.72 

24.66 

11.49 
25.73 

22.29 

19.92 

17.55 

8.72 
19.40 

15.18 

4     X3M 

10.57 

23.62 

9.65 
21.51 

7.79 
17.29 

6.86 
15.18 

4     X3 

5/16 
3/4 

0.65 
0.64 

2.09 
4.69 

10.25 

22.86 

9.28 
20.67 

8.32 

18.47 

7.36 
16.27 

6.39 
14.07 

3HX3 

5/16 
3/8 

5/8 

l/4~" 

3/8 

1/2 

0.63 
0.62 
0.62 

1.93 
2.30 
3.67 

9.35 
11.07 
17.67 

8.43 
9.96 
15.90 

5.72 
8.38 
10.78 

7.51 

8.84 
14.12 

4.92 
7.21 
9.22 

6.59 
7.74 
12.35 





3^X2^ 
3     X2y2 

0.54 
0.54 
0.53 

0.53 
0.52 
0.52 

1.44 
2.11 

2.75 

6.52 
9.55 
12.34 

1/4 

3/8 
1/2 

1.31 
1.92 
2.50 

5.88 
8.52 
11.10 

5.13 

7  42 
9.66 

4.39 
6.31 

8.22 

3     X2 

1/4 

3/8 
1/2 

0.43 
0.43 
0.43 

1.19 
1.73 
2.25 

4.71 
6.85 
8.91 

3.88 
5.64 
7.34 

2^X2 

1/4 
3/8 
1/2 

0.42 
0.42 
0.42 

1.06 
1.55 
2.00 

4.13 
6.03 

7.79 

3.37 
4.93 
6.36 

*  Axis  diagonal,  see  p.  304. 


STRENGTH  OF  ANGLE  STRUTS. 


469 


TABLE     XIV.— SAFE    LOADS    IN    TONS    FOR    SINGLE 

ANGLE  STRUTS  (continued). 

B.  ANGLES  WITH  EQUAL  LEGS. 

Strains  per  square  inch: 
11,000  Ibs.  for  lengths  of  50  radii  and  under; 

KH/ 

13,500-  —  for  lengths  over  50  radii. 


Size. 
6     X6 

Thick- 
ness. 

r 

Axis 
EF* 

1.19 
1.18 
1.17 

Area. 

4.36 
7.11 
9.74 

Length  in  feet. 

4 

5 

6 

22.83 
37.14 
50.77 

7 

8 

9 

19.54 
31.72 
43.26 

10 

18.44 
29.93 
40.78 

3/8 
5/8 
7/8 

23.98 
39.10 
53.57 

19.85 
32.23 
43.94 

23.93 
38.96 
53.27 

18.89 
30.50 
41.44 

21.74 
35.35 

48.28 

20.64 
33.54 
45.77 

5     X5 

3/8 
5/8 
7/8 

3/8 
1/2 
5/8 
3/4 

0.99 
0.97 
0.96 

0.79 
0.78 
0.77 
0.77 

3.61 
5.86 
7.99 

2.86 
3.75 
4.61 
5.44 

2.09 
3.25 
3.98 
4.69 

1.44 
2.11 
2.75 
3.36 

17.80 
28.68 
38.95 

16.71 
26.86 
36.45 

11.71 
15.22 
18.55 
21.89 

15.64 
25.06 
33.95 

10.61 
13.78 
16.75 
19.77 

14.53 
23.24 
31.46 

13.42 
21.43 

28.96 

4     X4 

14.96 
19.54 
23.98 

28.24 

10.47 
16.20 
19.74 
13.26 

6.79 
9.88 
12.87 
15.60 

13.88 
18.10 
22.13 
26.12 

12.79 
16.65 
20.33 
23.99 

9.53 
12.33 
14.95 
17.65 

VAXVA 

5/16 

1/2 
5/8 
3/4 

1/4 

3/8 
1/2 
5/8 

0.69 
0.68 
0.67 
0.67 

9.56 
14.77 
17.95 
21.16 

6.06 
8.78 
11.45 
13.84 

8.65 
13.34 
16.17 
19.06 

7.74 
11.90 
14.39 
16.96 

6.83 
10.47 
12.61 
14.86 

3     X3 

0.59 
0.58 
0.58 
0.57 

5.32 
7.69 
10.03 
12.07 

4.59 
6.60 
8.60 
10.30 

2lAX2y2 

3/16 
1/4 

3/8 

1/2 

0.49 
0.49 
0.48 
0.47 

0.90 
1.19 
1.73 
2.25 

3.87 
5.10 
7.35 
9.44 

3.32 
4.39 

6.27 
8.01 

2.76 
3.66 
5.19 
6.57 

2MX2M 

3/16 
1/4 

3/8 
7/16 

0.44 
0.44 
0.43 
0.43 

0.81 
1.06 
1.55 

1.78 

3.26 
4.26 
6.13 
7.14 

2.70 
3.54 
5.05 
5.80 

2.80 
3.95 
4.53 

2      X2 

3/16 
1/4 

0.40 
0.39 

0.72 
0.94 

2.70 
3.45 

2.16 
2.72 

2.CO 

*  Axis  diagonal,  see  p.  309. 


470 


STRENGTH  OF  ANGLE  STRUTS. 


TABLE  XV.— SAFE  LOADS  IN  TONS  FOR  TWO  ANGLE 

STRUTS. 
LONG  LEGS  PARALLEL  AND  J  INCH  APART. 

Strains  per  square  inch : 
11,000  Ibs.  for  lengths  of  50  radii  and  under; 

KQ7 

13,500-- — for  lengths  over  50  radii. 


Size. 

Thick- 
ness. 

Least 
r 

Area 
of 
two 
an- 
gles. 

Length  in  feet. 

5 

6 

7 

8 

10 

11 

12 

8     X6 
6     X4 

1/2 

3/8 
13/16 

2.49 
2.65 
1.67 
1.74 

13.52 

26.82 
7.22 
14.94 

6.84 
9.00 
11.10 
14.12 

74.36 
147.51 
39.71 
82.17 

37.62 
49.50 
61.05 

77.66 

74.36 
147.51 
39.71 
82.17 

37.57 
49.50 
61.05 

77.66 

74.36 
147.51 
39.65 

82.17 

36.13 
47.81 
59.27 

75.82 

74.36 
147.51 
38.35 
80.26 

34.69 
45.97 
57.05 
73.03 

74.36 
147.51 
35.77 
75.07 

31.82 
42.27 
52.51 
67.42 

73.34 
147.51 
34.47 
72.50 

30.38 
40.41 
50.29 
64.65 

71.72 
144.62 
33.14 
69.91 

29.00 

38.56 
48.07 
61.88 

6     X3K 

3/8 
1/2 
5/8 
13/16 

1.43 
1.46 
1.49 
1.52 

5     X4 
5     X3H 

5     X3 

3/8 
3/4 
3/8 
3/4 

1.59 
1.54 
1.51 
1.55 

6.46 
12.38 
6.10 
11.62 

35.53 
68.09 
33.55 
63.91 

31.46 
41.25 
50.71 
59.84 

35*53 
68.08 
33.55 
63.91 

30.50 
40.23 
49.76 
58.94 

35.07 
66.69 
32.70 
62.69 

33.86 
64.28 
31.49 
60.45 

31.41 
59.45 
29.05 
55.95 

30.20 
57.04 
27.84 
53.71 

28.99 
54.62 
26.64 
51.44 

22.39 
29.85 
37.29 
44.66 

3/8 
1/2 
5/8 
3/4 

1.27 
1.30 
1.33 
1.36 

5.72 
7.50 
9.22 
10.88 

29.15 
38.51 
47.69 
56.63 

27.80 
36.78 
45.59 
54.23 

25.09 
33.32 
41.40 
49.42 

23.75 
31.59 
39.30 
47.05 

4     X3K 
4     X3 

3/8 
3/4 
3/8 
3/4 

1/4 
3/8 
1/2 
11/16 

1.25 
1.20 
1.26 
1.22 

5.34 
10.12 
4.96 
9.38 

2.88 
4.22 
5.50 
7.30 

29.37 

55.66 
27.28 
51.59 

15.58 
22.73 
29.56 
38.92 

28.35 
53.13 

26.28 
49.47 

27.07 
50.60 
25.12 

47.18 

14.03 
20.42 
26.53 
34.78 

25.79 
48.07 
24.00 

44.85 

23.23 
43.01 
21.64 
40.24 

21.94 
40.48 
20.49 
37.94 

10.95 
15.82 
20.47 
26.51 

20.66 
39.95 
19.30 
35.64 

10.18 
14.67 
18.96 
24.43 

3^X2^ 

1.12 
1.10 
1.09 
1.06 

14.81 
21.59 
28.05 
36.86 

13.26 
19.28 
25.02 
32.74 

11.72 
16.97 
21.98 

28.58 

3     X2 

2^X2 

1/4 
1/2 
3/16 

1/2 

0.93 
0.92 
0.79 
0.75 

2.38 
4.50 
1.62 
4.00 

1.44 

1.88 

12.22 
23.04 

7.86 
19.00 

11.45 
21.58 

7.24 
17.40 

10.69 
20.10 
6.63 
15.80 

9.92 
18.64 
6.01 
14.20 

4.13 
5.26 

8.39 
15.70 

7.62 
14.23 

2      X2 
2      X2 

3/16 

1/4 

0.62 
0.61 

6.22 
8.08 

5.54 
7.14 

4.82 
6.20 

Two  ANGLE  STRUTS  OF  — 'p  SECTION,  p.  471. 


3/16 

1.07 

1.80 

9.63 

9.13 

8.64 

8.10 

7.11 

6.61 

6.12 

*/2  X  .4/2 

1/4 

1.11 

2.38 

12.85 

12.19 

1154 

10.88 

9.63 

8.98 

8.63 

3/16 

1.03 

1.62 

8.58 

8.10 

7.65 

7.16 

6.23 

5.75 

5.26 

/4            4 

1/4 

1.01 

2.12 

11.13 

10.54 

9.91 

9.27 

8.  CO 

7.42 

6.78 

9        V  9 

3/16 

0.93 

1.44 

7.37 

6.94 

6.48 

6.01 

5.07 

4.60 

4.13 

1/4 

0.94 

1.88 

9.68 

9.07 

8.46 

7.89 

6.67 

6.11 

5.49 

STRENGTH  OF  I-BEAM  STRUTS. 


471 


TABLE  XVI.— SAFE  LOADS  IN  TONS  FOR  STANDARD 
STEEL    BEAMS   USED   AS   COLUMNS   OR   STRUTS. 

Strains  per  square  inch:    13,500  —  50-. 
BEAMS  UNSUPPORTED  SIDEWAYS. 


Size, 
ins. 

H 

Weight, 
Ibs. 

r 

1.08 
1.04 
1.21 

Area 
of 

section. 

12.48 
14.71 
17.67 

Length  in  feet. 

9 

53.04 
61.12 

79.87 

10 

11 

12 

42.65 
48.38 
66.70 

13 

39.19 
44.13 
62.33 

14 

42.00 
50.00 
60.00 

49.57 
56.85 
75.45 

46.11 
52.62 
71.12 

57.95 

H 

ur| 

31.50 
35.00 
40.00 

25.00 
40.00 

21.00 
35.00 

1.01 
0.99 
1.08 

0.97 
0.90 

0  90 
0.84 

9.26 
10.29 
11.84 

7  37 
11.76 

37.76 
41.39 
50.32 

29.24 
44.10 

23.66 
36.40 

35.00 
38.28 
47.03 

26.95 
40.19 

21.56 
32.72 

32.24 
35.16 
43.75 

29.50 
32.05 
40.46 

37.18 



24.67 
36.28 

19.46 

22.40 

9"1 

6.31 
10.29 



*>\ 

18.00 
25.50 

0,84 
0.80 

5.33 
7.50 

18.85 
25.31 

16.95 
22.50 

BEAMS  SUPPORTED  SIDEWAYS. 

»( 
'i 

18.00 
25.50 

3.27 

3.02 

5.33 

7.50 

31.58 
43.93 

31.08 
43.17 

30.59 
42.43 

30.11 
41.68 

29.62 
40.95 

29.14 
40.20 

15.00 
20.00 

2.86 
2.68 

4.42 

5.88 

25.67 
33.76 

25.20 
33.10 

24.74 
32.45 

24.27 
31.79 

23.81 
31.13 

18.64 
22.09 
25.51 

13.91 
17.06 
20.24 

23  .  35 
30.47 

18.20 
21.53 

24.84 

•I 
•\ 

12.25 
14.75 
17.25 

2.46 
2.35 
2.27 

3.61 
4.34 
5.07 

20.40 
24.31 
28.19 

19.96 
23  .  76 
27.52 

19  .  53 
23.21 
26.86 

19.09 
22.65 
26.18 

14.33 
17.62 
20.94 

9.75 
12.25 
14.75 

2.05! 
1.94 

1.87 

2.87 
3.60 
4.34 

15.59 
19.29 
23.03 

15.17 
18.73 
22.33 

14.75 
18.18 
21.63 

13.49 
16.50 
19.55 

«i 

7.50 
10.50 

1.64 
1.52 

2.21 
3.09 

11.28 
15.37 

10.87 
14.76 

10.47 
14.15 

10.06 
13.54 

9.66 
12.93 

9.26 
12.32 

>i 

5.50 
7.50 

1.23 
1.15 

1.63 
2.21 

7.42 
9.73 

7.02 
9.15 

6.63 
8.57 

6.23 
8.00 

5.83 
7.42 

5.43 
6.84 

NOTE. — The  safe  loads  given  on  bottom  of 
p.  470  refer  to  two  angles  connected  by 
plates  so  as  to  form  a  cross- section,  as  in 
accompanying  figure.  This  form  of  strut  is 
frequently  used  in  light  steel  trusses. 


472 


STRENGTH  OF  CHANNEL  COLUMNS. 


TABLE  XVII.— SAFE  LOADS  IN  TONS  OF  2,000  LBS. 
FOR  CHANNEL  COLUMNS. 


Allowed  stresses  per  square  inch; 
12,000  Ibs.  for  lengths  of  90  radii  or  under; 


17,100  —  57-  for  lengths  over  90  radii,  and  less  than  125  radii,    afc 


Size  of 
plates, 
ins. 

Weight  of 
channels 
and 
plates. 

r 

Length  in  feet. 

14 

16 

18 

20 

22 

24 

6"  —  8-LB.  CHANNELS.     B  =  3J^".     C  =  5%". 

Lattice.  . 

5/itx8 

16.0 
29.6 
33.0 
36.4 
39.8 

2.33 
2.32 
2.32 
2.32 
2.32 

28.6 
52  .  6 
58.6 
64.6 
70.6 

28.6 
52.6 
58.6 
64.6 
70.6 

28.1 
51.7 
57.5 
63.4 
69.3 

26.7 
49.1 
54.7 
60.3 
65.8 

25.3 
46.5 
51.8 
57.1 
62.4 

23.9 
43.9 
48.9 
53.9 
58.9 

6"  —  15.5-LB.  CHANNELS.     B=3J^".     C  =  5M". 

Lattice.  . 

31.0 
48.0 
51.4 

54.8 
58.2 

2.00 
2.12 
2.13 
2.14 
2.15 

54.7 
84.7 
90.7 
96.7 
102.7 

53.0 
84.2 
90.4 
96.7 
102.7 

49.9 
79.7 
85.6 
91.5 
97.4 

46.8 
75.1 
80.7 
86.4 
92.0 

70.5 
75.9 
81.2 
86.5 

7"_g  .75-LB.  CHANNELS.     B  =  4^".     C  =  6M". 

Lattice.  . 

5/i6X9 
3^X9 

19.5 
34.8 
38.6 
42.5 
46.3 

2.72 
2.67 
2.67 
2.66 
2.66 

34.2 
61.2 
67.9 
74.7 
81.5 

34.2 
61.2 
67.9 

74.7 
81.5 

34.2 
61.2 
67.9 

74.7 
81.5 

34.2 
61.2 
67.9 
74.4 
81.1 

32.8 
58.5 
65.0 
71.2 
77.6 

31.4 
55.9 
62.0 
68.0 
74.1 

7"  —  17.25-LB.  CHANNELS.     B=4^".     C  =  6M". 

Lattice.  . 

3^X9 

34.5 
53.6 
57.5 
61.3 
65.1 

2.43 
2.49  - 
2.50 
2.50 
2.51 

60.8 
94.6 
101.3 
108.1 
114.8 

60.8 
94.6 
101.3 
108.1 
114.8 

60.8 
94.6 
101.3 
108.1 
114.8 

58.1 
91.4 
98.2 
104.8 
111.5 

55.3 

87.1 
93.5 
99.9 
106.3 

52.4 
82.8 
88.9 
95.0 
101.1 

To  weight  of  channels  and  plates  add  the  weight  of  rivets  and  lattice- 
bars.  The  size  of  lattice-bars  should  not  be  less  than  l^X^e  ins.  for 
6-inch  channels,  1%X%«  inch  for  7-  and  8-inch  channels,  or  2X5A&  ins. 
for  9-  and  10-inch  columns.  See  page  43°- 


STRENGTH  OF  CHANNEL  COLUMNS. 


473 


TABLE    XVII.— SAFE    LOADS    IN    TONS    OF  2,000  LBS. 

FOR  CHANNEL  COLUMNS  (continued). 

.- 

Allowed  stresses  per  square  inch: 
12,000  Ibs.  for  lengths  of  90  radii  or  under; 


17,100  —  57-—  for  lengths  over  90  radii,  and  less  than  125  radii.     — 


--B-- 


Size  of 
plates, 
ins. 

Weight  of 
channels 
and 
plates. 

r 

Length  in  feet. 

20 

22 

24 

26 

28 

30 

8"—  11.25-LB.  CHANNELS.     B  =  5%6".     C  =  73^". 

Lattice.  . 
HXIQ 
%6X10 

i^xio 

22.5 
39.5 

43.7 
48.0 

3.11 
3.03 
3.02 
3.01 

40.2 
70.2 
77.7 
85.2 

40.2 
70.2 

77.7 
85.2 

39.6 

68.4 
75.5 

82.7 

38.1 
65.7 
72.6 
79.4 

36.6 
63.1 
69.7 
76.2 

35.2 
60.5 
66.7 
73.0 

8"—  16.25-LB.  CHANNELS.     B  =  57/i6".     C  =  7^". 

Lattice.  . 
HX10 
%eX10 

HXIO 

32.5 
58.0 
62.3 
66.5 

2.89 
2.92 
2.91 
2.91 

57.4 

102.4 
109.9 
117.4 

56.8 
101.9 
109.3 
116.7 

54.6 
97.9 
105.0 
112.1 

52.3 
93.9 

100.7 
107.5 

50.1 

89.9 
96.4 
102.9 

47.8 
85.9 
92.1 
98.3 

9"—  13.25-LB.  CHANNELS.     B  =  63/46".     C  =  8^". 

Lattice.  . 

Kxn 

5AeXH 

Hxii 

26.5 
45.2 
49.9 
54.6 

3.49 

3.40 
3.38 
3.36 

46.7 
79.7 
88.0 
96.2 

46.7 
79.7 
88.0 
96.2 

46.7 
79.7 
88.0 
96.2 

46.7 
78.8 
86.7 
94.6 

45.2 
76.1 

83.8 
91.4 

43.6 
73.4 
80.8 
88.1 

9"—  20-LB.  CHANNELS.     B  =  68/4e".     C  =  83/£". 

Lattice.  . 
NXli 
7/4eXH 
HXll 

40.0 
68.1 

72.7 
77.4 

3.21 
3.25 
3.25 
3.24 

70.6 
120.1 
128.3 
136.6 

70.6 
120.1 

128.3 
136.6 

70.6 
120.1 
128.3 
136.6 

68.0 
116.3 
124.2 
132.1 

65.5 
112.1 
119.7 
127.3 

63.0 
107.9 
115.2 
122.5 

10''—  15-LB.  CHANNELS.     B  =  7".     C  =  9J^". 

Lattice.  . 
5AeXl2 

^X12 

30.0 
55.5 
60.6 

3.87 
3.74 
3.72 

53.5 

98.5 
107.5 

53.5 
98.5 
107.5 

53.5 

98.5 
107.5 

53.5 

98.5 

53.5 
98.5 

107.5 

52.6 
95.3 
107.0 

10"—  25-LB.  CHANNELS.     B  =  7".     C  =  9>£". 

Lattice.  . 
9/16X12 
MX12 

50.0 
95.9 
101.0 

3.52 
3.56 
3.55 

88.2 
169.2 
178.2 

88.2 
169.2 
178.2 

88.2 
169.2 
178.2 

88.2 
169.2 
178.2 

85.7 
165.3 
173.9 

82.8 
159.8 
168.2 

474 


DIMENSIONS  OF   Z-BAR  COLUMNS. 


DIMENSIONS  OF  Z-BAR  COLUMNS. 
CARNEGIE  SECTIONS. 


6"   COLUMNS. 
4  Z-bars  3-3}ie"  deep  and  1  web-plate  5%"X  thickness  of  Z-bars. 


&• 


Thick- 
ness of 
metal. 

1/4 
5/16 

3/8 
7/16 
1/2 
9/16 


12%6 

123/16 

12^ 

121/16 


B 


3%2 


3*1/32 


2% 
2% 


E 


G 


23Vl6 

211^6 

2M 


H 


3M 


8"    COLUMNS. 
4  Z-bars  4-4K"  deep  and  1  web-plate  6^r/  X  thickness  of  Z-bars. 


Thick- 
ness of 
metal. 

1/4 

5/16 

3/8 

7/16 

1/2 

9/16 

5/8 

11/16 

3/4 


141M6 
1434 


14%6 

145/16 


4%2 

413JL 


51- 

51^6 


3M 


IH 

1*4 


I 


H 


I 
4M 


4H/16 


4M 
4% 


STRENGTH  OF  Z-BAR  COLUMNS. 


475 


TABLE  XVIII.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.  FOR 
Z-BAR  COLUMNS  WITH  SQUARE  ENDS. 

\  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  stresses  per  square  inch,  ^^  _  ^  l_  for  lengths  ^ 


6"    Z-BAR    COLUMNS. 

Section:   4  Z-bars  3"  deep  and  one  web-plate  5%"  X  thickness  of  Z-bars. 

*"  S'co 

GO  c" 

<N  d 

CO      JH 

d 

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818 

<£>""•£§ 

2J"".§ 

oj'^oi 

Length 

j?57 

ii  iL 

ill 

•a!* 

^ll 

||     03  '~l 

of 
column 

IT? 

§7  d 

8?| 

•sS'd 

in  feet. 

S  I'  g 

«!'£ 

S,!:'§ 

111 

a  ".'a 

.13 

Xo. 

i^^  v 

N'£  *. 

t-^jO  j. 

sgi. 

*T3  ** 

12  and 
under 

55.9 

70.3 

81.6 

95.8 

105.7 

119.8 

14 

55.7 

70.3 

81.6 

95.8 

105.7 

119.8 

16 

52.3 

66.5 

76.6 

91.3 

99.9 

114.8 

18 

48.8 

62.3 

71.7 

85.6 

93.6 

107.8 

20 

45.4 

58.1 

66.7 

79.9 

87.2 

100.8 

22 

42.0 

53.9 

61.8 

74.3 

80.9 

93.8 

24 

38.6 

49.7 

56.9 

68.6 

74.6 

86.8 

26 

35.2 

45.5 

51.9 

63.0 

68.2 

79.8 

28 

31.7 

41.3 

47.0 

57.3 

61.9 

72.8 

30 

28.3 

37.1 

42.0 

51.7 

55.5 

65.8 

Section: 


8"    Z-BAR    COLUMNS. 
4  Z-bars  4"  deep  and  1  web-plate  6W  X  thickness  of  Z-bars. 


G 

G* 

G 
GO  C31"? 

G 

G 

^  cr^. 

.s  • 

G 
"-J'^O 

G 

oo.S    . 
gcr^ 

G 
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GO  <B^ 

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7  «<N 

O    K<>j 

£ 

7°^  ii 

7^7 

Jl^   " 

vsl 

II  «  II 

T^  " 

JLq  ii 

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3^? 

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i^ 

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a  ii  -g 

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18 

and 

under 

67.5 

84.8 

102.4 

114.2 

131.2 

148.5 

157.5 

174.3 

191.2 

20 

65,0 

82.5 

100.5 

110.5 

128.2 

146.4 

153.3 

171.3 

189.6 

22 

61.9 

78.7 

95.9 

105.3 

122.4 

139.9 

146.2 

163.5 

181.3 

24 

58.8 

74.8 

91.3 

100.1 

116.5 

133.4 

139.1 

155.8 

173.0 

26 

55.7 

71.0 

86.8 

94.8 

110.6 

126.9 

132.0 

148.1 

164.7 

28 

52.6 

67.1 

82.3 

89.6 

104.7 

•120.3 

124.8 

140.4 

156.4 

30 

49.4 

63.3 

77.7 

84.4 

98.8 

113.8 

117.7 

132.7 

148.2 

32 

46.3 

59.5 

73.2 

79.2 

93.0 

107.3 

110.6 

125.0 

139.9 

34 

43.2 

55.6 

68.7 

74.0 

87.1 

100.8 

103.5 

117.3 

131.6 

36 

40.1 

51.8 

64.1 

68.7 

81.2 

94.3 

96.4 

109.6 

123.3 

38 

37.0 

48.0 

59.6 

63.5 

75  .  3 

87.8 

89.4 

101.9 

115.0 

40 

33.9 

44.1 

55.0 

58.3 

69.5 

81.3 

82.2 

94.2 

106.7 

To  the  above  weights  of  column  shafts  add  the  weight  of  rivets. 


476  DIMENSIONS  OF  Z-BAR  COLUMNS. 

DIMENSIONS  OF  Z-BAR  COLUMNS. 
CARNEGIE  SECTIONS. 


10"    COLUMNS. 
4  Z-bars  5-5H"  deep  and  one  web-plate  7"  X  thickness  of  Z-bars. 


Thick- 
ness of 
metal. 

5/16 

3/8 

7/16 

1/2 

9/16 

5/8 

11/16 

3/4 

13/16 


16%6 
16kC 
165/16 


B 

sip 

511/3 

54 


C 


6M 


3M 


314 

3M 


IV* 


I 


3K 


3M 


314 

35/16 


H 


10H 
10 


5%« 
5^ 

5% 


12"    COLUMNS. 
4  Z-bars  6-6H"  deep  and  one  web-plate  8"X  thickness  of  Z-bars. 


Thick- 

Ui 

ness  of 

A 

B 

C 

D 

E 

F 

G 

H 

I 

o 

metal. 

'o    . 
^2^ 

3/8 

18~< 

6%6 

7H 

4 

4 

2 

m 

llkC 

6% 

*o 

7/16 

18i%« 

6%2 

73^ 

4 

4 

2 

3%  6 

11% 

6H 

fc-l  -ij' 
O  CD 

1/2 
9/16 

19 

18iVi6 

6% 

6%2 

7^ 
6is/1(5 

4 
4 

4 
4 

2 
2 

3% 
3H 

11 
10J^ 

6% 
6%a 

OJ.C 

5/8 

mi 

(\'< 

6i%(! 

4 

4 

2 

3%o 

KBi 

6H/16 

s  u 

11/16 

18i%0 

()!%2 

615/16 

4 

4 

2 

3% 

10% 

61%6 

.~i 

3/4 

18%  6 

6% 

6M 

4 

4 

2 

3M 

1034 

6^ 

Q 

13/16 

18% 

6i%2 

6|| 

4 

4 

2 

3%o 

10:j| 

6^ 

7/8 

18i%6 

6%o 

6M 

4 

4 

2 

3% 

10M 

7 

STRENGTH  OF  Z-BAR  COLUMNS. 


477 


TABLE  XVIII.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.  FOR 
Z-BAR  COLUMNS  WITH  SQUARE  ENDS  (continued). 

(  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  stresses  per  square  inch-j  ^^  _  ^  ]_  ^  lengths  Qf  over  gQ  ^^ 

10"  Z-BAR    COLUMNS. 
Section:   4  Z-bars  5"  deep  and  one  web-plate  7"  X thickness  of  Z-bars. 


a 

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d   . 

d 

d 

d   . 

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94.7 

114.2 

133.9 

147.0 

166.2 

185.6 

196.0 

214.9 

234.0 

24 

92.8 

112.6 

133.1 

144.6 

164.8 

185  .  3 

193.6 

213.9 

234.0 

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89.3 

108.6 

128.3 

139.2 

158.7 

178.7 

186.5 

206.2 

226.6 

28 

85.8 

104.4 

123.5 

133.8 

152.7 

172.1 

179.3 

198.5 

218.4 

30 

82.3 

100.2 

118.7 

128.4 

146.7 

165.5 

172.2 

190.8 

210.2 

32 

78.8 

96.1 

113.8 

123.0 

140.7 

158.9 

165.0 

183.1 

202.0 

34 

75.3 

91.9 

109.1 

117.6 

134.7 

152.3 

157.9 

175.4 

193.8 

33 

71.8 

87.8 

104.3 

112.2 

128.7 

145.7 

150.7 

167.8 

185.6 

38 

68.3 

83.6 

99.5 

106.8 

122.7 

139.1 

143.6 

160.0 

177.4 

40 

64.8 

79.4 

94.7 

101.4 

116.7 

132.5 

136.5 

152.3 

169.1 

42 

61.3 

75.3 

89.9 

96.0 

110.6 

125.9 

129.4 

144.6 

160.9 

44 

57.7 

71.1 

85.1 

90.6 

104.6 

119.3 

122.2 

136.9 

152.7 

46 

54.2 

67.0 

80.3 

85.2 

98.6 

112.7 

115.1 

129.2 

144.5 

48 

50.7 

62.8 

75.5 

79.8 

92.6 

106  .  1 

107.9 

121.5 

136.3 

50 

47.2 

58.6 

70.7 

74.4 

86.6 

99.5 

100.8 

113.8 

128.1 

12"    Z-BAR   COLUMNS. 
Section:    4  Z-bars  6"  deep  and  one  web-plate  8"  X  thickness  of  Z-bars. 


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128.3 

150.3 

172.6 

187.3 

209.1 

231.0 

243.0 

264.5 

286  .  1 

28 

127.0 

149.7 

172.5 

186.0 

208.9 

230  .  3 

240.8 

261.4 

282.1 

30 

123.0 

145.1 

167.6 

180.2 

202.5 

223.3 

233.2 

253.2 

273.2 

32 

119.0 

140.5 

162.4 

174.5 

196.1 

216.3 

225  .  7 

245.0 

264  .  2 

34 

115.1 

135.9 

157.2 

168.7 

189.8 

209  .  2 

218.2 

236.7 

255.2 

36 

111.1 

131.3 

152.0 

162.9 

1  S3  .  4 

202.1 

210.6 

228.4 

246.3 

38 

107.1 

126.7 

146.8 

157.1 

177.0 

195.1 

203.1 

220.2 

237  .  3 

40 

103.1 

122  1 

141.5 

151.4 

170.7 

188.0 

195.6 

211.9 

228.3 

42 

99.1 

117.5 

136.3 

145.5 

164.4 

180.9 

188.0 

203.7 

219.4 

44 

95.1 

112.9 

131.1 

139.8 

158.0 

1  73  .  9 

180.5 

195.5 

210.4 

46 

91.2 

108.3 

126.2 

134.0 

151.6 

166.8 

172.9 

187.2 

201.4 

48 

87.2 

103.6 

120.7 

128.2 

145.3 

159.8 

165  4 

179.0 

192.4 

50 

83.2 

99.1 

115.5 

122.4 

1  38  .  9 

152.7 

157  Q 

170.7 

183.5 

To  the  above  weights  of  column  shafts  add  the  weight  of  rivets. 


478 


DIMENSIONS  OF  Z-BAR  COLUMNS. 


DIMENSIONS  OF  Z-BAR  COLUMNS. 
CARNEGIE  SECTIONS. 


n 


Section:  4  Z-bars 


14"   COLUMNS. 
.  1  web-plate  8"  X 


ie".  2  side  plates  14"  wide. 


H 

o 

Thickness 
of 
side  plates. 

A 

B 

C 

D 

Diameter  of  bo 
rivet,  %". 

3/8 
7/16 
1/2 
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5/8 
11/16 
3/4 
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19»/16 

1911/10 

19M 
19J£ 
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20K 
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Section:   4  Z-bars  6" 


14"    COLUMNS. 

^".    1  web-plate  8"  X  'X".    2  side  plates  14"  wide 


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A 

B 

C 

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o 

side  plates. 

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634 

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73/16 

l^ 

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7/8 

2oy8 

7M 

IOK 

STRENGTH   OF   Z-BAR   COLUMNS. 


479 


TABLE  XVIII.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.  FOR 
STEEL    Z-BAR    COLUMNS,   WITH    SQUARE    ENFS 

(continued). 

(  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  strains  per  square  inch 


\  17,100-57  —  for  lengths  over  90  radii, 
i  f 

14"  Z-BAR    COLUMNS. 
Section :  4  Z-bars  &/$"  X  Hie".  1  web-plate  8"  X  Hie".  2  side  plates  14"  wide. 


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307.7 

318.3 

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298.3 

308.6 

318.9 

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349.5 

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338.6 

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289.2 

298.9 

308.6 

318.2 

327.7 

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270.1 

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289.0 

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269.7 

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242.5 

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275.8 

284.2 

292.6 

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Section:   4  Z-bars 


Z-BAR    COLUMNS. 
1  web-plate  8"XM"-     2  side  plates  ! 


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296.7 

307.2 

317.8 

328.3 

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349.4 

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287.4 

297.6 

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318.2 

328.4 

338.7 

348.9 

359.1 

369.4 

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278.1 

288.0 

298.0 

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318.0 

327  .  9 

337.8 

347.8 

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268.8 

278.4 

288.2 

297.9 

307.4 

317.2 

326.8 

336  .  4 

346.1 

38 

259.5 

268.8 

278.3 

287.7 

297.0 

306.4 

315.7 

325  .  1 

334.5 

40 

250  .  2 

259.3 

268.4 

277  .  5 

286.5 

295.6 

304.7 

313.7 

322.8 

42 

240.9 

249.7 

258.5 

267  .  3 

276.1 

284.8 

293.6 

302.4 

311.2 

44 

231.6 

240  .  1 

248.6 

257  .  1 

265  .  6 

274.1 

282  .  5 

291.0 

299.6 

46 

222.4 

230  .  5 

238  .  7 

246.9 

255  .  1 

203  .  4 

271.5 

279.7 

287.9 

48 

213.0 

220.9 

228.8 

236.8 

244.7 

252  .  6 

260.4 

268  .  3 

276.2 

50 

203.7 

211.3 

219.0 

226.6 

234.2 

241.8 

249.4 

257.0 

264.6 

To  the  above  weight  of  column  shafts  add  the  weight  of  rivets, 


480 


DIMENSIONS   OF   Z-BAR   COLUMNS. 


DIMENSIONS  OF  Z-BAR  COLUMNS. 

CARNEGIE  SECTIONS. 

16"  COLUMNS. 

Section:  4  Z-bars  6V£"  X  H".     1  web-plate  10"  X  1".     2  side  plates  16"  wide, 


Thicknes 
of  side 
plates. 


1/2 

9/16 

5/8 

11/16 
3/4 

13/16 
7/8 

15/16 
1 


2 

219/10 

211  Ho 


i 

7-r/io 

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12M 
12M 
12^ 
12k 


IS"  COLUMNS. 

Section:  4  Z-bars  6K"XK".     1  web-plate  12"  XI". 
2  side  plates  18"  wide. 


"T  I 


SM-  5 

•i  'J 


Thickness 
of  side 
plates. 


1/2 

9/16 

5/8 

11/16 
3/4 

13/16 
7/8 

15/16 
1 


A 

23 

23Vie 
234 
23%  o 
23'  ' 


B 


m 

m 
w% 


m 


14M 

14J4 
14^ 
14k 
14^ 
14k 
14M 


STRENGTH   OF  Z-BAR  COLtlMNS. 


481 


TABLE   XV1IL— SAFE   LOADS  IN  TONS   OF  2,000  LBS, 
FOR  STEEL  Z-BAR  COLUMNS  WITH  SQUARE  ENDS 

(continued) 

(  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  strains  per  square  inch:^17)10()_,57^  for  lengths  over  90  radii. 

16"    Z-BAR    COLUMNS. 
Section:  4  Z-bars  6V6"  X  7A".     1  web-plate  10" X  1".     2  side  plates  16"  wide 


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316.6 

326.3 

336.0 

345.7 

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365.1 

374.8 

384.5 

394.2 

18"    Z-BAR    COLUMNS. 
Section:  4  Z-bars  6^"X>s".     1  web-plate  12"  X  1".     2  side  plates  18"  wide. 


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428.1 

443.9 

458.1 

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482       CONSTANT-DIMENSION   Z-BAR  COLUMNS. 


DIMENSIONS  OF  CONSTANT-DIMENSION' 
Z-BAR   COLUMNS. 

(CARNEGIE  SECTIONS.) 


Constant  dimensions  are  given  on  the  sketch  above  for  all  columns. 

Variable  dimensions,  see  below.     All  rivets  %"  diameter.     Open  holes  for 

%"  rivets  or  bolts. 

Sgt]trpt1ea3teS99"$l«^°ot:8n"ffor  all  columns  less  than  «'' metal. 

For  all  columns  %"  metal  and  over,  tie-plates  are  %"  thick. 

All  tie-plates  spaced  about  3'-0"  centre  to  centre. 


Size  of  Z-bars. 


4k" 

4" 


B 


4" 
41/iG" 


D 


5" 

4T^ 
4-M' 
5" 


G 


3V16" 


3^10 
3M' 

3^6 


STRENGTH   OF  Z-BAR   COLUMNS. 


483 


TABLE  XIX.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.  FOR 
CONSTANT-DIMENSION  Z-BAR  COLUMNS,  SQUARE 
ENDS. 

12,000  Ibs.  for  lengths  of  90  radii  or  under. 
17,100-57—  for  lengths  over  90  radii. 


Allowed  stresses  per  square  inch: 

Section:  4  Z-bars  4"  deep  with  tie-plates. 


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30 

226.9 

236.3 

245.7    254.9 

264.2 

273.4 

282.6 

291.7 

300.7 

32 

218.7 

227.5 

236.4    245.2 

253.9 

262.6 

271.2 

279.8 

288  .  3 

34 

210.4 

218.8 

227.1     235.4 

243.6 

251.7 

259.8 

267  .  8 

275.9 

36 

202.2 

210.0 

217.8    225.6 

233  .  2 

240.9 

248.4 

255  .  9 

263  .  4 

40 

185.7 

192.5 

199.3    206.0 

212.6 

219.2 

225.7 

232  .  1 

238  .  5 

484    STRENGTH  OF  PHCENIX  STEEL  COLUMNS. 


TABLE   XX.— DIMENSIONS    AND    SAFE    CONCENTRIC 
LOADS  FOR  PHCENIX  STEEL  COLUMNS. 

(For  description  of  column,  see  page  440.) 
The  dimensions  given  in  the  following  table  are  subject  to 
such  slight  variations  as  are  unavoidable  in  the  manufacture  of 
these  shapes. 

The  weights  given  are  those  of  the  segments  composing  the 
columns,  and  from  2  to  5  per  cent,  must  be  added  for  weight  of 
the  rivet-heads. 

The  A,  B1,  B2,  and  C  columns  have  each  4  segments,  the  E 
have  6,  and  the  G  have  8  segments. 

Any  desired  thickness  between  the  minimum  and  maximum 
can  be  furnished. 

(  14,000  Ibs.     for    lengths    of   70 
radii  or  under. 

Allowed  strains  per  sq.  inch  <   ,  ,nl 

I   17,100  —  57—,    for    lengths  over 

^      70  radii. 


One  segment. 

Diameters  in  inches. 

One  column. 

Safe  load  in 
net  tons  for 

a 

.3  . 

d 

D 

Z)i 

B?j 

t-t 

»fl    • 

If 

31 

•+s  !>» 

d 

"S'U 

e3  CJ 

°-.s4 

Ill 

oJ 

+3    W 

£« 
11 

Us 

go, 

fH 

-a 

1 

3 

Is 

<u  M  o 

•*|| 

||| 

i£§ 

lj*3 

ii 

s  ^ 

H 

£ 

M 

o 

? 

H^  o>rH 

%6 

9.7 

- 

4 

6^6 

3.8 

12.9 

1.45 

21.7 

18.1 

12.2 

4Vg 

6'^  6 

4.8 

16.3 

1.50 

27.9 

23.9 

5,^6 

14.8 

3|j- 

4J4 

65/10 

5.8 

19.7 

1.55 

34.2 

29.0 

^8 

17.3 

&YS 

6.8 

23.1 

1.59 

40.5 

34.7 

H 

16.3 

5% 

g^ 

6.4 

21.8 

1.95 

41.2 

36.6 

5/16 

19.9 

5}4 

8%o 

7.8 

26.5 

2.00 

50.7 

45.3 

23.5 

B.I 

5^8 

85/16 

9.2 

31.3 

2.04 

59.8 

54.0 

7/16 

27.0 

A7 

5M 

10.6 

36.0 

2.09 

69.5 

62.8 

30.6 

48 

5Jlj 

S^2 

12.0 

40.8 

2.13 

84.0 

71.7 

%6 

34.2 

6 

8%  6 

13.4 

45.6 

2.18 

93.8 

80.9 

N 

37.7 

QYs 

SiVie 

14.8 

50.3 

2.23 

103.6 

90.2 

1A 

18.9 

6%6 

95€ 

7.4 

25.2 

2.39 

51.8 

46.3 

%B 

22.9 

61Vi6 

91^ 

9.0 

30.6 

2.43 

63.0 

56.7 

H 

27.0 

B.2 

6i-%6 

9%  6 

10.6 

36.0 

2.48 

74.2 

67.2 

31.1 

61  5/i(5 

Ql^ 

12.2 

41.5 

2.52 

85.4 

77.8 

;Mj 

35.2 

^  l^f 

7^6 

95^ 

13.8 

46.9 

2.57 

96.6 

88.6 

%6 

39  .  3 

7%  6 

Q;J/ 

15.  -4 

52.4 

2.61 

107.8 

99.4 

43.3 

75/16 

91%6 

17.0 

57.8 

2.66 

119.0 

110.4 

Least  radius  of  gyration  equals  D  X  .3636. 


STRENGTH  OF  PHCENIX  STEEL  COLUMNS.     485 


TABLE  XX.— SAFE  LOAD  IN  TONS  OF  2,000  LBS.  PHCENIX 

STEEL   COLUMNS  (continued). 
ALLOWED  STRAINS  PER  SQUARE  INCH,  14,000  LBS. 


One  segment. 

Diameters  in  inches. 

One  column. 

| 

"B 

d 

D 

Di 

rt 

n 

Sa  . 

|I| 

I  8 

II 

Weight  i 
Ibs.  per  ya 

Inside. 

Outside. 

1 

O  «3 

Area  of 
cross-secti< 
sq.  in. 

Weight 
per  foot 
in  pounds 

Least  radi 
of  gy  ratio 
in  inches 

M 

25% 

713Ae 

lin^e 

10.0 

34.0 

2.84 

70.0 

%6 

31 

715/16 

11x4 

12.1 

41.3 

2.88 

84.7 

% 

36 

1113/16 

14.1 

48.0 

2.93 

98.7 

H« 

41 

83/46 

11% 

16.0 

54.6 

2.97 

112.0 

46 

8^6 

111%6 

18.0 

61.3 

3.01 

126.0 

sJ46 

51 

8^4  6 

12 

19.9 

68.0 

3.06 

139.3 

% 

56 

C 

8^46 

12146 

21.9 

74.6 

3.11 

153.3 

i-Vie 

62 

7-3- 

8H/16 

123/46 

24.3 

82.6 

3.16 

170.1 

» 

68 

•  8 

8i  3/4  6 

125/16 

26.6 

90.6 

3.20 

186.2 

73 

815/46 

12V16 

28.6 

97.3 

3.24 

200.3 

% 

78 

9^6 

30.6 

104.0 

3.29 

214.2 

1 

89 

95/16 

12% 

34.8 

118.6 

3.34 

243.6 

1% 

99 

994  6 

38.8 

132.0 

3.48 

271.7 

IX 

109 

9H/16 

13 

42.7 

145.3 

3.57 

298.9 

X 

28 

119/46 

15% 

16.5 

56.0 

4.20 

115.3 

5A& 

32% 

11H/46 

15% 

19.1 

65.0 

4.25 

133.8 

% 

37 

1113,46 

15M 

21.7 

74.0 

4.29 

152.0 

TAo 

42 

1  115/16 

15% 

24.7 

84.0 

4.34 

173.0 

% 

47 

121/16 

1515/46 

27.6 

94.0 

4.38 

193.2 

%6 

52 

123/46 

161/16 

30.6 

104.0 

4.43 

214.1 

% 

57 

125/4  6 

163/16 

33.5 

114.0 

4.48 

234.7 

IVjft 

62 

1  -i  j  / 

127/46 

165/16 

36.4 

124.0 

4.52 

255.0 

M 

68 

/K> 

12%6 

16^/16 

40.0 

136.0 

4.56 

280.0 

13/16 

73 

1211/16 

16%o 

43.0 

146.0 

4.61 

300.6 

78 

45.9 

156.0 

4.66 

321.2 

1    8 

88 

131/4  6 

161346 

51.7 

176.0 

4.73 

362.0 

1% 

98 

135/16 

17^46 

57.6 

196.0 

4.84 

403.2 

108 

13»/16 

175/16 

63.5 

216.0 

4.93 

444.7 

5/16 

31 

15M 

19% 

24.2 

82.6 

5.54 

17.0 

36 

15% 

19^ 

28.1 

96.0 

5.59 

190.7 

T/^6 

41 

15% 

19% 

32.0 

109.3 

5.64 

226.0 

% 

46 

15% 

191V16 

36.0 

122.6 

5.68 

254.0 

9/16 

51 
56 

15M 

15% 

19% 

39.9 
43.8 

136.0 
149.3 

5.73 

5.77 

282.0 
300.4 

l-Vl6 

61 

16i 

20 

47.7 

162.6 

5.82 

337.9 

94! 

66 

1  /l^ 

20% 

51.7 

176.0 

5.88 

363.0 

13/16 

71 

8 

Igi^ 

20^ 

55.6 

189.3 

5.91 

382.2 

76 

16% 

20% 

59.6 

202.6 

5.95 

419.3 

1 

86 

16% 

20% 

67.4 

229.3 

6.04 

477.0 

1% 

96 

16% 

20% 

75.3 

256.0 

6.13 

522.3 

106 

17% 

21 

83.1 

282.6 

6.27 

587.0 

1% 

116 

17% 

21X 

90.9 

309.3 

6.32 

636.3 

Least  radius  of  gyration  equals  D  X  .3636. 


486    STRENGTH   OF  LARIMER  STEEL  COLUMNS. 


TABLE  XXI.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.,  LARI- 
MER STEEL  COLUMNS. 

(  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  strain  per  square  inch,-|  17>100_57  j_for  lengths  over  90  radii. 

16"    COLUMNS. 
Made  of  15"  beams.      Weight  of  filler  bar  10.5  Ibs.  per  foot.      %"  rivets. 


"c  B 

ij 

+J   O 

o-d 
«£.£ 

o 

03 
V 

3 
|j 

I*v-, 

jts 

'   n  fl  M 

Id 

Length  of  column 

1     / 

^  « 

ad  So 
**  y  fl 

£S 

if 

in  feet. 

~y    : 

"82 

&  9.S 

.*fo£ 

0,2 

'42  O 

SM 

/    ? 

O>  C'43 

o  o 

s  ° 

.. 

£ 

£ 

02 

s 

"  V 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

32  and 
under. 

36 

40 

A 

B 

C 

60 

131.25 

38.4 

4.36 

232 

220 

208 

16" 

171^6" 

6" 

55 

121.25 

35.7 

4.10 

210 

198 

186 

16%6 

17Vie 

5M 

50 

111.25 

32.8 

4.18 

195 

184 

173 

16 

17 

52V32 

45 

101.25 

29.8 

4.28 

179 

169 

160 

1529/32 

16i«H6 

5%a 

42 

95.25 

28.1 

4.32 

169 

160 

151 

13"    COLUMNS. 

Made  of  12"  beams.     Weight  of  filler  bar  10.5  Ibs.  per  foot.     %"  rivets. 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

24  and 
under. 

28 

32 

A 

B 

C 

45 

101.25 

29.7 

3.40 

178 

170 

158 

13" 

141/16" 

53^" 

40 

91.25 

26.8 

3.50 

161 

156 

145 

12T^ 

131%  6 

514 

35 

81.25 

23.7 

3.42 

142 

136 

127 

12% 

131%6 

5%2 

31.5 

74.25 

21.6 

3.51 

130 

126 

118 

121946 

13M 

o 

11"   COLUMNS. 

Made  of  10"  beams.     Weight  of  filler  bar  10.5  Ibs.  per  foot.     %"  rivets. 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

22  and 
under. 

24 

28 

A 

B 

C 

30 

71.25 

20.8 

2.84 

123 

118 

108 

10%" 

H^/ie" 

41%e" 

25 

61.25 

17.8 

2.94 

107 

103 

94 

102%, 

11-K 

4-'^ 

10"    COLUMNS. 

Made  of  9"  beams.     Weight  of  filler  bar  10.5  Ibs.  per  foot.     ?<±"  rivets. 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

20  and 
under. 

24 

28 

A 

B 

C 

25 

61.25 

18.1 

2.57 

106 

97 

87 

9H" 

W%Q" 

4i%«" 

21 

53.25 

15.7 

2.66 

94 

86 

78 

QH 

lOH/16 

41^2 

STRENGTH   OF  LARIMER  STEEL    COLUMNS.    487 


TABLE  XXI.— SAFE  LOADS  IN  TONS  OF  2,000  LBS.,  LARI- 
MER STEEL  COLUMNS  (continued). 

(  12,000  Ibs.  for  lengths  of  90  radii  or  under. 
Allowed  strain  per  square  incM  I7fl00_67!  for  lengths  over  90  radii. 

r 

9"    COLUMNS. 

Made  of  8"  beams.       Weight  of  filler  bar  6  Ibs.  per  foot.     %"  rivets  in 
web.     %"  rivets  in  flange. 


-a 

-*e  o 

'o 

3 

h*1 

t  per  foo 
ngle  bea 

gg 
tl.'S 

nal  area 
mn. 

13  a 

Sg 

3  ^ 

Length  of  column 
in  feet. 

U'       X? 

)7 

ft        * 

•fl'S 

r£      3.-H 

o  P 

a& 

!    \                 ''    •' 

.£?*« 

*•£  o 

£°' 

1" 

S° 

"-W 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

18  and 
under. 

20 

24 

A 

B 

C 

22.75 

52.0 

15.4 

2.37 

91 

86 

77 

9    " 

9i5/io" 

4%a" 

20  .  25 

47.0 

13.9 

2.41 

83 

79 

71 

Slij/lG 

91  'tie 

4%a 

17.75 

42.0 

12.4 

2.47 

75 

72 

65 

8J/8 

9M 

4 

8"   COLUMNS. 

Made  of  1"  beams.     Weight  of  filler  bar  6  Ibs.  per  foot,     ^g"  rivets. 

Lbs. 

Lbs. 

Sq.ins. 

Inches 

16  and 
under. 

20 

24 

A 

B 

C 

20.0 

46.5 

13.6 

2.10 

81 

72 

63 

8    " 

8W 

3J^/r 

17.5 

41.5 

12.1 

2   12 

72 

64 

56 

715/io 

8/^C 

3^ 

15.0 

36.5 

10.6 

2.16 

64 

57 

50 

727/32 

8^ 

32V32 

7"    COLUMNS. 

Mad 

e  of  6"  beams.     Weight  of  filler  bar  6  Ibs.  per  foot.     %"  rivets. 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

14  and 
under. 

16 

20 

A 

B 

C 

14.75 

36 

10.5 

1.85 

62 

58 

50 

615Ae" 

7M" 

37/io'/ 

12.25 

31 

9.0 

1.88 

54 

51 

44 

613/16 

7%o 

311/32 

6"   COLUMNS. 

Made  of  5"  beams.     Weight  of  filler  bar  6  Ibs.  per  foot.     y%"  rivets  in 

web.     Yz'  rivets  in  flange. 

Lbs. 

Lbs. 

Sq.ins. 

Inches. 

12  and 
under. 

16 

20 

A 

B 

C 

12.25 

31 

9.0 

1.56 

53 

45 

37 

51H6// 

g3/// 

3  1/// 

9.75 

26 

7.5 

1.62 

45 

39 

32 

513/10 

60/16 

3 

488     STRENGTH  OF  NURICK  STEEL   COLUMNS. 


TABLE  XXII.--DIMENSIONS   AND    SAFE    LOADS    FOR 
NURICK  STEEL  COLUMNS. 

(JONES  <fe  LAUGHLINS,  PROPRIETORS.) 

P 


,  I 


17,100-57—  for  lengths  over  90    radii,   and    12,000  Ibs.  for  90  radii 
and  under. 


/\ 

\ 

'o   . 

"83 

•M 

QJ 

"1 

\ 

CD 

•*a'o 

4J     O 

o 

J 

•£ 

//~^~ 

•""•NX 

1 

!l 

8g 

T3  d 

N/^ 

/ 

y^ 

Ej 

03     . 

11 

<§^ 

o£!  oi 

}  A 

O 

5° 

*  1  & 

*g 
fl  " 

|"S 

w 

TJ^  c! 

XVM 

1 

r 

to'§ 

•f^ 

J3  3  -5 

0.3 

S  be 

•5  "Si 

O  "&„-» 

i 

vX  

-J) 

o>  2« 

N   "^ 

b£  C! 

•s-58 

'5  8<£ 

'-£  O 

'.§"0 

5  s 

•2!  § 

i 
i 

^ 

^/ 

as 

^ 

E* 

M 

s 

^^ 

QQ 

(<_ 
i 

—  c 

—  1 

Inches 

Lbs. 

Lbs. 

Sq.ins. 

Inches 

Tons. 

Tons. 

A 

B 

c 

15 

45 

183 

53.8 

6.58 

323 

323 

15%e 

21^ 

2215/32 

40 

163 

47.9 

6.50 

287 

287 

21-H 

225/16 

33 

135 

39.6 

6.45 

237 

237 

15%6 

21%2 

22%2 

12 

35 

143 

41.18 

5.41 

247 

247 

12%6 

30 
25 

123 
103 

35.38 
29.39 

5.43 
5.43 

212 
176 

212 
176 

ii546 

1615/16 

181Vl6 

1&A 

20% 

85 

24.12 

5.45 

145 

145 

12%e 

16% 

18%6 

10 

20 

83 

23.40 

4.59 

140 

140 

10% 

14^16 

16 

15 

63 

17.84 

4.53 

107 

107 

10% 

1315/^6 

151%  6 

9 

20 

83 

23.51 

4.09 

134 

141 

91  %o 

1234 

1423,^2 

15 

63 

17.60 

4.10 

100 

105 

9%« 

12^8 

1417,^2 

13^ 

53 

15.55 

4.11 

89 

93 

9^8 

12% 

14% 

8 

1614 

68 

19.29 

3.57 

102 

116 

glS/32 

Il54e 

13%2 

13*4 

58 

16.35 

3.63 

87 

98 

8%  6 

H%e 

11M 

48 

13.40 

3.65 

72 

80 

8^ 

11% 

13>| 

7 

62 

17.20 

3.21 

85 

103 

71  %2 

92%2 

121/82 

12J4 

52 

14.26 

3.23 

70 

85 

7fl6 

9-M 

1H5/16 

9*4 

42 

11.39 

3.25 

56 

68 

7^ 

91  -VI  6 

Hl%6 

18ft. 

24  ft. 

and 

under 

6 

10% 

44 

12.48 

2.76 

69 

75 

go/ 

gsr 

102V 

8 

34 

9.52 

2.85 

54 

57 

623-00 

8%o 

100/16 

5 

9 

38 

10.73 

2.36 

54 

63 

51^2 

6% 

28 

7.79 

2.42 

40 

46 

52%2 

6i%e 

9%2 

'  rivets  in  last  four  sections,  %"  rivets  in  all  others. 


STRENGTH  OF  GRAY  STEEL  COLUMNS.        489 


TABLE  XXIII.— SAFE  LOADS  FOR  GRAY  COLUMNS. 

Computed  by  the  formula  TF=  17,100 -57-. 
12"    SQUARE    COLUMNS. 


I 

Dimensions 
of  angles. 

Properties. 

Safe  loads  in  thousands  of 
pounds. 

Qi 

Column  lengths. 

i 

Length 
of  legs. 

Thick. 

Area, 
square 
ins. 

7. 

r. 

12ft. 

16ft. 

20ft. 

30ft. 

8 

2^X2^ 

5/16 

11.76 

172 

3.8 

175 

165 

160 

140 

8 

2^X2^ 

3/8 

13.84 

202 

3.8 

205 

195 

185 

160 

8 

3     X2^ 

5/16 

12.96 

198 

3.9 

195 

185 

175 

150 

8 

3     X2y2 

3/8 

15.36 

234 

3.9 

230 

220 

205 

180 

8 

3     X3 

5/16 

14.24 

206 

3.8 

210 

200 

190 

165 

8 

3     X3 

3/8 

16.88 

241 

3.8 

250 

240 

225 

195 

8 

3     X3 

7/16 

19.52 

276 

3.8 

290 

275 

260 

225 

8 

3     X3y2 

5/16 

15.44 

209 

3.7 

230 

215 

205 

180 

a 

8 

3     X31A 

3/8 

18.40 

245 

3.7 

270 

260 

245 

210 

8 

3     X3^ 

7/16 

21.20 

282 

3.7 

315 

300 

280 

245 

8 

3     X3*^ 

1/2 

24.00 

318 

3.7 

355 

340 

320 

275 

8 

3     X4 

5/16 

16.72 

213 

3.5 

245 

230 

220 

185 

8 

3     X4 

3/8 

19.84 

249 

3.5 

290 

275 

260 

220 

8 

3     X4 

7/16 

22.96 

285 

3.5 

335 

320 

300 

255 

8 

3     X4 

1/2 

26.00 

321 

3.5 

380 

360 

340 

290 

18 

3     X4 

9/16 

28.96 

357 

3.5 

425 

405 

380 

325 

f8 

3     X5 

3/8 

22.88 

255 

3.3 

335 

315 

295 

250 

8 

3     X5 

7/16 

26.48 

291 

3  3 

385 

365 

340 

290 

&18 

3     X5 

1/2 

30.00 

327 

3.3 

435 

410 

385 

325 

Is 

3     X5 

9/16 

33.44 

363 

3.3 

485 

460 

430 

365 

14"    SQUARE    COLUMNS. 

8 

2^X2^ 

5/16 

11.76 

238 

4.5 

180 

170 

165 

145 

8 

2^X2^ 

3/8 

13.84 

280 

4.5 

210 

200 

195 

170 

8 

3     X2^ 

5/16 

12.96 

274 

4.6 

195 

190 

180 

160 

. 

8 

3     X2^ 

3/8 

15.36 

325 

4.6 

235 

225 

215 

190 

!8 

3     X3 

5/16 

14.24 

286 

4.5 

215 

205 

200 

180 

a\  8 

3     X3 

3/8 

16.88 

336 

4.5 

255 

245 

235 

210 

18 

3     X3 

7/16 

19.52 

386 

4.5 

295 

285 

275 

245 

8 

3     X3?^ 

5/16 

15.44 

293 

4.3 

235 

225 

215 

190 

8 

3     X3^ 

3/8 

18.40 

340 

4.3 

280 

265 

255 

225 

8 

3     X3^ 

7/16 

21.20 

386 

4.3 

320 

305 

295 

260 

18 

3     X3^ 

1/2 

24.00 

433 

4.3 

365 

350 

330 

295 

f8 

3     X3H 

9/16 

26.72 

479 

4.3 

405 

385 

370 

330 

18 

3     XS1^ 

5/8 

29  .  36 

526 

4.3 

445 

425 

405 

360 

6-18 

3     X3^ 

11/16 

32.00 

572 

4.3 

485 

465 

445 

395 

8 

3     X3^ 

3/4 

34.48 

619 

4.3 

520 

500 

480 

425 

18 

3     X3H 

13/16 

36.96 

666 

4.3 

560 

535 

515 

455 

8 

3     X4 

5/16 

16.72 

300 

4.2 

250 

240 

230 

205 

8 

3     X4 

3/8 

19.84 

348 

4.2 

300 

285 

275 

240 

Cl 

8 

3     X4 

7/16 

22.96 

396 

4.2 

345 

330 

315 

280 

8 

3     X4 

1/2 

26.00 

444 

4.2 

390 

375 

360 

315 

:8 

3     X4 

9/16 

28.96 

491 

4.2 

435 

420 

400 

350 

8 

3     X4 

5/8 

31.84 

539 

4.2 

480 

460 

440 

385 

b 

0 

3     X4 

11/16 

34.72 

587 

4.2 

525 

500 

480 

420 

is 

3     X4 

3/4 

37.52 

635 

4.2 

565 

540 

520 

455 

18 

3     X4 

13/16 

40.24 

683 

4.2 

605 

580 

555 

490 

a,  tie-plates  8  inches  wide,  2'  6"  C.  to  C. 

b,  tie-plates  9  inches  wide,  2'  6"  C.  to  C. 


490         STRENGTH  OF  GRAY  STEEL   COLUMNS. 


SAFE  LOADS  FOR  GRAY  COLUMNS. 
14"  SQUARE  COLUMNS  (continued). 


Dimensions 
of  angles. 

Properties. 

Safe  loads. 

s 

"c* 

*o 

Column  lengths  in  thou 

d 

sands  of  pounds. 

*K 

Length 
of  legs. 

Thick. 

Area, 
square 
ins. 

7. 

r. 

12ft. 

16ft. 

20ft. 

30ft. 

oooooo 
e 

3     X5 
3     X5 
3     X5 

3/8 
7/16 

1/2 

22.88 
26.48 
30.00 

365 

414 
463 

4.0 
4.0 
4.0 

345 
395 
450 

325 

380 
430 

310 
360 
410 

370 
315 
355 

f8 

3     X5 

9/16 

33.44 

512 

4.0 

500 

480 

455 

400 

8 

3     X5 

5/8 

36.88 

560 

4.0 

555 

530 

505 

440 

6-J8 

3     X5 

11/16 

40.24 

609 

4.0 

605 

575 

550 

480 

]8 

3     X5 

3/4 

43.52 

658 

4.0 

655 

625 

595 

520 

1.8 

3     X5 

13/16 

46.72 

706 

4.0 

700 

670 

635 

560 

f8 

3^X3 

5/16 

15.44 

320 

4.5 

235 

225 

215 

190 

fl    8 

3^X3 

3/8 

18.40 

373 

4.5 

280 

270 

255 

230 

a]8 

3HX3 

7/16 

21.20 

425 

4.5 

320 

310 

295 

265 

8 

3HX3 

1/2 

24.00 

477 

4.5 

365 

350 

335 

300 

:8 

3^X3 

9/16 

26.72 

529 

4.5 

405 

390 

375 

335 

h    8 

3HX3 

5/8 

29.36 

581 

4.5 

445 

430 

410 

365 

6    8 

3^X3 

11/16 

32.00 

633 

4.5 

485 

470 

450 

400 

.8 

3^X3 

3/4 

34.48 

685 

4.5 

525 

505 

485 

430 

(8 

3^X3^ 

3/8 

19.84 

389 

4.4 

300 

290 

275 

245 

a-{8 

3HX3^ 

7/16 

22.96 

441 

4.4 

350 

335 

320 

285 

Is 

3^X3^ 

1/2 

26.00 

493 

4.4 

395 

380 

360 

320 

f8 

31^X3^ 

9/16 

28.96 

545 

4.4 

440 

420 

405 

360 

8 

3^X3^ 

5/8 

31.92 

597 

4.4 

485 

465 

445 

395 

6-|8 

3^X3^ 

11/16 

34.72 

649 

4.4 

525 

505 

485 

430 

8 

3^X3^ 

3/4 

37.52 

701 

4.4 

570 

545 

525 

465 

u 

^AX&A 

13/16 

40.24 

753 

4.4 

610 

585 

560 

500 

(8 

3^X5 

3/8 

24.40 

407 

4.0 

365 

350 

330 

290 

o«8 

3MX5 

7/16 

28.24 

461 

4.0 

425 

405 

385 

340 

\s 

3^X5 

1/2 

32.00 

515 

4.0 

480 

460 

435 

385 

rs 

3^X5 

9/16 

35.76 

570 

4.0 

535 

510 

490 

425 

8 

3^X5 

5/8 

39.36 

624 

4.0 

590 

565 

535 

470 

7,J8 

3^X5 

11/16 

42.96 

678 

4.0 

645 

615 

585 

515 

Ms 

3HX5 

3/4 

46.48 

732 

4.0 

700 

665 

635 

555 

8 

3^X5 

13/16 

50.00 

786 

4.0 

750 

715 

680 

600 

18 

3^X5 

7/8 

53.36 

840 

4.0 

800 

765 

730 

640 

,J8 

3^X6 

3/8 

27.36 

410 

3.8 

405 

385 

370 

320 

°18 

3HX6 

7/16 

31.76 

468 

3.8 

475 

450 

430 

370 

rs 

3^X6 

1/2 

36.00 

526 

3.8 

535 

510 

485 

420 

h\s 

3^X6 

9/16 

40.24 

584 

3.8 

600 

570 

540 

470 

b]s 

3^X6 

5/8 

44.40 

641 

3.8 

660 

630 

600 

520 

8 

3^X6 

11/16 

48.48 

698 

3.8 

725 

690 

655 

565 

a,  tie-plates  8  inches  wide,  2'  6"  C.  to  C. 
6,  tie-plates  9  inches  wide,  2'  6"  C.  to  C. 


STRENGTH  OF  GRAY  STEEL   COLUMNS.        491 
SAFE  LOADS  FOR  GRAY  COLUMNS. 

16"    SQUARE    COLUMNS. 
Tie-plates  9  inches  wide,  2'  6"   C.  to  C. 


Safe  loads  in  thousands  of 

pounds. 

Dimensions  of 

g 

angles. 

Properties. 

0 

OJ 

'a 

Column  lengths. 

o 

6 

Area, 

Length 
of  legs. 

Thick. 

square 
ins. 

I. 

r. 

12  ft. 

16ft. 

20ft. 

30ft. 

8 

WX2K 

5/16 

11.76 

320 

5.2 

180 

175 

170 

155 

8 

2^2  x2]^>, 

3/8 

13.84 

374 

5.2 

215 

205 

200 

180 

8 

2]/2  X2j/£ 

7/16 

16.00 

427 

5.2 

245 

240 

230 

210 

8 

2^2X2^2 

1/2 

18.00 

481 

5.2 

280 

270 

260 

235 

8 

3     X3 

5/16 

14.24 

380 

5.1 

220 

210 

205 

185 

8 

3     X3 

3/8 

16.88 

443 

5.1 

260 

250 

240 

220 

8 

3     X3 

7/16 

19.52 

507 

5  1 

300 

290 

280 

255 

8 

3     X3 

1/2 

22.00 

570 

5.1 

340 

325 

315 

285 

8 

3     X3 

9/16 

24.48 

633 

5.1 

380 

365 

350 

320 

8 

3     X3 

5/8 

26.88 

696 

5.1 

415 

400 

385 

350 

8 

3^X3^ 

3/8 

19.84 

517 

5.0 

305 

295 

285 

255 

8 

3^X3^ 

7/16 

22.96 

588 

5.0 

355 

340 

330 

300 

8 

1/2 

26.00 

660 

5.0 

400 

385 

370 

335 

8 

31^  x  31^ 

9/16 

28.96 

731 

5.0 

445 

430 

415 

375 

8 

3/^2  X  3^ 

5/8 

31.92 

802 

5.0 

490 

475 

455 

415 

8 

31^  x  31^ 

11/16 

34.72 

873 

5.0 

535 

515 

500 

450 

8 

3HX3H 

3/4 

37.52 

944 

5.0 

580 

560 

540 

485 

8 

4     X4 

3/8 

22.88 

588 

5.0 

350 

340 

325 

300 

8 

4     X4 

7/16 

26.48 

669 

5.0 

410 

395 

380 

345 

8 

4     X4 

1/2 

30.00 

750 

5.0 

460 

445 

430 

390 

8 

4     X4 

9/16 

33.44 

831 

5.0 

515 

500 

480 

435 

8 

4     X4 

5/8 

36.88 

912 

5.0 

570 

550 

530 

480 

8 

4     X4 

11/16 

40.24 

994 

5.0 

620 

600 

575 

520 

8 

4     X4 

3/4 

43.52 

1075 

5.0 

670 

650 

625 

565 

8 

4     X4 

13/16 

46.72 

1156 

5.0 

720 

695 

670 

605 

8 

4     X6 

7/16 

33.44 

730 

4.6 

510 

490 

470 

420 

8 

4     X6 

1/2 

38.00 

810 

4.6 

580 

560 

535 

480 

8 

4     X6 

9/16 

42.48 

891 

4.6 

650 

625 

600 

535 

8 

4     X6 

5/8 

46.88 

972 

4.6 

715 

690 

660 

590 

8 

4     X6 

11/16 

51.28 

1053 

4.6 

785 

755 

720 

645 

8 

4     X6 

3/4 

55  .  52 

1134 

4.6 

850 

815 

780 

700 

8 

4     X6 

13/16 

59.76 

1215 

4.6 

915 

880 

840 

755 

8 

4     X6 

7/8 

63.92 

1296 

4.6 

975 

940 

900 

805 

492       STRENGTH  OF  GRAY  STEEL  COLUMNS. 


SAFE  LOADS  FOR  GRAY  COLUMNS. 

16"   WALL   COLUMNS. 
Tie-plates  9  inches  wide,  2'  6"  C.  to  C. 


Safe  loads  in  thousands  of 

pounds. 

Dimensions  of 

M 

o 

angles. 

Properties. 

0 

o 

a   { 
*o 

Column  lengths. 

4 

Length 
of  legs. 

Thick- 
ness. 

Area, 
square 
Ins. 

I. 

r. 

12ft. 

16ft. 

20ft. 

30ft. 

6 

2HX2^ 

5/16 

8.82 

Ill 

3.6 

130 

120 

115 

100 

6 

2Y2X2y2 

3/8 

10.38 

120 

3.6 

150 

145 

135 

115 

6 

2y2X2Y2 

7/16 

12.00 

139 

3.6 

175 

165 

160 

135 

6 

2%X2y2 

1/2 

13.50 

167 

3.6 

200 

185 

180 

150 

6 

3     X3 

5/16 

10.68 

131 

3.5 

155 

150 

140 

120 

6 

3     X3 

3/8 

12.66 

157 

3.5 

185 

175 

165 

140 

6 

3     X3 

7/16 

14.64 

179 

3.5 

215 

205 

190 

165 

6 

3     X3 

1/2 

16.50 

200 

3.5 

240 

230 

215 

185 

6 

3     X3 

9/16 

18.36 

222 

3.5 

270 

255 

240 

205 

6 

3     X3 

5/8 

20.16 

244 

3.5 

295 

280 

265 

225 

6 

VAX&A 

3/8 

14.88 

188 

3.5 

220 

205 

195 

165 

6 

3l/2X3l/2 

7/16 

17.22 

215 

3.5 

255 

240 

225 

190 

6 

3}AX31A 

1/2 

19.50 

241 

3.5 

285 

270 

255 

220 

6 

3^X3^ 

9/16 

21.72 

268 

3.5 

320 

300 

285 

245 

6 

3^X3^ 

5/8 

23.94 

294 

3.5 

350 

335 

315 

270 

6 

3J^  X3^ 

11/16 

26.04 

321 

3.5 

385 

365 

340 

290 

6 

3^X3^ 

3/4 

28.14 

347 

3.5 

415 

395 

370 

315 

6 

4     X4 

3/8 

17.16 

221 

3.5 

250 

240 

225 

190 

6 

4     X4 

7/16 

19.86 

252 

3.5 

290 

275 

260 

225 

6 

4     X4 

1/2 

22.50 

283 

3.5 

330 

315 

295 

250 

6 

4     X4 

9/16 

25.08 

314 

3.5 

370 

350 

330 

280 

6 

4     X4 

5/8 

27.66 

345 

3.5 

405 

385 

365 

310 

6 

4     X4 

11/16 

30.18 

376 

3.5 

445 

420 

400 

340 

6 

4     X4 

3/4 

32.64 

407 

3.5 

480 

455 

430 

365 

6 

4     X4 

13/16 

35.04 

439 

3.5 

515 

490 

460 

395 

6 

4     X6 

7/16 

25.08 

279 

3.3 

365 

345 

325 

270 

6 

4     X6 

1/2 

28.50 

311 

3.3 

415 

390 

370 

310 

6 

4     X6 

9/16 

31.86 

343 

3.3 

465 

440 

410 

345 

6 

4     X6 

5/8 

35.16 

375 

3.3 

510 

485 

455 

380 

6 

4     X6 

11/16 

38.46 

407 

3.3 

560 

530 

500 

415 

6 

4     X6 

3/4 

41.64 

440 

3.3 

605 

570 

540 

450 

6 

4     X6 

13/16 

44.82 

472 

3.3 

655 

615 

580 

485 

6 

4     X6 

7/8 

47.94 

504 

3.3 

700 

660 

620 

520 

i 

STRENGTH  OF  GRAY  STEEL  COLUMNS.        493 


SAFE  LOADS  FOR  GRAY  COLUMNS. 

I0i"    CORNER    COLUMNS. 


)ieces. 

Dimensions  of 
angles. 

Properties. 

Safe  loads  in  thousands 
of  pounds. 

o 

Length 

Thick- 

Area, 

r 

Column  lengths. 

o 

of  legs. 

ness. 

i  . 

1*. 

__?_ 

inches. 

12ft. 

16ft. 

20ft. 

30ft. 

'4 

3  2X3 

5/16 

3/8 

[    9.83 

118 

3.5 

145 

135 

130 

110 

Cl 

4 

1 

3^X3 
3     X3 

3/8 
3/8 

[ll.31 

139 

3.5 

165 

155 

150 

125 

4 
1 

3^X3 
3     X3 

7/16 

1/2 

[l3.35 

145 

3.5 

195 

185 

175 

150 

4 
1 

3^X3 
3     X3 

1/2 
1/2 

[l4.75 

159 

3.5 

215 

205 

195 

165 

(4 
1 

3^X3 
3     X3 

9/16 

5/8 

[l6.72 

172 

3.5 

245 

230 

220 

185 

Jt 

3HX3 
3     X3 

5/8 
5/8 

J18.04 

186 

3.5 

265 

250 

235 

200 

1  4 
1 

3  2X3 

11/16 

5/8 

[l9.36 

199 

3.5 

285 

270 

255 

215 

Li 

3  2X3 

3/4 
5/8 

[20.60 

213 

3.5 

305 

285 

270 

230 

I1 

3  2X3  2 

3/8 
3/8 

[l2.  03 

139 

3.4 

175 

165 

155 

130 

HI 

3  2X3  2 

7/16 

1/2 

[14.23 

158 

3.4 

205 

195 

185 

155 

I  4 

U 

3  2X3  2 

1/2 
1/2 

[l5.75 

177 

3.4 

230 

215 

205 

175 

4 

1 

3^X3^ 
3     X3 

9/16 

5/8 

[17.84 

196 

3.4 

260 

245 

230 

195 

4 
1 

3  2X3/2 

5/8 
5/8 

[l9.32 

215 

3.4 

280 

265 

250 

210 

6 

4 

3%  X  3M 
3     X3 

11/16 
5/8 

[20.72 

234 

3.4 

305 

285 

270 

230 

4 
1 

3  2X3  2 

3/4 

5/8 

[22.12 

253 

3.4 

325 

305 

290 

245 

1 

3  2X32 

13/16 

5/8 

[23.48 

272 

3.4 

345 

325 

305 

260 

f4 
1 

3^X4 
3     X3 

3/8 
3/8 

[l2.79 

141 

3.3 

185 

175 

165 

140 

4 

7/16 

a1i 

3     X3 

1/2 

j-  15.11 

160 

3.3 

220 

205 

195 

165 

14 
U 

3KX4 
3  "X3 

1/2 
1/2 

[l6.75 

180 

3.3 

245 

230 

215 

180 

f4 
1 

3^X4 
3     X3 

9/16 

5/8 

Ug.  96 

199 

3.3 

275 

260 

245 

205 

4 
1 

3^X4 
3     X3 

5/8 
5/8 

[20.56 

219 

3.3 

300 

280 

265 

220 

Hi 

3^X4 
3     X3 

11/16 

5/8 

[22.08 

238 

3.3 

320 

305 

285 

240 

4 

1 

3^X4 
3     X3 

3/4 

5/8 

[23.60 

258 

3.3 

345 

325 

305 

255 

.1 

3^X4 
3     X3 

13/16 

5/8 

[25.08 

277 

3.3 

365 

345 

325 

270 

f4 

3^X5 
3     X3 

3/8 
3/8 

[14.31 

145 

3.2 

205 

195 

180 

150 

•1 

3^X5 
3     X3 

7/16 
3/8 

[l6.23 

165 

3.2 

235 

220 

205 

170 

4 
U 

3)3X5 
3     X3 

1/2 
1/2 

[l8.75 

185 

3.2 

270 

255 

240 

200 

a,  tie-plates  8  inches  wide,  2'  6"  C.  to  C 

0,  tie-plates  9  inches  wide,  2'  6"  C.  to  C. 

494        COLUMN  SHAPES  IN  TALL  BUILDINGS. 


KINDS  OF  COLUMNS  USED  IN  THE  PRINCIPAL  OFFICE 
BUILDINGS  OF  CHICAGO  AND  NEW  YORK. 

CHICAGO. 


Architect. 

Building. 

No.  of 
stories. 

Kind 
of  column. 

W.  L.  B.  Jenney 

Manhattan 

16 

Cast 

** 

"The  Fair" 

9 

Z-bar 

•• 

Y.  M.  C.  A. 

13 

Z-bar 

« 

Isabella 

10 

Z-bar 

Jenney  &  Mundie 

New  York  Life 

12 

Steel;  plates  and 

angles 

** 

Fort  Dearborn 

12 

Channels      and 

plates 

Holabird  &  Roche 

Tacoma 

13 

Cast 

•• 

Pontiac 

14 

Z-bar 

«« 

Venetian 

13 

Z-bar 

•• 

Monadnock  Block,  new 

17 

Z-bar 

part 

•t 

Old  Colony 

17 

Z-bar  and 

Phcenix 

«« 

Champlain 

15 

Z-bar 

" 

Marquette 

16 

Z-bar 

Adler  &  Sullivan 

Auditorium 

10  &  17 

Cast 

Schiller  Theatre 

13  &  17 

Z-bar  and 

Phcenix 

M 

Stock  Exchange 

13 

Z-bar 

Burnham  &  Root 

Rookery 

12 

Cast 

" 

Woman's  Temple 

13 

Z-bar 

** 

Masonic  Temple 

20 

Plates  and  angles 

M 

Ashland 

16 

Z-bar 

D.  H.  Burnham  &  Co 

Reliance 

15 

Gray 

Fisher 

18 

Gray 

11 

Great  Northern  Theatre 

16 

Gray  _ 

Henry  Ives  Cobb 

Title  &  Trust 

16 

Phcenix 

O  wings 

14 

Cast 

Bruce  Price 

American  Surety 

21 

Angles      and 

plates  —  Z-bar 

Kimball  &  Thompson 

Manhattan  Life  Ins. 

18 

Cast,    5    stories: 

plates   and   an- 

gles above 

Geo.  B.  Post 

Meyer,  Jonasson 

14 

Plates    and    an- 

M 

Havemeyer  (Cortland 

15 

gles 
Plates     and   an- 

St.) 

gles 

(( 

St.  Paul  Building 

26 

Plates    and    an- 

gles 

M 

New  York  World 

22 

Phcenix 

«t 

Union  Trust 

10 

Phoenix 

Harding  &  Gooch 

Postal  Telegraph 

14 

Cast 

«* 

Dunn  Building 

15 

Phcenix 

*• 

Park  Row  Building 

29 

Plates    and    an- 

gles 

•• 

Commercial  Cable 

20 

Phcenix 

R.  H.  Robertson 

American  Tract  Society 

20 

Riveted 

H.  J.  Hardenberg 

Hotel  Waldorf 

12 

Cast 

COMPARISON   OF  FORMULAS.  495 

FORMULAS   FOR   STEEL  COLUMNS   AND   STRUTS, 

GIVEN   IN  VARIOUS  BUILDING  LAWS,   AND   RECOMMENDED     BY 
LEADING  ENGINEERS. 

p=  working  stress  in  pounds  per  square  inch  of  cross-section. 
1=  length  in  inches.     r=  least  radius  of  gyration. 
Chicago  Building  Law: 

For  columns  more  than  60  radii  in  length,  p=  17,000  —  — . 

For  columns  less  than  60  radii  in  length,  p=  13,500  Ibs. 
Greater  New  York  Law  (1899) : 

p=  15,200  -58-. 

Boston  Law: 

p=  12,000  Ibs.  reduced  by  approved  modern  formulae. 

Buffalo  Building  Law  (1896) : 

For  columns  more  than  90  radii  in  length,  p=  17,100-  57—. 

For  columns  less  than  90  radii   in  length,  p=  12,000  Ibs. 
Denver  Building  Ordinance: 
Same  as   Buffalo. 
Carnegie  Steel  Co.;  Jones  &  Laughlins: 

p=  17,100  —  57—  for  lengths  over  90  radii. 
p=  12,000  for  lengths  of  90  radii  and  under. 
Passaic  Rolling  Mill  Co.     Geo.  H.  Blakeley,  C.E. 

rj  ,  ,  ,         (  P=  12,000  for  lengths  up  to  50  radii. 

Z/-bar  and  box  )  , 

columns.       |  p=  i5;QOO-57-  for  lengths  over  50  radii. 

(  12,000  for  lengths  up  to  30  radii. 
Steel  Struts.      •{  I 

I  13,500-50-  for  lengths  over  30  radii. 

Charles  Evan  Fowler,  C.E.     General  specifications  for  steel 
roofs  and  buildings: 

For  struts  with  flat  and  fixed  ends,  p=12,500-41f-. 


496  COMPARISON   OF   FORMULAS. 

Theodore  Cooper,  M.  Am.  Soc.  C.  E.     General  specifications  for 
iron  and  steel  railroad  bridges  and  viaducts : 

p=   8,000-30-  for  live  load  stresses. 
For  chords.       ^ 

p=  16.000  —  60—  for  dead  load  stresses. 
r 


For  posts. 


p=   7>000  — 40-  for  live  load  stresses. 
r 

p=  14,000  —  80—   for  dead  load  stresses. 
£>=  10,000  —  60—  for  wind  load  stresses. 


Formula  proposed  by  Mr.  Thomas  H.  Johnson,  M.  Am.  Soc. 
C.  E. : 

5    Hinged  ends,  p=  13,125 -55-, 
For  mild  steel.  J 

Flat  ends,  p=  13, 125  -45-^. 

Mr.  Joseph  K.  Freitag,  in  commenting  on  the  allowed  working 
stress  for  steel  columns  in  buildings  says : 

"The  writer  believes  that  with  the  use  of  a  mild  steel  of  an 
ultimate  strength  of  from  65,000  to  68,000  Ibs.  per  square  inch, 
15,000  or  16,000  Ibs.  per.  square  inch  may  safely  be  used  for  all 
concentric  dead,  live,  and  wind  loads  combined  (with  an  addi- 
tional allowance  for  eccentric  loading),  provided  that  the  wind 
pressure  is  taken  at  not  less  than  30  Ibs.  per  square  foot  and  that 
the  live  loads  on  the  floors  are  assumed  as  required  by  municipal 
building  laws." 


PRINCIPLES  OF  THE  STRENGTH  OF  BEAMS.  497 


CHAPTER  XV. 

GENERAL  PRINCIPLES  OP  THE  STRENGTH  OP 
BEAMS,  AND  STRENGTH  OP  STEEL  BEAMS. 

STEEL-BEAM    BOX    GIRDERS— FRAMING    AND     CON- 
NECTING OF  STEEL  BEAMS. 

BY  the  term  "beam"  is  meant  any  piece  of  material  which 
supports  a  load  whose  tendency  is  to  break  the  piece  across,  or  at 
right  angles  to,  the  fibres,  and  which  also  causes  the  piece  to  bend 
before  breaking.  A  simple  beam  is  one  which  rests  upon  sup- 
ports at  both  ends.  When  a  beam  is  supported  at  its  centre  it 
is  a  cantilever  beam,  or  if  a  part  of  a  beam  projects  from  a  wall 
or  beyond  a  support,  the  projecting  part  is  called  a  cantilever. 
In  a  simple  beam  the  lower  part  is  in  tension  and  the  upper 
part  in  compression;  in  a  cantilever  beam  the  reverse  is  the 
case. 

When  a  transverse  load  of  any  kind  is  applied  to  any  beam  it 
will  cause  the  beam  to  bend  by  a  certain  amount,  and  as  it  is  im- 
possible to  bend  a  piece  of  any  material  without  stretching  the 
fibres  on  the  outer  side,  and  compressing  the  fibres  on  the  inner 
side,  the  bending  of  the  beam  will  produce  tension  in  the  stretched 
side  and  compression  of  the  fibres  of  the  opposite  side.  Be- 
tween the  stretched  and  compressed  fibres  is  a  neutral  surface 
wrhich  is  unchanged  in  length.  From  experiments  it  has  been 
found  that  the  amount  of  elongation  or  shortening  of  any  fibre 
?s  directly  proportional  to  its  distance  from  the  neutral  surface; 
hence,  if  the  elastic  limit  be  not  surpassed,  the  stresses  are  also 
proportional  to  their  distance  from  the  neutral  surface.  The 
line  where  the  neutral  surface  would  cut  through  the  side  or 
cross-section  of  the  beam  is  called  the  neutral  axis.  Within  the 
safe  strength  of  the  material  the  neutral  axis  passes  through 
the  centre  of  gravity  of  the  cross-section  of  the  beam  for  all 
materials. 

To  determine  the  strength  of  any  beam  to  resist  the  effects  of 
any  load,  or  series  of  loads,  we  must  determine  two  things :  first, 


498  PRINCIPLES   OF  THE   STRENGTH   OF  BEAMS. 

the  destructive  force  tending  to  bend  and  break  the  beam,  which 
is  called  the  "Pending-moment"]  and,  second,  the  combined  re- 
sistance of  all  the  fibres  of  the  beam  to  being  broken,  which  is 
called  the  "moment  of  resistance." 

The  methods  for  finding  the  bending-moments  for  any  load,  or 
series  of  loads,  have  been  given  in  Chap.  IX.  The  moment  of 
resistance  is  equal  to  the  "moment  of  resistance  area"  or  " sec- 
tion modulus,"  multiplied  by  the  strength  of  the  material. 
Formulas  for  finding  the  section  modulus  of  common  shapes  are 
given  in  Chap.  X.,  and  the  value,  R,  for  the  section  modulus  of 
merchant  shapes  of  structural  steel  is  given  in  the  tables,  pages 
296  to  315. 

The  "coefficient  of  strength"  usually  given  in  tables  of  steel 
beams  is  the  maximum  distributed  load  that  a  beam  of  one  foot 
span  would  support  without  producing  a  fibre  stress  exceeding 
the  safe  limit,  generally  16,000  Ibs.  As  the  strength  of  a  beam  is 
inversely  as  its  span,  the  safe  load  for  any  span  may  be  obtained 
by  dividing  the  coefficient  by  the  span  in  feet. 

Now,  that  a  beam  shall  just  be  able  to  resist  the  load,  and  not 
break,  we  must  have  a  condition  where  the  bending-moment  in 
the  beam  is  equal  to  the  section  modulus  multiplied  by  the 
strength  of  the  material.  That  the  beam  may  be  abundantly 
safe  to  resist  the  given  load,  this  product  must  be  several  times 
as  great  as  the  bending-moment;  and  the  ratio  in  which  this 
product  exceeds  the  bending-moment,  or  in  which  the  breaking- 
load  exceeds  the  safe  load,  is  known  as  the  "factor  of  safety." 

By  "the  strength  of  the  material"  is  meant  a  certain  constant 
quantity,  which  is  determined  by  experiment,  and  which  is  known 
as  the  "Modulus  of  Rupture."  Of  course  this  value  is  different 
for  each  different  material.  The  following  table  contains  the 
values  of  this  constant  divided  by  the  factor  of  safety,  for  most 
of  the  materials  used  in  building  construction.  The  section 
modulus  multiplied  by  these  values  will  give  the  safe  resisting- 
power  of  the  beam. 

The  term  "Modulus  of  Rupture"  is  now  seldom  seen  in  the 
various  handbooks  published  by  the  rolling-mill  companies,  the 
term  "fibre  stress"  being  used  instead.  The  two  terms,  how- 
ever, are  synonymous. 

The  following  values  of  S  for  wrought  iron  and  steel  are  one- 
fourth  that  for  the  breaking-loads ;  for  cast  iron,  one-sixth ;  for 
wood,  one-third;  and  for  stone,  one-sixth.  The  constrnts  for 
wood  are  based  upon  tests  made  at  the  Massachusetts  Institute  of 


PRINCIPLES  OF  THE  STRENGTH  OF  BEAMS.  499 


MODULUS  OF  RUPTURE  (S)  FOR  SAFE  STRENGTH.* 


Material. 

Value  of 
S, 
in  Ibs. 

Material. 

Value  of 

.  5. 
in  Ibs. 

Cast  iron 

5,544 

American  White  pine 

1,080 

\Vrought  iron 

12,000 

American  yellow  pine 

1,800 

Steel   . 

16,000 

American  spruce.  .         ... 

1,260 

Oregon  pine 

1,620 

Amer  can  ash  
Amer  can  red  beech.  .  .  . 
Amer  can  yellow  birch  . 

2,000 
1,800 
1,620 

Bluestone    flagging  (Hud- 
son River)  

450 

1  000 

Cement    1    3*6 

370 

Amer  can  elm  

1,400 
1  080 

Granite,  average  
Limestone          .      

300 
250 

Hemlock 

990 

Marble  

300 

1  350 

Sandstone  »  •  •  

150to20:) 

Slate  

900 

*  For  a  comparison  of  values  given  in  different  Building  Laws  see  last 
pages  of  Chapter  XVI. 

Technology  upon  full-size  timbers  of  the  usual  quality  found  in 
buildings.  The  figures  given  in  the  above  table  are  believed  to 
be  amply  safe  for  beams  in  floors  of  dwellings,  public  halls,  roofs, 
etc. ;  but  for  floors  in  mills,  and  warehouse  floors,  the  author 
recommends  that  not  more  than  two-thirds  of  the  above  values  be 
used.  The  safe  loads  for  the  steel  sections  given  in  the  following 
tables  are  all  computed  on  the  value  of  16,000  Ibs  for  S.  For 
angles,  tees,  and  deck-beams  it  was  customary,  previous  to  1898, 
to  use  a  somewhat  lower  value  for  S,  about  12,000  Ibs.,  on  account 
of  the  section  not  being  symmetrical.  All  but  one  of  the  steel 
companies  now  use  16,000  Ibs.  for  all  shapes,  and  the  author  has 
therefore  revised  the  tables  in  this  book  to  correspond ;  but  these 
full  loads  should  be  used  with  caution,  and  reduced  under  the 
conditions  noted.  For  riveted  steel  girders  the  value  of  S  is 
generally  taken  at  13,000  Ibs. 

There  are  certain  cases  of  beams  which  most  frequently  occur 
in  building  construction,  for  which  formulas  can  be  given  by 
which  the  safe  loads  of  the  beams  may  be  determined  directly; 
but  it  often  happens  that  we  may  have  either  a  regularly  shaped 
beam  irregularly  loaded,  or  a  beam  of  irregular  shape  but  with 
a  common  method  of  loading.  For  such  cases  it  is  impossible 
to  give  tables  for  strength,  as  each  case  must  be  computed  by 
determining  either  the  section  modulus  required  to  resist  the 
bending-moment,  or  the  greatest  bendirig-moment  that  may  be 
allowed  for  a  given  value  of  R  (section  modulus). 

The  general  formula  for  any  beam  under  any  system. of  loading 
is  as  follows: 


500    FORMULAS   FOR  THE  STRENGTH  OF  BEAMS. 

Greatest  bending-moment  (inch-lbs.)  =  section  modulus  X$,   (a) 
or 

Q     ,.             ,   ,       fT)     N  bending  moment  (inch-lbs.) 
Section  modulus  (R  =  ) ~ —         — .       (b) 

o 

If  the  bending-moment  is  computed  in  foot-pounds,  these 
formulas  become : 

-,  section  modulus  X  S 

Greatest  bending-moment  =  —  — ,  (c) 

iju 

or 

,  ,      /TVV     12  X  bending-moment 

Section  modulus  (R)  ==' — =»  — •        (a) 

o 

By  substituting  for  the  bending-moment  its  value  in  terms  of 
the  load  and  span,  the  following  formulse  may  readily  be  deduced 
which  apply  to  any  shape  of  beam. 


FORMULAE  FOR  STRENGTH   OF  BEAMS   FOR  DIFFERENT  CONDITIONS 
OF    SUPPORT    AND    LOADING. 

R= section  modulus;    $=safe  modulus  of  rupture,  or  fibre 
stress  in  pounds  (p.  499). 

W=  total  load  on  beam  in  pounds. 

L=span  in  feet. 

C=  coefficient  of  strength  given  in  tables. 

Values  for  R  for  the  various  shapes  and  sizes  of  structural  steel 
bars  will  be  found  in  the  tables  on  pages  296-315. 

CASE  1. — Beams  fixed  at  one  end  and  loaded  at  the  other  (Fig.  1). 


Safe  l°ad  m  pounds = 

SL*S>  or  8- 


(1A) 

A3 

w 

Fig.  1. 

EXAMPLE. — A  steel  T-bar  is  fixed  at  one  end  in  a  brick  wall, 
and  loaded  at  the  other  end  with  600  Ibs.,  the  distance  L  being 
4  ft.  What  size  bar  should  be  used  to  support  the  load  with 
safety? 

*  When  C  is  given  in  tons,  safe  load  will  be  tons. 


FORMULAS  FOR  THE  STRENGTH  OF  BEAMS.  501 


Ans.     We  will  allow  12,000  Ibs.  for  the  value  of  £;  then  R= 

12  X  600  X  4 

~T2~onn —  =  2.4.     Now  we  must  ascertain  what  size  T-bar  has 

a  section  modulus  equal  to  2.4.  Looking  in  the  table  giving 
the  properties  of  tees  (p.  313,  col.  VII.),  we  find  2.43  opposite  a 
4X5Xf  tee,  and  2.55  opposite  a  4X4JXJ  tee;  hence  either 
size  will  have  sufficient  strength,  the  first,  however,  being  the 
cheapest,  as  it  weighs  the  least. 

For  an  I-beam  we  could  have  used  16,000  Ibs.  for  S;  then  R 

,  12X600X4 

would  equal  —  — =1.8,  which  would  permit  of  using  a 

lo,OUU 

3-inch  6i-lb.  beam. 

CASE  2. — Beams  fixed  at  one  end,  loaded  with  uniformly  dis- 
tributed load  (Fig.  2). 


Safe  load  in  pounds = 

•fij-XS,     or    ~Y. 
,     QWXL 


Fig.  2. 

CASE  3. — Beams  supported  at  both  ends,  loaded  at  middle  (Fig.  3). 

R  C* 

Saf e  load  in  pounds  =~f  xS,    or     ^-Y.  (3) 

6L  £Li 


R- 


3WXL 

s    • 

W 


Fig.  3. 


*  When  C  is  given  in  tons,  safe  load  will  be  tons. 


502    FORMULAS   FOR  THE  STRENGTH   OF  BEAMS. 

CASE  4. — Beams  supported  at  both  ends,  load  uniformly  dis- 
tributed (Fig.  4). 


27?  C1* 

Safe  load  in  pounds  =  —  r  X  S,     or     -=-. 
6L  Li 


R= 


2S     ' 


(4) 
(4A) 


CASE  4A. — Beams  supported  at  both  ends,  with  a  distributed  load 
over  only  a  portion  of  the  span,  as  in  Fig.  4a. 


Fig,  4a. 

In  this  case  the  load  is  generally  given,  and  the  problem  will 
be  to  determine  the  size  of  the  beam.  This  can  be  accurately 
done  only  by  computing  the  bending-moment  as  explained  in 
Chapter  IX.,  and  substituting  the  value  thus  found  in  formulas 
(6)  or  (d),  page  500.  If,  however,  the  length  Li  is  very  short  in 
comparison  with  Z/,  then  the  load  may  be  considered  as  concen- 
trated at  its  centre,  and  R  may  be  found  by  formula  (3 A)  if  the 
load  is  at  the  centre  of  the  beam,  or  by  formula  (5.4 )  if  the  load 
is  at  one  side  of  the  centre.  The  error  will  be  on  the  safe  side. 


*  When  C  is  given  in  tons,  safe  load  will  be  tons. 


FORMULAS   FOR   THE    STRENGTH   OF   BEAMS.     503 


CASE  5.     Beams  supported  at  both  ends,  loaded  with  concentrated 
load  not  at  centre  (Fig.  5). 


R-- 


Fig.  5. 

T?  V  7" 
Safe  load  in  pounds^         ^ X& 


!2W_XmXn 
LXS 


,  m  and  n  being  measured  in  feet.        (5  A) 


EXAMPLE. — A  steel  I-beam  of  20  feet  span  has  to  support  a 
concentrated  load  of  24,000  Ibs.  at  a  distance  of  6  feel  from  one 
support.  What  must  be  the  size  and  weight  of  the  beam? 

Ans.  In  this  case  W=  24,000,  L=20,  ra=6,  ra=14,  and  we 
will  allow  16,000  Ibs.  for  S. 


Then 


R- 


12X24,000X6X14 
20X16,000 


=  75.6. 


Looking  down  column  VII.  of  the  Properties  of  Steel  I-beams 
(p.  296),  we  find  that  the  nearest  value  (above)  to  75.6  is  81.2  for 
a  15-inch  60-lb.  beam,  and  117.0  for  a  20-inch  65-lb.  beam,  or  we 
might  use  two  12-inch  35-lb.  beams.  The  15-inch  60-lb.  beam 
would,  however,  be  the  cheapest  beam  to  use,  although  the  20- 
inch  beam  would  deflect  much  less  under  the  load. 

CASE  6. — Beams  supported  at  both  ends,  loaded  with  W  pounds, 
at  the  same  distance  m  from  each  end  (Fig.  6). 


f|W 
Fig.  6. 

Safe  load  W,  in  pounds,  at  each  point = 

]2 
•K — 


I 


R 


XS,          (6) 
(6A) 


504     FORMULAS   FOR   THE   STRENGTH   OF  BEAMS. 

EXAMPLE. — A  12-inch  standard  steel  channel  of  12  ft.  span 
supports  the  ends  of  two  10-inch  beams  4  ft.  from  each  support. 
Each  10-inch  beam  is  designed  to  carry  16,000  Ibs.  What  should 
be  the  weight  of  the  channel  to  support  the  beams? 

Ans,  The  channel  would  have  to  support  only  one-half  of  the 
load  on  the  beams,  whence  TF  =  8,000;  w=4;  £=16,000;  and 

12X8,000X4 

**s=s T«~nAn =  24,  which  is  the  value  of  the  section  modulus 

ID, ULKJ 

of  a  12-inch  25-lb.  channel.     (Col.  VII.,  p.  298.) 

It  will  be  noticed  that  in  formulas  (6)  and  (QA)  the  span  of  the 
beam  is  not  taken  into  account,  and  if  the  beam  itself  had  no 
weight  it  would  make  no  difference  in  the  fibre  strains  how  far 
apart  the  loads  W  are  placed.  In  reality,  however,  steel  beams 
do  weigh  considerable,  and  to  be  absolutely  correct  an  example 
such  as  the  above  should  be  calculated  for  the  weight  of  the 
beam,  as  well  as  for  the  weights  W.  The  weight  of  the  beam 
would,  of  course,  be  a  distributed  load,  and  to  be  absolutely  cor- 
rect the  maximum  bending-moment  on  the  beam  should  be  found 
graphically  in  a  manner  similar  to  that  explained  on  the  lower 
half  of  page  272,  and  the  value  of  R  computed  by  formula  (7). 
Where  the  loads,  however,  are  spaced  so  as  to  divide  the  beam 
into  three  equal  parts,  as  in  the  last  example,  one-third  of  the 
weight  of  the  beam  may  be  added  to  W  with  sufficient  accuracy; 
thus,  the  weight  of  the  channel  in  the  above  example  between 
supports  would  be  12x25,  or  300  Ibs.,  and  W  should  be  taken  at 
8,100  Ibs.,  which  would  give  a  value  for  R  of  24.1. 

Generally  there  is  a  sufficient  factor  of  safety  in  the  loads 
allowed  to  offset  the  slight  effect  produced  by  the  weight  of  the 
beam ;  but  if  the  full  load  assumed  is  likely  to  be  imposed  on 
the  beam,  then  allowance  must  be  made  for  the  weight  of  the 
beam  itself. 

CASE  7. — Beam  loaded  with  several  loads. — In  such  a  case  as 
this  it  will  be  necessary  to  compute  the  maximum  bending- 
moment  on  the  beam  and  proportion  the  beam  by  the  formula 

max.  bending-moment  (ft. -Ibs.)  X12 
R=  -g-  (7) 

EXAMPLE. — A  steel  beam  girder  is  to  be  used  to  support  a 
brick  wall,  16  inches  thick  and  weighing  138,000  Ibs.,  over  an 
opening  22  ft.  wide.  The  girder  must  also  support  the  ends  of 
four  10-inch  floor-beams  spaced  as  in  Fig.  7,  each  beam  being 


FORMULAS   FOR  THE  STRENGTH  OF  BEAMS.     505 

assumed  to  carry  16,000  Ibs.;    what  should  be  the  size  of  the 
beams  forming  the  girder? 

Ans.  The  first  step  should  be  to  determine  on  the  allowance 
for  the  weight  of  the  girder.  The  total  load  on  the  girder = 
138,000  +  4x8,000  (one-half  the  load  on  each  beam)  =  170,000 
Ibs.,  or  85  tons.  As  we  must  use  a  pair  of  beams  the  load  on 


f     f 

5---*t< 5- »K > 

Fig.  7. 

each  beam  will  be  42.5  tons.  For  our  present  purpose  we  may 
consider  the  entire  load  as  distributed,  and  from  the  table  of 
strength  of  I-beams,  we  find  that  to  support  42.5  tons  with 
a  span  of  22  feet  would  require  a  24-inch  85-lb.  beam.  Our 
girder  would  then  weigh  between  supports  2x85X22  =  3,740 
Ibs.,  or  say  4,000  Ibs.  Adding  this  to  the  wreight  of  the  wall  we 
have  for  the  total  distributed  load  142,000  Ibs.  The  next  step 
will  be  to  determine  the  maximum  bending-moment. 

By  the  formulas  given  in  Chapter  IX.  we  find  the  bending- 
moments  for  the  various  loads  to  be  as  follows : 


For  weight  of  wall,     M  =  -  ?A^±»^  =  390,500  ft.  -Ibs. 

o 

For  beam  B,,  M1  =  8'°°°>^iXl84=23,545  ft.-lbs. 


For  beam  B2,  M^,  =41>m  ft_.lbs-. 

The  beams  being  spaced  symmetrically  from  the  centre  of  the 
span,  the  bending-moments  for  B3  and  B4  will  be  equal  to  those 
of  B2  and  Bj  respectively.  Platting  the  bending-moments  to  a 
scale,  in  the  manner  explained  on  pages  272,  273,  we  obtain  the 
diagram  shown  in  Fig.  8,  the  greatest  bending-moment  being  the 
line  M0,  which  scales  485,000  Ibs.  Multiplying  this  moment  by 
12  and  dividing  by  S  (=  16,000  Ibs.),  we  have  363.7  as  the  value 
for  R  for  both  beams,  or  181.8  for  one  beam.  From  column  VII., 
p.  296,  Properties  of  I-beams,  we  find  that  a  24-inch  90-lb. 
beam  has  a  section  modulus  of  186.6,  therefore  two  90-lb.  beams 
will  just  answer.  The  maximum  load  for  a  single  beam  is  50.9 


506 


THE   STRENGTH   OF  STEEL   BEAMS. 


tons,  which  is  greater  than  the  load  we  wish  to  carry,  so  that 
there  is  no  danger  of  the  web  buckling.  The  two  beams  should 
be  securely  bolted  together  with  separators  near  each  connection 
of  beams  Blf  B2,  B3,  B4,  and  at  each  end  of  the  girder.  , 


The  method  above  indicated  applies  to  any  method  of  loading, 
the  only  difference  in  the  calculation  being  in  determining  the 
beriding-moment. 

INCLINED  BEAMS. — The  strength  of  beams  inclined  to  the 
horizon  may  be  computed,  with  sufficient  accuracy  for  most  pur- 
poses, by  using  the  formulas  given  for  horizontal  beams,  and 
taking  the  horizontal  projection  of  the  beam  as  its  span. 


Steel  Beams. 

Practically  the  only  materials  used  in  structural  work  for 
beams,  at  the  present  day,  are  wood  and  steel.  Wooden  beams 
being  always  rectangular  in  cross-section,  the  general  formula  can 
be  much  simplified  by  substituting  for  R  its  value  in  terms  of  the 
breadth  and  depth  of  the  beam.  Formulas  for  wooden  beams 
will  therefore  be  found  in  Chapter  XVI.  Cast  iron  is  also  occa- 
sionally used  for  beams  or  lintels,  but  as  this  material  is  much 
stronger  to  resist  compression  than  tension,  the  beam  must  be  of 
a  special  shape  in  order  to  use  the  material  to  advantage.  The 


THE   STRENGTH  OF  STEEL  BEAMS.  507 

strength  of  cast-iron  beams  is  therefore  considered  under  a 
special  heading  in  Chapter  XVI.  Formulas  for  concrete-steel 
beams  are  given  in  Chapter  XXIV. 

Since  1893,  steel  beams  have  practically  superseded  wrought- 
iron  beams,  and  the  latter  are  now  seldom,  if  ever,  used.  The 
same  formulas  apply  to  wrought-iron  as  to  steel  beams,  however, 
by  simply  changing  the  value  of  S.  Any  shape  of  rolled  steel 
may  be  used  as  a  beam,  but  the  I  shape  is  the  most  economical, 
as  it  possesses  the  greatest  resistance  for  a  given  weight  of  metal. 
Next  to  the  I-beam,  in  economy,  is  the  channel,  then  the  deck- 
beam,  and  angles  and  tees  are  the  least  economical  of  all  shapes. 
The  following  figures  show  the  safe  load  per  pound  of  steel,  for 
the  various  sections,  for  a  10-foot  span;  the  same  ratio  would 
hold  for  other  spans. 

10"  I-beam         10"  channel         10"  deck-beam         4X6  angle         4X5  tee 
104  94.6  83.0  28.7  21.6 

Deepest  Beams  StifFest  and  most  Economical. — 

The  strength  of  a  wrought-iron,  wooden,  or  steel  beam  of  rectan- 
gular shape  varies  as  the  square  of  the  depth,  and  directly  as  the 
breadth ;  hence  the  deeper  beam  will  have  the  greatest  strength 
in  proportion  to  its  sectional  area.  With  I-beams  this  rule  in 
regard  to  the  square  of  the  depth  does  not  hold  strictly  true,  on  ac- 
count of  the  variation  in  the  sections,  but  it  is  approximately  true. 

It  therefore  follows  that,  for  any  given  span,  it  is  more  economi- 
cal, where  other  conditions  will  permit,  to  use  deep  beams  spaced 
farther  apart  in  floors,  or  to  use  one  deep  beam  in  place  of  two 
shallower  beams.  Thus  if  we  wished  to  support  a  distributed 
load  of  39  tons  with  a  16-ft.  span,  we  might  use  one  20-inch  70-lb. 
beam,  two  15-inch  42-lb.  beams,  or  three  12-inch  40-lb.  beams, 
but  the  20-inch  beam  would  weigh  only  1,190  Ibs.  (allowing  for 
6-inch  bearings)  as  compared  with  1,428  Ibs.  for  the  15-inch 
beams  and  2,040  Ibs.  for  the  12-inch  beams,  besides  the  saving 
in  bolts  and  separators. 

Light  beams  are  also  more  economical  than  heavy  beams  of  the 
same  defth,  except  when  the  span  is  so  short  that  the  safe  load 
is  governed  by  the  resistance  of  the  web  to  buckling,  in  which 
case  the  heavy  beams  are  the  more  economical. 

Maximum  Safe  Load  for  Steel  Beams. — All  beams 
are  subject  in  a  greater  or  less  degree  to  three  kinds  of  strains. 
The  most  destructive  of  these  is  generally  the  bending-moment, 
which  has  already  been  considered.  The  second  kind  is  that 


508  THE  STRENGTH  OF  STEEL   BEAMS. 

which  tends  to  shear  the  beam,  or  make  one  part  slide  on  the 
other  vertically.  This  strain,  however,  seldom  needs-  to  be  con- 
sidered except  in  the  case  of  riveted  girders,  and  short  beams  with 
very  thick  webs.  The  third  strain  is  that  which  tends  to  cause 
the  web  of  the  beam  to  buckle,  and  for  steel  beams,  where  the 
span  is  very  short  in  proportion  to  the  depth  of  the  beam,  the 
resistance  of  the  web  to  buckling  generally  determines  the  maxi- 
mum load  that  the  beam  will  support,  without  stiffening  the 
webs. 

In  the  tables  giving  the  safe  loads  for  I-beams,  channels, 
and  deck-beams,  the  column  headed  Max.  Load  gives  the  great- 
est load  that  should  be  put  on  the  beam,  no  matter  how  short  the 
span,  unless  the  web  is  stiffened  by  riveting  plates  or  angles  to 
the  web.  This  load  may  be  either  distributed  or  concentrated 
at  the  centre,  provided  it  does  not  exceed  the  safe  load  as  deter- 
mined by  the  bending-moment.  In  the  tables  giving  safe  loads  for 
I-beams  and  channels  the  loads  to  the  left  of  the  dotted  line 
exceed  the  maximum  distributed  loads,  and  hence  the  beam 
should  not  be  used  for  those  spans,  unless  stiffening  is  resorted 
to.  For  concentrated  loads  very  much  shorter  spans  may  be 
used  than  for  distributed  loads.  Thus  for  a  24-inch  SO-lb.  beam 
the  shortest  span  for  a  full  distributed  load  is  25  feet,  while  for  a 
concentrated  load  at  the  centre  12  feet  would  be  the  shortest 
span.  In  using  the  tables  for  safe  loads,  therefore,  the  maxi- 
mum load  should  always  be  considered.  The  maximum  loads 
in  the  table  are  such  that  the  greatest  shear  will  not  exceed 
10,000  Ibs.  per.  sq.  inch,  nor  the  total  load  exceed  that  obtained 
by  the  formula 


Max.  load  in  tons— 


1   I 
" 


in  which  d—  depth  of  beam  and  t—  thickness  of  web,  both  in 
inches. 

This  formula  is  that  used  by  the  engineers  of  the  Pencoyd  Iron 
Works,  and  gives  results  considerably  less  than  formulas  used  by 
some  of  the  other  steel  companies. 

It  is  based  on  Gordon's  formula  for  long  columns,  considering 
the  length  of  the  column  equal  to  the  diagonal  depth  of  the  beam, 
and  using  8,000  Ibs.  as  the  unit  strength  of  the  material  instead 
of  ten  or  twelve  thousand  pounds,  as  used  for  columns  and  the 
webs  of  riveted  girders. 


THE  STRENGTH  OF  STEEL   BEAMS.  509 

In  comparing  this  formula  with  formulas  giving  the  safe  resist- 
ance to  buckling,  it  should  be  remembered  that  these  formulas 
give  the  maximum  shear,  and  that  the  maximum  shear  is  only 
one-half  of  the  safe  load,  when  the  load  is  either  distributed  or 
concentrated  at  the  centre. 

For  beams  unsymmetrically  loaded  the  maximum  shear  should 
not  exceed  one-half  of  the  maximum  load. 

Short  lengths  of  beams  used  as  blocking  or  bolsters  should  not 
be  loaded  to  more  than  one-half  the  maximum  load,  given  in  the 
tables. 

Lateral  Strength. — As  has  been  stated,  the  effect  of  the 
bending-moment  on  a  beam  is  to  produce  compression  in  the  top 
flange  and  tension  in  the  lower  flange;  the  top  flange  therefore 
becomes  in  effect  a  strut,  and  when  its  length  exceeds  20  times  its 
width  the  compression  tends  to  deflect  the  beam  sideways.  Pro- 
vision should  therefore  be  made  for  bracing  the  beam  sidewa}^s 
at  intervals  not  exceeding  20  times  the  width  of  the  flange. 
Floor-beams  are  generally  sufficiently  braced  by  the  filling  be- 
tween the  beams  and  by  the  tie-rods.  In  the  case  of  a  pair  of 
beams  bolted  together  the  total  width  may  be  taken  in  determin- 
ing the  maximum  length, 

In  cases  where  it  is  not  practical  to  support  the  beams  sideways, 
the  loads  given  in  the  tables  should  be  reduced  as  indicated  in  the 
following  table: 

BEAMS  WITHOUT  LATERAL  SUPPORT. 

T    ^   *u     fu  n  Proportion  of  tabular  load 

Length  of  beam.  forming  greatest  safe  load. 

20  times  flange  width Whole  tabular  load. 

20  to  30      "  "  "     9/10 

30  to  40      "  "  "     .•.  .  8/10 

40  to  50      "  "  "    7/10  " 

50  to  60      "  "  "    6/10  " 

CO  to  70      "  "  "     5/10 

EXAMPLE. — What  is  the  maximum  distributed  load  that  should 
be  allowed  for  a  15-inch  42-lb.  beam  25-foot  clear  span,  the  beam 
being  unsupported  sideways? 

Ans.  The  flange  width  of  this  beam  (see  table  of  properties  of 
standard  beams)  is  54  in.  25  ft.  (300  in.)  4-54  =  54.  We  should 
therefore  use  only  .65  of  the  load  given  in  the  table,  or  8.12  tons 
Froni  this  the  weight  of  the  beam  (1,050  Ibs.)  should  also  be  sub- 
tracted, reducing  the  maximum  safe  load  to  7.6  tons. 


510 


DEFLECTION  OF  STEEL   BEAMS. 


Deflection  of  Steel  Beams. — The  principles  and  gen- 
eral formula  for  the  deflections  of  beams  are  given  in  Chapter 
XVIII.,  and  the  deflection  of  any  beam  under  any  load  may  be 
found  by  the  formula  there  given.  A  shorter  and  sufficiently 
accurate  method  of  finding  the  deflection  of  steel  beams  under 
the  safe  loads  given  in  the  tables  is  afforded  by  the  following 
table,  taken  from  the  " Pocket  Companion"  of  the  Carnegie  Steel 
Company : 

DEFLECTION   COEFFICIENTS   FOR   SYMMETRICAL 
SHAPES  GIVEN  IN  64THS  OF  AN  INCH. 


Coeffi- 

Distance between  supports  in  feet. 

cient 

index. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

c 

38.0 

68.0 

106.0 

152.5 

208.0    271.0 

343.0 

424.0 

513.0 

C" 

30.0 

53.0 

83.0 

119.0 

162.0 

212.0 

268.0 

331.0 

400.5 

Distance  between  supports  in  feet. 

24 

26 

28 

30 

32 

34 

36 

38 

40 

c 

610.0 

716.0 

830.5 

953.0 

1085.0 

1225.0 

1373.0 

1530.0 

1695.0 

C' 

477.0 

559  .  0 

649.0 

748.0 

847.0 

957.0 

1073.0 

1195.0 

1324.0 

The  figures  given  opposite  C  arid  C'  are  the  Deflection  Coeffi- 
cients for  steel  shapes  subject  to  transverse  strain  for  varying 
spans,  under  their  maximum  uniformly  distributed  safe  loads, 
derived  from  a  fibre  strain  of  16,000  and  12,500  respectively,  the 
modulus  of  elasticity  being  taken  at  29,000,000  Ibs. 

To  find  the  deflection  of  any  symmetrical  shape  used  as  a  beam, 
under  its  corresponding  safe  load*  divide  the  coefficients  given  in 
the  above  tables  by  the  depth  of  the  beam ;  the  result  will  be  the 
deflection  in  64ths  of  an  inch.  This  applies  to  such  shapes  as 
beams,  channels,  etc.  For  those  shapes  having  unsymmetrical 
sections,  such  as  tees,  angles,  etc.,  divide  by  twice  the  greatest 
distance  of  the  neutral  axis  from  the  outside  fibre. 

For  a  beam  supported  at  both  ends  and  loaded  at  the  centre 


*  This  applies  only  to  the  loads  at  the  left  of  the  heavy  line  in  the  tables 
following;  the  loads  to  the  right  of  this  line  being  reduced  by  the  rule  fo? 
stiffness,  the  deflections  obtained  by  this  rule  would  be  excessive. 


STRENGTH   OF  STRUT   BEAMS.  511 

with  one-half  the  distributed  load  the  deflection  will  be  .8  that 
obtained  by  the  above  table. 

EXAMPLE. — Required  the  deflection  of  a  10-inch  25-lb.  steel 
beam,  10-foot  span,  under  its  maximum  distributed  load  of  13 
tons  (16,000  Ibs.  fibre  strain).  The  above  table  gives  106  as  the 
deflection  coefficient;  dividing  by  the  depth  of  the  beam  (10)  we 

have  — rj-  for  the  deflection  at  the  centre.     This  is  equivalent  to 

.165  in.     By  formula  1,  Chapter  XVIII.,  we  find  the  deflection  for 

26,000  X  1,728,000  X  .013 
the  same  beam,  span,  and  load  =        29;OQ0,QQQX  122.1 

in.,  the  two  results  agreeing  perfectly.     For  the  same  beam  and 
18-ft.  span,  with  a  load  of  7.2  tons,  we  find  the  deflection  by  the 

34  3 

above  table  to  be  ^r~°r  -536  in.,  and  by  formula  1,  .532,  or  prac- 
tically the  same. 

For  a  concentrated  load  of  6,500  Ibs.  at  centre  of  18-ft.  span  the 
deflection  would  be  .8X.53  or  .42  in.  As  a  rule  it  is  not  desir- 
able to  subject  any  beam  to  a  load  which  will  produce  a  deflection 
at  the  centre  exceeding  3^  th  of  the  span,  or  g^th  of  an  inch  per 
foot  of  span.  A  greater  deflection  is  liable  to  produce  cracks  in 
plastered  ceilings,  and  if  the  beam  is  exposed  the  deflection  is 
painful  to  the  eye. 

In  the  tables  giving  the  safe  loads  for  I-beams  and  channels  all 
of  the  loads  given  are  within  this  limit,  the  loads  to  the  right  of 
the  heavy  line  having  been  reduced  to  conform  with  the  rule  for 
stiffness.* 

When  the  deflection  is  of  no  particular  consequence  these 
loads  may  be  increased  to  the  value  obtained  by  dividing  the 
coefficient,  (7,  by  the  span,  but  as  a  general  rule,  the  loads  should 
not  exceed  those  given  in  the  table. 

Strut  Beams. — It  cannot  be  considered  as  good  engineering 
to  subject  a  strut  to  a  cross-strain,  as  any  such  strain  must  pro- 
duce a  certain  amount  of  flexure  in  the  strut,  which  the  compress- 
ive  stress  tends  to  increase. 

There  are  often  cases,  however,  where  practical  considerations 
make  it  desirable  to  use  a  strut  as  a  beam  also,  as  in  the  top  chord 
or  principals  of  trusses.  For  determining  the  size  of  the  section 
in  such  cases  the  following  method  should  be  used: 

*This  rule  is  as  follows: — Multiply  the  load  given  immediately  to  the 
left  of  the  heavy  line  by  the  square  of  the  corresponding  span,  and  divide 
by  the  square  of  the  required  span ;  the  result  will  be  the  required  load. 


512  STRENGTH    OF   TIE    BEAMS. 

1st.  Find  the  section  modulus  for  the  transverse  load  by  for- 
mulas 2 A  to  6A,  using  12,000  Ibs.  as  the  value  of  S,  and  find  the 
area  of  a  section  corresponding  to  the  value  of  R  thus  found. 

2d.  Find  the  section  area  required  by  a  section  of  the  size 
found  to  resist  the  compression  stress  by  dividing  the  stress  by 

the  value  opposite  —  in  column  II.,  Table  XL,  Chapter  XIV. 

3d.  Add  the  two  areas  thus  found  together  and  use  the  next 
larger  section  having  the  required  area. 

EXAMPLE. — The  principal  rafter  in  a  truss,  8-|  ft.  long  between 
joints,  supports  the  end  of  a  purlin  at  the  centre  of  the  span;  the 
weight  from  the  purlin  is  2,800  Ibs.  and  the  compressive  stress  is 
30,000  Ibs.  It  is  desired  to  use  two  angles,  with  long  legs  vertical 
and  J  inch  apart  for  the  principal.  What  should  be  their  size  ? 

Ans.   By  formula  (3A),  jg=  3X2;8^X8^5.95. 

LZjUOO 

As  two  angles  will  be  used,  R  for  each  will  be  2.98.  From  the 
table  of  properties  of  angles  (p.  304,  col.  VII.),  we  find  that  the 
angle  having  a  value  next  above  2.98  is  a  5X3X9/16  inch. 
The  area  of  this  angle  is  4.18  in.,  and  from  the  table  on  page  317 
we  find  the  least  value  of  r0  for  a  pair  to  be  about  1.58  (the  strut 

I       102 
being  braced  sideways) ;  then  —  =  -——  =  64.5,  and  pfrom  column 

T  l.OO 

II.,  Table  XL,  p.  463,  =10,756  Ibs.  30, 000 -f-1 0,756  =  2. 79 
sq.  in.,  or  1.40  in.  for  each  angle.  The  area  of  the  angle  found 
for  the  beam  was  4.18;  adding  to  this  1.40,  we  have  5.58  as 
the  required  area  for  each  angle,  which  is  found  in  the 
5X3XH"  size. 

As  the  area  in  both  steps  considerably  exceeds  that  required 
by  the  calculation,  we  need  not  make  further  allowance  for  the 
weight  of  the  angles. 

Tie  Beams. — Steel  beams  subject  to  both  tensile  and  trans- 
verse strain  should  be  calculated  in  a  similar  way  to  that  ex- 
plained above  for  strut  beams.  The  section  necessary  to  resist 
the  transverse  strain  should  first  be  found,  and  then  the  sectional 
area  necessary  to  resist  the  tensile  strain,  and  the  two  added 
together. 

EXAMPLE. — One  span  of  a  tie  beam,  10  ft.  between  joints,  has 
to  support  a  load  at  the  centre  of  three  tons,  and  a  tensile  stress  of 
84,000  Ibs.  Two  steel  channels  will  be  used  for  the  tie.  What 
should  be  their  size  and  weight? 


STRENGTH  OF  STEEL   BEAMS.  513 

Ans.  A  centre  load  of  3  tons  corresponds  with  a  distributed 
load  of  6  tons,  or  3  tons  for  each  channel.  From  the  table  giving 
the  strength  of  channels,  we  find  that  a  light  7-inch  channel  will 
be  required,  the  sectional  area  being  2.85  sq.  in.  The  area  re- 

84  000 
quired  to  resist  the  tensile  stress  =  TTT^TT^^  scl'  m->  or  3  in.  for 

each  channel,  and  the  total  area  for  each  channel  should  be 
2.85  +  3=5.85  sq.  in.  A  7-in.  19}-lb.  channel  has  an  area  of 
5.81  sq.  in.  which  will  answer,  as  we  do  not  use  the  full  strength 
of  the  light  channel.  If  a  sufficiently  heavy  section  could  not  be 
found  in  the  7-inch  channels,  we  should  use  the  next  size,  or 
8-inch. 


Explanation  of  Tables  for  the  Strength  of 
Steel  Beams. 

The  following  tables  give  the  greatest  safe  loads  for  all  of  the 
standard  sections  of  beams,  channels,  and  angles,  and  for  the 
Carnegie  deck-beams  and  tees,  and  also  the  limits  for  deflection 
and  buckling  of  the  beams  and  channels.  By  following  the  ex- 
planations given  below  these  tables  may  be  used  with  simple  or 
no  computations  (other  than  those  required  for  determining  the 
load  they  will  have  to  support)  for  the  usual  conditions  of  build- 
ing construction.  For  several  concentrated  loads  or  for  a  con- 
bination  of  distributed  and  concentrated  loads  it  will  be  neces- 
sary to  use  the  methods  previously  explained  under  Case  7. 

In  using  any  of  the  following  tables  allowance  should  be  made  for 
the  weight  of  the  beam  itself. 

I-beams  and  channels  having  loads  and  spans  to  the  left  of  the 
dotted  line,  should  have  the  web  stiffened. 

The  loads  to  the  right  of  heavy  line  (I-beams  and  channels) 
were  computed  by  formula  for  deflection.  "Max.  Load"  is  the 
greatest  distributed  load  that  should  be  used  without  stiffening 
the  web  by  plates  or  angles.  (See  page  508.)  To  find  the  safe 
load  for  any  other  span  than  those  given  in  the  table,  divide  the 
number  in  column  headed  C  by  the  given  span  in  feet  and 
decimals  of  a  foot,  and  the  answer  will  be  the  safe  load  for  that 
span,  provided  it  is  less  than  the  max.  load  and  within  the  limits 
of  deflection,  and  is  stayed  laterally. 

To  use  any  of  the  following  tables  for  CONCENTRATED  LOADS, 
find  the  equivalent  distributed  load  by  multiplying  the  con- 


514  STRENGTH  OF  STEEL   BEAMS. 

centrated  load  by  the  factor  given  below,  and  then  use  the  size 
of  beam  having  a  safe  load  equal  to  the  load  thus  found. 
For  concentrated  load  at  centre,  multiply  by  2. 

For  load  applied  one-third     the  span  from  one  end,  m'ply  by  1.78 

"  "  "  one-fourth  "  "  "  "  "  "  '  "  1.5 

"  "  "  one-fifth  "  "  "  "  "  "  "  1.28 

"  "  "  one-sixth  "  "  "  "  "  "  "  1J 

"  "  "  one-seventh  "  u  "  "  "  "  "        .98 

"  "  "  one-eighth  "  "  "  "  "  "  "           -J 

"  "  "  one-ninth  "  "  "  "  "  "  "        .79 

"  "  "  one-tenth  "  "  "  "  "  "  "        .72 

For  two  equal  loads  applied  one-third  the  span  from  each  end, 

multiply  one  load  by  2§. 
For  two  equal  loads  applied  one-fourth  the  span  from  each  end 

multiply  one  load  by  2. 

For  beam  fixed  at  one  end,  and  loaded  at  the  other,  multiply  by  8. 
For  beam  fixed  at  one  end,  and  uniformly  loaded  over  entire 

length,  multiply  by  four. 

Examples  of  Application. 

EXAMPLE  1. — A  steel  I-beam  of  15-foot  span  has  to  support  a 
load  of  4  tons  at  a  point  5  feet  from  one  support.  What  should 
be  the  size  of  the  beam? 

Ans.  Five  feet  is  one-third  of  the  span.  Multiplying  the  load 
by  1.78,  we  have  7.12  tons.  Looking  in  the  following  table  for 
the  strength  of  steel  I-beams,  we  find  that  a  9-inch  25-lb.  beam 
15-ft.  span  has  a  safe  load  of  7.2  tons,  hence  this  beam  will  just 
answer. 

EXAMPLE  2. — A  steel  I-beam  of  15-ft.  span  supports  two  equal 
loads  of  three  tons  each,  applied  5  feet  from  each  end.  What 
should  be  the  size  of  the  beam? 

Ans.  Five  feet  being  one-third  of  the  span,  multiply  one  load 
by  2§,  which  gives  8  tons  as  the  equivalent  distributed  load. 
This  will  require  a  9-inch  30-lb.  beam. 

[NOTE. — The  same  results  should  be  obtained  by  using  the 
formula  6A,  page  503.] 

Following  the  tables  giving  the  safe  loads  for  channels  is  a  table 
computed  by  the  author,  giving  the  strength  of  small  rectangular 
steel  bars.  These  bars  are  often  used  for  supporting  metal  lath 
in  suspended  ceilings,  and  the  table  will  be  found  useful  in  deter- 
mining the  size  of  bar  to  use  for  any  given  span  and  spacing. 


STANDARD   STEEL    I-BEAMS. 


515 


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516 


STANDARD  STEEL   I-BEAMS. 


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STANDARD   STEEL  I-BEAMS. 


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Depth  of  beam 
in  inches. 

OS                       CO 

1>               CO 

518 


DECK-BEAMS. 


SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR  STANDARD 

STEEL  I-BEAMS   (continued). 

(See  pages  513  and  515.) 


Depth  of 
beam  in 
inches. 

B 

C. 

I 
1 

Span  in  feet. 

4 

5 

6 

6V* 

7 

8         9 

10 

11 

5 
4 

9.75 
12.25 
14.75 

7.50 
8.50 
9.50 
10.50 

5.50 
6.50 
7.50 

25  .  80 
29.05 
32  .  30 

15.90 
16.95 
18.00 
19.05 

8.80 
9.55 
10.35 

5.5 

12.1 

18.4 

4.1 
6.7 
9.2 
11.7 

2.7 
5.3 

7.8 

6.45 

5.16 
5.81 
6.46 

3.18 
3.39 
3.60 
3.81 

1.76 
1.91 
2.07 

4.30 
4.84 
5.38 

2.65 
2.82 
3.00 
3.17 

1.46 
1.59 
1.72 

3.97 
4.47 
4.97 

2.44 
2.60 

2.77 
2.93 

1.25 
1.35 
1.47 

3.68 
4.15 
4.61 

2.27 
2.42 
2.57 
2.72 

1  .08 
1.17 
1.27 

3.221 
3.63 
,4  .  03| 

1.74 
1.85 
1.97 

2.08 

0.82 
0.89 
0.97 

2.54 

2.87 
3.19 

1.37 
1.46 
1.55 
1.64 

0.65 
0.71 
0.76 

2.06 
2.32 

2.58 

1.11 
1.18 
1.26 
1.33 

0.53 
0.57 
0.62 

1.70 
1.92 
2.13 

7.26 

8.07 

3.97 
4.24 
4  .  50 
4.76 

2.20 
2.39 

2.58 

3 

SAFE  DISTRIBUTED  LOADS    IN  TONS  FOR  CARNEGIE 
DECK-BEAMS. 

(For  dead  loads  only.) 

(See  explanation,  page  513.) 
c  =  load  to  be  added  to  C  for  each  Ib.  increase  in  weight  of  beam. 


Maximum  fibre  strain,  16,000  Ibs.  per  square 

*o.S 

|«3 

1 

inch. 

Ho" 

"^Tr 

C. 

c. 

X 

Span  in  feet. 

Q  « 

cs 

£~ 

6 

8 

9 

10 

12 

14 

16 

18 

11M 

37.00 

163.2 

39.2 

27.21 

20.40 

18.14 

16.32 

13.60 

11.66 

10.20 

9.07 

nvl 

32.20 

147.4 

3.04 

25.7 

24.56 

18.42 

16.37 

14.74 

12.28 

10.53 

9.21 

8.19 

10 

35.70 

137.1 

43.4 

22.84 

17.13 

15.23 

13.71 

11.42 

9.79 

8.57 

7.61 

10 

27.23 

113.1 

2.45 

20.8 

18.84 

14.13 

12.56 

11.31 

9.42 

8.08 

7.07 

6.28 

9 

30.00 

104.3 

35.4 

17.37 

13.03 

11.59 

10.43 

8.69 

7.45 

6.52 

5.79 

9 

26.00 

94.5 

2.25 

24.7 

15.76 

11.81 

10.51 

9.45 

7.88 

6.75 

5.91 

5.25 

8 

24.48 

75.1 

25.3 

12.51 

9.39 

8.35 

7.51 

6.25 

5.36 

4.69 

~ 

8 

20.15 

64.9 

2.00 

13.7 

10.82 

8.11 

7.21 

6.49 

5.41 

4.64 

4.0(1 

3.20 

7 

23.46 

62.3 

27.2 

10.38 

7.79 

6.92 

6.23 

5.19 

4.45 

"•Ho 

2.69 

7 

18.11 

51.5 

1.7 

is!o 

8.58 

6.44 

5.72 

5.15 

4.29 

3.68 

2.81 

2  22 

6 

17.16 

38.4 

18.2 

6.40 

4.80 

4.27 

3.84 

3.20 

2  35 

1.80 

1.42 

6 

14.10 

32.5 

1.5 

10.3 

5.42 

4.07 

3.62 

3.25 

2.71 

1.99 

1.52 

1.20 

STANDARD   STEEL   CHANNELS. 


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10 

OOrHHH  t^CCO 

iO  »O  >O  CO  CO 

l>  CO-*  CO  CM 

Tf  rHOX 

i>ooo»o 

b.00050TH 

•^»OCOJ>00 

CO^t^to 

•* 

00  W  CD  O  "t  00 

TH^HCM^IO 

THQ050000 

CCO^O 

1-1 

>O  CO  l^  O5  C  TH 

^H  rH  rl  T-H  OI  (M 

OOO5OTHCM 

iOCOCOi>00 

^HTJUOIO 

iO  O5  CO  <M  00  'O 

iO  CO  O2  CO  CO 

OiOOTHCM 

COOC05 

~ 

222gcMCMCM 

^s^^^ 

^5b-X050 

^.OCOCO 

CM  t-  I-  CO  CO  CO' 

•*  GCCOO51O 

rHTf  1>OCO 

COCCM  -^ 

•-1 

CM  (M  ^f  CO  00  C 
(M  CM  01  CM  (M  CO 

^^^^.H 

1-G005THCM 

»OCOb-00 

•p«°I 

<M  r-  o  co  rf  t^ 

TH  (M   »O   "*  b- 

T-<  CM  CO  CO  -^ 

GCC^-CCO 
(M  CM  rf  iO 

TH  r-J  CO 

CM  IOTHI>COO5 

O5  O  t-  "<t  TH 

COCOTHCM 

THCMOOO 

CJ 

<M  t^  r-  co  cc  >o 

CM  CM  rf  CO  00  O 
Ol  CM  <M  (M  (>1  CO 

co  00  co  o:  "O 

TH  rf  t^  O  CO 
t-  00  Oi  —  CM 

CCOlMCO 
iO  CO  b-  00 

^qj 

888888 

S8888 

cccoo 
cccoc 

lOCCO 
C1CCO 

^I3PAV 

co»oc>»oo  >o 

0*00^00 
CM  CM  CO  CO  -^ 

SgwMW 

coiocio 

£8 

H 

10 

CM 

0 

Oi 

520 


STANDARD  STEEL   CHANNELS. 


CO 

CM    i—  •KT    CM  '-O 

IO     OOrH     -*b- 

CM    CM  CO    COCO 

co   C-0  XT  <rj  i^ 

rH    rHrHCMCM 

«O 

00    CM  to    00  CM 

t^  os  CM  ^r  co 

CM    COCO    CO"* 

rH     rH  CM  CM  CM 

2 

b-    CMO    b-  to 

O     -^00     rHIO 

O    CM  tOOOO 
CM    CMCMCMCO 

CO 

1     rH     OSOS     OO 

CO    COOSCM  to 
CM    CM  CM  CO  CO 

co  ujooo 

rH     rHrHCM 

CM 

1  OS   OCO    b-O 

to  o-*  ooco 

oo  i>  to  co  i—i 

b-    O  ^  00  (M 

O     00  rH  Tfl 

CO   ^TH    TH.O 

CM    COCOCO^ti 

rH     rHC-QCM 

^ 

I     rH     COCO     rHO 

as  co  oo  co  oo 

CO    IOCCOOO 
O    CO  b-  r-i  CO 

S  ^^So 

O    CM  Tf 

1 

O 

O    O  CM    •<*  b- 
CO    OOCO    OOCO 

CO     COrH  COO 

co  ooi* 

|85t: 

a 

^   ^to   tOCO 

CO   CO^tO 

CM    (MOO  CO 

L® 

0 

00    COOS    lOrH 

rH    OS  O  rH  CM 

b-     OCOrHCO 

b-    Os  CM  CO 

to  as^t  oo 

ICO   b-OS 
tO     OOrH 

b-  CC«O 
OOOSO 

a 

T*   to  to   CO  b- 

CO   -^^toto 

CM    (M  CO  CO 

i~* 

^ 

"f    OCO   COOS 

rH     COrHb-CO 

00    CO  to^r 

oo  coooco 

o  c^b^: 

10  04  CO 
rHCM  CO 

to  coco  b-b- 

Th     ^OtOCO 

CM    COCOTt< 

rH     CM  CM 

rH     OSCO     COrH 

bl   CMOU7CM 

CO    OOr^OS 

CM     b-rH 

^Ot- 

Ios  l^-  to 

co  cOb-  00  OS 

«    tOtOCOb- 

CO    00^. 

CM    CM  CO 

rHrHrH 

rHJOOS  b-O 

»O    rH  OS  CO  ^ 

to  oocoos 

GO    -*  i-l  b- 

CO    COO 

CO     rHb- 

oo  co  co 
coooo 

i                         rH 

to  coco  b-  oo 

CO    rt^toto- 

CM    COCO 

rHrHCM 

1   I 

i 

CO   OS'* 

CM  CO'* 

c^-l- 

to 

OOJOs'OrHCM 

tC\l-~OG&C> 

T^I   to  CO  CO 

CO    COTjH 

01  CM  CM 

rH^'rH 

b-joco  coos 

co  !  .rt  oc  to  co 

ooib-b-b- 

OS  b-to 

CM  00  tO 
iO  b-O 

^cooo 

O-CMCO    TfiO 

00  !  OS  O  1-1  CM 

tOicOb-00 

CO    TJI  to 

CM  CMOO 

rHrHrH 

CO    Ob-i^CM 

rH  icO'tfCOOO 

b-  i  OS  CM  CO 

CM  ico-*1 

COrH  CO 

co  b-o 

co  oo  to 

rH      rH  r-l  ;  rH  CM 

rH  !CM  CO  IOCO 

b-JGOO^ 

tojcob- 

CO  COT* 

rHCMC-1 

• 

3 

00   CM  rf    O  tO 

CO    CMOCOOS 

•^i    O  to  OS 

co   1-1  b- 

rHb-CM 

OtOO 

Sj 

I 

CO    COtO    CMOO 

rHrH     CM  CM 

CO   CO  CO  <M  00 

rH  rHCM  CM 

iO    CCOCM 

rHrHCM 

^     r^2 

•^  COOs 

CO  to  00 

O    OCM    -*b- 

§  83S8 

O    O  O  to 

rH     OSCOb- 

So   ScM 

o  too 

I-H  r-i  CM 

oo  to  co 

O 

CO    OOCO    OOCO 
"*    rt  10    10  CO 

CO     COr-J  COO 

co  coo'* 

CM    CM  CO  CO 

tO    OOCM 

OrH  CM 

iO  COb- 

•eqi 

CM    b^  CM    b-  CM 

l^    0)  b-  CM  b- 

8  §8S 

§   0§ 

iO  iO  to 
CM(MCM 

888 

c^ijSta 

\\ 

rH      CO  CO      OOrH 

0     rH^2 

oo  oco  to 

CO     OSrH 

tOcOb- 

**  iO  CO 

a 

1 

o 

.5 

a 

o 
ft 

00 

- 

CO 

10 

CO 

STANDARD  STEEL  CHANNELS. 


521 


SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR  STANDARD 
STEEL  CHANNELS— SET  FLATWAYS 

or  with  the  load  acting  at  right  angles  to  the  plane  of  the  web. 

(Computed  by  the  Pencoyd  Iron  Works.) 
(Fibre  Stress  16,000  Ibs.  per  Square  Inch.) 


Length  of  span  in  feet. 

Wt. 

Size 

in 

in 

Ibs. 

4 

5 

6 

8 

9 

10 

11 

12 

13 

ins. 

per 

foot. 

Safe  load  in  net  tons. 

15 

33.0 

4.141  3.31 

2.76 

2.36 

2.07 

1.84 

1.66 

1.50 

1.38 

1.27 

15 

35.0 

4.28 

3.42 

2.85 

2.45 

2.14 

1.90 

1.71 

1.56 

1.43 

1.32 

15 

40.0 

4.56 

3.65 

3.04 

2.61 

2.28 

2.03 

1.82 

1.66 

1  .  52 

1.40 

15 

45.0 

4.83 

3.86 

3.22 

2.76 

2.41 

2.15 

1.93 

1.76 

1.61 

1.49 

15 

50.0 

6.92 

5.53 

4.61 

3.95 

3.46 

3.07 

2.77 

2.51 

2.31 

2.13 

15 

55.0 

7.30 

5.84 

4.87 

4.17 

3.65 

3.25 

2.92 

2.66 

2.43 

2.25 

12 

20.5 

2.32 

1.86 

1.55 

1.33 

1.16 

1.03 

0.93 

0.84 

0.77 

0.71 

12 

25.0 

2.53 

2.03 

1.69 

1.4.5 

1.27 

1.13 

1.01 

0.92 

0.84 

0.78 

12 

30.0 

2.77 

2.22 

1.85 

1.58 

1.39 

1.23 

1.11 

1.01 

0.92 

0.85 

12 

35.0 

4.76 

3.81 

3.17 

2.72 

2.38 

2.12 

1.90 

1.73 

1.59 

1.46 

12 

40.0 

5.12 

4.10 

3.41 

2.93 

2.56 

2.28 

2.05 

1.86 

1.71 

1.58 

10 

15.0 

1.55 

1.24 

1.03 

0.88 

0.77 

0.69 

0.62 

0.56 

0.52 

0.48 

10 

20.0 

1.77 

1.42 

.1.18 

1.01 

0.89 

0.79 

0.71 

0.64 

0.59 

0.54 

10 

25.0 

2.66 

2.13 

1.77 

1.52 

1.33 

1.18 

1.06 

0.97 

0.89 

0.82 

10 

30.0 

2.95 

2.36 

1.97 

1.69 

1.47 

1.31 

1.18 

1.07 

0.98 

0.91 

10 

35.0 

3.26 

2.61 

2.17 

1.86 

1.63 

1.45 

1.30 

1.19 

1.09 

1.00 

9 

13.25 

1.29 

1.03 

0.86 

0.74 

0.65 

0.57 

0.52 

0.47 

0.43 

0.40 

9 

15.00 

1.37 

1.10 

0.92 

0.79 

0.69 

0.61 

0.55 

0.50 

0.46 

0.42 

9 

20.00 

2.08 

1.67 

1.39 

1.19 

1.04 

0.92 

0.83 

0.76 

0.69 

0.64 

9 

25.00 

2.37 

1.89 

1.58 

1.35 

1.18 

1.05 

0.95 

0.86 

0.79 

0.73 

8 

11.25 

1.04 

0.83 

0.70 

0.60 

0.52 

0.46 

0.42 

0.38 

0.35 

0.32 

8 

13.75 

1.16 

0.92 

0.77 

0.66 

0.58 

0.51 

0.46 

0.42 

0.39 

0.36 

8 

16.25 

1.64 

1.31 

1.09 

0.94 

0.82 

0.73 

0.66 

0.59 

0.55 

0.50 

8 

18.75 

1.77 

1.42 

1.18 

1.01 

0.89 

0.79 

0.71 

0.64 

0.59 

0.55 

8 

21.25 

1.90 

1.52 

1.27 

1.09 

0.95 

0.85 

0.76 

0.69 

0.63 

0.59 

7 

9.75 

0.84 

0.67 

0.56 

0.48 

0.42 

0.37 

0.34 

0.31 

0.28 

0.26 

7 

12.25 

0.95 

0.76 

0.63 

0.54 

0.47 

0.42 

0.38 

0.34 

0.32 

0.29 

7 

14.75 

1.37 

1.10 

0.91 

0.78 

0.69 

0.61 

0.55 

0.50 

0.46 

0.42 

7 

17.25 

1.51 

1.20 

1.00 

0.86 

0.75 

0.67 

0.60 

0.55 

0.50 

0.46 

7 

19.75 

1.64    1.31 

1.10 

0.94 

0.82 

0.73 

0.66 

0.60 

0.55 

0.50 

6 

8.00 

0.65 

0.52 

0.44 

0.37 

0.33 

0.29 

0.26 

0.24 

0.22 

0.20 

6 

10.50 

0.91i   0.73 

0.61 

0.52 

0.45 

0.41 

0.36 

0.33 

0.30 

0.28 

6 

13.00 

1.04 

0.83 

0.69 

0.59 

0.52 

0.46 

0.41 

0.38 

0.35 

0.32 

6 

15.50 

1.16 

0.93 

0.78 

0.66 

0.58 

0.52 

0.46 

0.42 

0.39 

0.36 

5 

6.50 

0.50 

0.40 

0.33 

0.28 

0.25 

0.22 

0.20 

0.18 

0.16 

0.15 

5 

9.00 

0.61 

0.49 

0.41 

0.35 

0.30 

0.27 

0.25 

0.22 

0.20 

0.19 

5 

11.50 

0.72 

0.57 

0.48 

0.41 

0.36 

0.32 

0.29 

0  .  26 

0.24 

0.22 

522 


SMALL  STEEL  CHANNELS. 


SAFE  DISTRIBUTED  LOADS  IN  POUNDS  FOR  SMALL 
STEEL  CHANNELS,  OR  GROOVED  STEEL. 

(Computed  for  fibre  strain  of  16,000  Ibs.)  . 
(For  dimensions  of  sections  see  page  300.) 


Sec- 
tion 
No. 

D'pth 
in 

ins. 

wt. 

per 
foot, 
Ibs. 

C 
Ibs. 

2 

Span  in  feet. 

4.5 

2.5 

3 

3.5 

4 

5 

6 

1 

2M 

3.80 

7570 

3785 

3028 

2523 

2163 

1892 

1682 

1514 

1261 

2 

2 

2.90 

5120 

2560 

2048 

1706 

1463 

1280 

1138 

1024 

853 

3 

2 

3.60 

5760 

2880 

2304 

1920 

1643 

1440 

1280 

1152 

960 

4 

2 

3.60 

6240 

3120 

2496 

2080 

1783 

1560 

1386 

1248 

1040 

5 

2 

2.60 

4512 

2256 

1804 

1504 

1289 

1128 

1000 

902 

752 

6 

2 

2.00 

2836 

1418 

1134 

945 

810 

709 

630 

567 

472 

7 

w, 

1.13 

1815 

907 

726 

605 

518 

454 

403 

363 

302 

8 

IK 

1.32 

1536 

768 

614 

512 

439 

384 

341 

307 

256 

9 

iy2 

1.46 

1736 

868 

694 

578 

496 

434 

386 

347 

289 

10 

V4 

0.94 

950 

475 

380 

316 

271 

237 

211 

190 

11 

ll/s 

1.12 

939 

469 

375 

313 

268 

234 

208 

188 

12 

VA 

1.00 

874 

437 

350 

291 

250 

218 

194 

175 

13 

1 

0.83 

672 

336 

268 

224 

192 

168 

14 

1 

0.68 

532 

266 

212 

177 

152 

133 

15 

H 

0.67 

448 

224 

180 

149 

128 

112 

16 

7A 

0.69 

458 

229 

183 

152 

130 

17 

M 

0.53 

266 

133 

106 

88 

RECTANGULAR  STEEL   BARS. 


523 


SAFE  DISTRIBUTED  LOADS  IN  POUNDS  FOR  RECTAN- 
GULAR STEEL  BARS,  ON  EDGE,  USED  AS  BEAMS. 

(Computed  for  a  fibre  stress  of  16,200  Ibs.) 


1 

Depth 
in  ins. 

Thick- 
ness. 

Span  in  Feet. 

2 

2y2 

3 

3^ 

4 

4l/2 

5 

5H 

1 

1 

225 

180 

150 

1 

X 

281 

225 

187 

1 

t 

337 

270 

225 

li 

350 

280 

234 

200 

175 

1J 

& 

438 

350 

292 

250 

219 

H  ' 

1 

526 

420 

350 

300 

262 

1$ 

1 

506 

405 

338 

289 

253 

225 

li 

% 

632 

506 

422 

361 

316 

281 

11 

t 

759 

607 

506 

433 

379 

337 

if 

i 

689 

551 

459 

393 

344 

306 

275 

,1} 

% 

861 

688 

573 

491 

430 

382 

343 

if 

I 

1033 

826 

688 

589 

516 

459 

412 

2 

% 

1125 

900 

750 

642 

562 

500 

450 

409 

2 

3 

8 

1350 

1080 

900 

781 

675 

600 

540 

490 

2 

& 

1575 

1260 

1050 

914 

787 

700 

630 

572 

2i 

% 

1423 

1138 

948 

813 

711 

632 

569 

517 

2i 

1 

1708 

1366 

1138 

976 

853 

759 

683 

621 

2i 

% 

1993 

1594 

1328 

1139 

996 

885 

797 

724 

2i 

% 

1757 

1406 

1171 

1004 

878 

781 

703 

639 

2i 

I 

2109 

1687 

1406 

1205 

1054 

937 

843 

747 

2i 

& 

2460 

1968 

1540 

1406 

1230 

1093 

984 

855 

3 

I 

3037 

2430 

2025 

1736 

1518 

1350 

1215 

1104 

3 

% 

3543 

2835 

2362 

2025 

1771 

1575 

1417 

1288 

3 

4050 

3240 

2700 

2314 

2025 

1800 

1620 

1472 

524 


COMMON  SIZES  OF  STEEL  ANGLES. 


SAFE   DISTRIBUTED   LOADS  IN  TONS   FOR  COMMON 
SIZES  OF  STEEL  ANGLES. 

Computed  for  fibre  stress  of  16,000  Ibs.      For  permanent  and  live  loads 
reduce  20  per  cent.     See  further  explanation  on  page  513. 

ANGLES   WITH   EQUAL   LEGS. 


Size  of  angle. 

c. 

Span  in  feet. 

2 

3 

4 

5 

8    X8    X14 

93.49 

46.74 

31.16 

23.37 

18.70 

8   X8    X    i 

44.64 

22.32 

14.88 

11.16 

8.93 

6   X6   Xl 

45.72 

22.86 

15.24 

11.43 

9.44 

6   X6   X    | 

18.82 

9.41 

6.27 

4.70 

3.76 

5   X5   Xl 

30.91 

15.45 

10.30 

7.73 

6.18 

5   X5   X   f 

12.91 

6.45 

4.30 

3.23 

2.58 

4   X4   X% 

16.05 

8.03 

5.35 

4.01 

3.21 

4   X4   X% 

6.88 

3.44 

2.29 

1.72 

1.38 

34X3£X% 

12.00 

6.00 

4.00 

3.00 

2.40 

3iX3^X% 

5.20 

2.60 

1.73 

1.30 

1.04 

3   X3   X    f 

6.93 

3.47 

2.31 

1.73 

1.39 

3   X3   X   i 

3.09 

1.55 

1.03 

0.77 

0.62 

2fX2fX    i 

4.75 

2.37 

1.58 

1.19 

0.95 

2JX2JX    i 

2.56 

1.28 

0.85 

0.64 

0.51 

2iX2JX   i 

3.89 

1.95 

1.29 

0.97 

0.78 

2iX2iX% 

1.61 

0.81 

0.54 

0.40 

0.32 

2£x2iX    * 

3.09 

1.55 

1.03 

0.77 

0.62 

2iX2iX% 

1.30 

0.65 

0.43 

0.32 

0.26 

2   X2   Xji^o 

2.13 

1.07 

0.71 

0.53 

0.43 

2   X2   X% 

1.01 

0.51 

0.34 

•  0.25 

0.20 

IfXlJXjfi 

1.60 

0.80 

0.53 

0.40 

0.32 

iixi}x% 

0.75 

0.37 

0.25 

0.19 

0.15 

lixijx  i 

1.01 

0.51 

0.34 

0.25 

0.20 

ilxiix  4 

0.38 

0.19 

0.13 

0.096 

0.077 

HxHx% 

0.58 

0.29 

0.19 

0.150 

0.120 

HxHx  i 

0.26 

0.13 

0.087 

0.065 

0.052 

1    Xl    X   i 

0.30 

0.15 

0.100 

0.075 

0.060 

1    Xl    X   i 

0.17 

0.083 

0.055 

0.041 

0.033 

IX   |X% 

0.18 

0.088 

0.059 

0.044 

|x  |x  i 

0.12 

0.061 

0.041 

0.031 

fx  f  xJiB 

0.13 

0.064 

0.043 

0.032 

tx  fx  4 

0.091 

0.045 

0.030 

0.023 

COMMON  SIZES  OF  STEEL  ANGLES. 


525 


SAFE  DISTRIBUTED    LOADS   IN  TONS   FOR    COMMON 
SIZES  OF  STEEL  ANGLES  (continued). 

Computed  for  fibre  stress  of  16,000  Ibs.     For  permanent  and  live   loads 
reduce  20  per  cent.     See  further  explanation  on  page  513. 

ANGLES  WITH  EQUAL  LEGS. 


Size  of  angle. 

Span  in  feet. 

6 

7 

8 

9 

10 

8    X8    X1J 

15.58 

13.36 

11.69 

10.39 

9.35 

8   X8   X    i 

7.44 

6.38 

5.58 

4.96 

4.46 

6   X6   XI 

7.62 

6.53 

5.72 

5.08 

4.57 

6   X6   X    | 

3.14 

2.69 

2.35 

2.09 

1.88 

5   X5   Xl 

5.15 

4.42 

3.86 

3.43 

3.09 

5   X5   X   f 

2.15 

1.84 

1.61 

1.43 

1.29 

4   X4   x% 

2.68 

2.29 

2.01 

1.78 

1.61 

4   X4   X   % 

1.15 

0.98 

0.86 

0.76 

0.69 

3iX3iX% 

2.00 

1.71 

1.50 

1.33 

1.20 

34X3iX% 

0.87 

0.74 

0.65 

0.58 

0.52 

3   X3   X    f 

1.16 

0.99 

0.87 

0.77 

0.69 

3   X3   X   J 

0.52 

0.44 

0.39 

0.34 

0.31 

2|X2|X   i 

0.79 

0.68 

0.59 

0.53 

0.47 

2|X2|X   i 

0.43 

0.37 

0.32 

0.28 

0.26 

24X21X    \ 

0.65 

0.56 

0.49 

0.43 

0.39 

2JX2JXJ6 

0.27 

0.23 

0.20 

0.18 

0.16 

2iX2|-X    * 

0.52 

0.44 

0.39 

0.34 

0.31 

2iX2i-X% 

0.22 

0.19 

0.16 

0.14 

0.13 

2   X2   X% 

0.36 

0.30 

0.27 

0.24 

0.21 

2   X2    X% 

0.17 

0.14 

0.13 

0.11 

0.10 

ilxifx^ 

0.27 

0.23 

0.20 

0.18 

0.16 

ijxifxji 

0.12 

0.11 

0.093 

0.083 

0.075 

lixijx  t 

0.17 

0.14 

0.130 

0.110 

lixiix  i 

0.064 

0.055 

0.048 

0.043 

Hxiix% 

0.097 

0.083 

0.073 

0.065 

Hxiix  -1 

0.044 

0.037 

0.033 

0.029 

1    XI    X   i 

0.050 

1    XI    X   i 

0.028 

526 


COMMON   SIZES  OF  STEEL  ANGLES. 


SAFE   DISTRIBUTED   LOADS   IN   TONS   FOR   COMMON 
SIZES  OF  STEEL  ANGLES. 

Computed  for  fibre  stress  of  16,000  Ibs.     For  permanent  and  live  loads 
reduce  20  per  cent.     See  further  explanation  on  page  513. 

ANGLES    WITH   UNEQUAL   LEGS. LONG    LEG   VERTICAL. 


Size  of  angle. 

c. 

Span  i 

n  fee 

t. 

2 

3 

4 

5 

6 

7 

8 

9 

10 

7     X3}^X1 

56.43 

28.21 

18.81 

14.11 

11.29 

9.40 

8.06 

7.05 

6.27 

5.64 

7     X&AX  %6 

26.72 

13.36 

8.91 

6.68 

5.34 

4.45 

3.82 

3.34 

2.97 

2.67 

6     X4     XI 

42.77 

21.39 

14.26 

10.69 

8.55 

7.13 

6.11 

5.35 

4.75 

4.28 

6     X4     X   Y% 

17.71 

8.85 

5.90 

4.43 

3.54 

2.95 

2.53 

2.21 

1.97 

1.77 

6     X3^X1 

41.76 

20.88 

13.92 

10.44 

8.35 

6.96 

5.97 

5.22 

4.64 

4.18 

6     X3^X    YB 

17.33 

8.67 

5.78 

4.33 

3.47 

2.89 

2.48 

2.17 

1.93 

1.73 

5     X4     X    14 

26.61 

13.31 

8.87 

6.65 

5.32 

4.44 

3.80 

3.33 

2.96 

2.66 

5    X4    X  H 

12.48 

6.24 

4.16 

3.12 

2.50 

2.08 

1.78 

1.56 

1.39 

1.25 

5     X3HX   V* 

26.03 

13.01 

8.68 

6.51 

5.21 

4.34 

3.72 

3.25 

2.89 

2.60 

5     X3^X  5/i6 

10.35 

5.18 

3.45 

2.59 

2.07 

1.73 

1.48 

1.29 

1.15 

1.04 

5     X3     X  13/i6 

23.73 

11.87 

7.91 

5.93 

4.75 

3.96 

3.39 

2.97 

2.64 

2.37 

5     X3     X   5/i6 

10.08 

5.04 

3.36 

2.52 

2.02 

1.68 

1.44 

1.26 

1.12 

1.01 

4^X3     X   13/io 

19.31 

9.65 

6.44 

4.83 

3.86 

3.22 

2.76 

2.41 

2.15 

1.93 

4^X3     X  -Ho 

8.21 

4.11 

2.74 

2.05 

1.64 

1.37 

1.17 

1.03 

0.91 

0.82 

4     X3^X  i3/ie 

15.57 

7.79 

5.19 

3.89 

3.11 

2.60 

2.22 

1.95 

1.73 

1.56 

4     X3^X   5/i6 

6.72 

3.36 

2.24 

1.68 

1.34 

1.12 

0.96 

0.84 

0.75 

0.67 

4     X3     X  13/io 

15.31 

7.65 

5.10 

3.83 

3.06 

2.55 

2.19 

1.91 

1.70 

1.53 

4     X3     X   5/i6 

6.56 

3.28 

2.19 

1.64 

1.31 

1.10 

0.94 

0.82 

0.73 

0.66 

3^X3     X  13/i6 

11.73 

5.87 

3.91 

2.93 

2.35 

1.96 

1.68 

1.47 

1.30 

1.17 

3HX3     X   5/io 

5.12 

2.56 

1.71 

1.28 

1.02 

0.85 

0.73 

0.64 

0.57 

0.51 

3^X2^X  n/16 

9.87 

4.93 

3.29 

2.47 

1.97 

1.64 

1.41 

1.23 

1.10 

0.99 

3^X2^X   ^ 

4.00 

2.00 

1.33 

1.00 

0.80 

0.67 

0.57 

0.50 

0.44 

0.40 

314X2     X  fi/i6 
3MX2     X   M 

6.93 
3.36 

3.47 
1.68 

2.31 
1.12 

1.73 
0.84 

1.39 
0.67 

1.16 
0.56 

0.99 
0.48 

0.87 
0.42 

0.77 
0.37 

0.69 
0.34 

3     X2V£X   9/i6 

6.13 

3.07 

2.04 

1.53 

1.23 

1.02 

0.88 

0.77 

0.68 

0.61 

3     X2^X   M 

2.99 

1.50 

1.00 

0.75 

0.60 

0.50 

0.43 

0.37 

0.33 

0.30 

3     X2     X   H 

5.33 

2.67 

1.78 

1.33 

1.07 

0.89 

0.76 

0.67 

0.59 

0.53 

3     X2     X   M 

2.88 

1.44 

0.96 

0.72 

0.58 

0.48 

0.41 

0.36 

0.32 

0.29 

2^X2     X   ^ 

3.73 

1.87 

1.24 

0.93 

0.75 

0.62 

0.53 

0.47 

0.41 

0.37 

2.^X2     X  3/io 

1.55 

0.77 

0.52 

0.39 

0.31 

0.26 

0.22 

0.19 

0.17 

0.16 

2^X1^X   M 

3.15 

1.57 

0.05 

0.79 

0.63 

0.52 

0.45 

0.39 

0.35 

0.32 

2MX1^X  3/16 

1.23 

0.61 

0.41 

0.31 

0.25 

0.21 

0.18 

0.15 

0.14 

0.12 

2     Xl'^X   K 

1.23 

0.61 

0.41 

0.31 

0.25 

0.21 

0.18 

0.15 

0.14 

0.12 

2     Xl^X  3/i6 

0.96 

0.48 

0.32 

0.24 

0.19 

0.16 

0.14 

0.12 

0.11 

0.10 

B-gXl     X  M 

0.48 

0.24 

0.16 

0.12 

0.10 

0.08 

0.07 

0.06 

0.05 

0.05 

1^X1     X   Y* 

0.32 

0.16 

0.11 

0.08 

0.06 

0.05 

0.05 

0.04 

0.04 

0.03 

COMMON   SIZES  OF   STEEL   ANGLES. 


527 


SAFE   DISTRIBUTED   LOADS   IN   TONS   FOR   COMMON 
SIZES  OF  STEEL  ANGLES. 

Computed  for  fibre  stress  of  16,000  Ibs.     For  permanent  and  live  loads 
reduce  20  per  cent.     See  further  explanation  on  page  513. 

ANGLES    WITH    UNEQUAL   LEGS. SHORT   LEG   VERTICAL. 


Size  of  angle. 
Inches. 

c. 

Span  in  feet. 

2 

3 

4 

5 

6 

7 

8 

9 

10 

7     X  &A  X  I 

15.79 

7.89 

5.26 

3.95 

3.16'2.63 

2.26 

1.97 

1.75 

1.58 

7     XS^Xtte 

7.84 

3.92 

2.61 

1.96 

1.57:1.31 

1.12 

0.98 

0.87 

0  .  78 

6     X4     XI 

20.21 

10.11 

6.74 

5.05 

4.04'3.37 

2.89 

2.53 

2.25 

2.02 

6     X4     X   % 

8.53 

4.27 

2.84 

•2.13 

1.71 

1.42 

1.22 

1.07 

0.95 

0.85 

6     X3KX1 

15.47 

7.74 

5.16 

3.87 

3.09 

2.58 

2.21 

1.93 

1.72 

1.55 

6     X3HX   H 

6.56 

3.28 

2.19 

1.64 

1.31 

1.09 

0.94 

0.82 

0.73 

0.66 

5     X4     X   !/% 

17.65 

8.83 

5  .88 

4.41 

3.53 

2.94 

2.52 

2.21 

1.96 

1.77 

5     X4     X   Y% 

8.37 

4.19 

2.79 

2.09 

1.67 

1.40 

1.20 

1.05 

0.93 

0.84 

5     X&AX   7A 

13.44 

6.72 

4.48 

3.36 

2.69 

2.24 

1.92 

1.68 

1.49 

1.34 

5     X&AX  %6 

5.44 

2.72 

1.81 

1.36 

1.090.91 

0.78 

0.68 

0.60 

0.54 

5     X3     X   i%6 

9.28 

4.64 

3.09 

2.32 

1.86  1.55 

1.33 

1.16 

1.03 

0.93 

5     X3     X  5/ie 

4.00 

2.00 

1.33 

1.00 

0.800.67 

0.57 

0.50 

0.44 

0.40 

4^X3     X   i-Tio 

9.12 

4.56 

3.04 

2.28 

1.82  1.52 

1.30 

1.14 

1.01 

0.91 

4MX3X       %6 

4.05 

2.03 

1.35 

1.01 

0.81  0.68 

0.5S 

0.51 

0.45 

0.41 

4     X3HX   13/ie 

12.27 

6.13 

4.09 

3.07 

2.45 

2.05 

1.75 

1.53 

1.36 

1.23 

4     X3HX  5/ie 

5.39 

2.69 

1.80 

1.35 

1.08 

0.90 

0.77 

0.67 

0.60 

0.54 

4     X3     X   13/i6 

8.96 

4.48 

2.99 

2.24 

1.79 

1.49 

1.28 

1.12 

1.00 

0.90 

4     X3     X  5/i6 

3.95 

1.97 

1.32 

0.99 

0.79 

0.66 

0.56 

0.49 

0.44 

0.39 

3^X3     X   i3/i6 

8.80 

4.40 

2.93 

2.20 

1.76 

1.47 

1.26 

1.10 

0.98 

0.88 

3KX3     X  5/i6 

3.84 

1.92 

1.28 

0.96 

0.77 

0.64 

0.55 

0.48 

0.43 

0.38 

3^X2^X   Hie 

5.28 

2.64 

1.76 

1.32 

1.06 

0.88 

0.75 

0.66 

0.59 

0.53 

3KX2MX   1A 

2.19 

1.09 

0.73 

0.55 

0.44 

0.36 

0.31 

0.27 

0.24 

0.22 

3J4X2       X    9/16 

2.83 

1.41 

0.94 

0.71 

0.57 

0.47 

0.40 

0.35 

0.31 

0.28 

3^X2     X    M 

1.39 

0.69 

0.46 

0.35 

0.28 

0.23 

0.20 

0.17 

0.15 

0.14 

3     X2^X  9/i6 

4.37 

2.19 

1.46 

1.09 

0.87 

0.73 

0.62 

0.55 

0.49 

0.44 

3     X2^X   M 

2.13 

1.07 

0.71 

0.53 

0.43 

0.36 

0.30 

0.27 

0.24 

0.21 

3     X2     X  K 

2.51 

1.25 

0.84 

0.63 

0.50 

0.42 

0.36 

0.31 

0.28 

0.25 

3     X2     X   H 

1.33 

0.67 

0.44 

0.33 

0.27 

0.22 

0.19 

0.17 

0.15 

0.13 

2.^X2     X   V2 

2.45 

1.23 

0.82 

0.61 

0.49 

0.41 

0.35 

0.31 

0.27 

0.25 

2y2X2     X  3/i6 

1.07 

0.53 

0.36 

0.27 

0.21  0.18 

0.15 

0.13 

0.12 

0.11 

2MX1.^X   3^ 

1.39 

0.69 

0.46 

0.35 

0.280.23 

0.20 

0.17 

2MX1HX 

0.59 

0.29 

0.20 

0.15 

0.12 

0.10 

2     Xl'^X    \i 

0.64 

0.32 

0.21 

0.16 

0.13 

2     Xl^X  -Vie 

0.48 

0.24 

0.16 

0.12 

1:HX1     X   M 

0.27 

0.13 

0.09 

0sXl     X   >s 

0.16 

0.08 

0.05 

528 


COEFFICIENT  FOR   STEEL   ANGLES. 


COEFFICIENT  OF  STRENGTH  IN  TONS  FOR  ALL  SIZES 
AND  THICKNESSES  OF  STEEL  ANGLES. 

Computed  for  fibre  stress  of  16,000  Ibs. 

For  permanent  or  live  loads  reduce  20  per  cent. 

To  find  safe  distributed  load  for  any  span,  divide  C  by  span  in 
feet :  result  will  be  load  in  tons ;  or,  to  find  size  of  angle  for 
any  distributed  load  and  span,  multiply  the  load  by  the  span, 
and  select  an  angle  having  a  value  for  C  equal  or  larger  than 
the  product. 

For  load  at  centre  of  span  multiply  twice  the  load  by  the  span. 

For  further  explanation  see  page  513. 

ANGLES   WITH   EQUAL  LEGS. 


Size  in 
inches. 

Thick- 
ness of 
metal. 

C. 

Size  in 
inches. 

Thick- 
iess  of 
metal 

C. 

Size  in 
inches. 

Thick- 
ness oi 
metal. 

C. 

ii 

93.49 

% 

25.87 

% 

12.00 

*« 

88.91 

'i 

24.16 

\ 

11.25 

i 

84.26 

1% 

22.40 

10.45 

! 

79.52 
74.72 

5X5 

gf 

20.58 

18.72 

3^X3* 

1 

9.65 

8.80 

8X8 

% 

70.92 

i 

16.80 

J 

7.95 

'3 

64.93 

xle 

14.88 

7.04 

60.00 

| 

12.91 

f 

6.13 

jj 

54.93 

5/^ 

5.22 

9X 

49.81 

| 

16.48 

X16 

/It) 

44,64 

14*98 
13.49 

3JX3i 

| 

7.25 

5.28 

-j 

45.71 

4  -j  X  4  -o 

7/ 

11.95 

,/io 

43*25 

J 

10.40 

| 

6.93 

J 

40.75 

8.75 

/le 

6.35 

9710 

c  71 

3 

4 

O  t  .  J-  O 

35.52 

!^T 

16.05 

3X3 

7I 

O.  /  1 

5.07 

6X6 

32.91 

i 

15.18 

5* 

4.43 

| 

30.19 

i|^ 

13.92 

3.78 

/ie 

30.75 

J 

12.80 

X  1 

3.09 

i 

24.95 

4X4 

11.68 



7^ 

21.71 

^ 

10.51 

i 

4.75 

| 

18.82 

Jl6 

9.33 

716 

4.21 

J 

8.11 

2|X2f 

J 

3.68 

1 

30.93 

6.88 

3.15 

5X5 

1-V> 

29.28 

i 

2.56 

7 
t 

27.57 

For  Weight  and  Properties  of  these  angles,  see  Tables  Chapter  XX. 


COEFFICIENT  FOR  STEEL  ANGLES. 


529 


COEFFICIENT  OF  STRENGTH  IN  TONS  FOR  ALL  SIZES 

AND  THICKNESSES  OF  STEEL  ANGLES  (continued). 

Reduce  20  per  cent,  for  permanent  and  live  loads. 

See  explanation  on  opposite  page. 

ANGLES  WITH  EQUAL  LEGS. 


Size  in 
i-.chss. 

Thick- 
ness or 
metal. 

c. 

Size  in 
inches. 

Thick- 
ness oi 
metal. 

C. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

C. 

21X21 

"4 

'  i 
4 

1 
It 

si 

3.89 
3.47 
3.04 
2.56 
2.13 
1.60 

3.09 

2.77 
2.40 
2.08 
1.71 
1.28 

2X2 

5! 
'* 

J 
# 

•\ 

2.13 

1.87 
1.60 
1.33 
1.01 

1.60 
1.39 
1.23 
1.01 
0.75 

1.01 
.864' 
.715 

ilxii 

I 

\ 

0.555 
.373 

.581 
.485 
.378 
.261 

.298 
.234 
.165 

.176 
.123 

.128 
.091 

HxH 

ifxif 

21X2! 

ixi 

i!xii 

fxj 

fxf 

ANGLES  WITH  UNEQUAL  LEGS. LONG  LEG  VERTICAL. 


iX  61 

8X6 


7X3J 


6?X4f 
61X4 


6X4 


82.29 

62.56 
42.83 

56.42 
53.33 
50.24 
47.04 
43.50 
40.53 
37.17 
33.76 
30.29 
26.72 

51.09 
20.64 

42.77 
40.48 
38.13 


6X4 


6X31 


35.73 
33.33 
30.62 

28.32 
25.76 
23.04 
20.43 
17.71 

41. 7f 
39.52 
37.22 
34.93 

32.5; 

30.13 
27.68 
25.17 
22.61 
20.00 
17.33 


5fX5 
5|X3f 


5X4 


5X31 


28.21 

18.72 

24.85 
14.72 

26.61 
23.31 
19.89 
16.26 
12.48 

26.02 
24.42 
22.82 
21.17 
19.46 
17.70 
15.94 
14.08 
12.21 


For  Weight  and  Properties  of  these  angles,  see  Tables  Chapter  XX. 


530 


COEFFICIENT  FOR  STEEL  ANGLES. 


COEFFICIENT  OF  STRENGTH  IN  TONS  FOR  ALL  SIZES 

AND  THICKNESSES  OF  STEEL  ANGLES  (continued). 

Reduce  20  per  cent,  for  permanent  and  live  loads. 

See  explanation  at  beginning  of  table. 

ANGLES    WITH  UNEQUAL    LEGS. LONG   LEG   VERTICAL    (cont'd). 


Size  in 
inches. 

Thick- 
ness of 
metal. 

c. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

(7. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

(7. 

5X3^ 

%, 

10.34 

3JX2| 

i 

12.21 

f\  79 

3X2 

i 

2.88 

13/ 

9*3  7^ 

8 

i 

^  7^ 

5X3 

I 

! 

Ye 
i 

22.18 
20.58 
18.93 
17.22 
15.92 

1  q  7fi 

3iX3 

n* 

1 

/Ye 

11.73 
10.93 
10.58 
9.38 

8.58 
7  7^ 

2iX2 

2 

$ 

Ye 
% 

3.30 
2.93 
2.50 
2.02 
1.54 

A 

11.94 
10.08 

2 

Ye 
f 

6.88 
6.02 
^  19 

24x1} 

4 

1.97 
1.54 

vy 

1Q  °,1 

/16 

, 

9  77 

2. 
4 

18.02 

1  fi  74. 

9.86 

91  O 

24x14 

1.49 

41X3 

gs 

15.41 
14.08 

i  o  «4 

3JX2J 

1 

7/ 

8.32 
7.52 

ft  79 

24X11 

f 
% 

2.66 
1.44 

/Ye 
Ye 

11.20 
9.76 
8.21 

/16 

5* 

XJL 

5.81 
4.96 
4.00 

21x14 

I 

8Z 

3.14 
2.24 
1.60 
1  22 

l-V 

1  K    C7 

05  V  9  * 

3 

^  81 

716 

1 

14.66 
13.65 

0  -8  A  ^  8 

3^X2 

8 
1 
4 

3.84 

2Xl| 

Ye 

/Vo 

1.60 
1.013 

4X3J 

•1 

12.53 
11.45 
i  n  9Q 

3JX2 

j 

6.93 
6.24 

4  S^ 

2X14 

/ie 

1.546 
0.960 

9.17 

o  nn 

. 

i 

3.36 

2X1| 

O        J  3 

i 

1.226 
OQf\n 

.  .Ye 

6.72 

?r6 

6.13 
5  54 

1 

1.920 
0  960 

\y 

15  30 

^  V9t 

7^ 

4  Qft 

4 

716 

4y  ** 

i 

f 

14.29 
13.28 
12.26 
11  14 

5f 
1 

4 

4.32 

3.68 
2.98 

ifxit 

ifxi 

1  3  y  1 

7l6 

i 

0.8 
.320 
.480 
"390 

i 

1  n  ns 

t 

K  qq 

8 

2~ 
J 

8.96 

7.78 
6.56 

3X2 

3 

4.74 
4.16 
3.52 

ifxl 

ixf 

1 

.304 
.149 

For  Weight  and  Properties  of  these  angles,  see  Tables  Chapter  XX. 


COEFFICIENT  FOR  STEEL  ANGLES. 


531 


COEFFICIENT  OF  STRENGTH  IN  TONS  FOR  ALL  SIZES 

AND  THICKNESSES  OF  STEEL  ANGLES  (continued). 

Reduce  20  per  cent,  for  permanent  and  live  loads. 

See  explanation  at  beginning  of  table. 

ANGLES  WITH    UNEQUAL  LEGS.       SHORT    LEG  VERTICAL. 


Size  in 
inches. 

fhick- 
ness  of 
metal. 

C. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

C. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

c. 

8JX6J 
8JX6J 

1 

f 

49.06 
37.33 

5fX5 

1 

22.77 
15.14 

^Lx_!_ 

V- 

,•  lo 

4.05 

8   X6 

25.60 

% 

12.26 

5fX3f 

f 

11.20 

a 
f 

11.46 

1 

15.78 

5iX3| 

6.50 

% 

10.66 

% 

14.93 

j 

9.81 

,  1 

14.08 

{ 

17.65 

4x31 

8.96 

13.22 

3 

4 

15.46 

J 

8.10 

t 

3 

12.32 

5X4 

f 

13.22 

7.20 

7Xo^ 

11.41 

1 

10.88 

| 

6.29 

5 

8 

10.50 

} 

8.37 

%> 

5.38 

?| 

9.60 

i 

8.64 

£ 

13.44 

?1G 

8.96 

K 

7.84 

v''\c 

12.64 

'  £ 
1 

8.37 

ilf 

11.84 

% 

7.78 

6  -J  X  4  J 

is/ 

21.70 

10.98 

| 

7.20 

61X4 

f 

8.64 

5X31 

3 

10.13 

9.22 

4X3 

J^ 

6.56 
5.97 

i 

20.21 

xii 

8.32 

2 

/i6 

5*28 

!^6 

19.14 

^6 

7.41 

1 

4.64 

! 

18.08 

'  't 

6.45 

% 

3.94 

16.96 

/16 

5.44 

j 

6X4 

J 

15.84 
14.72 

13/ 

9.28 

3fX2f 

1 

t 

6.29 
3.52 

I1 

13.54 

'I 

8.69 



12.32 

%6 

8.05 

l%> 

8.80 

1 

11.09 

s 

7.41 

"t 

8.21 

Jie 

9.86 

5X3 

% 

6.77 

% 

7.68 

1 

8.53 

1 

6.13 

1 

7.09 

/ir 

5.44 

31x3 

% 

6.45 

1 

15.46 

I 

4.74 

i 

5.86 

% 

14.61 

xle 

4.00 

Jl6 

5.22 

* 

13.81 

J 

4.53 

12.96 

l/{c 

9.12 

3.84 

^ 

i 

12.10 

\ 

8.53 

6X31 

11.25 

794 

/Ir 

5.28 

gl 

10.34 
9.44 

41X3 

1 

7.30 
6.66 

31X21 

1 

4.90 

4.48 

1 

8.48 

1 

6.02 

31x21 

7* 

4.05 

Jie 

7.52 

Ji6 

5.38 

3.62 

1 

6.56 

1 

4,69 

| 

3.14 

For  Weight  and  Properties  of  these  angles,  see  Tables  Chapter  XX. 


532 


COEFFICIENT  FOR  STEEL   ANGLES. 


COEFFICIENT  OF  STRENGTH  IN  TONS  FOR  ALL  SIZES 

AND  THICKNESSES  OF  STEEL  ANGLES  (continued). 

Reduce  20  per  cent,  for  permanent  and  live  loads. 

See  explanation  at  beginning  of  table. 

ANGLES  WITH  UNEQUAL  LEGS. SHORT  LEG  VERTICAL  (continued). 


Size  in 
inches. 

3JX2J 

Thick- 
ness of 
metal. 

C. 

2.66 
2.18 

2.18 
1.12 

2.82 
2.56 
1.97 
1.38 

4.37 
3.94 
3.52 
3.09 
2.61 
2.13 

2.50 
2.24 
1.97 
1.70 
1.33 

Size  in 
inches. 

Thick- 
ness  of 
metal. 

C. 

Size  in 
inches. 

Thick- 
ness of 
metal. 

% 

/($ 

SA 
a 

X 

xYo 

1 

i 

1 

c. 

0.906 
.586 

.640 
.480 

.906 
.373 

.533 
.213 

.266 
.160 

.128 
.064 

* 

I 

% 

I 

% 
i 
% 
l 
ft 

.Ye 

1 

2JX2 

4 

4 

% 

%, 
§ 

9f 

•1 

1 
I 

% 

% 
% 

2.45 
2.18 
1.92 
1.65 
1.33 
1.06 

1.06 

.80 

1.06 

.586 

.746 
.426 

1.386 
1.066 
.746 

.586 

1.226 

.800 

2X1J 

3§X2i 
3^X2 

2Xlf 

3ix2 

2%xl^ 
2XH 

2iXl| 

ifxit 

2JX1J 

3X21 

11  XI 

2JX1J 

1   X* 

1    Xf 

2iXli 

3X2 

2X1'| 

For  Weight  and  Properties  of  these  angles,  see  Tables  Chapter  XIII. 


LOADS  IN   TONS  FOR  CARNEGIE  TEES.        533 


SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR  CARNEGIE 
TEES. 

Computed  for  fibre  stress  of  16,000  Ibs.     For  permanent  and  live  loads, 
reduce  20  per  cent.     See  further  explanation  page  513. 


Size. 
Flange 

Wt. 
per 

c. 

Span  in  feet. 

by  stem. 

foot. 

2 

3 

4 

5 

6 

7 

8 

9 

10 

5     X3 

13.6 

6.29 

3.15 

2.10 

1.57 

1.26 

1.05 

0.90 

0.79 

0.70 

0.63 

5     X2^ 

11.0 

4.59 

2.29 

1.53 

1.15 

0.92 

0.76 

0.66 

0.57 

0.51 

0.46 

4MX3K 

15.8 

11.36 

5.68 

3.79 

2.84 

2.27 

1.89 

1.62 

1.42 

1.26 

1.14 

4>iX3 

8.5 

4.32 

2.16 

1.44 

1.08 

0.86 

0.72 

0.62 

0.54 

0.48 

0.43 

4^X3 

10.0 

5.01 

2.51 

1.67 

1.25 

1.00 

0.84 

0.72 

0.63 

0.56 

0.50 

4^X2^ 

8.0 

2.99 

1.49 

0.96 

0.75 

0.60 

0.48 

0.43 

0.37 

0.32 

0.30 

4M  X  2}4 

9.3 

3.47 

1.73 

1.16 

0.87 

0.69 

0.58 

0.50 

0.43 

0.39 

0.35 

4     X5 

15.6 

16.53 

8.27 

5.51 

4.13 

3.31 

2.76 

2.36 

2.07 

1.84 

1.65 

4     X5 

12.0 

12.96 

6.48 

4.32 

3.24 

2.59 

2.16 

1.85 

1.62 

1.44 

1.30 

4     X4^ 

14.6 

13.60 

6.80 

4.53 

3.40 

2.72 

2.27 

1.94 

1.70 

1.51 

1.36 

4     X4^ 

11.4 

10.56 

5.28 

3.52 

2.64 

2.11 

1.76 

1.51 

1.32 

1.17 

1.06 

4     X4 

13.7 

10.77 

5.39 

3.59 

2.69 

2.15 

1.80 

1.54 

1.35 

1.20 

1.08 

4     X4 

10.9 

8.75 

4.37 

2.92 

2.19 

1.75 

1.46 

1.25 

1.09 

0.97 

0.87 

4     X3 

9.3 

4.69 

2.35 

1.56 

1.17 

0.94 

0.78 

0.67 

0.59 

0.52 

0.47 

4     X2Y2 

8.6 

3.31 

1.65 

1.10 

0.83 

0.66 

0.55 

0.47 

0.41 

0.37 

0.33 

4     X2^ 

7.3 

2.93 

1.47 

0.98 

0.73 

0.59 

0.49 

0.42 

0.37 

0.33 

0.29 

4     X2 

7.9 

2.13 

1.07 

0.71 

0.53 

0.43 

0.36 

0  .  30 

0.27 

0.24 

0.21 

4     X2 

6.6 

1.81 

0.91 

0.60 

0.45 

0.36 

0.30 

0.26 

0.23 

0.20 

0.18 

3^X4 

12.8 

10.56 

5.28 

3.52 

2.64 

2.11 

1.76 

1.51 

1.32 

1.17 

1.06 

33^X4 

9.9 

8.27 

4.13 

2.76 

2.07 

1.65 

1.38 

1.18 

1  03 

0.92 

0.83 

3j^X3^ 

11.7 

8.11 

4.05 

2.70 

2.03 

1.62 

1.35 

1.16 

1.01 

0.90 

0.81 

3H  X  3^ 

9.2 

6  .  35 

3.17 

212 

1.59 

1  .  27 

1.06 

0.91 

0.79 

0.71 

0.63 

3^X3 

10.9 

6.03 

3.01 

2!oi 

1.51 

1.21 

1.00 

0  .  86 

0.75 

0.67 

0.60 

3^X3 

8.5 

4.69 

2  .  35 

1.56 

1.17 

0.94 

0.78 

0.67 

0.59 

0.52 

0.47 

3^X3 

7.8 

3.84 

1.92 

1.28 

0.96 

0.77 

0.64 

0.55 

0.48 

0.43 

0.38 

3     X4 

11.8 

10.35 

5.17 

3.45 

2.59 

2.07 

1.72 

1.48 

1   29 

1.15 

1  .03 

3     X4 

10.6 

9.49 

4.75 

3.16 

2.37 

1.90 

1.58 

1  .  36 

1.19 

I  .05 

0  .  95 

3     X4 

9.3 

8.37 

4.19 

2.79 

2.09 

1.67 

1.40 

1  .20 

1.05 

0.93 

0.84 

3     X3K 

10.9 

7.95 

3.97 

2.65 

1.99 

1.59 

1.32 

1.14 

0.99 

0.88 

0.79 

3     X3y2 

9.8 

7.31 

3.65 

2.44 

1.83 

1.46 

1.22 

1.04 

0.91 

0  81 

0.73 

3     X3^ 

8.5 

6.45 

3.23 

2.15 

1.61 

1.29 

1.08 

0.92 

0.81 

0.72 

0.65 

3     X3 

10.0 

5.87 

2.93 

1.96 

1.47 

1.17 

0.98 

0.84 

0.73 

0.65 

0.59 

534       LOADS  IN   TONS  FOR  CARNEGIE  TEES. 

SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR  CARNEGIE 
TEES  (continued). 

Computed  for  fibre  stress  of  16,000  Ibs.     For  permanent  and  live  loads, 
reduce  20  per  cent.     For  further  explanation  see  page  513. 


Size. 
Flange 

wt. 

per 

C. 

Span  in  feet. 

by  stem 

foot. 

2 

3 

4 

5 

6 

7 

8 

9 

10 

3     X3 

9.1 

5.39 

2.69 

1.80 

1.35 

1.08 

0.90 

0.77 

0.67 

0.60 

0.54 

3     X3 

7.8 

4.59 

2.29 

1.53 

1.15 

0.92 

0.76 

0.66 

0.57J0.51 

0.46 

3     X3 

6.6 

3.95 

1.97 

1.32 

0.99 

0.79 

0.66 

0.56 

0.49(0.44 

0  .  39 

3     X2*4 

7.2 

3.20 

1.60 

1.07 

0.80 

0.64 

0.53 

0.46 

0.40 

0.36 

0.32 

3     X2^ 

6.1 

2.77 

1.39 

0.92 

0  69 

0.55 

0.46 

0.40 

0.35 

0.31 

0.28 

2*4X2 

7.4 

4.00 

2.00 

1  .  33 

1.00 

0.80 

0.67 

0.57 

0.50 

0.44 

0.40 

2V£  X  3 

7.2 

4.64 

2.32 

1.55 

1.16 

0.93 

0.77 

0.66 

0.58 

0.52 

0.46 

2^X3 

6.1 

4.05 

2.03 

1.35 

1.01 

0.81 

0.68 

0.58 

0.51 

0.45 

0.41 

2*4  X  2*4 

6.7 

3.89 

1.95 

1.30 

0.97 

0.78 

0.65 

0.56 

0.49 

0.43 

0.39 

2*4X2% 

5.8 

3.20 

1.60 

1.07 

0.80 

0.64 

0  .  53 

0.46 

0.40 

0.36 

0.32 

2*4X2*^ 

6.4 

3.15 

1.57 

1.05 

0.79 

0.63 

0.52 

0.45 

0.39 

0.35 

0.31 

2*^X2*^ 

5.5 

2.67 

1.33 

0.89 

0.67 

0.53 

0.44 

0.38 

0.33 

0.30 

0.27 

2*4x1*4 

2.9 

0.48 

0.24 

0.16 

0.12 

0.10 

2*4X2*4 

4.9 

2.24 

1.12 

0.75 

0.56 

0.45 

0.37 

0.32 

0.28 

0.25 

0.22 

2*4X2/4 

4.1 

1.71 

0.85 

0.57 

0.43 

0.34 

0.28 

0.24 

0.21 

0.19 

0.17 

2     X2 

4.3 

1.76 

0.88 

0.59 

0.44 

0.35 

0.29 

0.25 

0.22 

0.20 

0.18 

2     X2 

3.7 

1.33 

0.67 

0.44 

0  .  33 

0.27 

0.22 

0.19 

0  .  17 

0.15 

0.13 

2     Xl*4 

3.1 

0  80 

•  0.40 

0.27 

0.20 

0.16 

0  .  1  3 

0.11 

0.10 

i*4xi% 
1*4X1*4 

3.1 
3.6 

1.01 
0.80 

0.51 
0.40 

0.34 
0.27 

0.25 
0.20 

0.20 
0.16 

0.17 
0.13 

0.14 
0.11 

0.13 
0.10 

i*4xm 

2.4 

0.75 

0.37 

0.25 

0.19 

0.15 

0.12 

[*4Xl*/2 

1.84 

0.59 

0.29 

0.20 

0.15 

0.12 

1*4X1*4 

2.04 

0.53 

0.27 

0.18 

0.13 

0.11 

1*AX1*4 

1.53 

0.37 

0.19 

0.12 

0.09 

0.07 

1     XI 

1.23 

0.27 

0.13 

0.09 

0.07 

0.05 

1     XI 

0.87 

0.16 

0.08 

0.05 

0.04 

0.03 

LOADS   IN   TONS   FOR   Z-BARS. 


535 


SAFE   DISTRIBUTED   LOADS  IN  TONS  FOR  CAMBRIA 
AND  CARNEGIE  Z-BARS. 

For  fibre  stress  of  16,000  Ibs.  per  square  inch. 

To  use  this  table  for  other  spans,  or  other  methods  of  loading,  see  ex- 
planation page  513. 


Size, 
ins. 

Thick 
ness 
of 
meta] 

c. 

45.0 
52.4 
59.9 

Span  in  feet. 

4 

5 

6 

7 

8 

9 

10 

12 

14 

6 

6^16 

1 

11.25 
13.11 
14.96 

9.00 
10.48 
11.97 

7.50 
8.73 
9.97 

6.43 

7.48 
8.55 

5.63 
6.55 

7.48 

5.00 
5.82 
6.65 

4.50 
5.24 
5.99 

3.75 
4.37 
4.99 

3.21 
3.74 

4.28 

6 

|l6 
11/16 

61.6 
68.4 
75.2 

15.40 
17.09 
18.80 

12.32 
13.67 
15.04 

10.27 
11.40 
12.53 

8.80 
9.76 
10.74 

7.70 
8.55 
9.40 

6.84 
7.60 
8.36 

6.16 
6.84 
7.52 

5.13 
5.70 
6.27 

4.40 
4.88 
5.37 

6 

l« 

74.9 
81.2 
87.5 

18.72 
20.29 
21.86 

14.98 
16.23 
17.49 

12.48 
13.53 
14.57 

10.70 
11.59 
12.49 

9.36 

10.15 
10.93 

8.32 
9.02 
9.72 

7.49 
8.12 
8.75 

6.24 

6.76 
7.29 

5.35 
5.80 
6.25 

5 

'I6 

7/46 

28.5 
34.1 
39.7 

7.12 
8.52 
9.92 

5.70 
6.82 
7.94 

4.75 
5.68 
6.62 

4.07 

4.87 
5.67 

3.56 
4.26 
4.96 

3.17 
3.79 
4.41 

2.85 
3.41 
3.97 

2.37 

2.84 
3.31 

2.03 
2.43 
2.83 

5 

K 

40.9 
46.0 
51.1 

10.24 
11.49 
12.76 

8.19 
9.19 
10.21 

6.83 
7.66 
8.51 

5.85 
6.56 
7.29 

5.12 
5.75 
6.38 

4.55 
5.11 
5.67 

4.09 
4.60 
5.11 

3.41 
3.83 
4.25 

2.92 
3.28 
3.65 

5 

51£6 

3; 

50.5 
55.2 
59.7 

12.63 
13.79 
14.94 

10.10 
11.03 
11.95 

8.42 
9.19 
9.96 

7.21 

7.88 
8.54 

6.32 
6.89 

7.47 

5.61 
6.13 
6.64 

5.05 
5.52 
5.97 

4.21 
4.60 
4.98 

3.61 
3.94 

4.27 

4 

H* 

16.8 
20.8 
24.9 

4.19 
5.21 
6.22 

3.35 
4.17 
4.98 

2.79 
3.48 
4.15 

2.39 
2.98 
3.56 

2.09 
2.60 
3.11 

1.86 
2.32 

2.77 

1.68 
2.08 
2.49 

1.40 
1.74 
2.08 

1  .20 
1.49 

1.78 

4 

1 

25.7 
29.3 
32.9 

6.44 
7.33 
8.24 

5.15 
5.87 
6.59 

4.29 
4.89 
5.49 

3.68 
4.19 
4.71 

3.22 
3.67 
4.12 

2.86 
3.26 
3.66 

2.57 
2.93 
3.29 

2.15 
2.44 
2.75 

1.84 
2.09 
2.35 

4 

11/16 

32.3 
35  .  5 
38.7 

8.06 
8.86 
9.68 

6.45 
7.09 

7.74 

5.37 
5.91 
6.45 

4.61 
5.06 
5.53 

4.03 
4.43 
4.84 

3.58 
3.95 
4.30 

3.23 
3  .  55 

3.87 

2.69 
2.96 
3.23 

2.31 
2.53 
2.76 

3 

3^6 

5/i6 

10.3 
12.7 

2.56 
3.17 

2.05 
2.54 

1.71 
2.12 

1.46 
1.81 

1.28 
1.58 

1.14 
1.41 

3 

31/16 

%6 

13.7 
15.9 

3.44 
3.97 

2.74 
3.18 

2.28 
2.65 

1.96 
2.27 

1.72 
1.98 

1.52 
1.77 

3 

31/16 

9/16 

16.3 
18.3 

4.08 
4.57 

3.26 
3.66 

2.72 
3.05 

2.33 
2.62 

2.04 

2.28 

1.81 
2.03 

Steel-beam  Girders. 

A  box  girder  consisting  of  a  pair  of  steel  I-beams  with  top  and 
bottom  flange-plates,  furnishes  an  economical  girder  for   short 


536  STEEL-BEAM   BOX-GIRDERS. 

spans.  The  flange-plates  are  riveted  to  the  beams  with  rivets 
f"  diameter,  spaced  from  6  to  9  inches  on  centres.  In  short 
girders  care  must  be  taken  to  have  a  sufficient  number  of  rivets 
in  each  plate,  between  the  end  of  the  girder  and  the  centre  of  the 
span,  to  develop  the  full  tensile  or  compressive  strength  of  the 
plate,  figured  at  13,000  Ibs.  per  square  inch. 

The  following  tables  give  the  safe  loads  for  the  sizes  of  beams 
most  likely  to  be  used  in  this  way.  The  values  given  in  the 
tables  are  founded  upon  the  moments  of  inertia  of  the  various 
sections,  deductions  being  made  for  the  rivet-holes  in  both  flanges. 
In  order  to  amply  compensate  for  the  deterioration  of  the  metal 
around  the  rivet-holes  from  punching,  and  also  because  these 
girders  are  more  often  used  to  support  permanent  loads,  such 
as  brick  or  stone  walls,  the  maximum  fibre  stress  was  limited  to 
13,000  Ibs.,  although  it  is  but  right  to  state  that  most  of  the 
latest  handbooks  of  the  steel  manufacturers  gi  ve  tables  for  such 
girders  based  on  15,000  Ibs.  fibre  stress.  The  author  advises 
that  for  loads  of  masonry,  which  usually  come  very  closely  to 
the  estimated  load,  arid  which  are  constantly  exerted,  the  girders 
be  not  loaded  beyond  the  values  given  in  the  following  tables, 
while  for  ordinary  floor  loads,  which  seldom  reach  the  estimated 
load,  an  addition  of  -Jth  may  be  added  to  the  values  given  in  the 
tables. 

EXAMPLE. — A  13"  brick  wall,  15  feet  high,  is  to  be  built  over  an 
opening  of  24  feet.  What  will  be  the  section  of  the  girder  re- 
quired? 

Ans.  Assuming  25  feet  as  the  distance,  centre  to  centre  of 
bearings,  the  weight  of  the  wall  will  be  25 X 15  X 121  =  45,375  Ibs., 
or  22.68  tons. 

From  the  tables  we  find  that  a  girder  composed  of  two  12" 
steel  beams,  each  weighing  31.5  Ibs.  per  foot,  and  two  14"  Xl" 
lange-plates  will  carry  safely,  for  a  span  of  25  feet,  a  uniformly 
distributed  load  of  23.23  tons,  including  its  own  weight.  Deduct- 
ing the  latter,  1.42  tons,  given  in  the  next  column,  we  find  21.81 
tons  for  the  value  of  the  safe  net  load,  which  is  1.07  tons  less  than 
required.  From  the  following  column  we  find  that  by  inci easing 
the  thickness  of  the  flange-plates  %ff  we  may  add  1.52  tons  to  the 
allowable  load.  This  will  more  than  cover  the  difference.  Hence 
the  required  section  will  be  two  12"  steel  beams  31.5  Ibs.  per  foot, 
and  two  14" 'X%"  steel  cover-plates. 


STEEL-BEAM   BOX-GIRDERS. 


537 


STEEL-BEAM  BOX-GIRDERS.     SAFE  LOADS  IN  TONS, 
UNIFORMLY  DISTRIBUTED. 

2-20"  steel  I-beams  and  2  steel  plates  1 


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176.72 

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181.51 

1.34 

6.56 

160.66 

1.16 

6.68 

0.04 

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166.39 

1.46 

6.02 

147.26 

1.27 

6.12 

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153.60 

1.58 

5.56 

135.95 

1.37 

5.65 

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142.64 

1.70 

5.16 

126.24 

1.48 

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133.12 

1.83 

4.81 

117.82 

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124.80 

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110.45 

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117.47 

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103.96 

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110.94 

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98.18 

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105.10 

2.31 

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93.01 

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99.83 

2.43 

3.61 

88.36 

2.11 

3.67 

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95.08 

2.56 

3.44 

84.15 

2.22 

3.50 

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90.77 

2.68 

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80.33 

2.32 

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86.82 

2.80 

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76.84 

2.43 

3.19 

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83.20 

2.92 

3.01 

73.64 

2.53 

3.06 

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79.87 

3.04 

2.89 

70.69 

2.64 

2.94 

0.08 

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76.80 

3.16 

2.78 

67.97 

2.75 

2.82 

0.09 

27 

73.96 

3.29 

•2.68 

65.46 

2.85 

2.72 

0.09 

28 

71.32 

3.41 

2.58 

63.12 

2.96 

2.62 

0.09 

29 

68.86 

3.53 

2.49 

60.94 

3.06 

2.53 

0.10 

30 

66.56 

3.65 

2.41 

58.91 

3.17 

2.45 

0.10 

31 

64.41 

3.77 

2.33 

57.01 

3.27 

2.37 

0.10 

32 

62.41 

3.89 

2.26 

55.22 

3.38 

2.29 

0.11 

33 

60.51 

4.02 

2.19 

53.56 

3.48 

2.22 

0.11 

34 

58.73 

4.14 

2.12 

51.98 

3.59 

2.16 

0.11 

35 

57.05 

4.26 

2.06    . 

50.50 

3.70 

2.10 

0.12 

36 

55.46 

4.38 

2.01 

49.09 

3.80 

2.04 

0.12 

37 

53  .  96 

4  .  50 

1.95 

47.77 

3.91 

1.98 

0.12 

38 

52.54 

4.62 

1.90 

46.51 

4.01 

1.93 

0.13 

39 

51.20 

4.75 

1.85 

45.32 

4.12 

1.88 

0.13 

Above  values  are  based  on  maximum  fibre  strain  of  13,000  Ibs.  per 
square  inch,  rivet-holes  in  both  flanges  deducted.  Weights  of  girders 
correspond  to  lengths,  centre  to  centre  of  bearings. 


538 


STEEL-BEAM  BOX-GIRDERS 


STEEL-BEAM  BOX-GIRDERS.     SAFE  LOADS  IN   TONS, 
UNIFORMLY  DISTRIBUTED. 

2-18"  steel  I-beams  and  2  steel  plates  16"  Xf". 


bo 

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4.66 

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4.35 

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4.07 

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1.80 

3.43 

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3.26 

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3.26 

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75.5 

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3.10 

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2.96 

67.0 

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2.96 

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69.0 

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64.1 

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2.83 

156 

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66.1 

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2.72 

61.5 

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2.72 

163 

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2.61 

59.0 

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2.61 

170 

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61.0 

5876 

2.51 

56.7 

5096 

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2.51 

177 

27 

58.8 

6102 

2.41 

54.6 

5292 

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2.41 

184 

28 

56.6 

6328 

2.33 

52.7 

5488 

1.21 

2.33 

190 

29 

54.7 

6554 

2.25 

50.9 

5684 

1.17 

2.25 

197 

30 

52.9 

6780 

2.17 

49.2 

5880 

1.13 

2.17 

204 

31 

51.8 

7006 

2.10 

47.6 

6076 

1.10 

2.10 

211 

32 

49.6 

7232 

2.04 

46.1 

6272 

1.06 

2.04 

218 

33 

48.1 

7458 

1.98 

44.7 

6468 

1.03 

1.98 

224 

34 

46.7 

7684 

1.92 

43.4 

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1.00 

1.92 

231 

35 

45.3 

7910 

1.86 

42.1 

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1.86 

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1.81 

41.0 

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1.81 

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42.9 

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1.76 

39.9 

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1.76 

252 

38 

41.2 

8588 

1.72 

38  .  8 

7448 

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1.72 

258 

Above  values  are  based  on  maximum  fibre  strain  of  13,000  Ibs.  per  sq.  in., 
rivet-holes  in  both  flanges  deducted.  Weights  correspond  to  lengths,  centre 
to  centre  of  bearings. 


STEEL-BEAM  BOX-GIRDERS. 


STEEL-BEAM  BOX-GIRDERS.     SAFE  LOADS    IN  TONS, 
UNIFORMLY  DISTRIBUTED. 

2-15"  steel  I-beams  and  2  steel  plates  14"  X$i". 


M 

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122.33 

1.06 

111  .01 

0.91 

90  .  29 

0.72 

4.63 

0  .  03 

11 

111.21 

1.17 

100.92 

1  .  00 

82.08 

0.79 

4.21 

0.03 

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101.95 

1.27 

92.51 

1  .09 

75.24 

0.86 

3.86 

0.03 

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94.10 

1.38 

85.40 

1.18 

69.45 

0.93 

3.57 

0.04 

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87.38 

1.48 

79  .  30 

1.27 

64.50 

1.00 

3.31 

0.04 

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81.56 

1.59 

74.01 

1.36 

60.19 

1.08 

3.09 

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76.46 

1.70 

69.38 

1.45 

56.43 

1.15 

2.90 

0.05 

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71.96 

1.80 

65.30 

1.54 

53.11 

1.22 

2.72 

0.05 

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67.96 

1.91 

61.67 

1.63 

50.16 

1.29 

2  57 

0.05 

19 

64.39 

2.01 

58.43 

1.72 

47.52 

1.36 

2.43 

0.05 

20 

61.17 

2.12 

55.50 

1.81 

45.14 

1.44 

2.32 

0.06 

21 

58.25 

2.22 

52.86 

1.90 

42.99 

1.51 

2.21 

0.06 

22 

55.60 

2.33 

50.46 

2.00 

41.04 

1.58 

2.11 

0.06 

23 

53.19 

2.43 

48.27 

2.09 

39.25 

1.65 

2.02 

0.07 

24 

50.97 

2.54 

46.25 

2.18 

37.62 

1.72 

1.93 

0.07 

25 

48.93 

2.65 

44.40 

2.27 

36.12 

1.79 

1.85 

0.07 

26 

47.05 

2.76 

42.70 

2.36 

34.72 

1.87 

1.78 

0.08 

27 

45.31 

2.86 

41.12 

2.45 

33.44 

1.94 

1.71 

0.08 

28 

43.69 

2.96 

39.65 

2.54 

32.25 

2.01 

1.66 

0.08 

29 

42.18 

3.07 

38.28 

2.63 

31.13 

2.08 

1.60 

0.08 

30 

40.78 

3.17 

37.00 

2.72 

30.09 

2.15 

1.54 

0.09 

31 

39.46 

3.23 

35.81 

2.81 

29.12 

2.23 

1.49 

0.09 

32 

38.23 

3.38 

34.69 

2.80 

28.21 

2.30 

1.45 

0.09 

33 

37.07 

3.46 

33  .  64 

2.99 

27.36 

2.37 

1.41 

0.10 

34 

35.98 

3.60 

32.65 

3.08 

26.55 

2.44 

1.37 

0.10 

35 

34.95 

3.70 

31.72 

3.17 

25.80 

2.51 

1.33 

0.10 

36 

33.98 

3.81 

30.84 

3.27 

25.08 

2.58 

1.29 

0.10 

37 

33.06 

3.91 

30.00 

3.36 

24.40 

2.66 

1.25 

0.11 

38 

32.20 

4.02 

29.21 

3.45 

23  .  76 

2  73 

1.22 

0.11 

39 

31.37 

4.13 

28.47 

3.54 

23.15 

2.80 

1.19 

0.11 

Above  values  are  based  on  maximum  fibre  strains  of  13,000  Ibs.  per.  sq.  in., 
rivet-holes  in  both  flanges  deducted.  Weights  of  girders  correspond  to 
lengths,  centre  to  centre  of  bearings. 


540 


STEEL-BEAM  BOX-GIRDERS. 


STEEL    BEAM   BOX-GIRDERS.      SAFE  LOAD  IN  TONS, 
UNIFORMLY  DISTRIBUTED. 

2-12"  steel  I-beams  and  2  steel  plates  14"  XJ^". 


W) 

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64.94 

0.65 

3.75 

58.08 

0.57 

3.81 

0.03 

11 

59.02 

0.71 

3.40 

52.80 

0.63 

3.45 

0.03 

12 

54.12 

0.78 

3.12 

48.40 

0.68 

3.17 

0.03 

13 

49.95 

0.84 

2.88 

44.68 

0.74 

2.93 

0.04 

14 

46.39 

0.91 

2.68 

41.48 

0.80 

2.72 

0.04 

15 

43.29 

0.97 

2.50 

38.72 

0.85 

2.53 

0.04 

16 

40.59 

1.04 

2.34 

36  .  30 

0.91 

2.38 

0.05 

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38.20 

1.10 

2.21 

34.16 

0.97 

2.24 

0.05 

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36.08 

1.17 

2.03 

32.27 

1.03 

2.11 

0.05 

19 

34.18 

1.23 

1.97 

30.57 

1.08 

2.00 

0.05 

20 

32.47 

1.30 

1.87 

29.04 

1.14 

1.90 

0.06 

21 

30.93 

1.36 

1.78 

27.66 

1.20 

1.81 

0.06 

22 

29.52 

1.43 

1  .  70 

26.40 

1.25 

1.73 

0.06 

23 

28.23 

1.49 

1.63 

25.25 

1.31 

1.65 

0.07 

24 

27.06 

1.56 

1.56 

24.20 

1.37 

1.58 

0.07 

25 

25.98 

1.62 

1.50 

23  .  23 

1.42 

1.52 

0.07 

26 

24.98 

1.69 

1.44 

22  .  34 

1.48 

1.46 

0.08 

27 

24,05 

1  .  75 

1.38 

21.51 

1.54 

1.41 

0.08 

28 

23.19 

1.82 

1.34 

20.74 

1.60 

1.36 

0.08 

29 

22.39 

1.88 

1.29 

20.03 

1.65 

1.31 

0.08 

30 

21.65 

1.95 

1.25 

19.36 

1.71 

1.27 

0.09 

31 

20.95 

2.01 

1.21 

18.73 

1.77 

1.23 

0.09 

32 

20.29 

2.08 

1.17 

18.15 

1.82 

1.19 

0.09 

33 

19.68 

2.14 

1   14 

17.60 

1.88 

1.15 

0.10 

34 

19.10 

2  21 

1.10 

17.08 

1.94 

1.12 

0.10 

35 

18.55 

2^27 

1.07 

16.59 

1.99 

1.09 

0.10 

36 

18.04 

2  .  34 

1.04 

16.13 

2.05 

1.06 

0.10 

37 

17.55 

2.40 

1.01 

15.70 

2.11 

1.03 

0.11 

38 

17.09 

2.47 

0  99 

15.28 

2.17 

1  .00 

0.11 

39 

16.65 

2.53 

0.96 

14.89 

2  22 

0.98 

0.11 

Above  values  are  based  on  maximum  fibre  strains  of  13,000  Ibs.  per 
sq.  in.,  rivetholes  in  both  flanges  deducted.  Weights  of  girders  correspond 
*.o  lengths,  centre  to  centre  of  bearings. 


STEEL-BEAM   BOX-GIRDERS. 


541 


STEEL-BEAM  BOX-GIRDERS.      SAFE  LOADS  IN  TONS, 
UNIFORMLY  DISTRIBUTED. 

2-10"  steel  I-beams  and  2  steel  plates  12"  X^". 


1 

/( 

^ 

T-^J'^r1 

~r~ji~T2? 

50  QJ 

1 

^t~ 
2  steel 

plates, 

10"  steel 
[-beams, 
35.0  Ibs. 

2  steel 
plates, 

f? 

10"  steel 
I-beams, 
25.0  Ibs. 

4 

I 

1.2"  XH" 
& 

L4 

per  foot. 

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per  foot. 

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0.55 

2.59 

39.23 

0.47 

2.64 

0.02 

11 

40.32 

0.60 

2.36 

35.66 

0.52 

2.40 

0.03 

12 

36.96 

0.65 

2.16 

32.69 

0.56 

2.20 

0.03 

13 

34.12 

0.71 

1.99 

30.18 

0.61 

2.03 

0.03 

14 

31.68 

0.76 

1.85 

28.02 

0.66 

1.89 

0.03 

15 

29.57 

0.82 

1.73 

26.15 

0.71 

1.76 

0.04 

16 

27.72 

0.87 

1.62 

24.52 

0.75 

1.65 

0.04 

17 

26.09 

0.93 

1.52 

23.08 

0.80 

1.55 

0.04 

18 

24.64 

0.98 

1.44 

21.79 

0.85 

1.47 

0.04 

19 

23.34 

1.04 

1.36 

20.65 

0.89 

1.39 

0.05 

20 

22.18 

1.09 

1.30 

19.62 

0.94 

1.32 

0.05 

21 

21.12 

1.15 

1.23 

18.68 

0.99 

1.26 

0.05 

22 

20.16 

1.20 

.18 

17.83 

1.04 

1.20 

0.05 

23 

19.28 

1.26 

.13 

17.06 

1.08 

1.15 

0.06 

24 

18.48 

1.31 

.08 

16.35 

1.13 

1.10 

0.06 

25 

17.74 

1.36 

.04 

15.69 

1.18 

1.06 

0.06 

26 

17.06 

1.42 

.00 

15.09 

1.22 

1.02 

0.06 

27 

16.43 

1.47 

0.96 

14.53 

1.27 

0.98 

0.07 

28 

15.84 

1.53 

0.93 

14.01 

1.32 

0.94 

0.07 

29 

15.29 

1.58 

0.89 

13.53 

1.37 

0.91 

0.07 

30 

14.78 

1.64 

0.86 

13.08 

1.41 

0.88 

0.07 

31 

14.31 

1.69 

0.84 

12.65 

1.46 

0.85 

0.08 

32 

13.86 

1.75 

0.81 

12.26 

1.51 

0.82 

0.08 

33 

13.44 

1.80 

0.78 

11.89 

1.55 

0.80 

0.08 

34 

13.04 

1.86 

0.76 

11.54 

1.60 

0.78 

0.08 

35 

12.67 

1.91 

0.74 

11.21 

1.65 

0.75 

0.09 

36 

12.32 

1.96 

0.72 

10.90 

1.70 

0.73 

0.09 

37 

11.99 

2.02 

0.70 

10.60 

1.74 

0.71 

0.09 

38 

11.67 

2.07 

0.68 

10.32 

1.79 

0.69 

0.09 

39 

11.37 

2.13 

0.66 

10.06 

1.84 

0.67 

0.10 

Above  values  are  based  on  maximum  fibre  strains  of  13,000  Ibs.  per 
square  inch,  rivet-holes  in  both  flanges  deducted.  Weights  of  girders 
correspond  to  lengths,  centre  to  centre  of  bearings 


542 


BEAMS  SUPPORTING  BRICK  WALLS. 


BEAMS  SUPPORTING  BRICK  WALLS. 

In  calculating  the  size  of  a  girder  to  support  a  brick  wall,  the 
structure  of  the  wall  should  be  carefully  considered.  If  the  wall 
is  without  openings,  and  does  not  support  floor  beams,  only  the 


Fig.   10 

portion  of  the  wall  included  within  the  dotted  lines,  Fig.  10,  need 
be  considered  as  being  supported  by  the  girder.  The  beams  in 
that  case,  however,  should  be  made  very  stiff,  so  as  to  have  little 
deflection.  If  there  are  several  openings  above  the  girder,  and 
especially  if  there  be  a  pier  over  the  centre  of  the  girder,  as 
shown  in  Fig.  11,  then  the  manner  in  which  the  weight  bears  on 
the  girder  should  be  carefully  considered.  In  a  case  such  as  this 
the  entire  dead  weight  included  between  the  dotted  lines  A  A 
and  B  B  should  be  considered  as  coming  on  the  girder,  and 
proper  allowance  made  for  the  load  being  mostly  concentrated  at 
the  centre. 

When  beams  are  used  to  support  a  watt  entirely  (that  is,  the 
beams  run  under  the  whole  length  of  the  wall),  and  the  wall  is 
more  than  sixteen  or  eighteen  feet  long,  the  whole  weight  of 
the  wall  should  be  taken  as  coming  upon  the  beams;  for,  if  the 
beams  should  bend,  the  wall  would  settle,  and  might  push  out 
the  supports,  and  thus  cause  the  whole  structure  to  fall. 


FRAMING  AND  CONNECTING  STEEL  BEAMS.  543 


FRAMING-  AND  CONNECTING  STEEL  BEAMS. 

Separators. — When  beams  are  used  to  support  walls,  or  as 
girders  to  carry  floor  beams,  they  are  often  placed  side  by  side; 
and  should  in  such  cases  be  connected  by  means  of  bolts,  and 
cast-iron  separators  fitting  closely  between  the  flanges  of  the 
foeams.  The  office  of  these  separators  is,  in  a  measure,  to  hold  in 
position  the  compression  flanges  of  the  beams,  preventing  side 

A        B 


Fig.  II 


deflection  or  buckling,  and  also  to  unite  the  beams  so  as  to  cause 
them  to  act  in  unison  as  regards  vertical  deflection.  Separators 
should  be  provided  near  the  supports  and  at  points  where  heavy 
loads  are  imposed,  otherwise  at  regular  intervals  of  from  5  to  6 
feet. 

The  illustrations  on  the  following  page  show  a  pair  of  beams 
connected  by  separators,  and  also  the  pattern  of  separators  now 


514        CAST-IRON  SEPARATORS   FOR  I-BEAMS. 
CAST-IRON  SEPARATORS  FOR  I-BEAMS. 


c  4 
-U 


Beams. 

Separators. 

Bolts,  square  heads 
and  hex  nuts. 

.2  S 

"o 

to 

^  1 

o 

1 

£ 

H-° 

o 

-5 

S^ 

Sec- 
tion 

No. 

1 

eight  per  fo 

to  out  of  fla 
of  beams. 

ntre  to  cent 
of  beams. 

Thickness 

,jd 

J53 

of  wt.  for  e 
al  spread  of 

Diameter 

'e  to  centre 

W) 
J 

of  bolts  an 

.  of  bolts  fyi 
al  spread  oJ 

P 

•g 

3 

!»    O 

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d 

£ 

£   0 

O 

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CD 

O 

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d 

4 

£ 

£ 

G& 

C 

JB 

^ce 

Ins. 

Lbs. 

Inches 

Inches 

In. 

Lbs. 

Lbs. 

In. 

^ns. 

Ins. 

Lbs. 

Lbs. 

SEPARATORS  WITH  ONE  BOLT. 


B      5 

3 

5.5 

5%e 

3 

v% 

1.1 

.29 

% 

37,< 

.94 

.085 

B      9 

4 

7.5 

5^ 

3^ 

ys 

1.6 

.38 

% 

4M 

.98 

.123 

B    13 

5 

9  .  75 

6^ 

3>3 

% 

2.0 

.49 

3, 

4^ 

1.01 

.123 

B    17 

6 

12.25 

7%  G 

4 

1A 

3.3 

.78 

V 

5 

1.07 

.1:3 

B    21 

7 

15.0 

7<78 

414 

y* 

3.9 

.92 

3 

5J^ 

.10 

.  12:- 

B    25 

8 

17.75 

sy2 

VA 

X 

4.7 

1.06 

3 

5H 

.15 

.12; 

B    29 

9 

21.0 

95/1  e 

5 

5.9 

1.20 

3 

61A 

.21 

.12S 

B    33 

10 

25.0 

9^ 

5M 

Yz 

6.8 

1.33 

3 

GH 

.24 

.122 

B    41 

12 

31.5 

10K 

5§| 

y> 

8.8 

1.61 

;5 

W/s 

.30 

.  i2r 

B  105 

12 

40.0 

11M 

6 

y> 

8.9 

1.58 

3 

7M 

.35 

.  12,': 

SEPARATORS  WITH  Two  BOLTS. 


B    41 

12 

31  .  5 

10M 

5% 

H 

9.5 

L.61 

V 

&i 

QH 

2.61 

.246 

B  105 

12 

40.0 

\\14 

6 

H 

9.5 

1.58 

V 

VA 

7k 

2.70 

.246 

B    53 

15 

42.0 

\\H 

614 

\i 

12.5 

2.02 

3 

7 

7^2 

2.76 

.246 

B  109 

15 

60.0 

12M 

&4 

Yz 

13.0 

1.97 

:; 

7 

SH 

2.92 

.246 

B  113 

15 

80.0 

13H 

714 

X 

13.2 

1.91 

y 

7 

8H 

3.10 

.246 

B    65 

18 

55.0 

12% 

V4 

y* 

19.8 

2.41 

3 

9 

8 

2.89 

.246 

B    73 

20 

65.0 

1314 

7 

% 

22.9 

3  .  37 

y 

10 

8^ 

4.20 

.334 

B  121 

20 

80.0 

14% 

7% 

y* 

24.6 

3.34 

% 

10 

9U 

4.49 

.334 

B    89 

24 

80.0 

14*4 

ry± 

% 

30.3 

4.07 

% 

12 

9.^ 

4.45 

.334 

Lengths  and  weights  of  separator  bolts  in  above  tables  are  for  o 

composed  of  two  beams  of  minimum  section  as  shown.  Lengths  of  bolts  for 
intermediate  and  maximum  sizes  of  beams  may  be  obtained  by  adding  twice 
the  increase,  of  web  thickness  to  the  lengths  given. 


BEAM  CONNECTIONS. 


545 


in  common  use.  The  table  below  the  cuts  gives  the  various 
dimensions  and  weights  as  adopted  by  the  Cambria  Steel  Co. 
The  weights  vary  slightly  from  those  given  by  other  manufac- 
turers, but  the  table  is  probably  as  near  an  average  of  current 
practice  as  any  that  could  be  given. 

Separators  formed  of  pieces  of  steam  or  gas  pipe,  cut  to  the 
desired  length  and  slipped  over  the  bolts  are  often  used  by  con- 
tractors. Such  separators  permit  the  beams  to  act  independently/ 
of  each  other,  and  should  not  be  used  in  any  place  where  one! 
beam  is  liable  to  receive  a  greater  load  than  the  other,  and  as 
this  condition  occurs  in  almost  every  case  where  two  or  more 
beams  are  used  together,  it  follows  that  "cast-iron  separators, 
made  to  fit  the  space  between  the  beams,"  should  be  specified 
in  almost  every  instance.  Separators  with  two  bolts  should  be 
used  for  beams  over  12  ins.  in  depth.  For  12-inch  beams  either 
one  or  two  bolts  may  be  used,  according  to  the  load;  for  beams 
under  12  inches  in  height  one  bolt  is  sufficient. 

Beam  Connections. — Steel  beams  and  channels  are 
framed  together  by  means  of  short  pieces  of  angle-bars,  which 


Fig.  12 


are  usually  riveted  to  the  floor  or  tail  beam  and  bolted  to  the 
girder.  The  angles  are  always  used  in  pairs,  one  on  each  side  of 
the  floor  beam. 


546  BEAM  CONNECTIONS. 

If  the  floor  beam  is  framed  flush,  either  with  the  top  or  botcom 
of  the  girder,  or  where  two  beams  of  the  same  height  are  framed 
together,  the  end  of  the  beam  supported  should  be  " coped,"  or 
cut  to  fit  the  shape  of  the  girder  or  supporting  beam.  The 
maximum  clearance  space  allowed  between  end  of  beam  and  web 
varies  from  %>  inch  in  the  smaller  beams  to  J  inch  in  the  larger 
ones. 

Figs.  12  to  14  show  beams  of  different  depths  framed  in  dif- 
ferent positions,  and  Fig  15.  shows  a  beam  framed  into  a  girder 
of  the  same  depth. 

When  a  floor  beam  rests  on  top  of  another  beam  or  girder,  as 
in  Fig.  17,  the  beam  should  be  secured  by  means  of  a  pair  of 
wrought-iron  clips,  shown  in  Fig.  16,  shaped  so  as  to  fit  closely 


Fig.  16     .  Fig.  17 

the  top  flange  of  the  girder,  and  either  bolted  or  riveted  to  the 
lower  flange  of  the  floor  beam,  on  opposite  sides  of  the  same. 

Fig.  18  shows  the  best  method  of  framing  the  ends  of  wooden 
floor  joist  to  steel  beams,  a  4x3x4  inch  angle  being  riveted 
%"IRON  DOG  ^e  wno^e  length   of  the   steel   beam, 

\r~-j=r=^^^f  u  ,1  by  f-inch  rivets,  about  6  ins.  apart. 
The  top  of  the  beam  is  usually  se- 
cured by  iron  dogs  or  clamps.  If  the 
floor  beams  are  over  3  feet  apart, 
short  lengths  of  angles  may  be  placed 
under  each  beam. 

Standard  Connection  An  gles 
for    I-"Beams    and.    Channels. 
Fig.  18  —The   size   of    the    angles    and    the 

number  of  the  rivets  used  for  connecting  steel  beams,  varies 
somewhat  with  different  shops  and  with  different  structural 
engineers,  so  that  there  cannot  be  said  to  be  a  universal  standard. 
The  variations  in  the  different  "standards,"  however,  are  not 
very  great,  and  as  the  connections  adopted  by  the  Carnegie 


BEAM  CONNECTIONS. 


547 


Steel  Co.  are  perhaps  the  most  used,  the  author  has  selected 
them  for  illustration  on  the  following  pages. 

These  connections  are  designed  on  the  basis  of  an  allowable 
shearing  stress  of  10,000  Ibs.  per  square  inch,  and  a  bearing 
stress  of  20,000  Ibs.  per  square  inch  on  rivets  or  bolts,  correspond- 
ing with  extreme  fibre  stresses  in  the  I-beams  of  16,000  Ibs.  per 
square  inch.  The  number  of  rivets  or  bolts  required  is  found  to 
be  dependent,  in  most  instances,  on  their  bearing  values. 

The  connections  have  been  proportioned  with  a  view  to  cover- 
ing most  cases  occurring  in  ordinary  practice,  with  the  usual 
relations  of  depth  of  beam  to  length  of  span.  In  extreme  in- 
stances, however,  where  beams  of  short  relative  span  lengths  are 
loaded  to  their  full  capacity,  or  when  beams  frame  opposite  each 
other  into  another  beam  with  web  thickness  less  than  %  inch, 
it  may  be  found  necessary  to  make  provision  for  additional 
strength  in  the  connections.  The  limiting  span  lengths,  at  and 
above  which  the  standard  connection  angles  may  be  used  with 
perfect  safety,  are  given  in  the  following  table : 

TABLE  OF  MINIMUM  SPANS  OF  I-BEAMS,  FOR  WHICH 
STANDARD  CONNECTION  ANGLES  MAY  BE  SAFELY 
USED  WITH  BEAMS  LOADED  TO  THEIR  FULL  CA- 
PACITY. 


Mini- 

Mini- 

Mini- 

Designation 
of  beam. 

mum 

safe 
span, 

Designation 
of  beam. 

mum 
safe 
span, 

Designation 
of  beam. 

mum 
safe 
span, 

in  feet. 

in  feet. 

in  feet. 

24"  —  80  Ibs. 

21.0 

15"  —  42  Ibs. 

10.5 

1"—  15  Ibs. 

20       80 

18.0 

12       40     " 

9.0 

6        12.25  Ibs. 

20       65 

17.0 

12       31.5  Ibs. 

7.5 

5       9.75  Ibs. 

18       55 

14.0 

10       25  Ibs. 

9.5 

4       7.5  Ibs. 

15       80 

16.0 

9       21    " 

8.0 

3       55    " 

15       60 

12.5 

8        18    " 

6.5 

For  shorter  spans  and  for  heavier  beams  the  number  of  rivets  required 
should  be  computed  by  the  method  explained  in  Chapter  XII. 


548 


STANDARD  CONNECTION  ANGLES. 


STANDARD  CONNECTION  ANGLES  FOR  I-BEAMS  AND 
CHANNELS.* 

q|  F  4"x  4"x  %"L— iVlg.  Weight  38.4  Ibs. 


S" 

4 

-+ 

-f- 

-+- 

-f 

+ 

-f 

for  18  and_20  Pi 


for  5  and  6  Ps 
and.  C's 


6  x  4  x  %  L— 0  1&  Ig-. 
g-|  F     Weight  5.6  Ibs. 


t 

.£. 


SIP 

Shop  I  Field. 

Rivets  or 
Bolts. 


for  3  and  4  Ps 
and  C's 


All  holes  for  %  Bolts  or  Rivets. 

The  weights  of  connections  include  shop  and  field  rivets. 
2/4  gauge  on  all  4  legs. 


*As  adopted  by  the  Carnegie  Steel  Co.,  Ltd. 


BEAM  CONNECTIONS. 


549 


CONNECTIONS    FOR    DIFFERENT  DEPTHS  OF  BEAMS 
FRAMING  OPPOSITE.* 


Cut  L's  for  I's  above    5# 

15"  I  and  12 "I 


12"!  and  10"! 


10"!  and  9"! 


Cut  L's  for  I's  above  55  # 

15" I  and  7" I 


Standard  connection  angles 
to  be  used  on  larger  beams 
unless  gauge  exceeds  %%" 
on  special  angles  of  smaller 
beams. 


12"  I  and  6"  I 

*  As  adopted  by  the  Carnegie  Steel  Co.,  Ltd. 


550 


CONNECTION  ANGLES  OF  I-BEAMS. 


STANDARD  SPACING  AND  DIMENSIONS  OF  RIVET  AND 
BOLT  HOLES  THROUGH  FLANGES  AND  CONNEC- 
TION ANGLES  OF  I-BEAMS. 


O 
O 


O 


3 

'Z!  •» 

ll 

$3 

Weight  per 
foot. 

Max.  size 
bolt  or  rivet 
in  flanges. 

in 

f! 
S.a 

a  c 

A" 

.  bib 

3§l 

305  1 

B 

OJ 

!*• 

a  5 

c 

CX  * 
'C.S 

fl 

G 

Depth  in 
inches. 

Weight  per 
foot. 

Max.  size 
bolt  or  rivet 
in  flanges. 

Gauge 
^in  inches. 

it 

SI 

B 

->  Distance  1 
^^in  inches.  | 

~-C 

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CJ  c 
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23/32 

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30 
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Weights  in  heavy  print  are  standard,  others  aro  snecial. 
All  holes  for  connections  to  h:i  for  V  rivets  of  bolls. 
*  From  centre  of  through  beam  to  end  of  tail  beam. 


CONNECTION  ANGLIC  OF   CHANNELS. 


STANDARD  SPACING  AND  DIMENSIONS  OF  RIVET  AND 
BOLT  HOLES  THROUGH  FLANGES  AND  CONNEC- 
TION ANGLES  OF  CHANNELS.* 


12 


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Weights  in  heavy  print  arc  Standard,  others  are  special. 
All  holes  for  connections  to  be  for  '-}\"  rivets  or  bolts. 
*Adopted  by  the  Carnegie  Steel  Co.i  Ltd. 


552  STANDARD  RIVET  GAUGES  FOR  ANGLES. 
STANDARD  GAUGES  FOR  ANGLES,  TEES  AND  Z-BARS. 


l__ 


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2  2 


Rivet. 


MINIMUM   GAUGE    FOR    MACHINE    RIVETING. 


A  must  not  be  less  than 
rivet-heads,  see  page  373. 


For  size  of 


*  For  4^'x  and  5"  legs  rivet-holes  should  be  staggered,  so  that  the  distance 
between  centres  of  rivets  shall  not  be  less  than  2"  for  %"  rivets,  or  2\"  for 


WALL  ANCHORS.  553 

WALL  ANCHORS  FOR  BEAMS  AND  CHANNELS. 


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All     weights     and     dimensions 
marked  V  are  variable,  as  are  also 

12  to  24 

3 

11 

other  figures  where  not  given. 

All  material  for  anchors  steel,  except  Nos.  7  and  8,  parts  of  which  may  be 
cast  or  malleable  iron.  All  anchors  are  shipped  loose  and  riveted  or  bolted  to 
beams  in  the  field;  and  in  order  to  avoid  two  size  holes  in  the  same  piece 
anchors  should  be  so  selected  that  holes  for  them  and  their  connections  may 
be  I%Q".  The  weights  given  above  include  the  bolts  or  rivets  for  field  con- 
nections. 

Anchors  Nos.  1,  2,3,4,  and  6  are  common  in  building  construction;  the 
split  anchor  bolts  No.  5,  with  or  without  wedges  are  mostly  used  for  bridge 
work  and  column  foundations;  the  washer  for  No.  7  on  outside  of  wall  may 
be  either  a  cast-iron  star  or  a  steel  plate ;  expansion  bolts  No.  8  are  of  use  in 
repair  work  to  fasten  channels,  etc.,  to  brick  walls. 


554 


STRENGTH  OF  CAST-IRON  BEAMS. 


CHAPTER  XVI. 

STRENGTH  OP  CAST-IRON,  WOODEN,  AND 
STONE  BEAMS. 

CAST-IRON  BEAMS. 

OWING  to  the  fact  that  the  resistance  of  cast-iron  to  tension  is 
only  about  one-fifth  of  its  resistance  to  compression ,  the  shapes 
of  beams  most  economical  for  wrought  iron  or  steel  would  be 
wasteful  if  made  of  cast-iron.  The  extreme  brittleness  of  cast 
iron,  and  its  liability  to  flaws  in  casting,  also  render  it  an  unde- 
sirable material  for  resisting  transverse  strain.  About  the  only 
form  in  which  cast-iron  beams  are  now  used  in  building  construc- 
tion in  this  country,  is  in  the  shape  of  lintels  for  supporting 
brick  or  stone  walls,  in  places  where  a  flat  soffit  is  desired,  and 
the  walls  are  not  to  be  plastered.  Cast-iron  lintels  are  also 
occasionally  used  over  store  fronts,  the  face  of  the  lintel  being 
panelled  and  moulded  for  architectural  effect. 

Before  wrought-iron  I-beams  were  manufactured,  cast-iron 
beams  were  frequently  used  as  the  only  available  material,  other 
than  wood  or  stone.  Early  in  the  nineteenth  century  Mr.  Eaton 
Hodgkinson,  an  English  engineer,  made  a  series  of  experiments 
with  cast-iron  beams  from  which  he  found  that  the  form  of 
cross-section  of  a  beam  which  will  resist 
the  greatest  transverse  strain  is  that 
shown  in  Fig.  1,  in  which  the  bottom 
flange  contains  six  times  as  much  metal 
as  the  top  flange. 

When  cast-iron  beams  are  subjected  to 
very  light  strains,  the  areas  of  the  two 
flanges  ought  to  be  nearly  equal.  As  in 
practice  it  is  usual  to  submit  beams  to 
strains  less  than  the  ultimate  load,  and 
yet  beyond  a  slight  strain,  it  is  found  that 


Fig.  I 


when  the  flanges  are  as  1  to  4,  we  have  a  proportion  which 
approximates  very  nearly  the  requirements  of  practice.     The 


STRENGTH  OF  CAST-IRON   BEAMS.  555 

thickness  of  the  three  parts — web,  top  flange,  and  bottom  flange 
— may  with  advantage  be  made  in  proportion  as  5,  6,  and  8. 

If  made  in  this  proportion,  the  width  of  the  top  flange  will  be 
equal  to  one-third  of  that  of  the  bottom  flange.  As  the  result  of 
his  experiments,  Mr.  Hodgkinson  gave  the  following  rule  for  the 
breaking-weight  at  the  centre  for  a  cast-iron  beam  of  the  above 
form: 

/Area  of  bot.  flangeA^/ 

i      •  •  Al 


Breaking-load  )  __  V    in  square  inches  /     \iiiins.> 
in  tons        j  clear  span  in  feet 

This  rule,  although  largely  empirical,  agreed  very  well  with  the 
few  experiments  that  were  made,  and  has  been  in  general  use 
even  to  the  present  day. 

Modern  structural  engineers,  however,  use  the  general  for- 
mula for  the  strength  of  beams,  as  given  in  Chapter  XV.,  except 
that  the  section  modulus  is  found  by  dividing  the  Moment  of 
Inertia  by  the  distance  of  the  neutral  axis  from  the  bottom  of 
the  beam,  and  the  safe  tensile  strength  is  used  for  the  modulus  of 
rupture. 

Thus  the  general  formula  for  a  beam  supported  at  both  ends, 
and  with  the  load  uniformly  distributed,  as  given  on  page  502, 
Chapter  XV.,  is: 

27? 
Safe  load  in  pounds  =—rX&     As  S,  for  cast  iron,  should  be 

O-L/ 

taken  at  3,000  Ibs.,  this  formula  becomes 

Safe  load  in  pounds  =-LT — ,  (2) 

Li 

and  R  for  either  section  given  below 

Moment  of  Inertia 


The  moment  of  inertia  is  computed  by  the  formula 

-y-fr)^  ^ 


556 


STRENGTH  OF  CAST-IRON   BEAMS. 


in  which  6  denotes  the  combined  thickness  of  the  webs,  and  the 
distances  d,  d±,  and  d2  are  measured  from  the  neutral  axis,  which 
must  pass  through  the  centre  of  gravity  of  the  section.  The  centre 
of  gravity  may  be  found  by  the  method  explained  in  Chapter  VI. 

This  formula  may  be  used  for  any  of  the  above  sections  when 
the  depth  does  not  exceed  the  width,  and  the  thickness  of  each 
web  is  at  least  equal  to  the  thickness  of  the  flange. 

In  lintels  with  a  single  web  it  is  well  to  make  the  thickness  of 
the  web  J  or  f  inch  greater  than  the  thickness  of  the  flange.  For 
a  beam  of  the  shape  shown  in  Fig.  1,  formula  (2)  agrees  very 
closely  with  formula  (1),  using  a  factor  of  safety  of  six. 

EXAMPLE. — The  following  example  will  illustrate  the  applica- 
tion of  formula  (2) :  Compute  the  safe  load  for  a  cast-iron  lintel 
having  a  section  as  shown  in  Fig.  2  and  a  clear  span  of  10  feet. 
The  load  to  be  uniformly  distributed,  and  the  thickness  of  the 


Fig.  2 

metal  to  be  one  inch.  The  first  step  is  to  find  the  distance  d  that 
the  centre  of  gravity  of  the  section  is  below  the  top  of  the  beam. 
This  is  found  by  taking  the  moments  of  the  webs  and  flange 
about  the  line  x-y,  and  dividing  their  sum  by  the  area  of  the 
section  (see  page  240).  Each  web  is  11  ins.  deep  and  1  in.  thick, 
hence  the  area  is  11  sq.  inches.  The  moments  of  the  three  webs 

about  x-y  will  then  be  3  X 1 1  X    5|  =  1 81 .5 

Moment  of  flange  about  x-y  =  28  X 1 H  =  322 


503.5 


Area  of  section  =61. 
503.5^-61  =8.25=d 


Then 


d  =8.25 


2  =2.  75 


d3  =561.5 
d,3=  52.7 
d*=  20.8 


6  =3 
^=28 


Next  find  Moment  of  Inertia  by  formula  (3) : 
r     3X561.5  +  28X52.7-25X20.8 

I  = - = 


STRENGTH  OF  CAST-IRON   BEAMS.  557 

fl=f^  =  234.6.    Safe  load  =  20Q°*f34>6  =46,920  Ibs. 

o.7o  J-U 

or  23.4  tons. 

Ends  and  Brackets. — When  T-shaped  lintels  are  used 
over  a  single  opening,  the  web  may  be  tapered  towards  the  ends, 
as  in  Fig.  3,  without  affecting  the  strength.  If  the  flange  is  more 
than  8  ins.  wide,  brackets  should  be  cast  in  the  middle,  as  at  A, 
Fig.  3. 


Fig.  3 

When  continuous  lintels  are  used  over  store  fronts  or  similar 
places,  ends  should  be  cast  on  the  lintels,  as  in  Fig.  4,  and  the 
ends  of  abutting  lintels  bolted  together. 


All  lintels  with  two  or  three  webs  should  have  solid  ends  con- 
necting the  webs. 

Tables  of  Strength  of  Cast-iron  Lintels. — The  tables 
on  the  following  pages  have  been  computed  in  accordance  with 
formula  (2).  The  weight  of  the  lintel  itself  should  be  deducted 
from  the  safe  load.  In  using  these  tables  it  should  be  remem- 


558  STRENGTH  OF  CAST-IRON   BEAMS. 

bered  that  the  values  are  for  loads  uniformly  distributed.  If  the 
load  is  concentrated  at  the  centre,  it  should  be  multiplied  by  2. 
If  at  some  other  point  than  the  centre,  multiply  by  the  value  on 
page  514  which  most  nearly  corresponds  with  the  position  of  the 
load.  For  other  spans  than  those  given  multiply  the  distributed 
load  by  the  span,  and  use  the  lintel  having  a  coefficient  C  just 
above  the  product  thus  obtained. 

EXAMPLE. — It  is  desired  to  support  a  12-inch  brick  wall,  10  ft. 
high,  over  an  opening  5  ft.  6  ins.  wide,  with  a  cast-iron  lintel; 
22  inches  from  one  support  a  girder  enters  the  wall,  which  may 
bring  a  load  of  9,600  Ibs.  on  the  lintel.  What  should  be  the  size 
of  the  lintel? 

Ans.  At  110  Ibs.  per  cubic  foot,  the  wall  above  the  lintel  will 
weigh  10  X  5J  X 1 10  =  6050  Ibs.  As  22  ins.  is  one-third  of  the  span, 
we  multiply  the  concentrated  load  by  1.78  (see  page  514),  which 
gives  17,088  Ibs.  The  total  equivalent  distributed  load  is  then 
23,138  Ibs.  Multiplying  this  by  the  span  we  have  127,259  Ibs. 
or  63.6  tons  as  the  least  value  for  the  coefficient  C.  Looking  in 
the  table,  we  find  that  a  12"XlO"  lintel,  1"  thick,  and  one  web, 
has  a  coefficient  of  72.2,  and  that  a  12"XS"Xli"  lintel  with 
two  webs  has  a  coefficient  of  69.9.  A  lintel  with  two  webs  is 
best  for  a  12"  wall,  and  interpolating  between  the  values  of  C 
for  V  and  If  thickness  of  the  12//X8//  lintel,  we  have  65.4  as 
the  value  of  C  for  a  thickness  of  1J".  This  exceeds  the  required 
value  by  enough  to  more  than  compensate  for  the  weight  of  the 
lintel  itself,  hence  we  will  use  a  12"X8"XlJ"  lintel  with  two 
webs. 

Owing  to  the  liability  of  flaws  in  the  castings,  cast-iron  beams 
should  always  be  tested  for  defects  before  being  set  in  place,  and 
if  there  is  any  doubt  at  all  as  to  their  safety,  they  should  be  tested 
up  to  the  full  load  they  may  have  to  support. 


STRENGTH  OF  CAST-IRON  LINTELS. 


559 


TABLE  I.— SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR 
CAST-IRON  LINTELS. 


LINTELS  OF 


SHAPES. 


Loads  include  weight  of  lintel.     Maximum  tensile  stress  3,000  Ibs.  per 
square  inch.     See  remarks  page  558. 


Size, 
width 
by 
depth, 

lickness  of 
aetal.  ins.  | 

Wt. 
per 

foot, 
Ibs 

c, 

Tons 

Span  in  feet. 

ins. 

SH 

5 

6 

7 

8 

9 

10 

11 

12 

24 

26.3 

15.9 

3.18 

2.65 

2.27 

1.98 

1.76 

1.59 

1.44 

1.32 

6X6 

1 

34.4 

19.0 

3.80 

3.16 

2.71 

2.37 

2.11 

1.90 

1.72 

1.58 

IK 

42.0 

21.5 

4.30 

3.58 

3.07 

2.68 

2.39 

2.15 

1.95 

1.79 

34 

28.6 

17.8 

3.56 

2.96 

2.54 

2.22 

1.98 

1.78 

1.61 

1.48 

7X6 

1 

37.5 

21.3 

4.26 

3.55 

3.04 

2.66 

2.36 

2.13 

1.93 

1.77 

IK 

45.9 

24.0 

4.80 

4.00 

3.43 

3.00 

2.66 

2.40 

2.18 

2.00 

H 

31.0 

22.6 

4.52 

3.76 

3.23 

2.82 

2.51 

2.26 

2.05 

1.88 

7X7 

1 

40.6 

27.5 

5.50 

4.58 

3.93 

3.43 

3.05 

2.75 

2.50 

2.29 

IK 

49.8 

31.4 

6.28 

5.23 

4.49 

3.92 

3.49 

3.14 

2.85 

2.36 

34 

31.0 

19.6 

3.92 

3.2C 

2.80 

2.45 

2.18 

1.96 

1.78 

1.63 

8X6 

I 

40.6 

23.4 

4.68 

3.90 

3.34 

2.92 

2.60 

2.34 

2.12 

1.95 

IK 

49.8 

26.4 

5.28 

4.40 

3.77 

3.30 

2.93 

2.64 

2.40 

2.20 

K 

33.3 

25.0 

5.00 

4.16 

3.57 

3.12 

2.77 

2.50 

2.27 

2.08 

8X7 

1 

43.7 

30.3 

6.06 

5.05 

4.33 

3.79 

3.36 

3.03 

2.75 

2.52 

IK 

53.7 

34.8 

6.96 

5.80 

4.97 

4.35 

3.86 

3.48 

3.16 

2.90 

% 

35.6 

30.6 

6.12 

5.10 

4.37 

3.82 

3.40 

3.06 

2.78 

2.55 

8X8 

1 

46.8 

37.6 

7.52 

6.2f 

5.37 

4.70 

4.18 

3.76 

3.41 

3.13 

IK 

57.6 

43.4 

8.68 

7.2? 

6.20 

5.42 

4.82 

4.34 

3.94 

3.61 

H 

38.0 

36.5 

7.30 

6.08 

5.21 

4.56 

4.05 

3.65 

3.31 

3.04 

8X9 

1 

50.0 

45.2 

9.04 

7.53 

6.45 

5.65 

5.02 

4.52 

4.11 

3.76 

IK 

61.5 

52.6 

10.52 

8.76 

7.51 

6.57 

5.84 

5.26 

4.41 

4.38 

34 

40.4 

26.5 

5.30 

4.41 

3.78 

3.31 

2.94 

2.65 

2.41 

2.21 

12X6 

l' 

53.1 

31.6 

6.32 

5.26 

4.51 

3.95 

3.51 

3.16 

2.87 

2.63 

IK 

65.4 

34.8 

6.96 

5.80 

4.97 

4.35 

3.86 

3.48 

3.16 

2.90 

H 

45.0 

41.7 

8.34 

6.95 

5.95 

5.21 

4.63 

4.17 

3.79 

3.48 

12X8 

l 

59.4 

51.2 

10.24 

8.53 

7.31 

6.40 

5.69 

5.12 

4.65 

4.26 

IK 

73.2 

58.5 

11.70 

9.75 

8.35 

7.31 

6.50 

5.85 

5.32 

4.87 

K 

49.8 

58.0 

11.60 

9.66 

8.28 

7.25 

6.44 

5.80 

5.27 

4.83 

12X10 

l 

65.6 

72.2 

14.44 

12.03 

10.31 

9.02 

8.02 

7.22 

6.56 

6.01 

IK 

81.0 

83.8 

16.76 

13.96 

11.97 

10.47 

9.31 

8.38 

7.62 

6.98 

K 

54.4 

75.2 

15.04 

12.53 

10.74 

9.40 

8.35 

7.52 

6.83 

6.26 

12X12 

l 

71.9 

94.8 

8.96 

15.80 

13.54 

11.85 

10.53 

9.48 

8.62 

7.90 

IK 

88.9 

11.5 

22.30 

18.58 

15.92 

13.93 

12.39 

11.15 

10.12 

9.29 

560 


STRENGTH   OF   CAST-IRON  LINTELS. 


TABLE  I.— SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR 
CAST-IRON    LINTELS—  (Continued). 


LINTELS  OP 


T 

DEPTH 

L= 

—  , 

SHAPES. 


Loads  include  weight  of  lintel.     Maximum  tensile  stress  3,000  Ibs.  per 
square  inch.     See  remarks  page  558. 


Size, 
width 
by 
depth, 
ins. 

Thickness  of  1 
metal,  ins. 

wt. 

per 
foot, 
Ibs. 

c, 

tons. 

Span  in  feet. 

5 

6 

7 

8 

3.96 
4.70 
5.37 

9 

10 

11 

12 

12X6 

1 

52.7 
68.8 
84.0 

31.7 
37.6 
43.0 

6.34 
7.52 
8.60 

5.28 
6.26 
7.16 

4.53 
5.37 
6.14 

3.52 

4.18 

4.77 

3.17 
3.76 
4.30 

2.88 
3.42 
3.91 

2.64 
3.13 
3.58 

12X8 

1  4 

62.1 
81.3 
99.6 

49.5 
60.9 
69.9 

9.90 
12.18 
13.98 

8.25 
10.15 
11.65 

7.07 
8.70 
9.98 

6.19 

7.61 

8.73 

5.50 
6.76 
7.76 

4.95 
6.09 
6.99 

4.50 
5.53 
6.35 

4.12 
5.07 

5.82 

14X6 

1  4 
1# 

57.4 
75.0 
91.8 

35.5 
42.0 
48.0 

7.10 
8.40 
9.60 

5.91 
7.00 
8.00 

5.07 
6.00 
6.85 

4.43 
5.25 
6.00 

3.94 
4.66 
5.33 

3.55 

4.20 
4.80 

3.22 
3.82 
4.36 

2.96 
3.50 
4.00 

14X8 

H 

66.8 
87.5 
107.4 

55.4 
68.1 
78.8 

11.08 
13.62 
15.76 

9.23 
11.35 
13.13 

7.91 
9.73 
11.25 

6.92 
8.51 
9.85 

6.15 
7.56 

8.75 

5.54 
6.81 

7.88 

5.03 
6.19 
7.16 

4.61 
5.67 
6.56 

16X6 

i 

62.1 
81.3 
99.6 

39.1 
46.8 
52.9 

7.82 
9.36 
10.58 

6.51 

7.80 
8.81 

5.58 
6.68 
7.55 

4.88 
5.85 
6.61 

4.34 
5.20 

5.88 

3.91 
4.68 
5.29 

3.55 
4.25 
4.81 

3.25 
3.90 
4.40 

16X8 

i  4 

71.5 
93.8 
115.2 

61.4 
74.6 
86.8 

12.28 
14.92 
17.36 

10.23 
12.43 
14.46 

8.77 
10.65 
12.40 

7.67 
9.32 
10.85 

6.82 
8.29 
9.64 

6.14 
7.46 
8.68 

5.58 

6.78 
7.89 

5.H 
6.21 

7.2? 

20X6 

i  4 

71.5 
93.8 
115.2 

47.2 
55.1 
62.0 

9.44 
11.02 
12.40 

7.86 
9.18 
10.33 

6.74 

7.87 
8.85 

5.90 

6.88 

7.75 

5.24 
6.12 

6.88 

4.72 
5.51 
6.20 

4.29 
5.01 
5.63 

3.93 
4  59 
5.16 

20X8 

i  4 

1M 

80.8 
106.2 
130.8 

72.6 
89.5 
102.5 

14.52 
17.90 
20.50 

12.10 
14.91 
17.08 

10.37 

12.78 
14.64 

9.07 
11.18 
12.81 

8.06 
9.94 
11.39 

7.26 
8.95 
10.25 

6.60 
8.13 
9.31 

6.05 

7.45 
8.54 

20X10 

H 

i 

90.2 
118.8 
146.5 

100.5 
125.4 

146.8 

20.10 
25.08 
29.36 

16.75 
20.90 
24.46 

14.35 
17.91 
20.97 

12.56 
15.67 
18.35 

11.16 
13.93 
16.31 

10.05 
12.54 
14.68 

9.13 
11.40 
13.34 

8.37 
10.45 
12.23 

20X12 

i 

1M 

99.6 
131.3 
162.1 

122.6 
158.0 
189.5 

24.52 
31.60 
37.90 

20.43 
26.33 
31.58 

17.51 
22.57 
27.07 

15.32 
19.75 
23.68 

13.62 
17.55 
21.05 

12.26 
15.80 
18.95 

11.14 
14.36 
17.22 

10.21 
13.16 
15.79 

24X8 

1M 

90.2 
118.8 
146.5 

83.4 
102.4 
117.0 

16.68 
20.48 
23.40 

13.90 
17.06 
19.50 

11.91 
14.63 
16.71 

10.42 
12.80 
14.62 

9.26 
11.37 
13.00 

8.34 
10.24 
11.70 

7.58 
9.31 
10.63 

6.95 
8.53 
9.75 

STRENGTH  OF  CAST-IRON   LINTELS. 


561 


TABLE  I.— SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR 
CAST-IRON  LINTRL&— (Continued). 


LlNTEI£    OP 


t 

DEPTH 
1 

—  -i 

SHAPES. 


Leads  include  weight  of  lintels.    Maximum  tensile  stress  3,000  Ibs.  per 
square  inch.     See  remarks  page  558. 


Size, 
width 
by 
depth, 

ickness  of 
tetal,  ins. 

Wt. 

per 
foot, 

c, 

tons. 

Span  in  feet. 

ins. 

X3S 
P 

Ibs. 

5 

6 

7 

8 

9 

10 

11 

12 

*4 

99.6 

116.0 

23  .  20 

19  .  33 

16.57 

14.50 

12.88 

11.60 

10.54 

9.66 

24X10 

1 

131.3 

144.4 

28.88 

24.06 

20.63 

18.05 

16.04 

14.44 

13.12 

12.03 

V4 

162.1 

167.6 

33.52 

27.93 

23.94 

20.95 

18.62 

16.76 

15.23 

13.96 

% 

109.0 

150.4 

30.08 

25.06 

21.48 

18.80 

16.71 

15.04 

13.67 

12.53 

24X12 

143.8 

189.6 

37.92 

31.60 

27.08 

23.70 

21.06 

18.96 

17.23 

15.80 

ll<i 

177.7 

223.0 

44.60 

37.16 

31.85 

27.87 

24.77 

22.30 

20.27 

18.58 

% 

99.6 

95.5 

19.10 

15.25 

13.64 

11.93 

10.61 

9.55 

8.68 

7.98 

28X8 

1 

131.3 

115.0 

23.00 

19.16 

16.43 

14.37 

12.77 

11.50 

10.45 

9.58 

IK 

162.1 

130.5 

26.10 

21.75 

18.64 

16.31 

14.50 

13.05 

11.86 

10.87 

H 

109.0 

140.5 

28.10 

23.41 

20.07 

17.56 

15.61 

14.05 

12.77 

11.70 

28X10 

143  8 

164.8 

32.96 

27.46 

23.54 

20.60 

18.31 

16.48 

14.98 

13.73 

IK 

177.7 

192.0 

38.40 

32.00 

27.43 

24.00 

21.33 

19.20 

17.45 

16.00 

% 

118.3 

171.4 

34  .  28 

28.56 

24.48 

21.82 

19.04 

17.14 

15.58 

14.28 

28X12 

i 

156.3 

216.1 

43.22 

36.01 

30.87 

27.01 

24.01 

21.61 

19.64 

18.00 

IK 

193.3 

256.7 

51.34 

42.78 

36.67 

32.08 

28.52 

25.67 

23.33 

21.39 

LINTELS  OP 


E 

DEPTH 
1 

SHAPES. 

H 

74.4 

43.3 

8.66 

7.21 

6.18 

5.41 

4.81 

4.33 

3.93 

3.60 

16X6 

1 

96.9 

52.4 

10.48 

8.73 

7.48 

6.55 

5.82 

5.24 

4.76 

4.36 

IK 

118.1 

59.3 

11.86 

9.88 

8.47 

7.41 

6.59 

5.93 

5.39 

4.86 

H 

88.5 

68.1 

13.62 

11.35 

9.73 

8.51 

7.56 

6.81 

6.19 

5.67 

16X8 

i 

115.6 

83.9 

16.75 

13.98 

11.98 

10.48 

9.32 

8.39 

7.62 

6.99 

IK 

141.6 

97.0 

19.40 

16.16 

13.85 

12.12 

10.77 

9.70 

88.1 

8.08 

H 

97.8 

80.2 

16.04 

13.36 

11.45 

10.02 

8.91 

8.02 

7.29 

6.68 

20X8 

1 

128.1 

98.7 

19.74 

16.45 

14.10 

12.33 

10.95 

9.87 

8.97 

S.22 

IK 

157.2 

113.9 

22.78 

18.98 

16.27 

14.23 

12.65 

11.39 

10.35 

9.49 

562 


STRENGTH  OF  CAST-IRON  LINTELS. 


TABLE  I.— SAFE  DISTRIBUTED  LOADS  IN  TONS  FOR 
CAST-IRON  LINTELS— (Continued). 


LINTELS  off 


DEPTH 

..L 


SHAPES. 


Loads  include  weight  of  lintel.      Maximum  tensile  stress  3,000  Ibs.  pel 
square  inch.     See  remarks  page  558. 


Size, 
width 
by 
depth, 
ins. 

*0  w 

33  a 

Wt. 
per 
foot, 
Ibs. 

111.9 
146.9 
180.7 

c, 

tons. 

112.0 
139.7 
163.5 

Span  in  feet. 

1 

IK 

5 

6 

7 

8 

9 

12.44 
15.52 
18.16 

10 

11.20 
13.97 
16.35 

11 

10.18 
12.70 
14.86 

12 

9.33 
11.64 
13.62 

20X10 

22.40 
27.94 
32.70 

18.66 
23.28 
27.25 

16.00 
19.95 
23.35 

14.00 
17.46 
20.43 

20X12 

1 

126.0 
165.6 
204.1 

146.7 

184.8 
218.8 

29  .  34 
36.96 
43.76 

24.45 
30.80 
36.46 

20.95 
26.40 
31.25 

18.33 
23.10 
27.35 

16.30 
20.53 
24.31 

14.67 

18.48 
21.88 

13.33 
16.80 
19.89 

12.22 
15.40 
18.33 

24X8 

1  4 

107.2 
140.6 
172.6 

91.9 

112.8 
130.2 

18.38 
22.56 
26.04 

15.31 

18.80 
21.70 

13.12 
16.11 
18.57 

11.49 
14.10 
16.27 

10.21 
12.53 
14.47 

9.19 

11.28 
13.02 

8.35 
10.25 
11.83 

7.66 
9.40 
10.85 

24X10 

1 
IK 

121.3 
159.4 
196.3 

127.8 
159.5 
183.6 

25.56 
31.90 
36.72 

21.30 
26.58 
30.60 

18.25 
22.78 
26.23 

15.97 
19.94 
22.95 

14.20 
17.72 
20.40 

12.78 
15.95 
18.36 

11.61 
14.50 
16.69 

10.65 
13.29 
15.30 

24X12 

1  4 
IK 

135.3 
178.1 
219.7 

166.6 
209.3 
247.7 

33.32 
41.86 
49.54 

27.76 
34.88 
41.28 

23.80 
29.90 
35.39 

20.82 
26.16 
30.96 

18.51 
23.25 
27.52 

16.66 
20.93 
24.77 

15.14 
19.02 
22.51 

13.88 
17.44 
20.64 

28X10 

l  4 
IK 

130.7 
171.9 
211.9 

141.4 
177.4 

207.8 

28.28 
35.48 
41.56 

23.57 
29.57 
34.63 

20.20 
25.34 
29.68 

17.67 
22.17 
25.97 

15.71 
19.71 
23.09 

14.14 
17.74 
20.78 

12.85 
16.12 
18.89 

11.78 
14.78 
1.7.31 

28X12 

1 

IK 

144.7 
190.6 
235.3 

186.0 
234.6 
277.9 

37.20 
46.92 
55  .  58 

31.00 
39.10 
46.31 

26.57 
33  .  51 
39.70 

23.25 
29.32 
34.74 

20.66 
26.06 
30.88 

18.60 
23.46 
27.79 

16.91 
21.32 
25.26 

15.50 
19.55 
23.16 

Strength   of  Wooden  Beams. 

Wooden  beams  are  almost  invariably  square  or  rectangular 
shaped  timbers,  and  we  shall  therefore  consider  only  that  shape 
in  the  following  rules  and  formulas. 

For  beams  with  a  rectangular  cross-section,  we  can  simplify 
our  formulas  for  strength  by  substituting  for  the  moment  of 

inertia  its  value,  viz.,  -  10   ,  where  6  =  breadth  of  beam   and  d 
its  depth. 


12 


STRENGTH  OF  WOODEN  BEAMS. 


563 


Then,  substituting  this  value  in  the  general  formulas  for  beams, 
we  have  for  rectangular  beams  of  any  material  the  following 
formulas : — 

Beams  fixed  at  one  end,  and  loaded  at  the  other  (Fig.  5). 


-L -I 


Fig.  5 


breadth X square  of  depthxA*     ,*<. 

Safe  load  in  pounds  =  —  — ? — TT~. — ? — -         — -,    (4) 

4  X  length  in  feet 


or 


Breadth  in  inches     = 


4  X  load  X  length  in  feet 
square  of  depth  X  A 


(5) 


Beams  fixed  at  one  end,  and  loaded  with  uniformly  distributed 
load  (Fig.  6). 


Safe  load  in  pounds  = 


Fig.  6 

breadth X square  of  depth X A* 
2  X  length  in  feet 


2  X  load  X  length  in  feet 

Breadth  in  inches      =  —  — . 

square  ot  depth  X  A 


,     (6) 

(7) 


*  For  value  of  A ,  see  Table  II. 


564 


STRENGTH  OF  WOODEN  BEAMS. 


Beams  supported  at  both  ends,  loaded  at  middle  (Fig.  7). 

W 


1 


Fig.  7 

c,  r   ,      ,  .  ,        breadth  X  square  of  depth  X  A  * 

Safe  load  in  pounds  =  — 

span  in  feet 


Breadth  in  inches   = 


span  in  fcet/Xload 


(8) 


(9) 


square  of  depth X  A' 
Beams    supported    at    both    ends,    load   uniformly    distributed 
(Fig.  8). 


0  r   *     j  .  , 

Safe  load  in  pounds  = 


Fig.  8 

2  X  bread  thX  square  of  de 
— 

span  in  ieet 


span  in  feetxload 

Breadth  in  inches  =~ —  — :=— , — rr -.. 

2  X  square  ot  depth  X  A 


,    (10) 


(11) 


Beams  supported  at  both  ends,  load  uniformly  distributed  over 
only  a  portion  of  the  span  (Fig.  9). 


Fig.  9 


*  For  value  of  A ,  see  Table  II. 


STRENGTH  OF  WOODEN  BEAMS. 


565 


In  this  case  the  dimensions  of  the  beam  required  to  carry  the 
load  can  be  accurately  determined  only  by  computing  the  bend- 
ing-moment,  as  explained  in  Chapter  IX.  and  substituting  the 
value  thus  found  in  formula  (16),  following.  If,  however,  the 
length  Ll  is  very  short  in  comparison  with  L,  then  the  load  may 
be  considered  as  concentrated  at  its  centre,  and  the  breadth  of  the 
beam  may  be  found  by  formula  (9),  if  the  load  is  at  the  centre  of 
the  span,  or  by  formula  (13),  if  it  is  at  one  side  of  the  centre.  The 
error  will  be  on  the  safe  side. 

Beams  supported  at  both  ends,  loaded  with  concentrated  load 
NOT  AT  CENTRE  (Fig.  10). 


Fig.   10 

breadth  Xsq.  of  depth  X  span  X  A  *     ,im 
Saf e  load  in  pounds  =  —  -1- —  — ,    (12) 

4  x  m  x  n 


Breadth  in  inches    = 


square  of  depthXspanxA* 

Beams  supported  at  both  ends,  and  loaded  with  W  pounds  at  a 
distance  m  from  each  end  (Fig.  11). 


Wl 


iw 


I 


Fig.  II 


Safe  load  W  in  pounds  _  breadth  X  square  of  depth  X -4* 
at  each  point  4.Xm 


or 


,    (14) 
(15) 


4  X  load  at  one  point  X  m 

Breadth  in  mches= F~r~Ti  — • 

sq.  of  depth  X  A 

NOTE. — In  the  last  two  cases  the  lengths  denoted  by  m  and  n  should  be 
taken  in  feet,  the  same  as  the  spans. 


*  For  value  of  A ,  see  Table  II. 


566      STRENGTH  OF  WOODEN  BEAMS. 


Application   of  the  foregoing  formulas. 

EXAMPLE  1.  —  What  load  will  an  8  inch  by  12  inch  hard  pine 
beam,  securely  fastened  into  a  brick  wall  at  one  end,  sustain 
with  safety,  6  feet  out  from  the  wall? 

Am.     Safe  load  in  pounds  (Formula  4)  equals 


EXAMPLE  2.  —  It  is  desired  to  suspend  two  loads  of  10,000 
pounds  each,  four  feet  from  each  end  of  an  oak  beam  20  feet  long. 
What  should  be  the  size  of  the  beam? 

Ans.     Assume  depth  of  beam  to  be  14  inches;  then  (Formula 

4X10,000X4 
15)  breadth  =  —  19^      5    -==11   inches,  nearly;      therefore   the 

beam  should  be  11  X  14  inches. 

To  find  the  size  of  beam  (supported  at  both  ends)  to  support 
several  concentrated  loads,  or  a  distributed  load  and  one  or  more 
concentrated  loads.  —  The  correct  method  of  finding  the  least  size 
of  beam  that  will  safely  support  a  combination  of  loads,  is  to 
first  find  the  maximum  bending-moment,  as  explained  in  Chapter 
IX.,  and  then  substitute  the  value  thus  found  for  the  bending- 
moment  in  the  following  formula: 

T>      J.LI,  •    •     t,         4  X  max.  bending  moment,  ft.  Ibs. 
Breadth  in  inches  =  -  —  .        (16) 

square  of  depth  X^.. 

An  example  of  this  kind  for  steel  beams  is  worked  on  pages 
504-506. 

A  shorter  and  easier  method  is  to  find  the  equivalent  distrib- 
uted load  for  each  concentrated  load,  and  then  find  the  size  of 
beam  required  to  support  the  total  equivalent  distributed  load 
thus  found.  The  equivalent  distributed  load  for  concentrated 
loads  applied  at  different  proportions  of  the  span  from  either  end, 
may  be  obtained  by  multiplying  the  concentrated  load  by  the 
following  factors: 


STRENGTH  OF  WOODEN  BEAMS. 


567 


For  concentrated  load  applied  at  centre  of  span,  multiply  by  2 


at  l/3d     the  span,  by 


at  l/4th 

at  1 /5th  " 

at  l/6th  " 

at  l/7th  " 

atl/8th  " 

at  l/9th  " 

at  l/10th  " 


by 
by 
by 
by 
by 
by 
by 


1.78 
1.5 
1.28 
H 

.98 

* 
.79 

.72 


Thus  a  concentrated  load  of  900  Ibs.  applied  at  one-sixth  of 
the  span  from  one  support,  will  produce  the  same  bending- 
moment  as  a  distributed  load  of  900  X  li  or  1,000  Ibs. 

The  above  method  of  finding  the  size  of  beam  for  a  combina- 
tion of  several  loads,  will  give  a  larger  beam  than  the  correct 
method,  by  formula  (1.6),  for  the  reason  that  the  maximum  bcnd- 
ing-moment  will  not  be  equal  to  the  sum  of  the  individual  bending- 
moments,  hence  when  there  are  several  heavy  loads  to  be  sup- 
ported, it  will  be  economy  to  compute  the  maximum  bending- 
moment  by  the  graphic  method  explained  in  Chapter  IX. 

EXAMPLE  3. — The  girder  G,  Fig.  12,  supports  the  rafters  of  a 
flat  roof,  and  also  three  heavy  beams,  A,  B,  C,  blocked  up  above 
the  roof  and  supporting  a  large 
tank  filled  with  water.  The  tim- 
ber is  to  be  longleaf  yellow  pine. 
The  weight  of  the  roof  and  allow- 
ance for  snow  will  be  7,500  Ibs. 
Each  of  the  beams  A,  B,  and  C 
will  impose  a  load  on  the  girder 
due  to  the  weight  of  the  tank 
and  its  contents  of  3,000  Ibs. 
What  should  be  the  size  of  the 
girder? 

Ans.  The  roof  load  may  be  considered  as  uniformly  dis- 
tributed. The  load  from  beam  A  is  applied  l/3d  the  span  from 
one  end;  the  load  from  B  5/12ths  the  span  from  the  other  end, 
and  the  load  from  C  l/6th  the  span.  The  fraction  5/12ths  is  half 
way  between  1/2  and  l/3d;  hence  the  load  from  B  should  be 
multiplied  by  1.89.  Multiplying  the  concentrated  loads  by  their 
proper  factors,  we  find  the  equivalent  distributed  load  to  be  as 
follows : 


Fig.  12 


568  STRUT   BEAMS  AND   TIE   BEAMS. 

Roof  load,  distributed  =  7,500 

Load  from  A,  3,000 X  1.78  =  5,340 

Load  from  B,  3,000X1.89  =  5,670 

Load  from  C,  3,000X1  J  =  3,333 


Equivalent  distributed  load=21,843  Ibs. 

Assuming  14  ins.  as  the  depth  of  the  beam,  and  using  formula 
(11),  we  have 

12X21,843 
Breadth  m  u^.—-e.?  ins. 


Assuming  12  ins.  for  the  depth,  we  obtain  9.1  ins.  for  the 
breadth,  hence  the  girder  must  be  10"Xl2",  or  7"X14". 

Strut  Beams  and  Tie  Beams. 

A  "strut  beam"  is  a  beam  that  is  subject  both  to  a  transverse 
strain  and  to  a  compressive  stress. 

A  "tie  beam"  is  one  that  is  subject  to  direct  tension  in  addition 
to  the  transverse  strain. 

To  find  the  strength  of  either,  first  find  the  size  of  beam 
required  to  resist  the  transverse  strain,  and  then  the  size  of 
timber,  of  the  same  depth  as  the  beam,  to  resist  the  direct  tension 
or  compression,  and  add  the  two  breadths  together. 

EXAMPLE  4. — A  spruce  tie  beam  10  feet  long  between  joints 
sustains  a  ceiling  load  of  2,000  Ibs.  and  a  direct  tensile  stress  of 
40,000  Ibs.  What  should  be  the  dimensions  of  the  beam? 

Ans.  As  a  ceiling  load  is  uniformly  distributed  we  determine 
the  size  of  the  beam  by  formula  (11).  Assuming  the  depth  as  8 
ins.,  the  breadth  should  be 

10X2,000 
2X64X70  °3 

The  resistance  of  spruce  to  tension  (see  Table  I.,  Chapter  XI.) 
is  1,600  Ibs.  40,000  divided  by  1,600=25  sq.  ins.,  which  is 
equivalent  to  3 J  X  8  ins. ;  therefore  it  will  require  a  beam  5  J"  X 
8"  to  resist  both  the  transverse  strain  and  the  direct  tension.  If 
the  tie  beam  is  cut  in  any  way  so  as  to  reduce  the  section  (except 
over  a  support)  the  dimensions  must  be  increased  accordingly. 

EXAMPLE  5. — -A  strut  beam  of  white  pine  10  feet  long  sup- 
ports a  distributed  roof  load  of  6,000  Ibs.,  and  is  also  subject  to  a 


STRUT   BEAMS   AND   TIE   BEAMS. 


569 


direct  compression  of  48,000  Ibs.     What  should  be  the  size  of  the 
beam? 

Ans.     Assuming  12  inches  for  the  depth,  we  find  the  breadth 
for  the  transverse  load  by  formula  11 


10X6,000 


3i  ins.  nearly. 


Looking  in  the  table  giving  the  strength  of  white  pine  posts, 
Chapter  XIV.,  we  find  that  an  8  X  12  post  10  feet  long  will  support 
51,450  Ibs.,  or  a  little  more  than  our  compressive  stress.  Hence 
it  will  require  an  8  X  12  beam  to  resist  the  compressive  stress  and 
a  beam  3JX12  to  resist  the  transverse  load.  We  should  there- 
fore make  the  beam  12  X  12  ins.  to  resist  them  both. 


VALUES  OF  THE  CONSTANT  A. 

The  letter  A  in  formulas  4-16  denotes  the  safe  load  for  a  unit 
beam  one  inch  square  and  one  foot  span,  loaded  at  the  centre. 
This  is  also  one-eighteenth  of  the  modulus  of  rupture  or  fibre 
stress  for  safe  loads.  The  following  are  the  values  of  A,  which  are 
obtained  by  dividing  the  moduli  of  rupture  in  Chap.  XV.  by  18. 

TABLE  II.— VALUES  OF  A.—  CO-EFFICIENT  FOR  BEAMS. 


Material. 

Albs. 

Material. 

Albs. 

Cast  iron                           .  .  . 

308 

Pine,  white,  Western.  .  . 

65 

Wrought  iron  

666 

Texas  yellow  

90 

Steel 

888 

Spruce 

70 

American  woods'        . 

Whitewood  (poplar)  
Redwood  (California) 

65 
60 

Chestnut    

60 

Bluestone  flagging  (Hudson 

Hemlock 

55 

River)   .  . 

25 

75 

Granite,  average  

17 

Pine   Georgia  yellow   . 

100 

Limestone  

14 

"      Oregon         

90 

17 

"      reel  or  Norway      .  . 

70 

Sandstone 

8  to  11 

"      white   Eastern  

60 

Slate  

50 

These  values  for  the  co-efficient  A  are  one-third  of  the  break- 
ing-weight of  timbers  of  the  same  size  and  quality  as  that  used 
in  first-class  buildings.  This  is  a  sufficient  allowance  for  timbers 
in  roof  trusses,  and  beams  which  do  not  have  to  carry  a  more 
severe  load  than  that  of  a  dwelling-house  floor,  and  small  halls, 
etc.  Where  there  is  likely  to  be  very  much  vibration,  as  in  the 
floor  of  a  mill,  or  a  gymnasium  floor,  or  floors  of  large  public  halls, 


570  STRENGTH  OF   WOODEN    BEAMS. 

the  author  recommends  that  only  four-fifths  of  the  above  values 
for  A  be  used. 

For  beams  supporting  permanent  loads,  such  as  masonry,  or 
water-tanks,  the  safe  load  should  be  reduced  ten  per  cent.,  as  such 
loads  are  not  usually  overestimated. 

The  values  for  stones  are  based  on  a  factor  of  safety  of  six. 

For  comparative  values  of  A,  as  given  in  Building  Laws,  see 
page  573. 


Relative  Strength  of  Rectangular  Beams. 

From  an  inspection  of  the  foregoing  formulas  it  will  be  found 
that  the  relative  strength  of  rectangular  beams  in  different  cases 
is  as  follows: 

Beam  supported  at  both  ends,  and  loaded  with  a  uniformly 

distributed  load 1 

Beams  supported  at  both  ends: 

Load  uniformly  distributed 1 

Concentrated  load  at  centre | 

"                     "     one-third  the  span ^ 

"                     "     one-fourth     "        f 

«                     "     one-fifth        "         f| 

«                     "     one-sixth       "         T% 

"                     "     one-seventh  "         f  f 

"                    "     one-eighth     "         f 

"                    "     one-ninth      "        ft 

«                     "     one-tenth       "        ff 

Beam  fixed   at  one  end,  and  loaded  with  a  uniformly  dis- 
tributed load i 

Beam  fixed  at  one  end,  and  loaded  at  the  other J 

Also  the  following  can  be  shown  to  be  true: 
Beam  firmly  fixed  at  both  ends,  and  loaded  at  the  centre. ...   1 
Beam  fixed  at  both  ends,  and  loaded  with  distributed  load .  . .  1J 

These  facts  are  also  true  of  a  uniform  beam  of  any  form  of  cross- 
section. 

When  a  square  beam  is  supported  on  its  edge,  instead  of  on  its 
side — that  is,  has  its  diagonal  vertical — it  will  bear  about  seven- 
tenths  as  great  a  breaking-load. 


STRENGTH  OF  WOODEN   BEAMS.  571 

The  strongest  beam  which  can  be  cut  out  of  a 
round  log  is  one  in  which  the  breadth  is  to  the       f 
depth  as  5  to  7,  very  nearly,  and  can  be  found      / 
graphically,  as  shown  in  margin.     Draw  any     \ 
diagonal,  as  ab}  and  divide  it  into  three  equal      \ 
parts  by  the  points  c  and  d]  from  these  points 
draw  perpendicular  lines,   and   connect   the 
points  e  and  /  with  a  and  b,  as  shown. 

CYLINDRICAL  BEAMS. — A  cylindrical  beam  is  only  \%  as 
strong  as  a  square  beam  whose  side  is  equal  to  the  diameter  of  the 
circle.  Hence,  to  find  the  load  for  a  cylindrical  beam,  first  find 
the  proper  load  for  the  corresponding  square  beam,  and  then 
divide  it  by  1.7. 

The  bearing  of  the  ends  of  a  beam  on  a  wall  beyond  a  certain 
amount  does  not  strengthen  the  beam  any.  In  general,  a  beam 
should  have  a  bearing  of  four  inches,  and  if  the  beam  be  very 
long,  the  bearing  should  be  6  ins. 

Weight  of  the  Beam  itself  to  be  taken  into  Account. — The  for- 
mulas we  have  given  for  the  strength  of  beams  do  not  take  into 
account  the  weight  of  the  beam  itself,  and  hence  the  safe  load  of 
the  formulas  includes  both  the  external  load  and  the  weight  of  the 
material  in  the  beam.  In  small  wooden  beams,  the  weight  of 
the  beam  is  generally  so  small,  compared  with  the  external  load, 
that  it  need  not  be  taken  into  account.  But  in  larger  wooden 
beams,  and  in  metal  and  stone  beams,  the  weight  of  the  beam 
should  be  subtracted  from  the  safe  load  if  the  load  is  distributed  ; 
and  if  the  load  is  applied  at  the  centre,  one-half  the  weight  of  the 
beam  should  be  subtracted. 

The  weight  per  cubic  foot  for  different  kinds  of  timber  may  be 
found  in  the  table  giving  the  Weight  of  Substances,  Part  III. 

Explanation  of  Tables  III.- VII. 

Tables  for  the  strength  of  yellow  and  white  pine,  Oregon  pine, 
spruce,  and  oak  beams,  are  given  on  the  following  pages  for  beams 
one  inch  wide.  These  tables  were  computed  by  the  author  from 
the  rules  and  coefficients  given  in  this  chapter,  and  are  believed 
to  be  perfectly  reliable  when  used  in  accordance  with  the  explana- 
tions. 

To  find  the  strength  of  a  given  beam  of  any  other  breadth,  it  is  only 
necessary  to  multiply  the  strength  given  in  the  table  by  the 
breadth  of  the  given  beam. 

EXAMPE  6. — What  is  the  safe  distributed  load  for  a  yellow-p 


572      STRENGTH  OF  WOODEN  BEAMS. 

beam,  supported  at  both  ends,  8  inches  by  12  inches,  20  feet  clear 
span? 

Ans.  "^rom  Table  III.,  safe  load  for  one  inch  thickness  is 
1,440  poling  1 .440X8=  11,520  pounds,  safe  load  for  beam. 

To  find  the  size  j^  a  beam  that  will  support  a  given  load  with  a 
given  span,  find  the  safe  load  for  a  beam  of  an  assumed  depth  one 
inch  wide,  and  divide  the  given  load  by  this  strength. 

EXAMPLE  7. — What  size  spruce  beam  will  be  required  to  carry 
a  distributed  load  of  8,640  pounds  for  a.  clear  span  of  18  feet? 

A-ns.  From  the  table  for  spruce  beams,  we  find  that  a  beam 
14  inches  deep  and  1  inch  thick,  18  feet  span,  will  support  1,524 
pounds;  and  dividing  the  load,  8,640  pounds,  by  1,524,  we  have 
5  J  for  the  breadth  of  the  beam  in  inches :  hence  the  beam  should 
be  6  X 14  inches,  to  carry  a  distributed  load  of  8,640  pounds  with 
a  span  of  18  feet. 

To  find  the  safe  centre  load  of  a  given  beam,  first  find  the  safe 
distributed  load  as  in  Example  6,  and  divide  by  two. 

To  find  the  safe  load  when  concentrated  at  some  point  other  than 
the  centre,  first  find  the  safe  distributed  load  for  the  given  span, 
and  divide  by  the  factors  given  011  page  567. 

To  find  the  size  of  beam  to  support  a  given  concentrated  load,  mul- 
tiply the  given  load  by  the  factor  corresponding  with  the  position 
of  the  load  as  given  on  page  567,  and  then  proceed  as  in  Example  7. 
If  in  doubt  as  to  the  application  of  the  tables,  in  special  cases, 
it  will  be  safer  to  use  the  appropriate  formula,  as  given  on  pages 
563  and  565.  The  formulas  and  tables  should  always  give  the 
same  result. 

To  use  the  tables  for  beams  thai  run  less  than  the  nominal  dimen- 
sions. In  many  localities  floor  joists  as  carried  in  stock  are  more 
or  less  scant  of  the  nominal  dimensions,  arid  for  such  joists  a 
reduction  in  the  safe  load  must  be  made  to  correspond  to  the 
reduction  in  size.  For  beams  J  inch  scant  in  both  dimensions 
the  safe  load  may  be  obtained  by  multiplying  the  safe  load  as 
given  in  the  table  by  the  following  factors : 

For  beams  lf"X5f"  by  1.6  For  beams  If'XllJ"  by  1.67 

2f"X5|"  "  2.52  2-|"XllJ"  "  2.63 

lf"X6i"  "      If  1J"X13|"  "   1.68 

2J"X6f"  "  2.55  2|"Xl3i"    "-2,65 

lJ"X7i"  "  1.64  !J"Xl4i"  "  1.69 

2J"X7f"  "  2.58  2f"Xl4J"  "  2.66 

l|"X9f"  "  1.66  1J"X15J"  "  1.7 

2i"X9$"  "  2.61  2f"Xl5|"  "  2.66 


STRENGTH  OF  WOODEN  BEAMS. 


573 


EXAMPLE.— What  is  the  safe  load  for  a  2f  "X13|' '  Oregon  pine 
beam,  20  feet  span? 

Ans.  From  Table  IV.  we  find  the  safe  load  for  a  1 X 14  beam 
to  be  1,764  Ibs.  Multiplying  this  by  2.65  we  have  4,674  Ibs.  as  the 
safe  distributed  load  for  a  beam  2|Xl3-|  ins.  For  a  beam  full 
3X 14  ins.  the  safe  load  is  5,292  Ibs. 

Stone  Beams. — The  same  formulas  apply  to  stone  as  to  wooden 
beams,  but  the  values  of  the  co-efficient  A  are  only  from  one- 
sixth  to  one-tenth  of  breaking-loads.  Sandstone  beams  should 
never  be  subjected  to  any  very  heavy  loads;  but,  where  used  as 
lintels,  the  stone  should  be  relieved  by  iron  beams  or  brick  arches 
back  of  the  stone. 

Comparison  of  the  values  of  A  (for  the  transverse  strength  of 
wooden  beams)  given  in  Building  Laws  with  those  of  Table  II. 
(A  as  used  by  the  author  is  -f^  of  the  fibre  stress,  and  ^  of  the 
constant  C,  given  in  the  Building  Laws  of  Buffalo  and  Chicago). 


Kind  of  wood. 

Maximum  working  values  for  A  . 

Buf- 
falo. 

Bos- 
ton. 

Chi- 
cago. 

Den- 
ver. 

New 
York. 

* 

66§ 
61 
40 
40 
554 
44^ 
33J 

Kid- 
der. 

Yellow  Pine  
Oregon  Pine.  .  . 

100 

69 

80 

100 
90 

75 

66 

'44i' 
44* 
55-| 
44i 
33J 

100 
90 
60-65 
70 
75 
60 
55 

White  Pine  

60 

50 

Spruce. 

42 

Oak  (White)  .... 
Chestnut  

75 

55J 

60 

90 

Hemlock  . 

60 

*  The  values  in  this  column  were  recommended  by  the  Committee  on 
Strength  of  Bridge  and  Trestle  Timbers  of  the  Association  of  Railway 
Superintendents  of  Bridges  and  Buildings,  in  1895,  and  are  supposed  to 
give  a  factor  of  safely  of  six.  With  a  factor  of  safety  of  four  they  agree 
very  closely  with  the  values  recommended  and  used  by  the  author  for 
ordinary  floor  beams  and  girders. 


574 


STRENGTH  OF  HAIID-PINE  BEAMS. 


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STRENGTH   OF  BUILT-UP  WOODEN    BEAMS.   579 


CHAPTER  XVII. 

STRENGTH    OF     BUILT-UP   WOODEN"     BEAMS, 
FLITCH-PLATES,  AND  TRUSSED  GIRDERS. 

Built-up  Wooden  Beams. — Wooden  beams  or  girders 
built  up  of  planks,  spiked  or  bolted  together  side  ~by  side,  will 
generally  be  somewhat  stronger  than  a  solid  beam  of  the  same 
dimensions,  because  the  planks  will  be  better  seasoned  and  more 
free  from  check  cracks  and  other  defects.  For  beams  or  girders 
10  ins.  or  less  in  depth  spikes  will  usually  be  sufficient  for  binding 
the  planks  together,  but  for  deeper  beams  bolts  should  be  used 
in  addition  to  the  spikes,  to  prevent  the  planks  from  separating 
and  the  outer  planks  from  warping  or  curling  away  from  the 
others. 

Two  bolts  should  be  placed  at  each  end  of  the  beam  and  about 
four  feet  apart  between. 

When  beams  are  built  up  in  this  way  each  plank  should  be  the 
full  length  of  the  beam,  or,  in  the  case  of  a  continuous  beam,  the 
planks  should  break  joint  over  the  supports.,  Built  beams 
should  always  be  set  with  the  planks  on  edge,  and  never  flatways. 

Compound  Wooden  Girders. — It  is  often  desirable  to 
use  a  wooden  girder  for  a  longer  span  or  greater  load  than  would 
be  safe  for  the  deepest  single  beam  that  can  be  obtained,  or  for 
a  beam  built  up  of  planks.  In  such  cases  compound  wooden 
beams  may  be  used. 

By  a  compound  wooden  beam  or  girder  is  meant  a  beam  built 
up  by  placing  two  or  more  single  beams  one  on  top  of  the  other, 
with  the  view  of  having  them  act  as  a  single  beam  having  tjie 
depth  of  the  combined  beams. 

Thus  if  two  10  X  10-inch  beams  were  placed  one  on  top  of  the 
other,  and  the  upper  one  loaded  at  the  centre,  the  beams  would 
act  as  two  separate  beams  (Fig.  1)  and  their  combined  strength 
would  be  no  greater  than  if  the  two  beams  were  placed  side  by 
side.  If,  however,  the  two  beams  can  be  joined  so  that  the  fibres 
of  the  lower  beam  will  be  extended  as  much  as  would  be  the  case 
jn  a  single  beam  of  the  same  depth  or  in  other  words,  so  that  the 


580     STRENGTH   OF  BUILT-UP  WOODEN   BEAMS. 

two  beams  will  not  slip  on  each  other,  the  compound  beam  will 
have  four  times  the  strength  of  the  single  beam. 

Various  attempts  have  been  made  to  join  beams  thus  placed 
so  as  to  prevent  the  two  parts  slipping  on  each  other,  but  until 
within  a  few  years  there  has  been  no  experimental  data  to  show 
how  far  such  methods  accomplish  their  object. 

During  the  years  1896-7,  however,  Prof.  Edgar  Kidwell,  of  the 
Michigan  College  of  Mines,  made  quite  an  extended  series  of  tests 


Fig.  I 

of  the  efficiency  of  compound  beams  of  different  patterns,  and 
from  these  tests  much  valuable  data  has  been  obtained.  A  full 
description  of  the  tests  accompanied  by  the  conclusions  of  the 
author,  and  rules  and  data  for  proportioning  the  bolts  and  keys, 
of  keyed  beams,  is  published  in  Vol.  XXVII.,  "  Transactions  of 
the  American  Institute  of  Mining  Engineers." 

Probably  the  most  common  form  of  compound  beam,  as  used 
in  American  building  construction,  is  that  shown  in  Fig.   2, 


Fig.  2 


diagonal  boards  in  opposite  directions  being  nailed  to  each  side 
of  the  two  timbers  to  prevent  their  slipping  on  each  other.  Mr. 
T.  M.  Clark,  in  his  "  Building  Superintendence/'  advocates  this 
as  one  of  the  best  forms  of  compound  beams,  and  places  its 
efficiency  at  about  95  per  cent,  of  a  solid  beam  of  the  same  depth. 
Prof.  Kidwell  made  nine  tests  of  this  style  of  beam,  six  having  a 
ratio  of  span  to  depth  of  beam  as  12  to  1,  and  three  as  24  to  1. 
The  shorter  beams  gave  an  average  efficiency  without  much 


STRENGTH  OF   BUILT-UP  WOODEN  BEAMS.   581 


variation,  of  71.4  per  cent.,  and 
the  longer  beams  an  efficiency 
of  80.7. 

It  was  found  that  the  beams 
failed  by  the  splitting  of  the 
diagonal  pieces  or  the  drawing 
of  the  nails — "in  every  case, 
long  before  the  beam  broke,  the 
struts  split  open  or  the  nails 
were  drawn  partly  out,  or  bent 
over  in  the  wood,  thereby  per- 
mitting the  component  beams 
to  slide  on  each  other.  It  was 
found  that  no  amount  of  nailing 
could  prevent  this." 

When  built  with  diagonal 
boards  1J  inches  thick,  nailed 
with  10  d  's  as  in  Fig.  2,  the  work- 
ing strength  of  such  a  beam  may 
be  taken  at  65  per  cent,  of  the 
strength  of  a  solid  beam  of  the 
same  depth,  and  of  a  breadth 
equal  to  the  breadth  of  the  tim- 
bers. The  deflection  of  the  beam, 
however,  will  be  about  double 
that  of  a  solid  beam  of  the 
same  size,  and  on  that  account 
this  style  of  beam  is  not  to  be 
recommended  for  supporting 
floors  with  plastered  ceilings  or 
carrying  plastered  partitions. 

Keyed  Beams.  —  Prof. 
Kidwell  also  tested  several 
styles  of  keyed  beams,  with  the 
result  that  a  compound  beam 
keyed  and  bolted  together,  as 
shown  in  Fig.  3,  was  found  to  be 
the  most  efficient  form  that  it 
is  practicable  to  build. 

It  was  found  that  with  oak 
keys  it  was  possible  to  obtain 
an  efficiency  for  spruce  beams 


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582    STRENGTH   OF   BUILT-UP  WOODEN  BEAMS. 


of  95  per  cent.,  while  the  deflection  varied  from  20  to  25  per 
cent,  more  than  would  be  expected  in  a  solid  beam. 

By  using  cast-iron  keys  the  deflection  was  found  to  be  but 
little,  if  any  more,  than  with  a  solid  beam.  The  keys  must  be 
wedge-shaped,  as  shown  in  Fig.  4,  so  that  they  can  be  driven 
tightly  against  the  end  wood. 

Prof.  Kidwell  recommends  that  for  ordinary  purposes  an 
efficiency  of  75  per  cent,  be  allowed  when  oak  keys  are  used  and 
80  per  cent,  when  the  keys  are  of  cast  iron.  The  width  of  oak 
keys  should  be  twice  the  height  of  the  key.  Numerous  small 
keys  closely  spaced  gave  better  results  than  fewer  large  keys. 
In  the  centre  of  the  span  a  space  equal  to  about  one-quarter  of 
the  length  of  the  beam  should  be  left  free  of  keys,  bolts,  etc.  In 

TABLE  I— SAFE  DISTRIBUTED  LOADS  IN  POUNDS  FOR 
COMPOUND  KEYED  BEAMS. 

16  and  20-inch  beams  to  have  l^X  3-inch  oak  keys,  %-inch  bolts,  3-inch 
washers. 

24-inch  beam  to  have  2  X  4-inch  oak  keys,  %-inch  bolts,  3>£-inch  washers. 

28-inch  beam  to  have  2>£  X  4^-inch  oak  keys,  K-inch  bolts,  3^-inch 
washers. 


Size  of  beam. 

Span  of  beam  in  feet. 

2O 

24 

28 

30 

32 

36 

(  White  pine.  
J  Spruce        .             .  . 

1,152 
1,344 

960 
,120 
,440 
,600 

,500 
,750 
2250 

823 
960 
1,234 
1,371 

1,285 

1,500 
1,928 
2,142 

1,851 
2,160 

2,777 
3,085 

2,520 

768 
896 
1,152 
1,280 

1,200 
1,400 
1,800 
2,000 

1,728 
2,016 
2,592 
2,880 

2,352 
2,744 
3,528 
3  920 

720 
840 
1,080 
1,200 

1,125 
1,312 

1,687 
1,875 

1,620 
1,890 
2,430 
2,700 

2,205 
2,572 
3,307 
3,675 

1,500 
1,666 

1,440 
1,680 
2,160 
2,400 

1,960 
2,286 
2,940 

3,266 

1  X  ID  -j  Qregon  pine  

1  Georgia  pine   .  .     . 

f  White  pine  
_  1  Spruce        

1,800 

X       1  Oregon  pine  

I  Georgia  pine.  .  . 

2,160 
2,520 

Georgia  pine  

f  White  pine  

i  v9«J  Spruce  

5  1  Oregon  pine  
(.Georgia  pine  

To  find  safe  loads  for  any  given  thickness  of  beam,  multiply  the  load  in 
the  table  by  breadth  of  beam  in  inches. 
For  centre  loads,  take  one-half  those  in  table.     For  concentrated  loads 
at  other  points  divide  by  the  factors  given  on  page  567. 
Beams  should  not  be  used  for  shorter  or  longer  spans  than  those  for  which 
safe  loads  are  given,  except  that  28-inch  beams  may  be  used  up  to  40  feet. 

STRENGTH  OF  BUILT-UP  WOODEN  BEAMS.    583 


his  report,  Prof.  Kidwell  also  gives  formulas  for  the  number  and 
spacing  of  the  keys. 

As  compound  beams,  if  used,  would  probably  be  built  of 
either  8, 10, 12,  or  14-inch  timbers,  the  author  has  prepared  Tables 
I.  and  II.,  giving  the  maximum  safe  load  that  may  be  allowed 
for  keyed  beams  16,  20,  24.  and  28  inches  in  depth,  put  together 
as  in  Figs.  3  and  4,  and  also  the  number  of  keys  required  on  each 
side  of  the  centre. 

TABLE  II.— NUMBER  OF  OAK  KEYS  REQUIRED  EACH 
SIDE  OF  CENTRE. 


Size  of  keys. 

White 
pine. 

Spruce. 

Oregon 
pine. 

Georgia 
pine. 

13-inch  beams  l^jX3    -inch  keys  . 
20-    "          "       1^X3    -    "        "      . 
24-   "         "       2     X4    -   "       "      . 
28-   "     e   /'      2MX414-    "       "      . 
Minimum  spacing  of  Keys. 
1KX3    -inch  keys  

7 
9 
8 
9 

1134  ins 

8 
11 
9 
10 

1134  ins 

11 
13 
12 
12 

9     ins 

12 
15 
13 
14 

9     ins 

2  X4  -  " 

15       " 

15       " 

UK    " 

HH   " 

2J4X4H-  "  "  

17       " 

17       " 

13 

13       " 

The  breadth  or  thickness  of  compound  beams  should  be  not 
less  than  two-fifths  of  the  depth.  The  number  of  keys  required 
is  not  affected  by  the  length  or  breadth  of  the  beam,  if  the  beam  is 
figured  for  the  full  safe  load. 

In  spacing  the  keys  (Fig.  4)  they  should  not  be  closer  than  the 
minimum  spacing  given  in  the  table.  For  beams  loaded  at  the 
centre,  the  spacing  of  the  keys  should  be  uniform  from  X  to  Y, 
Y  being  one-eighth  of  the  span  from  the  centre.  If  the  distance 
between  the  keys,  centre  to  centre,  works  out  less  than  the 
minimum  spacing,  the  safe  load  should  be  correspondingly  re- 
duced or  the  thickness  of  the  beam  increased. 

For  beams  uniformly  loaded,  the  first  four  or  five  keys  from 
the  ends  should  be  spaced  for  minimum  spacing,  and  the  spacing 
of  the  remaining  keys  increased  toward  the  point  Y.  When  the 
ratio  of  depth  to  span  is  greater  than  1  to  16,  the  inner  keys 
may  be  a  little  more  than  one-eighth  of  span  from  centre  for  dis- 
tributed loads. 

Fig.  3  shows  the  proper  spacing  for  a  20-inch  spruce  beam  of 
28  feet  span  and  for  a  Georgia  pine  beam  of  30  feet  span,  and  the 
following  table  gives  the  proper  spacing  for  spruce  beams  (figured 
from  the  end  of  the  beam)  of  longer  span.  For  other  woods  and 
spans  the  spacing  should  be  made  as  near  like  these  as  the  fixed 


584 


FLITCH  PLATE  GIRDERS. 


conditions  will  permit.     Four  examples  of  spacing  are  given 
below. 

The  sizes  of  bolts  and  washers  to  be  used  are  given  in  the  head- 
ing of  Table  I.     If  the  beam  is  not  over  10  inches  wide  the  bolts 


B  PLAN  OF  14"  X  24"  SPRUCE  BEAM  -36'  SPAN 
Fig.  4 

may  be  arranged  as  for  the  spruce  beam,  Fig.  3;  if  12  incnes  wide 
or  over  the  bolts  should  be  staggered  as  shown  for  the  hard  pine 
beam.  In  a  very  wide  beam  the  bolts  might  be  spaced  as  in 
detail  B,  Fig.  4. 

Spacing  of  keys  in  inches  (commencing  at  end)  for  distributed 
load: 


16-in.  spruce  beam,  32  feet  span,  10,  12,     12, 
20-  "        "          "        32    "       "      10,  11^,  IVA 
24-"        "         "        36    "       "       13,15,      15, 
28-  "        "         '*       36    fl       "      15,  17,     17, 


16,  19,  24,  32. 

11^,  12,  12,  12,  13,  15,  18,  24. 
15,     15,16,18,20,30. 

17,  17,  17,  17,  17,  17,  17, 


Flitch  Plate  Girders. 

A  Flitch  plate  girder  is  a  beam  composed  of  two  wooden  beams 
of  the  same  breadth  and  depth  with  a  wrought-iron  or  steel  plate 
of  the  same  length  and  depth  as  the  wooden  beams  bolted  be- 
tween them,  as  in  Fig.  5.  Such  beams  are  much  stronger  and 
stiffer  than  a  wooden  beam  of  the  same  depth,  and  may  often  be 
used  in  the  place  of  steel  beams,  where  the  latter  are  difficult  to 
obtain. 


FLITCH  PLATE  GIRDERS.  585 

Flitch  plate  beams  were  at  one  time  much  used,  but  with  steel 
at  3  or  3J  cents  a  pound  it  is  fully  as  cheap  and  better  to  use  a 
steel  beam. 

The  following  explanation  and  formulas  are  given,  however, 
for  the  benefit  of  any  one  who  might  have  occasion  to  use  a  beam 
of  this  kind.  It  has  been  found  by  practice  that  the  thickness 
of  the  iron  plate  should  be  about  one-twelfth  of  the  whole  thick- 


Fig.  5 

ness  of  the  beam,  or  the  thickness  of  the  wood  should  be  eleven 
times  the  thickness  of  the  iron.  As  the  elasticity  of  iron  is 
so  much  greater  than  that  of  wood,  we  must  proportion  the  load 
on  the  wood  so  that  it  shall  bend  the  same  amount  as  the  iron 
plate:  otherwise  the  whole  strain  might  be  thrown  on  the  iron 
plate.  The  modulus  of  elasticity  of  wrought-iron  is  about 
thirteen  times  that  of  hard  pine ;  or  a  beam  of  hard  pine  one  inch 
wide  would  bend  thirteen  times  as  much  as  a  plate  of  iron  of  the 
same  size  under  the  same  load.  Hence,  if  we  want  the  hard-pine 
beam  to  bend  the  same  as  the  iron  plate,  we  must  put  only  one- 
thirteenth  as  much  load  on  it.  If  the  wooden  beam  is  eleven 
times  as  thick  as  the  iron  one,  we  should  put  eleven-thirteenths 
of  its  safe  load  on  it,  or,  what  amounts  to  the  same  thing,  use  a 
constant  only  eleven-thirteenths  of  the  strength  of  the  wood. 
On  this  basis  the  following  formulas  have  been  made  up  for  the 
strength  of  Flitch  plate  girders,  in  which  the  thickness  of  the 
iron  is  one-twelfth  of  the  breadth  of  the  beam,  approximately : — 
Let  D=  Depth  of  beam. 

B=  Total  thickness  of  wood. 

L=  Clear  span  in  feet. 
t=  Thickness  of  wrought-iron  plate. 

f  82  pounds  for  hard  pine. 
f=  J  75  pounds  for  Oregon  pine. 
( 60  pounds  for  spruce. 

W=  Total  load  on  girder. 

Then,  for  beams  supported  at  both  ends, 

D2 

Safe  load  at  centre,  in  pounds  =  ~7-(/JB  +  700rt.  (1) 


586  TRUSSED   BEAMS, 


27)2 
Safe  distributed  load,  in  pounds  =  -=-(/£  +  7000-          (2) 


For  distributed  load,          *       D=  {/  __  WL  (3) 

V  25  +  1400* 


For  load  at  centre,  D  =  4/     WL     .  (4) 

V    B  +  700t 


The  bolts  should  be  f-inch  in  diameter,  and  spaced  2  feet  on 
centres.  Each  end  should  have  two  bolts,  as  in  Fig.  5. 

When  steel  plates  are  used,  the  thickness  of  the  timbers  should 
be  about  15  times  the  thickness  of  the  steel  plate.  Thus  with 
two  6"X  12"  beams  the  steel  plate  should  be  f  "  thick.  Instead 
of  using  two  beams  each  6  ins.  thick,  three  four-inch  beams  and 
two  f  "  plates  will  generally  be  better,  as  it  reduces  the  bending 
moment  on  the  bolts.  If  two  or  three  plates  are  used  t  should  be 
taken  as  the  total  thickness  of  the  plates. 

To  use  the  above  formulas  for  steel,  multiply  t,  in  formulas  1, 
2,  and  4  by  900  in  place  of  700,  and  in  formula  3,  by  1,800. 

EXAMPLE.  —  What  is  the  safe  load,  uniformly  distributed  for  a 
girder  composed  of  three  4"X  14"  Georgia  pine  timbers  and  two 
j"X  14"  Flitch  plates,  with  a  span  of  25  ft.? 

Ans.     By  formula  2,  safe  load 

os/  igg 
=  -^5—  (82X12  +900X1)  =26,013  lb& 

TRUSSED  BEAMS. 

Whenever  we  wish  to  support  a  floor  upon  girders  having  a 
span  of  more  than  thirty  feet,  we  must  use  either  a  trussed  girder, 
a  riveted  steel-plate  girder,  or  two  or  more  steel  beams.  The 
cheapest  and  most  convenient  way  is,  probably,  to  use  a  large 
wooden  girder,  and  truss  it,  either  as  in  Figs.  6  and  7,  or  Figs.  8 
and  9. 

In  all  these  forms  it  is  desirable  to  give  the  girders  as  much 
depth  as  the  conditions  of  the  case  will  permit;  as,  the  deeper 
the  girder,  the  less  strain  there  is  in  the  pieces. 

In  the  belly-rod  truss  we  either  have  two  beams,  and  one  rod 
which  runs  up  between  them  at  the  ends,  or  three  beams,  and  two 
rods  running  up  between  the  beams  in  the  same  way.  The  beams 
should  be  in  one  continuous  length  for  the  whole  span  of  the 
girder,  if  they  can  be  obtained  that  length.  The  requisite  dimen- 
sions of  the  tie-rod,  struts,  and  beam,  in  any  given  case,  must  be 
determined  by  first  finding  the  stresses  which  come  upon  these 


TRUSSED   BEAMS. 


587 


pieces,  and  then  the  area  of  cross-section  required  to  resist  these 
stresses.  For  SINGLE  STRUT  BELLY-ROD  TRUSSES,  such  as  is 
represented  by  Fig.  6,  the  strain  upon  the  pieces  may  be  obtained 
by  the  following  formulas : — 

For  DISTRIBUTED  LOAD  W  over  whole  girder. 


Tension  in  T 


Compression  in  C       —  f  W.* 
Compression  in  B        =  J 

For  CONCENTRATED  LOAD  W  OVCT  C, 

Tension  in  T 


length  ot  C 


length  of  B 


W    length  of  T 
"2" X  length  of  0* 


Compression  in  C=  W. 

W     length  of  B 

Compression  in  B  =  —  x  r-         ~ r>r 
2      length  ot  C 


(5) 
(6) 
(7) 

(8) 
(9) 


For  girder  trussed  as  represented  in  Fig.  7  under  a  DISTRIBUTED 
LOAD  W  over  whole  girder, 


Fig.  7 

Compression  in  S=  JTF  ; 
Tension  in  R  =  f  W.' 
Tension  in  B  =JTFX 


length  of  S 


length  of  B 
length  of  R 


(10) 


(11) 


*When  the  beam  B  is  in  one  piece,  the  full  length  of  span.      If  B  is  jointed 
over  the  strut  then  compression  in  C  or  tension  in  ft  =  %W- 


588  TRUSSED  BEAMS. 

For  CONCENTRATED  LOAD,  TF  at  centre, 

n  •       •     o     IF     length  of  S 

Compression  in  S=  -    ^ 

Tension  in  R 
Tension  in  B 


=  TF. 
W  v 
=  2      length  ofR 


(12) 


(13) 


For  double  strut  belly-rod  truss  (Fig.  8),  with  DISTRIBUTED  LOAD 
W  over  whole  girder  (beam  B  divided  into  three  equal  spans), 


Tension  in  T7         =— X 
Compression  in  C= 


Fig.  8 

length  of  T 
3  ' N  length  of  C' 
W 
3* 


.      .     ~     W    length  of  B 

Comp.  in  B  or  tension  in  D  =  --  -  X  r~        —  irx* 

3      length  ot  C 

For  CONCENTRATED  LOAD  W  over  each  of  the  struts  C, 

length  of  r 


Tension  in  T  =WX 

Compression  in  C  =  W. 

Comp.  in  B  or  tension  in  D=WX 


length  of  C' 


(14) 


(15) 


(16) 


(17) 


For  girder  trussed,  as  in  Fig.  9,  under  a  DISTRIBUTED  LOAD  TF 
over  whole  girder  (beam  B  divided  into  three  equal  spans), 

2  3 


Fig.  9 


Compression  in  S 


W  length  of  S 
—  X  ,—  —  F"?V 
3  length  oi  R 


Tension  in  R  ~^r- 

o 

™      .       .     D  .     n     TF     length  of  B 

Tension  in  B  or  comp.  in  Z)=  •— -Xr-        — — -. 

3     length  of  R 


(18) 


(19) 


TRUSSED  BEAMS.  589 

Under  CONCENTRATED  LOADS  W  applied  at  2  and  3. 

Cession  in*  =^X.  (20) 

Tension  in  R  =  W 

Tension  in  B  or  comp.  in  D  =  W  X  '  (21) 


Trusses  as  shown  in  Figs.  8  and  9  should  be  divided  so  that 
the  rods  R,  or  the  struts  C,  shall  divide  the  lengths  of  the  girder 
into  three  equal  or  nearly  equal  parts.  The  lengths  of  the  pieces 
T,  C,  B,  R,  S,  etc.,  should  be  measured  on  the  centres  of  the 
pieces.  Thus  the  length  of  R  should  be  taken  from  the  centre 
of  the  tie-beam  B  to  the  centre  of  the  strut  D  ;  and  the  length  of 
C  should  be  measured  from  the  centre  of  the  rod  to  the  centre  of 
the  strut-beam  B. 

After  determining  the  strains  in  the  pieces  by  these  formulas, 
we  may  compute  the  area  of  the  cross-sections  by  the  following 
rules  : 

c  ,.         ,,    ,  comp.  in  strut     ,__. 

Area  of  cross-section  of  short  struts  =  -  ;  —  -^  —    —  .    (22) 

C 

The  size  of  the  long  strut  D,  Fig.  9,  should  be  determined  by 
means  of  the  tables  on  pages  411,  412. 

The  diameter  of  the  tie-rods  may  be  obtained  from  the  table 
on  page  340. 

For  the  beam  B}  when  the  load  is  distributed,  we  must  compute 
its  necessary  area  of  cross-section  as  a  tie  or  strut  (according  to 
which  truss  we  use),  and  also  the  area  of  cross-section  required 
to  support  its  load  acting  as  a  beam,  and  give  a  section  to  the 
beam  equal  to  the  sum  of  the  two  sections  thus  obtained. 

Area  of  cross-section  of  B  to  )  _  tension  comp. 

resist  tension  or  compression  )  T  C 

In  trusses  6  and  7,  with  distributed  load, 

Breadth  of  B  (as  a  beam)  =  .^^    .  (24) 

*x./\JLf  /\A. 

In  trusses  8  and  9,  with  distributed  load, 

Breadth  of  B  (as  a  beam)*.  (25) 


W  denoting  the  full  distributed  load  on  the  girder  in  pounds,  and 
L  the  length  of  one  section  of  the  tie-beam  in  feet.     When  the 


590  TRUSSED   BEAMS. 

loads  are  concentrated  over  C,  or  at  R,  then  there  will  be  no 
transverse  strain  on  the  beam  B,  and  it  need  be.  proportioned 
only  for  the  tensile  or  compressive  stress,  as  the  case  may  be. 
In  formulas  23,  24,  and  25, 

C— 1,000  pounds  per  square  inch  for  hard  pine  and  Oregon  pine, 
800  pounds  per  square  inch  for  spruce  and  white  oak, 
700  pounds  per  square  inch  for  white  pine, 
13,000  pounds  per  square  inch  for  cast-iron. 
T  =2,000  pounds  per  square  inch  for  hard  pine  and  oak, 
1,800  pounds  per  square  inch  for  Oregon  pine, 
1,600  pounds  per  square  inch  for  spruce, 
1,400  pounds  per  square  inch  for  white  pine, 
12,500  pounds  per  square  inch  for  wrought-iron, 
15,000  pounds  per  square  inch  for  steel. 
A  =   100  pounds  per  square  inch  for  hard  pine, 

90  pounds  per  square  inch  for  Oregon  pine, 
70  pounds  per  square  inch  for  spruce, 
60  pounds  per  square  inch  for  white  pine. 

EXAMPLES. — To  illustrate  the  method  of  computing  the  dimen- 
sions of  the  different  parts  of  girders  of  this  kind,  we  will  take 
two  examples. 

1.  Computation  for  a  girder  such  as  is  shown  in  Fig.  6,  for  a  span 
of  30  feet,  the  trusses  to  be  12  feet  on  centres,  and  carrying  a 
floor  for  which  we  should  allow  100  pounds  per  square  foot. 
The  girder  will  consist  of  three  strut-beams  and  two  rods.  We 
can  allow  the  belly-rod  T  to  come  two  feet  below  the  beams  B, 
and  we  will  assume  that  the  depth  of  the  beams  B  will  be  12 
inches;  then  the  length  of  C  (which  is  measured  from  the  centre 
of  the  beam)  would  be  30  inches.  The  length  of  B  would,  of 
course,  be  15  feet,  and  by  computation,  or  by  scaling,  we  find  the 
length  of  T  to  be  15  feet  2J  inches. 

The  total  load  on  the  girder  equals  the  span  multiplied  by  the 
distance  of  girders  on  centres,  times  100  pounds =30X12X100 
*=  36,000  pounds. 

Then,  from  formula  5, 

36,000 vx  182J  inches      , 

Tension  in  T=—     —  X  — ^r4 — r =109,500  Ibs. 

2  30  inches 

or  54,750  Ibs.  on  each  of  two  rods.    For  such  a  large  stress  it  will 
be  best  to  upset  the  ends  of  the  rods,  and  allowing  15,000  Ibs. 


TRUSSED   BEAMS.  591 

per  square  inch  for  steel  rods,  we  find  from  the  table  on  page  340 
that  we  must  use  two  2 J -inch  steel  rods. 

The  strut-beam  we  will  make  of  Oregon  pine.     From  formula 

7  we  find  the  compressive  stress  in  B  =  —     — X  -577  =  108,000 

2i  oO 

pounds.  As  we  are  to  use  three  beams,  this  will  give  36,000  Ibs. 
on  each  beam, 

To  resist  the  compression  will  require      '        or  36  square  ins., 

J.,UU(J 

which  is  equal  to  3X12  inches. 

From  formula  24  we  find  the  total  breadth  required  to  resist 

36,000X15 
the  transverse  strain  =  — —=12  ins.,  or  each  beam  must 

be  4X12  inches  to  resist  the  transverse  strain,  and  3X12  ins.  to 
resist  the  compressive  strain.  Consequently  each  beam  must 
be  7X12  inches. 

As  this  would  make  the  girder  very  wide — 25J  ins. — we  will 
use  beams  14  ins.  deep,  increasing  the  depth  of  the  girder  one 
inch,  so  that  the  height  on  centres  will  still  be  30  ins. 

The  area  required  to  resist  the  compressive  stress  will  be  the 
same  as  before,  36  inches,  but  as  our  beam  is  14  inches  deep  the 
breadth  will  be  only  2-J  inches. 

The   total  breadth  to   resist  the   transverse   strain  will  be 

36,000X15  02  .       -• 

A  vxinAv/nr>=8  ins.,  or  2f  ins.  for  each  beam.     The  total  breadth 

4x  iyo  xyu 

for  each  beam  will  therefore  be  5J  inches.  A  6X14  beam 
when  dressed  will  run  about  5JXl3f  ins.,  which  will  just  about 
meet  the  requirements.  The  total  width  of  the  girder  will  then 
be  21  inches.  The  load  on  C=f  17=22,500  Ibs.,  or  11,250  Ibs. 
over  each  rod.  The  sectional  area  necessary  to  resist  this  load 

]  1  250  1 1  250 

=       '  *—  for  cast  iron  and  — '   '      for  oak.     As  the  struts  must 

lo,u(JU  oUU 

be  the  full  width  of  the  girder,  however,  it  will  be  necessary  to 
make  the  sectional  area  much  greater  than  the  theoretical 
requirements.  If  made  of  cast  iron  thte  strut  should  be  of  the 
shape  shown  in  Fig.  10,  and  if  of  oak,  of  the  shape  shown  in  Fig  11. 
The  cast-iron  strut  will  be  the  best,  but  an  oak  strut  will  answer. 
EXAMPLE  2. — It  is  desired  to  support  a  floor  over  a  lecture- 
room  forty  feet  wide,  by  means  of  a  trussed  girder;  and  as  the 
room  above  is  to  be  used  for  electrical  purposes  it  is  desired  to 
have  a  truss  with  very  little  iron  in  it,  and  hence  we  use  a  truss 
such  as  is  shown  in  Fig.  9.  Where  the  girders  rest  on  the  wall 


592 


TRUSSED  BEAMS. 


there  will  be  brick  pilasters  having  a  projection  of  six  inchest 
which  will  make  the  span  of  the  truss  39  feet;  and  we  will  space 
the  rods  R  R  so  as  to  divide  the  tie-beam  into  three  equal  spans 
of  13  feet  each.  The  tie-beam  will  consist  of  two  hard-pine 
beams,  with  the  struts  coming  between  them.  We  will  have 
two  rods,  instead  of  one,  at  R,  coming  down  each  side  of  the  strut, 
and  passing  through  an  iron  casting  below  the  beams,  forming 
supports  for  them.  The  height  of  truss  from  centre  to  centre  of 
timbers  we  must  limit  to  18  inches,  and  we  will  space  the  trusses 
8  feet  on  centres.  Then  the  total  floor-area  supported  by  one 


Fig.  10 


Fig.  II 


girder  equals  8  feet  by  39  feet,  equal  to  312  square  feet.  The 
heaviest  load  to  which  the  floor  will  be  subjected  will  be  the 
weight  of  students,  for  which  75  pounds  per  square  foot  will  be 
ample  allowance  ;  and  the  weight  of  the  floor  itself  will  be  about 
25  pounds  ;  so  that  the  total  weight  of  the  floor  and  load  will  be 
100  pounds  per  square  foot.  This  makes  the  total  weight  liable 
to  come  on  one  girder  31,200  pounds. 


The  compression  in  S  will  be,  from  formula  18,  ~ 

o 


* 


90,700  pounds. 

Tension  in  one  pair  of  rods 


=*  10,400  pounds. 


Tension  in  B  or  compression  in  D~ 


W      156  ins. 


TQ^~  — 
18  ins* 


=  90,130  Ibs. 


3  ^   18  ins. 

As  the  unsupported  length  of  D  is  greater  than  that  of  S,  a  beam 
that  will  resist  the  compression  in  D  will  be  ample  for  S.  From 
Table  III,  page  411,  we  find  that  it  will  require  a  10X12 


TRUSSED  BEAMS.  593 

beam  13  feet  long  to  resist  the  compression  in  D,  a  10X10  not 
being  quite  strong  enough.  The  tension  in  each  rod  will  be  only 
5,200  Ibs.,  but  as  the  rods  must  support  a  large  washer  at  the 
bottom  we  will  make  them  1  in.  in  diameter,  not  upset.  The 
tension  in  each  of  the  beams  B  will  be  45,065  Ibs.  This  divided 
by  2,000=22.6  square  ins.,  or  say  2X12  ins. 

The  total  breadth  of  the  tie-beam  to  resist  the  transverse  load 
we  find  from  formula  25,  assuming  12  inches  as  the  depth 

31,065X13 
=  - — '  =  4.7  ins.,  or  about  2f  ins.  for  each  beam. 

The  breadth  of  each  tie-beam  must  therefore  be  2"-f  2f"=4f". 
Hence  the  tie-beams  must  be  5X12  ins.  Therefore  our  girder 
must  be  built  with  10  X 12  in.  strut  beams,  and  two  5  X 12  in.  tie- 
beams,  each  42  ft.  long.  The  1-in.  rods  may  be  cut  J  in.  into  the 
strut-beam,  and  J  in.  into  the  tie-beams,  so  that  the  latter  will 
come  close  against  the  strut  S.  The  "kick"  of  strut  S  will  be 
equal  to  its  compressive  stress,  and  we  must  design  a  connection 
between  the  tie-beams  and  strut  that  will  be  capable  of  resisting 
the  kick,  which  in  this  case  is  90,700  Ibs.  As  the  inclination  of 
the  strut  is  very  slight  there  will  be  ample  room  for  bolts.  It 
will  be  best  to  use  bolts  at  least  li  ins.  in  diameter.  As  the  bolts 
will  be  in  double  shear,  the  resistance  to  shearing  of  one  bolt  will 
be  (Table  V,  page  376)  26,500  Ibs. 

The  bearing  area  of  a  IJ-inch  bolt  in  a  timber  10  inches  wide 
will  be  15  inches.  For  bearing  resistance  in  hard  pine  we  may 
allow  1,500  Ibs.  per  square  inch,  which  will  give  22,500  Ibs.  as  the 
bearing  resistance  of  one  1J"  bolt.  As  the  force  to  be  resisted  is 
90,700  Ibs.  it  will  require  four  1  J-inch  bolts  to  sustain  the  bearing 
pressure,  the  resistance  to  shearing  being  greater  than  the  stress. 

We  must  now  see  how  many  bolts  it  will  require  to  resist  the 
bending  moment.  The  total  bending  moment  to  be  resisted  (see 
page  390)  =90,700  times  the  distance  between  the  centres  of  the 

tie-beams  divided  by  12,  or  90,700 X  —  =  113,375  inch-pounds. 

12 

From  Table  IX,  Chapter  X,  we  find  that  the  maximum  bending 
moment  for  a  IJ-inch  pin  is  7,460  Ibs.  Hence  it  will  require 
fifteen  1 4-inch  bolts  to  resist  the  thrust  in  S  without  bending  the 
bolts.  It  would  be  impracticable  to  put  in  so  many  bolts,  hence 
we  must  use  larger  bolts.  For  a  2|-inch  bolt  the  maximum  bend- 
ing moment  is  29,600  Ibs.,  and  four  times  this  gives  118,400  Ibs., 
hence  four  2|-inch  bolts  will  be  sufficient  to  resist  the  bending 
strain,  and  also  the  shearing  and  bearing  stresses.  It  will  be 


594  TRUSSED  BEAMS. 

seen  from  this  example  that  it  is  much  more  difficult  and  expen- 
sive to  make  satisfactory  end  joints  for  girders  trussed  as  in 
Figs.  7  and  9  than  it  is  for  the  belly-rod  trusses.  The  belly- 
rod  trusses  are  to  be  preferred  when  the  conditions  will  admit  of 
their  use. 

These  four  cases  of  trussed  girders  are  but  special  examples  of 
trusses.  The  stresses  in  them  may  also  be  computed  by  the 
methods  explained  in  Chapter  XXVI,  and  where  the  divisions  of 
the  girder  cannot  be  made  uniform  the  stresses  should  be  com- 
puted by  the  general  method  there  explained. 


STIFFNESS  AND  DEFLECTION  OF  BEAMS.      595 


CHAPTER  XVIII. 
STIFFNESS  AND  DEFLECTION  OF   BEAMS. 

IN  Chapters  XV.  and  XVI.  we  have  considered  the  strength  of 
beams  to  resist  breaking  only;  but  in  all  first-class  buildings  it  is 
desired  that  those  beams  which  show,  or  which  support  a  ceiling, 
should  not  only  have  sufficient  strength  to  carry  the  load  with 
safety,  but  should  do  so  without  bending  enough  to  present  a  bad 
appearance  to  the  eye,  or  to  crack  the  ceiling;  hence,  in  calcu- 
lating the  dimensions  of  such  beams,  we  should  not  only  calculate 
them  with  regard  to  their  resistance  to  breaking,  but  also  to  bend- 
ing. Unfortunately  we  have  at  present  no  method  of  combining 
the  two  calculations  in  one  operation.  A  beam  apportioned  by 
the  rules  for  strength  will  not  bend  so  as  to  strain  the  fibres 
beyond  their  elastic  limit,  but  will,  in  many  cases,  bend  more 
than  a  due  regard  for  appearance  will  justify. 

The  amount  which  a  beam  bends  under  a  given  load  is  called  its 
deflection,  and  its  resistance  to  bending  is  called  its  stiffness; 
hence  the  stiffness  is  inversely  as  the  deflection. 

The  rules  for  the  stiffness  of  beams  are  derived  from  those  for 
the  deflection  of  beams;  and  the  latter  are  derived  partly  from 
mathematical  reasoning,  and  partly  from  experiments. 

We  can  find  the  deflection  at  the  centre  of  any  beam  not  strained 
beyond  the  elastic  limit,  by  the  following  formula : 

load  in  Ibs.  Xcube  of  span  in  inches  Xc       /1N 

Del.  in  inches  =  — -r-i ? — ; r-r: —  ; — «~. 77—.  (1) 

modulus  ot  elasticity  X  moment  ot  inertia 

The  values  of  c  are  as  follows: 

Beam  supported  at  both  ends,  loaded  at  centre  .  0 . 021 

uniformly  loaded    0.013 

"     fixed  at  one  end,  loaded  at  the  other 0 . 333 

uniformly  loaded 0 . 125 

By  making  the  proper  substitutions  in  Formula  1,  we  derive 


596    STIFFNESS  AND  DEFLECTION  OF  BEAMS. 

the  following  formula  for  a  rectangular  beam  supported,  at  both 
ends,  and  loaded  at  the  centre  : 

load  X  cube  of  span  in  feetX  1  ,728 
Def.  m  mches=  lP       of  • 


From  this  formula  the  value  of  the  modulus  of  elasticity,  E, 
for  different  materials,  has  been  calculated.  Thus  beams  of 
known  dimensions  are  supported  at  each  end,  and  a  known 
weight  applied  at  the  centre  of  the  beam.  The  deflection  of  the 
beam  is  then  carefully  measured  ;  and,  substituting  these  known 
quantities  in  Formula  2,  the  value  of  E  is  easily  obtained. 

1  728 
Formula  2  may  be  simplified  somewhat  by  representing     — 

by  ^,  which  gives  us  the  formula 


For  a  distributed  load  the  deflection  will  be  five-eighths  of  this. 
If  we  wish  to  find  the  load  which  shall  cause  a  given  deflection, 
we  can  transpose  Formula  2  so  that  the  load  shall  form  the  left- 
hand  member.     Thus: 

Load  at  centre  _  4  X  breadth  X  cube  of  depth  X  def.  in  ins.  X  E    ,  ^ 
in  pounds  cube  of  spanX  1,728 

Now,  that  this  formula  may  be  of  use  in  determining  the  load  to 
put  upon  a  beam,  the  value  of  the  deflection  must  in  some  way  be 
fixed.  This  is  generally  done  by  making  it  a  certain  proportion 
of  the  span. 

Thus  Tredgold  and  many  other  authorities  say  that  if  a  floor- 
beam  deflects  more  than  one-fortieth  of  an  inch  for  every  foot  of 
span,  it  is  liable  to  crack  the  ceiling  on  the  under  side ;  and  hence 
this  is  the  limit  which  is  often  given  to  the  deflection  of  beams 
in  first-class  buildings. 

Then,  if  we  substitute  for  " deflection"  the  value,  length  in  feet 
-i-40,  in  the  above  formula,  we  have, 

breadth  X  cube  of  depth  Xe  /-^ 

Load  at  centre  —  —  — ~ —    — -. — r. — 7 — 9  (p) 

square  ot  span  in  leet 

Tjl 

letting 


17,280* 


*The  constant  F  corresponds  to  Hatfield's  F,  in  his  Transverse  Strains. 


STIFFNESS  AND  DEFLECTION   OF   BEAMS.     597 

Most  engineers  and  architects  think  that  one-thirtieth  of  an  inch 
per  foot  of  span  is  not  too  much  to  allow  for  the  deflection  of  floor- 
beams,  as  a  floor  is  seldom  subjected  to  its  full  estimated  load,  and 
then  only  for  a  short  time. 

If  we  adopt  this  ratio,  we  shall  have  as  our  constant  for  deflec- 

tion,  e'=  12^60- 

In  either  of  the  above  cases  it  is  evident  that  the  values  used 
for  E}  Fj  e,  or  elf  should  be  derived  from  tests  on  timbers  of  the 
same  size  and  quality  as  those  to  be  used.  The  values  for  the 
various  woods  given  in  the  table  below  have  been  adopted  by  the 
author  after  careful  comparison  with  the  results  of  numerous 
tests  on  large  timbers  and  with  values  given  by  different  authori- 
ties. The  author  believes  that  they  are  perfectly  reliable  for 
first-class  merchantable  timber. 

TABLE  I.— VALUES    OF    CONSTANTS    FOR    STIFFNESS 

OR  DEFLECTION  OF  BEAMS. 
B=  Modulus  of  elasticity,  pounds  per  square  inch. 
F=  Constant  for  deflection  of  beam,  supported  at  both  ends,  and 

loaded  at  the  centre. 
e  =  Constant,  allowing  a  deflection  of  one-fortieth  of  an  inch  per 

foot  of  span. 
e±  —  Constant,  allowing  a  deflection  of  oner thirtieth  of  an  inch  per 

foot  span. 


7? 

F        E 

E 

E 

432 

'     17,280 

e'~12,960 

Cast  iron.  

15,700,000 

36  300 

907 

1  210 

Wrought  iron  

26,000,000 

60,000 

1,500 

2  000 

Steel  

31,000,000 

71,760 

1  794 

2  358 

Long-leaf  yellow  pine.  .  .  . 
Oregon  pine  or  Douglas  fir 
Spruce  o  

1,780,000 
1,425,000 
1,294,000 

4,120 
3,300 
3,000 

103 

82 
75 

137 
110 
100 

White  pine  

1,073,000 

2,480 

62 

82 

Hemlock  

1,045,000 

2,420 

60 

80 

White  oak  

1,240,000 

2,870 

72 

95 

Ash  

1,482,000 

3,430 

86 

114 

Chestnut  

944,000 

2,180 

54 

72 

Cypress  

900,000 

2,080 

52 

69 

Maple  .  . 

1,902,000 

4,400 

110 

146 

California  red-  wood  

700,000 

1,620 

40 

54 

598    STIFFNESS  AND  DEFLECTION   OF  BEAMS. 

Kules  for  Stiffness  of  Beams. 

Knowing  the  deflection  caused  by  a  weight  at  the  centre  of  a 
beam,  and  the  ratio  of  other  deflections,  caused  by  different 
modes  of  loading  and  supporting,  we  can  easily  deduce  the  for- 
mulas for  the  different  cases  considered  under  the  strength  of 
rectangular  beams.  These  cases  are: 

BEAMS  SUPPORTED  AT  BOTH  ENDS.* 
Loaded  at  the  centre, 

Safe  load=  breadth  X cube,  of  depth Xe 

square  of  span 
or, 

Breadth=  ^Xsquare  of  span 
cube  of  depth  X  e 

Loaded  at  a  point  other  than  the  centre,  m  and  n  being  the  seg- 
ments into  which  the  beam  is  divided, 

Safe  load  =  Breadth  X  cube  of  depth  X  square  of  span  X  e 

or, 

Breadth^      K          loadXm'Xn'XlB 

cube  oi  depth  X  square  of  span  X  e 

Load  uniformly  distributed, 

Safe  load=  ^  X  breadth  X  cnbe  of  depth  x«  „. 

5  X  square  of  span 
or, 

Breadth  =  ^Xload X square  of  span 
8  X  cube  of  depth  Xe 

Inclined  beam,  loaded  at  the  centre,^ 

breadth  X  cube  of  depth  X  e  ,.,  os 

Safe  load= r—  — - — ,  (12) 

spanXhor.  dist.  between  supports 

*  In  formulas  (6)  to  (17)  the  breadth  and  depth  are  to  be  taken  in  inches, 
and  the  length  or  span  in  feet.  The  load  is  always  in  Ibs. 

The  values  given  in  either  of  the  last  two  columns  of  Table  I.  may  be  used 
for  e,  according  to  the  degree  of  stiffness  desired,  but  the  values  in  the  last 
column  are  ample  under  ordinary  conditions. 

fTredgokTs  "Elements  of  Carpentry,"  p.  65. 


STIFFNESS  AND   DEFLECTION   OF   BEAMS.     599 


or, 

load  X  span  X  hor.  dist.  between  supports      /<g  ON 
Breadth  -  cube  of  depth  Xe  '   (13) 

BEAMS  FIXED  AT  ONE  END. 

Loaded  at  extreme  end, 

„   .      ,      bread  thX  cube  of  depth  Xe  /1yl>. 

Safe  load  =  —  —r.  —         —  ,  (14) 

16  X  square  ot  span 

or, 

•n      j^u         16  X  load  X  square  of  span  /t   . 

Breadth  =  -  r  —  rrr  -  •  (15) 

cube  ot  depth  Xe 

Load  uniformly  distributed, 

.    .      .      bread  thX  cube  of  depth  Xe  /1/3v 

Safe  load=  —  —r.  —      -  ,  (16) 

6  X  square  ot  span 

or, 

•D      J4.u        6  X  l°ad  X  square  of  span  n  „. 

Breadth  =•  —  ^,     ..          —  -.  (17) 

cube  of  depth  Xe 

NOTE.  —  Beams  whose  span  in  feet  is  less  than  the  depth  in  ins. 
should  not  be  calculated  by  formulas  for  stiffness,  but  by  those 
for  strength,  Chapter  XVI. 


Ratio  of  the  Stiffness  of  Beams. 

If  the  stiffness  of  a  beam  supported  at  both  ends  and  loaded 

at  the  centre  be  called 1 

Then  that  of  the  same  beam  with  the  same  load  uniformly 

distributed  will  be f 

Firmly  fixed  at  both  ends  and  loaded  at  the  centre,  according 

to  Moseley 5 

Firmly  fixed  at  both  ends  and  uniformly  loaded 8 

Fixed  at  one  end  and  loaded  at  the  other T\ 

Fixed  at  one  end  and  uniformly  loaded J 

The  stiffest  rectangular  beam  containing  a  given  amount  of 
material  is  that  in  which  the  ratio  of  depth  to  breadth  is  as  10  to 
6;  hence,  in  designing  beams,  the  depth  and  breadth  should  be 
to  approach  as  near  this  ratio  as  is  practicable. 


600    STIFFNESS  AND  DEFLECTION  OF  BEAMS. 

EXAMPLE  1. — What  is  the  greatest  distributed  load  that  an 
8  by  10  inch  white-pine  girder  of  12  foot  clear  span  will  support, 
without  deflecting  at  the  centre  more  than  -^  of  an  inch  per 
foot  of  span? 

Ans.  This  girder  comes  under  the  case  of  a  beam  supported 
at  both  ends  and  loaded  with  a  uniformly  distributed  load,  and 
hence  should  be  calculated  by  Formula  10.  Substituting  the 
given  dimensions  in  Formula  10  we  have, 

G  ,    ,  8X8X1,000X82 

Safe  load= '      =  7,288  pounds. 

O  X  144 


EXAMPLE  2.  —  What  should  be  the  dimensions  of  a  yellow-pine 
beam  of  10-foot  span  to  support  a  concentrated  load  of  4,250 
pounds,  without  deflecting  more  than  J  of  an  inch  at  the 
centre? 

Ans.  A  deflection  of  J  of  an  inch  in  a  span  of  10  feet  is  in  the 
proportion  of  ^  of  an  inch  per  foot  of  span;  and  as  the  load  is 
concentrated  and  applied  at  the  centre,  we  should  use  Formula  7, 
employing  for  e  the  value  given  in  the  fourth  column  opposite 
yellow  pine. 

Formula  7  gives  the  dimensions  of  the  breadth,  and  to  obtain 
it  we  must  assume  a  value  for  the  depth.  For  this  we  will  first 
try  10  inches. 

Substituting  in  Formula  7  we  have, 

4,250X100 


Hence  it  will  be  necessary  to  use  a  4//XlO//  beam.  As  the 
span  of  this  beam  in  feet  is  the  same  as  the  depth  in  ins.,  we 
should  see  if  it  also  meets  the  requirements  for  strength.  From 
Table  III,  Chapter  XVI,  we  find  that  the  safe  distributed  load 
for  a  1  X  10  beam  10  ft.  span  is  2,000  Ibs.,  and  for  a  4  X  10  beam 
the  safe  load  would  be  four  times  as  much,  or  8,000  Ibs.  The 
load  in  this  example,  however,  is  applied  at  the  centre  ;  hence  we 
must  divide  the  safe  distributed  load  by  2,  which  gives  4,000  Ibs. 
for  the  safe  centre  load.  As  this  is  a  little  less  than  the  load  we 
wish  to  support,  we  should  increase  the  size  of  the  beam  to 
5X  10  inches.  As  a  general  rule  it  is  not  safe  to  use  the  formulas 
for  stiffness  when  the  span  in  feet  does  not  exceed  the  depth  in 
inches. 


STIFFNESS  AND  DEFLECTION   OF   BEAMS.     601 

EXAMPLE  3. — What  is  the  largest  load  that  an  inclined  spruce 
beam  8X12  inches,  16  feet  long  between  supports,  will  carry  at 
the  centre,  consistent  with  stiffness,  the  horizontal  distance  be- 
tween the  supports  being  14  feet? 

Ans.  Formula  12  is  the  one  to  be  employed;  and  we  will  use 
the  value  of  e  given  in  the  last  column  opposite  spruce.  Making 
the  proper  substitutions  we  have, 

Safe  load=8X*'728*10°=6,170  pounds. 

J.O  /\  -L~t 


Cylindrical  Beams. 

For  cylindrical  beams  the  same  formulas  may  be  employed  as 
for  rectangular  beams,  only  instead  of  e  use  l.TXe;  that  is,  a 
cylindrical  beam  bends  1.7  times  as  much  as  the  circumscribing 
rectangle. 

Deflection  of  Steel  Beams. 

For  rolled  steel  beams  the  deflection  is  most  accurately  ob- 
tained by  Formula  1. 

A  shorter  and  sufficiently  accurate  method  for  determining  the 
deflection  of  the  standard  sections  under  their  full  safe  load  is 
given  on  pages  510  and  511. 

In  using  steel  beams  it  should  be  remembered  that  for  any 
given  span  the  deepest  beam  is  always  the  most  economical ;  and 
the  stiffness  of  a  floor  is  always  greater  when  a  suitable  number 
of  deep  beams  are  used. 


Tables  for  Wooden  Beams. 

The  following  tables  have  been  prepared  so  as  to  show  at  a 
glance  the  greatest  load  that  a  beam  one  inch  thick  will  support 
without  either  exceeding  the  limit  of  deflection  or  the  safe  strength, 
They  give  the  same  results  as  would  be  obtained  by  using  the 
above  formulas,  and  the  formulas  for  strength. 

To  find  the  corresponding  load  for  thicker  beams  multiply  the 
load  given  in  the  table  by  the  breadth  of  the  beam  in  inches.  The 
loads  thus  obtained,  however,  are  for  beams  that  will  run  full  to 
the  nominal  dimensions.  For  beams  that  are,  J-inch  scant  in 


602    STIFFNESS   AND   DEFLECTION    OF   BEAMS. 

both  dimensions  the  correct  load  may  be  obtained  by  multiplying 
the  load  given  in  the  tables  by  the  following  factors : 

For  If  X5f  by  1.5  Forljx   9}  by  1.6 

2fX5J  "  2.5  2JX  9J  "  2.55 

IfXTJ  "  1.6  liXllf  "  1.64 

2|X7i  "  2.5  2fXll|   "  2.6 

1JX13J  "  1§ 
2JXl3i  "  2.6 

Thus  the  maximum  load  consistent  with  stiffness  for  a  2 J  X  13f- 
inch  Oregon  pine  beam  of  20  f t.span  will  be  2.6  X  1,207=  3,138  Ibs. 


STIFFNESS  AND  DEFLECTION  OF  BEAMS.      603 


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608  CONTINUOUS  GIRDERS. 


CHAPTER  XIX. 

STRENGTH  AND  STIFFNESS    OF  CONTINUOUS 
GIRDERS. 

GIRDERS  resting  upon  three  or  more  supports  are  of  quite  fre- 
quent occurrence  in  building  construction;  and  a  great  variety 
of  opinions  are  held  as  to  the  relative  strength  and  stiffness  of 
continuous  and  non-continuous  girders ;  very  few  persons,  prob- 
ably, having  a  correct  knowledge  of  the  subject. 

In  almost  every  building  of  importance  it  is  necessary  to 
employ  girders  resting  upon  piers  or  columns  placed  from  eight  to 
fifteen  feet  apart;  and  in  many  cases  beams  can  conveniently  be 
obtained  which  will  span  two  and  even  three  of  the  spaces  be- 
tween the  piers  or  columns.  When  this  is  the  case  the  question 
arises,  whether  it  will  be  better  construction  to  use  a  long  con- 
tinuous girder,  or  to  have  each  girder  of  only  one  span. 

Most  architects  are  probably  aware  that  a  girder  of  two  or  more 
spans  is  stronger  and  stiffer  than  a  girder  of  the  same  section  of 
only  one  span;  but  just  how  much  stronger  and  stiffer  is  a  ques- 
tion they  are  unable  to  answer. 

As  it  is  seldom  that  a  girder  of  more  than  thn;e  spans  is  em- 
ployed in  ordinary  buildings  we  shall  consider  only  these  two 
cases.  In  all  structures  the  first  point  which  should  be  con- 
sidered is  the  resistance  required  of  the  supports;  and  we  will 
first  consider  the  resistance  offered  by  the  supports  of  a  continu- 
ous girder. 

In  this  chapter  we  shall  not  go  into  the  mathematical  discussion 
of  the  subject,  but  refer  any  readers  interested  in  the  derivation 
of  the  formulas  for  continuous  girders  to  an  article  on  that  sub- 
ject, by  the  author,  in  the  July  (1881)  number  of  Van  Nostrand's 
" Engineering  Magazine." 

Supporting  Forces. 

Girders  of  Two  Equal  Spans,  Loaded  at  the  Centre  of  Each  Span. 
— If  a  girder  of  two  spans,  I  and  llf  is  loaded  at  the  centre  of  the 


CONTINUOUS  GIRDERS.  609 

span  I  with  W  pounds,  and  at  the  centre  of  Zx  with  Wl  pounds, 
the  re-action  of  the  support  Ri  will  be  represented  by  the  formula 

13TT-3TF, 
R,=     —32        >  W 

the  re-action  of  the  support  R2  by 

(2) 


and  the  re-action  of  the  support  Rs  by  the  formula 

13TFt-3TF  m 

3==  —  32  --  * 

If  W=Wlf  then  each  of  the  end  supports  would  have  to  sustain 
•fs  of  one  of  the  loads,  and  the  centre  support  -V1-  of  W.  Were  the 
girder  cut  so  as  to  make  two  girders  of  one  span  each,  then  the  end 
supports  would  carry  \  or  ygTF,  and  the  centre  support  jf  TF; 
hence  we  see  that,  by  having  the  girder  continuous,  we  do  not 
require  so  much  resistance  from  the  end  supports,  but  more  from 
the  central  support. 


Fig.  I 

Girder  of  Two  Spans,  Uniformly  Distributed  Load  Over  Each 
Span.  —  Load  over  each  span  equals  w  pounds  per  unit  of  length. 
Re-action  of  left  support 


Re-action  of  central  support, 

R^wV  +  lJ-Rt-R,.  (5) 

Re-action  of  right  support, 


When  both  spans  are  equal  to  Z,  the  re-action  of  each  end  support 
is  %wlt  and  of  the  central  support  %wl;  hence  the  girder,  by  being 
continuous,  reduces  the  re-action  of  the  end  supports,  and  in- 


610  CONTINUOUS  GIRDERS. 

creases  that  of  the  central  support  by  one-fourth,  or  twenty-five 
per  cent. 

Continuous  Girder  of  Three  Equal  Spans,  Concentrated  Load  of 
W  Pounds  at  Centre  of  Each  Span. 

Re-action  of  either  abutment, 

B,=B.=ATT;  (7) 

Re-action  of  either  central  support, 

R?=R*=ttW;  (8) 

or  the  re-action  of  the  end  supports  is  lessened  three-tenths,  and 
that  of  the  central  supports  increased  three- twentieths  of  that 
which  they  would  have  been  had  three  separate  girders  of  the 
same  cross-section  been  used,  instead  of  one  continuous  girder. 


Fig.2 


Continuous  Girder  of  Three  Equal  Spans  Uniformly  Loaded  with 
w  Pounds  per  Unit  of  Length. 
Re-action  of  either  end  support, 

E^R^lwl;  (9) 

Re-action  of  either  central  support, 

do) 


hence  the  re  -actions  of  the  end  supports  are  one-fifth  less,  and  of 
the  central  supports  one-tenth  more,  than  if  the  girder  were  not 
continuous. 

Strength  of  Continuous  Girders.  —  Having  determined  the  re- 
action of  the  supports  we  will  now  consider  the  strength  of  the 
girder. 

The  strength  of  a  beam  depends  upon  the  material  and  shape 
of  the  beam,  and  upon  the  external  conditions  imposed  upon  the 
beam.  The  latter  give  rise  to  the  bending-moment  of  the  beam, 
or  the  amount  by  which  the  external  forces  (such  as  the  load  and 
supporting  forces)  tend  to  bend  and  break  the  beam. 

It  is  this  bending-moment  which  causes  the  difference  in  the 


CONTINUOUS  GIRDERS.  611 

bearing-strength  of  continuous  and  non-continuous  girders  of 
the  same  cross-section. 

Continuous  Girders  of  Two  Spans.  —  When  a  rectangular  beam 
is  at  the  point  of  breaking  we  have  the  following  conditions  : 

Bending-  _  Mod.  of  rupture  X  breadth  Xsq.  of  depth  t    ...... 

moment  6 

and,  that  the  beam  may  carry  its  load  with  perfect  safety,  we 
must  divide  the  load  by  a  proper  factor  of  safety. 

Hence,  if  we  can  determine  the  bending-moment  of  a  beam 
under  any  conditions,  we  can  easily  determine  the  required 
dimensions  of  the  beam  from  Formula  11. 

The  greatest  bending-moment  for  a  continuous  girder  of  two 
spans  is  almost  always  over  the  middle  support,  and  is  of  the 
opposite  kind  to  that  which  tends  to  break  an  ordinary  beam. 

Distributed  Load.  —  The  greatest  bending-moment  in  a  con- 
tinuous girder  of  two  spans,  I  and  Zt,  loaded  with  a  uniformly 
distributed  load  of  w  pounds  per  unit  of  length,  is 


Bending-moment  =   g1  .  (12) 

When  l=li,  or  both  spans  are  equal 

wl2 
Bending-moment  =—r-,  (12a) 

o 

which  is  the  same  as  the  bending-moment  of  a  beam  supported  at 
both  ends,  and  uniformly  loaded  over  its  whole  length;  hence  a 
continuous  girder  of  two  spans  uniformly  loaded  is  no  stronger  than 
if  non-continuous. 

Concentrated  Load.  —  The  greatest  bending-moment  in  a  con- 
tinuous girder  of  two  equal  spans,  each  of  length  /.  loaded  with  W 
pounds  at  centre  of  one  span,  and  with  Wl  pounds  at  the  centre  of 
the  other  span,  is 

Bending-moment  =  ¥y  (W  +  WJ.  (13) 

When  W=  Wlf  or  the  two  loads  are  equal,  this  becomes 

Bending-moment  =j\TT7,  (13a) 

or  one-fourth  less  than  what  it  would  be  were  the  beam  cut  at  the 
middle  support. 

Continuous  Girder  of  Three  Spans,  Distributed  Load,  —  The 
greatest  bending-moment  in  a  continuous  girder  of  three  spans 
loaded  with  a  uniformly  distributed  load  of.  w  pounds  per  unit  of 
length,  the  length  of  each  end  span  being  Z}  and  of  the  middle 


612  CONTINUOUS  GIRDERS. 

span  /,  is  at  either  of  the  central  supports,  and  is  represented 
by  the  formula, 

wl3  +  wl^ 
Bending-moment-  . 


When  the  three  spans  are  equal,  this  becomes 

wl2 
Bending-moment  =  —  ,  (14a) 

or  one-fifth  less  than  what  it  would  be  were  the  beam  not  con- 
tinuous. 

Concentrated  Loads.  —  The  greatest  bending-moment  in  a  con- 
tinuous girder  of  three  equal  spans,  each  of  a  length  Z,  and  each 
loaded  at  the  centre  with  W  pounds,  is 

Bending-moment  =  /$  Wl,  (15) 

or  two-fifths  less  than  that  of  a  non-continuous  girder. 

Deflection   of  Continuous  Girders. 

Continuous  Girder  of  Two  Equal  Spans.  —  The  greatest  deflec- 
tion of  a  continuous  girder  of  two  equal  spans  loaded  with  a 
uniformly  distributed  load  of  w  pounds  per  unit  of  length  is 

Deflection  =  0.005416^.  (16) 

(E  denotes  modulus  of  elasticity;  /,  moment  of  inertia.) 
The  deflection  of  a  similar  beam  supported  at  both  ends  and 

uniformly  loaded  is 

wn 
Deflection^  0.013020^?. 

£L1 

Hence  the  deflection  of  the  continuous  girder  is  only  about  two- 
fifths  that  of  a  non-continuous  girder.  The  greatest  deflection 
in  a  continuous  girder  is  also  not  at  the  centre  of  either  span,  but 
between  the  centre  and  the  abutments. 

The  greatest  deflection  of  a  continuous  girder  of  two  equal 
spans,  loaded  at  the  centre  of  one  span  with  a  load  of  W  pounds, 
and  at  the  centre  of  the  other  span  with  Wl  pounds,  is,  for  the 
span  with  load  W, 

(23W-9WJI* 
Deflection^  L_____i_;  (17) 

for  the  span  with  load  Wly 

(23TF1-9TF)Z3 

.  (17a) 


CONTINUOUS  GIRDERS.  613 

When  both  spans  have  the  same  load, 

Deflection^lf.  <™> 

The  deflection  of  a  beam  supported  at  both  ends  and  loaded  at 
the  centre  with  TF  pounds  is 

Wl* 


Deflection  = 


4SEI' 


or  the  deflection  of  the  continuous  girder  is  only  seven-sixteenths 
of  the  non-continuous  one. 

Continuous  Girder   of  Three  Equal     Spans. — Uniformly    dis- 
tributed load  of  w  pounds  per  unit  of  length 

wl* 
Deflection  at  centre  of  middle  span  =  0.00052  ^y.          (18) 

wn 
Greatest  deflection  in  end  spans       =0. 006884  ^y,        (19) 

or  the  greatest  deflection  in  the  girder  is  only  about  one-half  that 
of  a  non-continuous  girder. 

Concentrated  load  of  W  pounds  at  centre  of  each  span 

I  Wl3 
Deflection  at  centre  of  middle  span=--— •  -^r.  (20) 

II  Wl3 
Deflection  at  centre  of  end  spans     ^qpT)  ~^FJ  (21) 

or  only  eleven-twentieths  of  the  non-continuous  girder. 


Several  Observations  and  Formulas  for  Designing 
Continuous  Girders. 

From  the  foregoing  we  can  draw  many  observations  and  con- 
clusions, which  will  be  of  great  use  in  deciding  whether  it  will 
be  best  in  any  given  case  to  use  a  continuous  or  non-continuous 
girder. 

First  as  to  the  Supports. — We  see  from  the  formulas  given  for 
the  re-action  of  the  supporting  forces  in  the  different  cases  that  in 
all  cases  the  end  supports  do  not  have  as  much  load  brought  upon 
them  when  the  girder  is  continuous  as  when  it  is  not;  but  of 
course  the  difference  must  be  made  up  by  the  other  supports 
This  might  often  be  desirable  in  buildings  where  the  girders  run 
across  the  building,  the  ends  resting  on  the  side-walls,  and  the 
girders  being  supported  at  intermediate  points  by  columns  or 


614  CONTINUOUS  GIRDERS. 

piers.  In  such  a  case,  by  using  a  continuous  girder,  part  of  the 
load  could  be  taken  from  the  walls,  and  transferred  to  the 
columns  or  piers. 

But  there  is  another  question  to  be  considered  in  such  a  case, 
and  that  is  vibration.  Should  the  building  be  a  mill  or  factory 
in  which  the  girders  had  to  support  machines,  then  any  vibration 
given  to  the  middle  span  of  the  beam  would  be  carried  to  the  side- 
walls  if  the  beam  were  continuous,  while  if  separate  girders  were 
used,  with  their  ends  an  inch  or  so  apart,  but  little  if  any  vibra- 
tion would  be  carried  to  the  side-walls  from  the  middle  span. 

In  all  cases  of  important  construction  the  supporting  forces 
should  be  carefully  looked  after. 

Strength. — As  the  relative  strength  of  continuous  and  non- 
continuous  girders  of  the  same  size  and  span,  and  loaded  in  the 
same  way,  is  as  their  bending-moments,  we  can  easily  calculate 
the  strength  of  a  continuous  girder,  knowing  the  formula  for  its 
bending-moment.  From  the  values  given  for  the  bending- 
moments  of  the  various  cases  considered,  we  see  that  the  portion 
of  the  girder  most  strained  is  that  which  comes  over  the  middle 
supports;  also  that,  except  in  the  single  case  of  a  girder  of  two 
spans  uniformly  loaded,  the  strength  of  a  girder  is  greater  if  it  is 
continuous  than  if  it  is  not.  But  the  gain  in  strength  in  some 
instances  is  not  very  great,  although  it  is  generally  enough  to  pay 
for  making  the  girder  continuous. 

Stiffness. — The  stiffness  of  a  girder  is  indirectly  proportional  to 
its  deflection;  that  is,  the  less  the  deflection  under  a  given  load 
the  stiffer  the  girder. 

Now,  from  the  values  given  for  the  deflection  of  continuous 
girders,  we  see  that  a  girder  is  rendered  very  much  stiffer  by  being 
made  continuous;  and  this  may  be  considered  as  the  principal 
advantage  in  the  use  of  such  girders. 

It  is  often  the  case  in  building  construction  that  it  is  necessary 
to  use  beams  of  much  greater  strength  than  is  required  to  carry 
the  superimposed  load,-  because  the  deflections  would  be  too 
great  if  the  beam  were  made  smaller.  But,  if  we  can  use  con- 
tinuous girders,  we  may  make  the  beams  of  just  the  size  required 
for  strength,  as  the  deflections  will  be  lessened  by  the  fact  of  the 
girders  being  continuous.  It  should  therefore  be  remembered 
that,  where  great  stiffness  is  required,  continuous  beams  or 
girders  should  be  used  if  possible, 


CONTINUOUS   GIRDERS.  615 

Formulas  for  Strength  and  Stiffness. 

For  convenience  we  will  give  the  proper  formulas  for  calculat- 
ing the  strength  and  stiffness  of  continuous  girders  of  rectangular 
cross-section.  The  formulas  for  strength  are  deduced  from  the 
formula 


Bending-moment  =  --  -  ---  ,  (22) 

where  R  is  a  constant  known  as  the  modulus  of  rupture,  and  is 
eighteen  times  what  is  generally  known  as  the  co-efficient  of 
strength. 

STRENGTH.—  Continuous   girder   of   TWO   equal   spans,    loaded 
uniformly  over  each  span, 

2XBXD*XA 
Breakmg-weight*  =  —     —  v  —    —  ,  (23) 

where  B  denotes  the  breadth  of  the  girder,  D  the  depth  of  the 
girder  (both  in  inches),  and  L  the  length  of  one  span,  in  feet.  The 
values  of  the  constant  A  are  three  times  the  values  given  in  Table 
II.  of  Chapter  XVI.  For  yellow  pine,  300  pounds  ;  for  Oregon 
pine,  270  pounds;  for  spruce,  210  pounds;  and  for  white  pine, 
180  pounds,  may  be  taken  as  reliable  values  for  A. 

Continuous  girder  of  TWO  equal  spans,  loaded  equally  at  the  centre 
of  each  span, 

Breaking-weight^  |X  BxD^xA.  (24) 

Continuous  girder  of  THREE  equal  spans,  loaded  uniformly  over 
each  span, 

Breaking-  weight  =  fX  BxD*xA.  (25) 

A  Lt 

Continuous  girder  of  THREE  equal  spans,  loaded  equally  at  the 
centre  of  each  span, 


Breaking-weight=  |X  .  (26) 

STIFFNESS.—  The  following  formulas  give  the  loads  which  the 
beams  will  support  without  deflecting  more  than  one-thirtieth  of 
an  inch  per  foot  of  span. 

Continuous  girder  of  TWO  equal  spans,  loaded  uniformly  over 
each  span, 

(27) 

*  Breaking  weight  in  Ibs.  in  all  cases. 


616  CONTINUOUS  GIRDERS. 

Continuous  girder  of  TWO  equal  spans,  loaded  equally  at  centre 
of  each  span, 

16     £xD3Xe 
Load  on  one  span=  —  -  X  -  ^  -  .  (28) 


Continuous  girder  of  THREE  equal  spans,  loaded  uniformly  over 
each  spanf 


Load  on  one  span  =  Q33xL2-  (29) 

Continuous  girder  of  THREE  equal  spans,  loaded  equally  at  the 
Centre  of  each  span, 


20 
Load  on  one  span  =—X  -  j~2  -  •  (30) 

The  value  of  the  constant  e  is  obtained  by  dividing  the  modulus 
of  elasticity  by  12,960;  and,  for  the  three  woods  most  commonly 
used  as  beams,  the  following  values  may  be  taken  : 

Yellow  pine,  137;  white  pine,  82;  spruce,  100;  Oregon  pine, 
110.  (For  other  woods  see  table,  page  597.) 

For  continuous  steel  bea?ns  the  requisite  size  of  beam  may  be 
found  by  first  computing  the  bending-moment,  by  means  of 
Formulas  12—15,  and  then  selecting  a  beam  whose  section  modulus 

3  X  bending-  moment  (ft.  -Ibs.)      ,r  ,        £      ,,  ,. 

==  —  -  -  —  .     Values  for  the  section  modulus 

4,000 

for  the  different  shapes  of  rolled  steel  used  as  beams  are  given 
in  the  tables  in  Chapter  X. 

EXAMPLE  1.—  What  size  steel  beam  should  be  used  to  support 
two  loads  of  16,000  Ibs.  each,  concentrated  at  the  centre  of  two 
spans  of  10  feet  each,  the  beam  being  continuous? 

Ans.  Formula  13a  gives  the  bending  moment  as  i\Wl,  or 
30,000  ft.-lbs.  We  must  therefore  use  a  beam  having  a  section 

O  NX  OA    000 

modulus  equal  to  ^         -  or  22£.     From  the  table  on  page 
4,UUu 

297  we  find  that  a  9-inch  30-lb.  beam  has  a  section  modulus  of 
22.6,  and  a  10-inch  25-lb.  beam  a  section  modulus  of  24.  Either 
of  these  beams  will  therefore  answer,  the  10-inch  beam  being  the 
cheaper,  however. 

EXAMPLE  2.  —  A  steel  beam  continuous  over  three  spans  is  re- 
quired to  support  a  distributed  load  of  1,000  Ibs.  per  linear  foot. 
The  two  end  spans  are  12  feet  each,  and  the  centre  span  is  10  feet, 
what  size  and  weight  of  I-beam  should  be  used? 


CONTINUOUS  GIRDERS.  617 

Ans.  The  bending-moment  is  found  by  Formula  14,  and  will 
,     1,000X1,000  +  1,000X1,728  " 

~ 


O  v/  1O   ()Qf) 

The  section  modulus  must  equal  —  -—-     —  =9.47,  which  will 

4,UUU 
require  a  7-inch  15-lb.  beam. 

If  the  beam  were  not  continuous  an  8-inch  18-lb.  beam  would 
be  required  for  the  12-foot  spans,  and  a  7-inch  beam  for  the 
10-foot  span. 

For  beams  of  two  equal  spans,  loaded  uniformly,  the  strength 
of  the  beam  is  the  same  as  though  the  beam  were  not  continuous. 

The  formulas  given  for  the  re-actions  of  the  supports,  and  for 
the  deflections  of  continuous  girders  with  concentrated  loads, 
were  verified  by  the  author  by  means  of  careful  experiments  on 
small  steel  bars.  The  other  formulas  have  been  verified  by 
comparison  with  other  authorities  where  it  was  possible  to  do  so  ; 
though  one  or  two  of  the  cases  given  the  author  has  never  seen 
discussed  in  any  work  on  the  subject. 


618 


RIVETED  PLATE  AND  BOX  GIRDERS. 


CHAPTER  XX. 
RIVETED  STEEL  PLATE  AND  BOX  GIRDERS. 

GIRDERS  built  up  of  plates  and  angles,  in  the  manner  shown  in 
Figs.  1  to  4,  are  coming  more  extensively  into  use  every  year. 
This  is  undoubtedly  owing  to  the  simplicity  of  their  construction, 
comparatively  low  cost  of  the  shapes  of  which  they  are  composed, 
and  their  adaptability  to  any  arrangement  of  loads  or  to  any 
span  for  which  girders  are  usually  required. 

Riveted  girders,  however,  are  seldom  made  of  a  greater  span 
than  60  feet,  nor  of  a  greater  height  than  5  feet. 

The  most  common  forms  of  these  girders  are  those  showrn  in 
Figs.  2  and  4. 


nir 


Fig.  I 


Fig.  2 


Fig.  3 


Fig.  4 


The  sections  with  a  single  vertical  plate  (called  the  "web") 
are  usually  designated  as  "  plate-girders,"  and  those  with  double 
or  triple  webs  as  " box-girders." 

Plate-girders  are  more  economical  than  box-girders,  and  more 
accessible  for  painting  and  inspection ;  but  the  box-girders  are 
stiffer  laterally,  and  should  alwrays  be  used  where  great  length  of 
span  requires  a  wide  top  flange. 

In  general  it  may  be  said  that  plate-girders  should  be  used  for 
supporting  floor-beams  and  floor-arches,  and  walls  not  over  12 
inches  in  thickness,  and  that  box-girders  should  be  used  where  a 
greater  flange  width  than  12  inches  is  required. 

The  section  shown  in  Fig.  1.,  which  has  no  flange-plates,  should 
only  be  used  for  comparatively  light  loads  and  short  spans,  and 
never  for  supporting  masonry. 


RIVETED  PLATE  AND  BOX  GIRDERS.          619 

The  term  "flange,"  as  applied  to  riveted  girders,  embraces  all 
the  metal  in  top  or  bottom  of  girder,  exclusive  of  web-plate. 

By  the  "  depth"  of  a  riveted  girder  is  generally  meant  the  dis- 
tance between  the  centres  of  gravity  of  the  flanges;  in  practice 
this  is  taken  as  the  height  of  the  web-plate,  and  the  word  will  be 
so  used  in  this  chapter.  The  top  and  bottom  of  the  flange  angles 
are  always  on  a  line  with  the  top  and  bottom  of  the  web-plate. 

Stiffeners  are  short  pieces  of  angles  riveted  to  the  web  at  inter- 
vals, to  keep  the  web  from  buckling.  They  should  fit  closely 
against  the  horizontal  flanges  of  the  flange  angles,  and  should 
always  be  used  at  the  supports. 

Depth  and  Width  of  Girders. — The  depth  of  a  riveted  girder 
may  be  from  TV  to  fa  of  the  span.  The  greatest  economy  of 
materials  is  said  to  be  obtained  when  the  depth  is  fa  of  the  span. 
Thus  for  a  36-ft.  span  a  3-ft.  girder  should  be  used  if  the  con- 
ditions will  permit;  but  the  least  depth  should  be  fa  of  36,  or  2  ft. 
3  in. 

The  width  of  the  top  flange  should  not  be  less  than  fa  of  the 
distance  between  lateral  supports;  or  if  there  are  no  lateral 
supports,  then  not  less  than  fa  of  the  span. 

Arches  between  girders  or  floor  beams  riveted  to  the  sides  of 
girders  may  be  considered  as  lateral  supports. 

DETAILS  OF  CONSTRUCTION.* 

1.  All  the  connections  and  details  of  the  several  parts  shall  be 
of  such  strength  that,  upon  testing,  rupture  shall  occur  in  the 
body  of  the  members  rather  than  in  any  of  their  details  or  con- 
nections. 

In  members  subject  to  tensile  strain  full  allowance  shall  be 
made  for  the  reduction  of  section  by  rivet-holes. 

2.  The  webs  of  plate  girders,  when  they  cannot  be  had  in  one 
length,  must  be  spliced  at  all  joints  by  a  plate  on  each  side  of  the 
web. 

Tees  must  not  be  used  for  splices. 

3.  Stiffeners  shall  be  used  at  the  ends  of  all  girders  and  wher- 
ever concentrated  loads  occur,  and  elsewhere  when  the  shearing 
strain  is  greater  than  the  resistance  to  buckling. 

4.  The  pitch  (distance  between  centres)  of  rivets  shall  not  ex- 
ceed 6  in.,  nor  16  times  the  thickness  of  the  thinnest  outside  plate, 

*  The  following  twelve  points  are  taken  largely  from  Birktnire's  "  Coin- 
pound  Riveted  Girders." 


620         RIVETED  PLATE  AND  BOX  GIRDERS. 

nor  be  less  than  2J  in.  for  f -in.  rivets,  or  2f  in.  for  f-in.  rivets,  in 
a  straight  line. 

5.  The  rivets  used  should  be  f  in.  in  diameter  for  plates  from 
f  in.  to  f  in.  thick,  and  £  in.  in  diameter  for  greater  thickness  of 
plates. 

6.  The  distance  between  the  edge  of  any  piece  and  the  centre 
of  a  rivet-hole  must  never  be  less  than  1J  in. 

7.  In  punching  plates  or  other  iron,  the  diameter  of  the  die 
shall  in  no  case  exceed  the  diameter  of  the  punch  more  than  T^- 
of  an  inch. 

8.  All  rivet-holes  must  be  so  accurately  punched  that  when 
the  several  parts  forming  one  member  are  assembled  together,  a 
rivet  T^  inch  less  in  diameter  than  the  hole  can  be  entered,  hot, 
into  any  hole  without  reaming  or  straining  the  iron  by  " drifts." 

9.  The  rivets  when  driven  must  completely  fill  the  holes. 

10.  The  rivet-heads  must  be  hemispherical,  except  where  flush 
surfaces  are  required,   and  a  uniform  size  for  the  same-sized 
rivets  throughout  the   work.     They  must  be  full  and  neatly 
made,  and  be  concentric  to  the  rivet-holes. 

11.  Whenever  possible,  all  rivets  must  be  machine-driven. 

12.  The  several  pieces  forming  one  built  member  must  fit 
closely  together,  and,  when  riveted,  shall  be  free  from  twists, 
bends,  or  open  joints. 

Splicing. — "  Girders  40  feet  and  less  in  length  will  not  require 
any  splicing,  as  the  plates  and  angles  can  be  readily  handled  in 
one  length. 

"In  splicing  the  top  flange,  when  of  two  or  more  thicknesses, 
no  additional  cover-plate  will  be  required  over  the  joint,  but  the 
ends  should  be  planed  true  and  butt  solidly.  The  rivets  to  be 
closer  near  the  joint. 

"The  plate  covering  the  bottom  flange  must  be  of  the  same 
area  as  the  plates  joined,  and  of  sufficient  length  to  take  a  num- 
ber of  rivets  equal  to  the  strength  of  the  cover-plate." 

CALCULATIONS  FOR  RIVETED  GIRDERS. 

In  designing  a  riveted  girder  to  sustain  with  safety  a  given 
load,  the  following  steps  are  necessary : 

1.  To  determine  the  necessary  flange  area. 

2.  To  determine  the  thickness  of  the  web  to  resist  (a)  shearing, 
(&)  buckling. 

This  step  also  determines  whether  or  not  stiffeners  are  required. 

3.  To  determine  the  number  and  pitch  of  the  rivets. 


RIVETED  PLATE  AND   BOX  GIRDERS.         621 

4.  To  determine  the  length  of  the  outside  flange-plates.  When 
but  a  single  plate  is  used  in  the  flanges  this  step  is  not  required. 

1 .  Flange  Area. — For  determining  the  flange  area  of  riveted 
girders,  it  is  customary  to  assume  that  the  bending-moment  is 
resisted  entirely  by  the  upper  and  lower  flanges,  the  web-plate  bcii:g 
assumed  to  resist  only  the  shearing  strains.  Some  engineers 
include  J  of  the  section  of  the  web  in  the  flange  area,  and  some- 
times the  full  moment  of  inertia  of  the  section  is  taken.  The 
better  practice,  however,  appears  to  be  that  based  on  the  assump- 
tion first  given.  The  New  York  Building  Law  even  goes  further 
than  this,  and  requires  that  "No  part  of  the  web  shall  be  esti- 
mated as  flange  area,  nor  more  than  one-half  of  that  portion  of 
the  angle-iron  which  lies  against  the  iveb." 

As  used  in  this  chapter,  the  term  "flange  area"  will  include 
the  flange  or  cover-plates,  and  the  full  section  area  (less  rivet- 
holes)  of  the  angles  connecting  the  flange  with  the  web. 

In  the  flange  plates  and  angles  subjected  to  tensile  strain  full 
allowance  should  be  made  for  reduction  of  section  by  rivet-holes. 
For  the  compression  flange  the  gross  sectional  area  may  be  taken 
as  making  up  the  same,  provided  the  riveting  is  well  done,  so  as 
to  completely  fill  the  holes. 

The  general  formula  for  the  strength  of  beams  (see  page  500) 
is:  Max.  bending-moment  =  section  modulus  X$.  Assuming 
that  the  flanges  alone  resist  the  bending-moment  the  section 
modulus  will  be  equal  to  the  area  of  one  flange  multiplied  by 
the  height  of  the  girder  and  substituting  this  value  in  the  above 
equation  we  have 

Max.  bending-moment  =  area  of  one  flan geX  height  X$, 
or 

Area  of  one  flange  )   _  max,  bending-moment  (ft.-lbs.) 
in  square  in.        )  ~          height  of  web  in  feetX£. 

This  applies  to  any  condition  of  loading. 

Rules  for  finding  the  maximum  bending-moment  for  different 
conditions  of  loading  are  given  in  Chapter  IX. 

For  the  upper  or  compression  flange  S  should  be  taken  at 
12,000  Ibs.  for  steel  and  9,000  Ibs.  for  iron. 

For  the  bottom  or  tension  flange  S  should  be  taken  at  13,000 
Ibs.  for  steel  and  10,000  Ibs.  for  iron.* 

*Most  of  the  tables  giving  the  strength  of  riveted  girders,  found  in  the 
recent  editions  of  the  manuals  issued  by  the  rolling  mills,  are  based  on  o, 
fibre  stress  of  15,000  Ibs.  See  pages  648-050. 


622          RIVETED  PLATE  AND   BOX  GIRDERS. 

If  it  is  desired  to  compute  the  safe  distributed  load  for  a  girder 
already  constructed  or  designed,  the  following  formula  may  be 
used : 

Safe  load  in  Ibs.  uniformly  distributed  == 

SXnet  area  of  bottom  flange  X  height  in  ft.  XS 

— r — 7— —  .        (la) 

span  in  feet 

From  the  result  the  weight  of  the  girder  itself  should  be  sub- 
tracted. 

For  safe  centre  load  take  one-half  the  result  obtained  by  formula 
(la)  and  subtract  weight  of  girder. 

1.  Thickness  of  Web.— The  thickness  of  the  web  is  deter- 
mined by  its  resistance  to  shearing.  Whether  or  not  stiffeners 
shall  be  used  is  determined  by  the  resistance  of  the  web  to  buck- 
ling. 

SHEARING. — To  resist  shearing  the  net  sectional  area  of  web 
must 

_  maximum  shear 

-p         —, 

F  being  taken  at  6,000  Ibs.  for  iron  and  7,000  Ibs.  for  steel.* 
The  maximum  shear  in  any  beam  is  at  one  or  the  other  of  the 

supports,  and  in  a  girder  supported  at  both  ends  is  equal   to 

the  greater  of  the  supporting  forces. 

For  a   girder  supported  at  both  ends  and  uniformly  loaded, 

W 

maximum  shear  =  — -. 
2i 

For  a  girder  supported  at  both  ends  and  loaded  at  the  centre,  max- 
imum shear  =  —  ,  W  representing  the  total  load  on  the  girder. 
For  a  girder  supported  at  both  ends  and  loaded  as  in  Fig.  7, 

wx™ 

maximum  shear  =  — T —  =^V 
LJ 

For  a  girder  supported  at  both  ends  and  loaded  with  two  equal 
concentrated  loads  W,  W,  equally  distant  from  the  centre,  maxi- 
mum shear  =  TF. 

For  combinations  of  loads  the  maximum  shear  will  equal  the 
greater  supporting  force.  The  method  of  determining  the  sup- 
porting forces  in  a  beam  is  given  on  pages  274  and  275.  The 
shearing  force  at  any  given  vertical  section  between  the  supports 

*  These  are  very  conservative  values.  The  Carnegie  "Pocket  Com- 
panion "  and  several  building  laws  permit  10,0.00  Ibs.  for  steel. 


RIVETED  PLATE  AND  BOX  GIRDERS.        623 

may  be  determined  by  the  following  rule:  The  shearing  force  at 
any  given  cross-section  of  a  beam  is  the  algebraic  sum  of  all  the 
forces  acting  on  the  beam  from  the  origin  to  that  cross-section, 


.  ------  m  -------  • 


@ JL" 


fc__u 

...  3»    h 

"P 

dm     T                                         rmrnr 

III       ^'S  ® 

IT 

rig-  / 

PJ 

77"  ll                      I 

L           Jf 

7- 

jp. 

P 

/  / 

— 4—  4- 6- 


1 

4  

X                  Y                              Z 
ZQ'-—^  

...q. 

P          fr 

>0 

^l100 
i    L  on 

P2=140 


forces  acting  upwards  being  considered  as  minus,  and   those 
acting  downwards  being  considered  as  plus. 


624          RIVETED  PLATE  AND  BOX  GIRDERS. 

Thus  :  In  the  case  of  the  beam  shown  in  Fig.  9  the  reaction  at 
Pl  will  be  found,  by  the  method  explained  on  page  275,  to  be 
150,  and  that  at  P2  to  be  140. 

Taking  our  origin  at  P1}  we  would  have  for  the  shearing  force 
at  the  section  X}  by  the  foregoing  rule, 

Shear  at  X  =  -  150+  50  =  -  100  3 
Shear  at  Y  =  -  150+  50+  80  =  -  20.; 
Shear  at  Z  =  -  150+  50+  80+  100  =+  80  ; 
Shear  at   0  =  -  150+  50+  80+  100+  60  =  +  140. 

The  manner  in  which  the  shearing  force  varies  between  the 
supports,  under  different  methods  of  loading,  is  shown  by  the 
etched  areas  in  Figs.  5-9  ;  in  the  first  three  cases  W  has  the  same 
value. 

When  the  load  is  distributed  the  shearing  force  can  be  found 
by  laying  off  Pl  and  P2  to  a  scale  of  pounds,  and  drawing  the 
line  a&,  Fig.  5.  The  shear  at  X  will  then  be  represented  by  the 
ordinate  X1  and  the  shear  at  Y  by  Ylt  which  can  be  readily  scaled. 

The  resistance  of  the  web  to  buckling  is  determined  by  the  for- 
mula 

10,000  X  net  area  of  section 
Safe  resistance  to  buckling  =  —  -  --    -  ,    (3) 


where  /i=height,  and  £=thickness  of  web  in  inches. 

When  this  resistance  is  less  than  the  shearing  force,  at  any 
section,  stiffeners  must  be  used. 

STIFFENERS.  —  These  should  be  made  of  angles,  not  less  than 
3X3X1  in.  and  seldom  larger  than  4X4XJ  in.  They  should 
always  be  tightly  fitted  between  the  flange  angles,  so  as  to  sup- 
port the  horizontal  flange.  In  order  to  bring  the  stiffeners  in 
contact  with  the  web  and  vertical  leg  of  angle,  fillers  are  generally 
used  of  the  same  thickness  as  the  flange  angle,  as  shown  in  Fig. 
10.  Where  there  are  several  girders  exactly  alike,  something 
may  be  saved  by  omitting  the  fillers  and  bending  the  stiffeners, 
as  shown  in  Fig.  11.  This  bending  can  only  be  properly  done 
by  the  use  of  special  dies,  and  will  cost  more  than  the  fillers  unless 
there  are  many  stiffeners. 

As  to  the  spacing  of  stiffeners,  they  should  in  no  case  (where  the 
resistance  to  buckling  is  less  than  the  shear)  be  spaced  farther 
apart  than  1J  times  the  height  of  the  web,  and  it  is  safer  to  make 
the  distance  from  centres  equal  to  the  height  of  the  web. 


RIVETED  PLATE  AND   BOX  GIRDERS.         625 

On  girders  supporting  distributed  loads  they  are  generally 
placed  nearer  together  at  the  ends  than  towards  the  centre. 


Fig.  10  Fig.  II 

Stiffeners  should  always  be  placed  at  the  ends  and  directly  over 
the  edge  of  the  support,  as  shown  in  Fig.  18,  and  wherever  con- 
centrated loads  occur. 

On  plate  girders  the  stiffeners  are  always  placed  on  each  side  of 
the  web ;  on  box  girders  generally  on  the  outside  only. 

Bearing  of  Girders. — This  depends  somewhat  upon  the  load, 
but  a  safe  general  rule  is  to  make  the  bearing  of  the  girder  beyond 
the  edge  of  the  support  equal  to  one-half  the  height  of  the  girder. 

Spacing  of  Rivets. 

I.  RIVETS  IN  WEB  LEG  OF  ANGLES. 

It  will  readily  be  seen  that  when  a  plate  or  box  girder  is  loaded, 
the  tendency  of  the  bending-moment  is  to  cause  the  flange-plates 
and  angles  to  slide  horizontally  past  the  web;  this  tendency  is 
resisted  by  the  rivets  which  connect  the  angles  with  the  web. 

The  total  amount  of  this  tendency  to  slide  (called  the  " horizontal 
flange  strain"),  between  any  selected  point  of  the  flange  and  the 
nearer  end  of  the  girder,  is  equal  to  the  bending-moment  at  that 
point  divided  by  the  depth  of  the  web. 

The  total  number  of  rivets  between  the  selected  point  and  the 
nearer  end  must  be  such  that  their  combined  resistance  to  shear- 
ing or  bearing  (whichever  is  the  least)  shall  equal  the  "horizontal 
flange  strain"  at  the  selected  point;  or  number  of  rivets 

horizontal  flange  strain 
bearing  or  shearing  of  one  rivet' 
and  the  total  number  of  rivets  in  web-angle  from  end  to  end 

2Xmax.  bending-moment  fft.-lbs.) 

height  of  web  (in  ft.)  X least  resistance  of  one  rivet ' 


626         RIVETED  PLATE  AND   BOX  GIRDERS. 

If  the  number  of  rivets  determined  by  formula  (4)  is  such  that 
they  would  be  more  than  6  in.  apart,  then  the  number  must  be 
increased,  as  in  no  case  should  they  have  a  greater  "pitch"  than 
6  in. 

II.  FLANGE  LEG  OF  ANGLES. 

a.  With  single  cover-plate. — For  girders  with  a  single  cover- 
plate,  it  is  customary  to  put  the  same  number  of  rivets  in  the 
flange  leg  as  in  the  web  leg  for  a  distance  of  3  feet,  staggering  the 
rivets  as  in  Fig.  15.     Beyond  that  point  to  the  centre,  one-half 
the  number  of  rivets  will  be  sufficient,  provided  this  will  not 
give  them  a  greater  pitch  than  6  in. 

b.  With  two  or  more  cover-plates. — When  two  or  more  cover- 
plates  are  used,  each  plate  must  have  sufficient  rivets  between  the 
end  of  the  plate  and  the  point  where  its  resistance  is  required 
(that  is,  between  a  and  b,  Fig.  13)  to  transfer  to  the  angle  and 
flange  plates  between  an  amount  equal  to  the  safe  strength  of  the 
plate.     From  this  point  to  centre  the  rivets  can  be  spaced  accord- 
ing to  the  rule  for  greatest  pitch. 

III.  RIVETS  IN  STIFFENERS. 

The  spacing  of  rivets  in  the  stiffeners  is  generally  determined 
by  the  rules  given  for  the  pitch  of  rivets. 

Further  explanation  of  the  method  of  determining  the  spacing 
of  rivets  will  be  found  in  the  following  examples. 

Approximate  Weight  of  Girder. 

In  determining  the  size  of  a  riveted  girder  to  support  a  given 
load,  it  is  desirable  to  be  able  to  add  to  the  superimposed  load 
the  weight  of  the  girder  itself,  as  this  often  forms  quite  a  con- 
siderable portion  of  the  load  to  be  supported. 

Mr  William  H.  Birkmire,  in  his  book  on  "Compound  Riveted 
Girders,"  gives  the  following  empirical  rule  for  determining  the 
approximate  weight  of  plate  or  box  girders : 

W^Li  f£\ 

Weight  of  girder  between  support,  in  tons=    ^    , 

where  W  equals  load  to  be  supported  in  tons,  and  L  equals  span 

in  feet. 

The  constant  700  was  determined  for  girders  from  35  to  50  It. 
longr,  but  may  be  used  without  much  excess  for  girders  of  shorter 
span. 


RIVETED  PLATE  AND  BOX  GIRDERS.        627 

Tables. 

The  calculations  of  riveted  girders  may  be  greatly  facilitated 
by  Tables  I.,  II.,  and  III.  Table  I.  gives  the  sectional  area  that 
should  be  deducted  for  rivet-holes  in  plates  of  different  thick- 
nesses. In  computing  this  table  J  inch  was  added  to  the  diam- 
eter of  the  rivet  to  allow  for  the  injurious  effect  of  punching. 

Table  II.  gives  the  safe  shearing  value  for  web-plates  for 
various  depths  and  thicknesses,  and  the  deduction  to  be  made 
for  each  f-inch  or  -J-inch  rivet. 

Table  III.  gives  the  safe  resistance  to  buckling  per  square  inch 
of  net  section,  and  also  the  total  resistance  of  the  more  common 
sizes  of  web-plates,  fMth  two  rivet-holes  deducted. 

It  is  very  seldom  that  any  vertical  section  between  the  stif- 
feners  contains  more  than  two  rivet-holes.  Tables  giving  the 
dimensions  of  angles  will  be  found  in  Chapter  X.,  and  the  shear- 
ing and  bearing  value  of  rivets  is  given  on  page  371. 

Examples. 

EXAMPLE  I. — It  is  required  to  support  the  floor  over  a  room 
50  X  64  feet,  by  means  of  riveted  steel  plate  girders,  placed  across 
the  room  and  16  feet  on  centres.  The  floor  above  is  to  be  used 
for  general  assembly  purposes.  The  floor  joists  are  of  wood,  with 
plastered  ceiling  below.  Design  the  girder. 

First  Step:  Load. — The  first  step  will  be  to  determine  the  load 
to  be  supported  by  each  girder.  The  floor  area  supported  by  each 
girder  is  50'X16'  or  800  sq.  ft.  The  weight  of  the  floor  con- 
struction between  the  girders  will  be  not  over  25  Ibs.  per  sq.  foot, 
and  an  allowance  of  100  Ibs.  per  sq.  foot  for  live  load  will  be 
ample.  800  X 125  gives  100,000  Ibs.  or  50  tons  as  the  load  to  be 
carried  by  the  girder.  To  this  should  be  added  the  weight  of 
the  girder  itself.  The  rule  for  approximate  weight  of  girder  is 

load  in  tons  X  span      50X50 

w= — — —  =-  =3.57  tons,  or  about  7,000  Ibs., 

i uU  /UU 

making  the  total  load  107,000  Ibs.  This,  of  course,  will  be  dis- 
tributed. 

Second  Step:  Flange  Area. — The  next  step  will  be  to  determine 
the  flange  area.  Before  we  can  do  this,  however,  we  must  de- 
cide upon  the  width  and  depth  of  the  girder. 

As  it  is  desirable  to  keep  the  girder  as  shallow  as  possible,  con- 
sistent with  good  engineering,  we  will  make  the  depth,  or  height, 
of  the  web-plate  36  inches,  which  is  about  }{6ih  of  the  span. 


628         RIVETED  PLATE  AND  BOX  GIRDERS. 

As  the  girders  are  braced  sideways  by  the  floor  joists  we  will 
make  the  width  of  the  flange-plates  12  inches. 
The  flange  area  is  determined  by  formula  (1),  and  equals 
max,  bending-moment  in  ft.-lbs. 

height  of  web  in  ft.  X  S 
The  maximum  bending-moment  for  a  distributed  load  equals 

WXL        .      "; 

—5  —  -,  or  in  this  case 

o 

107,000X50     AftOP7KA4,   ,, 
-  -  -  =  668,750  ft.-lbs. 

o 

Substituting  this  in  the  above  formula  we  have, 

Gross  area  of  upper  flange  =2_=  18.57  sq.  in. 


Net  area  of  lower  flange=  —        —  =  17.15  sq.  in. 


We  will  first  consider  the  upper  flange. 

For  the  angles  we  will  use  two  5"X3J"Xi"  angles,  with  the 
long  leg  horizontal.*  The  area  of  these  two  angles  we  find  to  be 
8  sq.  in.,  which  leaves  10.57  sq.  in.  for  the  flange-plates.  Divid- 
ing this  by  the  width  of  the  plate,  12  in.,  we  have  .88,  or  say 
|  in.  as  the  required  thickness  of  the  plates.  We  will  divide  this 
into  two  plates,  one  J  inch  thick,  and  the  upper  one  f  inch  thick. 

We  will  now  see  if  these  plates  will  have  a  net  area,  after  de- 
ducting the  rivet-holes,  sufficient  for  the  lower  flange.  As  we 
shall  stagger  the  rivets  in  the  two  legs  of  the  angles,  we  will 
have  to  deduct  for  only  two  rivets  in  flange  legs  of  angles,  and 
two  in  the  flange-plates.  We  will  use  j-inch  rivets.  From 
Table  I.  we  find  that  the  area  to  be  deducted  for  two  J-inch  rivets 
in  a  J-inch  plate  is  1.53,  and  in  a  J-inch  plate  (thickness  of  angle) 
.87.  Adding  these,  we  have  2.40  sq.  in.  to  be  deducted  from 
18.50  sq.  in.,  the  gross  area  of  upper  flange,  which  leaves  16.  1  sq. 

*  For  the  flange-angles  of  plate  cirders  the  5"  X  3^"  size  is  most  com- 
monly used,  when  the  flange-plate  is  from  10^  to  12  inches  wide,  and 
6"X4"  angles  when  the  flange-plate  is  over  12  in.  wide.  For  box  girders 
5  X  4,  5  X  3f£,  4  X  3^,  and  3^  X  3V^  are  common  sizes  ;  while  for  very  heavily 
loaded  girders,  requiring  two  rows  of  rivets  in  the  web  leg,  6"X4"  angles 
are  often  used,  with,  the  long  leg  vertical.  For  most  riveted  girders,  in 
which  only  one  row  of  rivets  is  required,  the  short  leg  is  riveted  to  the  web, 
so  as  to  bring  most  of  the  material  as  far  from  the  centre  of  the  girder  as 
possible.  The  minimum  thickness  of  flange-angles  should  be  %  of  an  inch, 
and  the  maximum  thickness  for  ordinary  loads  %£  inch. 


RIVETED  PLATE  AND  BOX  GIRDERS.        629 

in.  as  the  net  area.     As  this  is  less  than  the  net  area  required  in 
the  lower  flange,  we  will  increase  the  thickness  of  outer  plate 
to  J  in.,  which  will  give  us  a  little  excess  of  area. 
Our  flanges  will  then  be  made  up  as  follows : 

Top  flange  =  2  angles  5"  X  3i"  X  J"  =  8     sq.  in.  gross  area 
1  plate  12"X   4"         =6      "    "      "        " 
1  plate  12"X   f"         =  4.5   "    "      "       " 

Total,  .18.5   "    "      "       " 

Bottom  flange  =  2  angles  5"X34"X4"*  net  area  7.13sq.  in. 
2  plates  12"XJ"  "     "      10.25  "    " 

Total,  17.38  "     " 

Third  Step:  Length  of  Flange-plates. — We  will  now  determine 
the  length  of  the  outer  plate  in  bottom  flange. 

To  do  this  we  must  first  determine  the  horizontal  flange  strain 
at  centre  of  girder.  This  is  equal  to  the  bending-moment 

divided  by  the  height  of  girder  in  feet,  or  668>75Q  =  222,910  Ibs. 

o 

The  bending-moment  in  a  beam  or  girder  loaded  with  a  uni- 
formly distributed  load  is  represented  by  the  ordinates  of  a 
parabola  having  its  height  equal  to  the  bending-moment  at  the 
centre.  The  horizontal  flange  strain  is  also  represented  by  the 
same  curve. 

If,  therefore,  we  draw  the  parabola  rht,  Fig.  12  making  ah= 
horizontal  flange  strain,  to  a  scale  of  pounds,  any  ordinate  drawn 
to  this  curve  will  represent  the  flange  strain  in  the  girder  at  the 
corresponding  point  on  the  girder. 

To  find  the  theoretical  length  of  the  flange-plates,  draw  the 
indefinite  horizontal  line  AD,  and  from  the  point  a  lay  off  the 
line  ad  equal  to  the  total  flange  area,  and  at  such  an  angle  that 
the  end  of  the  line  d  will  come  in  the  line  AD.  Then  divide  the 
line  ad  into  aZ>  =  area  of  two  angles;  6c=area  of  first  flange- 
plate;  cd=area  of  second  flange-plate. 

Draw  horizontal  lines  through  b  and  c;  then  the  line  ee'mll 
represent  the  theoretical  required  length  of  the  outer  flange- 
plate,  and  the  line  ff  the  length  of  the  first  flange-plate. 

The  plates  must  in  practice,  however,  be  extended  beyond  the 
points  e  and  /  a  distance  sufficient  to  catch  enough  rivets  to 
transmit  at  least  one-third  of  the  resistance  of  the  plate. 

The  first  flange-plate  we  will  make  the  full  length  of  the 


630        RIVETED  PLATE  AND  BOX  GIRDERS. 

girder,  as  it  greatly  strengthens  the  angles,  and  adds  but  a  small 
amount  to  the  cost  of  the  girder.  We  will  also  make  the  plates 
in  the  upper  flange  of  the  same  length  as  those  in  the  lower  flange. 
Fourth  Step:  Web. — The  maximum  shearing-stress  in  a  beam 
uniformly  loaded  is  equal  to  one-half  of  the  total  load,  or,  in  this 

107  000 
case,  £ —  =53,500  Ibs.     The  web  must  be  thick  enough  to 

a 

resist  the  shear.  From  Table  II.  we  find  that  the  resistance  to 
shearing  of  a  f"X36"  web-plate  is  94,500  Ibs.  As  this  greatly 
exceeds  the  total  shear,  we  will  use  a  §-inch  web-plate. 

Fifth  Step:  Stiffeners. — As  has  been  explained,  stiffeners  will 
be  required  wherever  the  shear  exceeds  the  safe  resistance  of  the 


web  to  buckling.  In  this  case  the  maximum  shear  is  53,500  Ibs. 
and  the  safe  resistance  of  a  |"X36"  web  with  two  f"  rivets  to 
buckling  (see  Table  III.)  is  31,560  Ibs.;  hence  stiffeners  wiU  be 
required  at  intervals  of  about  3  feet. 

To  determine  how  many  stiffeners  will  be  required,  we  draw 
the  horizontal  line  K-K,  Fig.  12,  and  at  each  end  lay  off  to  a 
scale  of  pounds  the  lines  Plt  P2,  each  equal  to  one-half  the  total 
load  on  the  girder.  The  shaded  triangles  will  represent  the 
shearing-stress  in  the  web.  At  3  ft.  from  the  end  the  shear  will 
equal  Sx~;  at6ft.,S2;  at  9  ft.,  S3;  and  so  on. 


RIVETED  PLATE  AND   BOX   GIRDERS.         631 

By  measuring  these  lines  with  our  scale  we  find  the  shear  at  m, 
n,  o,  p,  etc.  In  this  case  we  find  £^  =  46,200  Ibs.,  £2=  39,900 
Ibs.,  £3  =  33,600  Ibs.,  and  S4=  27,300  Ibs.  As  SB  is  greater  than 
the  safe  resistance  to  buckling,  and  $4  less,  we  might  stop  the 
stiffeners  at  p'}  but  as  the  floor-joists  are  framed  flush,  or  nearly 
so,  with  the  top  of  the  girder,  and  rest  on  angles  riveted  to  the 
web,  we  will  put  about  3  stiffeners  between  the  point  p  and  the 
corresponding  point  on  opposite  end. 

We  will  also  put  a  stiffener  at  each  end  and  directly  over  each 
support,  so  that  we  will  have  15  stiffeners  on  each  side  of  the 
girder.  These  we  will  make  of  4"  X  4"  X  I"  angles. 

Sixth  Step:  Rivets. — We  will  first  determine  the  number  of 
rivets  in  the  web  leg  of  the  angles.  As  we  should  put  a  rivet  in 
the  end  of  each  stiffener,  we  will  determine  the  number  of  rivets 
required  between  each  two  adjacent  stiffeners.  The  strain  on 
the  rivets  between  the  point  m  and  the  end  of  the  girder  is 
equal  to  the  line  H1')  between  m  and  ?i=//2;  between  n  and 
o=H3;  between  o  and  p=H^-  and  the  strain  between  p  arid 
the  centre  =  H&.  By  scaling  these  lines  we  find  H^  =  48,000  Ibs,, 
/f2  =  44,500  Ibs.,  7/3  =  38,000,  #4=  28,500,  and  #5  =  64,410. 

In  the  web  the  rivets  are  in  double  shear;  hence  each  rivet 
will  have  a  shearing  resistance  (see  Table  II.,  p.  371)  =  6, 620  Ibs. 
The  resistance  to  bearing  of  a  f  inch  rivet  on  a  f -inch  plate  (see 
same  table)  =  4,220  Ibs.,  and  the  latter  number  will  determine  the 
number  of  rivets. 

48,000  Ibs.  -=-4,220=11.4  rivets  or  12  rivets,  the  number 
required  between  m  and  the  end  of  girder.  We  will  put  1  rivet 
through  each  of  the  two  end  stiffeners,  3  between  the  end  stiffen- 
ers, and  7  between  the  stiffeners  at  r  and  m,  making  12  rivets  to 

the  left  of  m.     Between  m  and  n  we  must  have  -Hy^r  =  11  rivets. 

As  this  would  make  them  closer  together  between  m  and  n  than 
between  r  and  m,  we  will  space  the  18  rivets  evenly  between  r 
and  n,  putting  one  in  the  end  of  the  stiffener  at  n.  This  will 
make  the  pitch  just  4  in. 

OQ    f\f\f\ 

The  number  of  rivets  between  n  and  o  must  equal      '       =9y 

which  gives  the  same  pitch  as  before.     Between  o  and  p  we  must 

28  500 
have      '        =  7  rivets,  which  gives  a  pitch  of  5y  in. ;  and  between 

p  and  the  centre  we  must  have  —      —-,  or  16  rivets.     As  the  dis- 


632          RIVETED   PLATE  AND   BOX   GIRDERS. 

tance  is  13  ft.,  or  156  in.,  this  would  make  the  pitch  nearly  10  in, 
The  maximum  permissible  pitch  is  6  in.,  and  we  will  therefore 
use  that  pitch  from  t  to  the  corresponding  point  on  the  other  end. 

The  rivets  in  the  flange  leg  we  will  space  intermediate  with 
those  in  the  web  leg.  To  determine  the  length  of  the  outer 
plate,  we  have  the  net  area  of  outer  plate  in  lower  flange  =  5. 13 
sq.  in.  This  multiplied  by  13,000  =  66,690  Ibs.,  the  resistance  of 
the  plate.  One-third  of  this,  or  22,230  Ibs.,  must  be  transferred 
by  rivets  placed  beyond  the  points  e,  e',  Fig.  12.  As  the  rivets 
in  the  flange  are  in  single  shear,  the  shearing  strength  (3;310  Ibs. 
for  f-inch  rivets)  will  determine  the  number  22,230^3,310=7 
rivets,  or  say  3  in  each  angle. 

The  point  e,  Fig.  12,  comes  at  a,  Fig.  15,  and  we  will  extend 
the  plate  so  as  to  take  the  next  three  rivets  towards  the  end. 

The  rivets  in  the  stiffeners  we  will  space  as  near  6  in.  as  we 
can,  which  gives  five  rivets  between  the  ends. 

The  ends  of  the  floor-joist  we  will  support  on  4"X4"Xi" 
angles.  The  load  on  one  lineal  foot  of  this  angle,  on  each  side  of 
the  girdei,  =  8  ft.X125  Ibs.  =  1,000  Ibs. ;  and  as  the  same  rivets 
support  both  angles,  the  total  load  per  running  foot  will  be  2,000 
Ibs.,  which  is  only  about  one-half  of  the  resistance  of  a  single 
rivet.  We  will  therefore  pitch  the  rivets  about  6  in. 

Splices. 

As  the  total  length  of  the  girder  is  53  ft.,  it  will  probably  be 
necessary  to  splice  the  web  and  flange-plates. 

The  angles  should  not  be  spliced,  as  they  can  be  obtained  in 
one  length,*  and  it  is  difficult  to  make  a  good  splice  in  the  angles 
If  the  web  is  spliced,  the  joint  should  be  at  the  centre,  as  theoreti- 
cally there  is  no  strain  on  the  web  at  that  point  when  the  load  is 
distributed.  We  will  therefore  use  for  the  splice-plates  (one  on 
each  side  of  the  web)  \"  plates,  8"  wide,  and  of  such  length 
that  they  will  fit  closely  between  the  flange  angles.  These  plates 
will  serve  as  fillers  for  the  middle  stiffener.  If  there  was  a  shear- 
ing stress  at  this  point  of  the  web  the  number  of  rivets  on  each 
side  of  the  joint  should  be  sufficient  to  transfer  the  shear  from 
one  side  of  the  joint  to  the  other.  In  this  case  we  will  use  the 
same  number  of  rivets  as  we  determined  for  the  stiffener. 

The  outer  flange-plates  can  easily  be  obtained  in  one  length. 
The  first  flange-plate  it  may  be  necessary  to  splice. 

*  Angles  3"X3"  and  less  can  be  rolled  up  to  60  ft.  in  length.  Angles 
4"X4"  to  6"X6",  up  to  50  feet 


RIVETED   PLATE  AND  BOX   GIRDERS.         633 


Whenever  a  splice  is  required  in  a  flange-plate,  it  should  if 
possible  be  at  a  point  just  beyond  the  end  of  the  plate  above  it. 
The  joint  must  be  made  by  riveting  to  the  spliced  plate  a  plate  of 
the  same  thickness  and  of  sufficient  length  to  receive  a  number 
of  rivets  on  each  side  of  the  joint  equal  to  the  strength  of  the 
plate  that  is  spliced. 

When  the  flange  is  made  up  of  two  plates  of  the  same  thickness, 
the  simplest  method  of  splicing  the  inner  plate  is  shown  by  Fig. 
13.  Let  e  denote  the  theoretical  end  of  outer  plate,  as  deter- 
mined by  the  strain  diagram,  and  a  the  point  to  which  the  plate 
must  be  extended  to  receive  rivets  equal  to  one-third  the  strength 
of  the  plate.  Then  let  the  joint  in  inner  plate  be  just  under  a  and 
extend  the  outer  plate  to  b,  or  such  a  distance  that  it  can  receive 
a  number  of  rivets  equal  to  the  strength  of  one  plate. 

In  the  girder  in  question  we  will  use  a  separate  splice-plate 
\  in.  thick  and  12  in.  wide.  The  net  area  of  the  inner  plate  is 
5.13  sq.  in.,  and  its  safe  strength,  at  13.000  Ibs.  to  the  inch, 


0  j  O     O     p  (  O( 

o    o   p    o    o   o   o 

o    o   o    o 

'ti  1  1  1  II 

_.       .0       &> 

\ 

•Fig.  13 


0 
0 

OO        OOOOO        OOO 
OOOOO               OOOOO 

OOOOO               OOOOO 
OOO        OOOOO        OO 

o 

0  ' 

l«  SPLICE  PLATE  > 

Fig.  14 

66,690  Ibs.,  which  equals  the  resistance  of  20  rivets.     We  must 
therefore  have  20  rivets  through  the  splice-plate  on  each  side  of 


Jo,r-  c 

0 

- 

oooooo 

0 

0        0000        0     ' 

0                                               0    C 

oooooo 

0 

000 

i  3-V-  

,. 

c 
<_  —  3-V—  -\ 

c 

<  -3-V  

0 

<-,V- 

u/ 

Fig.  15 

the  joint.     These  rivets  we  will  space  as  shown  in  Fig.  14,  which 
shows  the  under  side  of  the  splice-plate.     The  splice-plate  should 


634          RIVETED  PLATE   AND   BOX   GIRDERS. 

be  placed  close  to  the  end  of  the  lower  plate  as  shown  in  Fig.  13. 
The  joint  in  the  upper  flange  we  will  make  as  shown  by  Fig.  15, 
extending  the  outer  plate  2'  4"  beyond  a. 

Fig.  15  shows  one  end  of  the  girder,  drawn  according  to  the 
foregoing  calculations,  the  joint  in  the  upper  flange  being  at  the 
other  end. 

For  the  construction  of  the  girder  we  shall  require  the  following 
bill  of  quantities : 

DETAIL  OF  GIRDER. 

Load  100,000  Ibs.  uniformly  distributed.  Span  50'.  Depth  3'. 
Upper  flange.  Two  angles  5"X3i"X  1"  53  ft.  long. 

One  plate      12"X    \"  40' 11"  long. 

One  plate      12"X    J"   12'  1"  long. 

One  plate      12"  X    f"  30'  6"  long. 
Lower  flange.  Two  angles    5"X3J"Xi"  53  ft.  long 

One  plate      12"X   V  43'  3"  long. 

One  plate      12"  X    i"   9' 9"  long. 

One  plate      12"X    J"  28' 10"  long. 
Web Two  plates  36"  X   f"  26'  6"  long,  spliced. 

30  stiffeners  4"X4"X|"  angles  2'  11"  long. 

28  filler-plates  4"X  i"X29"  long. 

92  ft.  8  in.  of  4"X4"Xi"  angles  for  supporting 
floor-joist. 

Two  splice-plates    for  web    8"Xf"   29  in.  long. 

One  splice-plate  on  bottom  flange    12"Xi",  4  ft. 

8"  long. 
Rivets f  in.  in  diameter. 

EXAMPLE  II. — It  is  required  to  support  the  wall  shown  in  Fig. 
16  by  a  riveted  steel  box  girder  at  the  height  indicated.  Design 
the  girder. 

First  Step:  Loads. — The  first  step  towards  designing  the  girder 
will  be  to  determine  the  load.  The  space  under  the  lower  win- 
dows is  too  shallow  to  permit  of  the  weight  from  the  piers  being 
distributed  over  the  girder,  so  that  the  only  safe  calculation  is  to 
assume  that  the  weight  of  the  wall  between  the  lines  A  and  B  is 
concentrated  at  W1}  the  weight  of  wall  between  lines  B  and  C  at 
TT2,  and  so  on. 

We  will  assume  that  the  floor-joists  run  across  the  building  so 
that  only  the  weight  of  the  waU  will  be  supported  by  the  girder. 


&1VETED  PLATE  AND  BOX  GIRDERS.      635 


Allowing  200  Ibs.  as  the  weight  of  one  square  foot  of  a  21-inch 
wall  plastered  on  the  inside,  and  165  Ibs.  per  sq.  ft.  for  the  17-inch 
wall,  we  shall  have. 


Load  at  Wl 

'3"X 
'3"X40'-(2'3"X14'+3'2"X7')]X165=25;795  f   Ibs. 


i  [?'  ?"x  10'~T'><2'  3"]X2OQ r- •  - Z>3?9  i 33>145 


f? 


1<- 

K 
T 

q 

ffl 

'I 

y^- 

N 

x  — 

\ 

rj 

'11-  -^ 

t28*i 

T4 

J 
1 

1 

-5-3"- 

/r---7-l'—r 

F—^-H 

:-i 

'o'^  ci' 
F 
I 

s"-  —  > 

*' 

Tl 

o"> 

2 

1  > 

(4-6 

_ 

<2  10> 

T3 

i-6 

:       i 

i 

4 

GIRDER  ^ 

T 

Mof 



Fig.  16 

i 

Load  at  TT72 

=  j[7/4'/XH/-4r6X7'0//]X200= 8,366)  40,720 

J  L7/4''X40'-(4/6X14'+-4/9"X7')]Xl65=32,354J'    Ibs. 

Load  at  TK3=  that  at  W 2= 40,720  Ibs. 


636          RIVETED  PLATE  AND  BOX  GIRDERS. 


Load  at  TF4 

_  j  [4'  ll"XlO'-2'  3"X7']X200= 6,683  ; 

~  j  [4'  11"X40'-(2'3"X14'+3'2"X7')]=23,595  p 

Total  load  on  girder  = 144,863  Ibs. 

or  72.4  tons 

Approximate  weight  of  girder 

About  one-third  of  this,  or  say  1,600  Ibs.,  should  be  added  to  W2 
and  W3,  and  900  Ibs.  to  TFj  and  W±.  This  will  give  us  the  fol- 
lowing loads  applied  as  in  Fig.  17: 

TF,  W2  -ppr 

ja'efc 7V 4^ 7-V-- b 7-3: ; 

_< — ± £ I- 

\     a 

\r 


Fig.  17 


^=34,000  Ibs. ;        TF2-  42,300  Ibs. ; 
W3=  42,300  Ibs. ;         TF4=  31,200  Ibs. 

Second  Step:  To  Determine  Maximum  Bending-moment. — By 
means  of  the  formula  under  Case  VI.,  p.  269,  we  find  the 
bending-moment  (in  foot  Ibs.)  for  each  of  the  loads  to  be  as 
follows : 

.  -     TT7      34,000  XI' 6" X  23' 4"     ^Qcnf,    «c 
Bending-moment  for  Wl  =  —      ^  ^T'lT)77 —     "^  =  47^980  f t-"1os« 

,  ,     TT7      42,3QOX8/11//X15/11//    949nnnff   «. 
Bending-moment  for  T72  =  —      — 9  ,  ^^  „ —          =  242,000  ft.  -Ibs 

Ti7      42,300Xl6/3//X8/7//    9Q7        ,    ,, 
Bending-moment  for  W 3=  —      — 24/  1Q// —         =237,900 ft. -Ibs. 

TT.      31,200Xl/4^X23/6^  ., 

Bending-moment  f  or  TF4=  04/  1Q// —          =39,420  it. -Ibs. 

Platting  these  moments  to  a  scale,  as  explained  on  page  271,  we 


&IVETED   PLATE   AND  BOX  GIRDERS.         637 

get  the  diagram  shown  in  Fig.  17.*  The  maximum  bending- 
moment  is  at  W2,  and  its  amount  equals  the  line  bb,  which  scales 
418,000  ft.  -Ibs. 

Third  Step:  To  Determine  Flange  Area  and  Length  of  Cover- 
plates.  —  Before  we  can  determine  the  flange  area  wre  must  decide 
upon  the  height  of  the  web-plate.  As  we  have  plenty  of  room 
for  our  girder,  we  will  make  the  height  of  the  web-plate  30  in., 
or  about  j^th  of  the  span. 

Then  by  formula  (1), 

Gross  area  of  upper  flange  =  x-K--^     -—  or  very  nearly  14  sq.  in.  ; 

^,000 


Net  area  of  lower  flange  =  —  ——       —  -  or  13  sq.  in. 

<6.OX  lO,(J(J(J 

As  the  thickness  of  the  wall  to  be  supported  is  21  inches,  we  will 
use  flange-plates  20  in.  wide.  The  least  thickness  of  cover-plate 
that  we  should  use  is  |  in.  The  area  of  a  f  X  20-inch  plate  is  7  J 
sq.  in.,  which  leaves  6J  sq.  in.  to  be  made  up  by  the  angles.  The 
area  of  two  §"X3J"Xj£"  angles  is  7.06,  which  gives  a  little 
excess  for  the  top  flange.  In  the  lower  flange  we  must  allow  for 
two  j-inch  rivet-holes  in  both  the  plate  and  angles.  From 
Table  I.,  we  find  that  the  area  to  be  deducted  for  two  f"  rivets, 
in  a  f"  plate,  is  0.65,  and  in  a  %-inch  plate  0.76  or  1.41  sq.  in.  in 
all.  The  gross  area  of  the  plate  and  angles  is  7J+7.06=14.56 
sq.  in.  Deducting  1.41  sq.  in.,  we  have  13.15  sq.  in.  for  net  area 
of  bottom  flange,  which  is  just  above  what  we  require. 

We  will  therefore  use  the  same  size  of  plate  and  angles  in  both 
flanges.  As  the  width  of  the  flange  is  more  than  one-twentieth 
of  the  span,  the  girder  will  not  require  lateral  support. 

Fourth  Step:  Web  and  Stiff  encrs.  —  The  least  thickness  that 
should  be  used  for  the  web-plates  is  §  in.  We  will  therefore  first 
determine  if  this  thickness  is  sufficient  to  resist  the  shearing 
stress. 

The  maximum  shearing  stress  will  be  at  the  left-hand  support, 
and  will  equal  the  reaction  of  that  support.  This  reaction  we 
must  determine  by  formula  (2),  page  275,  or 

(  34,000X23'  4"+  42,300X15'  11" 
Pl==  \  +42,300X8'  7"+  31,  200  XI7  4"  ,  =  75,450  Ibs. 

(  24'  10"  ) 

As  there  are  two  web-plates,  the  shearing  force  to  be  resisted 
by  each  plate  will  be  one-half  of  this,  or  37,725  Ibs.  From  Table 

*  The  ben  ding-moments  in  this  diagram  are  drawn  to  the  scale  of  400,000 
ft.  -Ibs.  to  the  inch. 


638         RIVETED  PLATE  AND  BOX  GIRDERS. 

II.  we  find  that  the  resistance  of  a  steel  plate  f  X30  in.  to  shear, 
ing  is  78,750  Ibs.,  or  twice  as  great  as  the  stress.     From  Table 

III.  we  find  the  safe  resistance  to  buckling,  deducting  for  two 
J-inch  rivets,  is  33,830  Ibs.     As  this  is  a  little  less  than  the  shear, 
we  will  place  4X4  stiffeners,   2'  4"  from   each   support,  and  5 
between  them,  about  3'  4"  on  centres. 

[NOTE. — If  our  loads  were  really  concentrated  at  the  points  Wl9 
W2,  etc.,  as  by  the  action  of  column  or  girder,  it  would  be  neces- 
sary to  put  stiffeners  at  each  of  those  points,  and  two  in  each  of 
the  7-foot  spaces.  But  as  in  this  case  the  load  is  partially  dis- 
tributed it  will  be  better  to  space  them  as  above  indicated.] 

There  will  also  be  two  stiffeners  over  each  support. 

The  only  remaining  point  to  determine  is  the 

SPACING  OF  RIVETS. 

We  will  first  determine  the  number  of  rivets  in  the  web  leg  of 
angle,  between  Wt  and  left-hand  end.  The  bending-moment  at 
W1  is  found  by  scaling  the  line  aa,  which  gives  110,000  Ibs. 
This  divided  by  the  height  of  the  girder  gives  44,000  Ibs.,  which 
is  the  horizontal  flange  strain  at  that  point.  As  there  are  two 
webs,  only  one-half  of  this  strain,  or  22,000  Ibs.,  will  come  on  one 
angle.  The  rivets  in  this  case  will  be  in  single  shear.  From 
table  on  page  371,  we  find  that  the  resistance  of  a  f  rivet  to  single 
shear  is  3,310  Ibs.,  and  the  bearing  value  on  a  f"  plate  4, 220  Ibs. 
The  resistance  to  shearing  will  therefore  determine  the  number  of 
rivets.  22,000-^-3,310  gives  7  as  the  number  of  rivets  required 
in  the  web  leg  of  each  angle  between  Wl  and  the  left-hand  end 
of  girder.  This  distance  is  40  in.,  which  would  make  the  pitch 
about  5J  in. 

Over  the  bearings,  however,  the  pitch  ought  not  to  exceed 
4  in. ;  we  will  therefore  increase  the  number  of  rivets  to  12, 
spacing  the  first  six  3f  in.  on  centres,  and  the  next  seven  4  in. 
on  centres. 

We  will  next  determine  the  number  of  rivets  between  Wl  and 

418  000 

W2.     The  horizontal  flange  strain  at  W2=  — ^~^=  167,200  Ibs., 

^.  o 

and  one-half  of  this  is  83,600  Ibs.  Dividing  83,600  by  3,310,  we 
have  26  as  the  number  of  rivets  required  between  W2  and  the 
left-hand  end  of  girder.  As  we  have  already  put  in  12  rivets 
we  shall  only  need  26  —  12  or  14  rivets  between  Wj_  and  W2  to 
resist  the  horizontal  strain.  This  distance  is  89  in.,  which 
divided  by  14  gives  6y\  in.  for  the  pitch.  As  for  practical  reasons 


RIVETED   PLATE  AND  BOX  GIRDERS. 


639 


the  pitch  should  not  exceed  6  in.,  we  will  give  the  rivets  that  pitch 
from  TJ7!  to  the  corresponding  distance  from  the  other  end,  mak- 
ing both  ends  of  the  girder  alike. 

Theoretically  the  number  of  rivets  between  W2  and  the  right- 
hand  end  should  be  the  same  as  on  the  other  side  of  W2,  and 
most  of  these  would  be  required  at  the  right  of  W3,  but  in  this 
case  the  number  of  rivets  is  determined  by  the  maximum  pitch. 

The  number  of  rivets  theoretically  required  in  the  flange  leg 
of  angle  equals  the  safe  strength  of  plate  divided  by  3,310.  The 
safe  strength  of  a  f  X20  inch  plate  at  13,000  Ibs.  unit  stress = 
13,000X1X20  =  97,500  Ibs.  This  divided  by  3,310  gives  30 
rivets  for  both  angles.  As  this  number  is  so  small,  we  must  be 
guided  by  the  rule  of  maximum  pitch,  and  will  use  the  same 
number  of  rivets,  less  one,  as  in  the  web  leg,  staggering  the  rivets. 

The  girder  will  then,  be  detailed  as  below : 


DETAIL  OF  GIRDER. 


CfjO~0~0~Ol 

0 

-xo"xo"o"o^o"o 

0 

"  0    ~   0 

0 

o 

o 

o 

6 

0 

0 

o 

o 

0 

0 

0 

o  p^o^o^p 

0 

£0O0O^O^O^  O 

0 

0         0 

Fig.1* 

Loads  34,000  Ibs.   1'    6"  from  left  support.     Span  24' 10". 
"     42,300    "     8'  11"  from  left  support.     Depth  30". 
"     42,300    "     8'    7"  from  right  support. 
"      31,200    "     1'    4"  from  right  support. 
Both  flanges :  4  angles,  5'  X  31"  X  %",  27'  6"  long. 

One  plate,  20"Xf",  27'  6"  long. 
Two  webs,  |"X30",  27'  6"  long. 
22  stiffeners,  4"X4"Xf",  29J"  long. 
22  filler-plates,  4"X  %",  23"  long. 
Rivets,  J  inch  diameter. 

By  the  rules  and  examples  above  given  it  is  possible  to  com- 
pute the  necessary  dimensions  and  details  for  riveted  girders 
under  any  conditions  of  loading.  If  further  examples  are  desired, 
the  reader  is  referred  '  to  "  Compound  Riveted  Girders,"  by 
William  H.  Birkmire,  in  which  eight  different  examples  of  load- 
ing are  fully  worked  and  explained. 


640 


RIVETED    PLATE   AND   BOX   GIRDERS. 


Detail  drawings,  with  strain  diagrams  of  one  of  the  heaviest 
plate  girders  ever  used  in  building  construction,  are  given  in  the 
Engineering  Record  of  Dec.  28,  1895.  This  girder  is  one  of  six 
plate  girders  used  in  the  construction  of  the  Tremont  Temple, 
Boston,  Mass.,  Messrs.  Blackall  &  Newton,  architects.  The 
girder  is  75  ft.  long  between  centres  of  columns  6  ft.  1  in.  high, 
with  flanges  28  in.  wide,  and  was  calculated  to  support  distributed 
and  concentrated  loads  aggregating  497.5  tons.  The  single  web- 
plate  is  64 J  in.  high,  and  |  in.  thick  at  the  ends;  the  flanges  are 
4i  in.  thick  at  centre;  flange  angles,  G"X8"X1". 


TABLE  I.— SECTIONAL  AREA  TO  BE  DEDUCTED  FROM 
PLATES  AND  ANGLES    FOR   RIVET-HOLES. 

(HIRKMIRE.) 
Taken  ^  inch  in  excess  of  diameter  of  rivet. 


Number  of  rivets,  1  inch 

Number  of  rivets,  Kinch 

Thickness  of 

diameter. 

diameter. 

1 

2 

3 

4 

1 

2 

3 

4 

1 

1.12 

2.25 

3.37 

4.50 

1  .00 

2.00 

3.00 

4.00 

15/16 

1.05 

2.10 

3.16 

4.21 

0.94 

1.87 

2.81 

3.75 

7/8 

0.98 

1.97 

2.95 

3.93 

0.87 

1.75 

2.62 

3.50 

13/16 

0.91 

1.83 

2.74 

3.65 

0.81 

1.62 

2.44 

3.25 

3/4 

0.84 

1.69 

2.53 

3.37 

0.75 

1.50 

2.25 

3.00 

il/16 

0.77 

1.55 

2.32 

3.09 

0.69 

1.37 

2.06 

2.75 

5/8 

0.70 

1.41 

2.11 

2.81 

0.62 

1.25 

1.87 

2.50 

9/16 

0.63 

1.26 

1.90 

2.53 

0.56 

1.12 

1.69 

2.25 

1/2 

0.56 

1.11 

1.69 

2.25 

0.50 

1.00 

1.50 

2.00 

7/16 

0.49 

0.98 

1.47 

1.97 

0.44 

0.87 

1.31 

1.75 

3/8 

0.42 

0.84 

1.26 

1.69 

0.37 

0.75 

1.12 

1.50 

Thickness  of 
plate. 

Number  of  rivets,  %  inch 
diameter. 

Number  of  rivets,  £-£  inch 
diameter. 

1 

o 

3 

4 

1 

2 

3 

4 

1 

0.87 

1.75 

2.62 

3.50 

0.75 

1.50 

2.25 

3.00 

15/16 

0.82 

1.64 

2.46 

3.28 

0.70 

1.40 

2.11 

2.81 

7/8 

0.77 

1.53 

2.30 

3.06 

0.65 

1.31 

1.96 

2.62 

13/16 

0.71 

1.42 

2.13 

2.84 

0.61 

1.22 

1.83 

2.44 

3/4 

0.66 

1.31 

1.96 

2.02 

0.56 

1.12 

1.69 

2.25 

11/16 

0.60 

1.20 

1  .80 

2.40 

0  51 

1.03 

1.54 

2.06 

5/8 

0  .  55 

1.09 

1.64 

2.19 

0.47 

0.94 

1.41 

.88 

9/16 

0.49 

0.98 

1.48 

1.96 

0.42 

€.84 

1.26 

.69 

1/2 

0.43 

0.87 

1.31 

1.75 

0.37 

0.75 

1.12 

.50 

7/16 

0.38 

0.76 

1.15 

1  .  53 

0.33 

0.66 

0.98 

.31 

3/8 

0.32 

0.65 

0.98 

1.31 

"0.28 

0.56 

0.84 

.12 

5/16 

0.27 

0  .  55 

0.82 

1  .09 

0.23 

0.47 

0.70 

0.94 

1/4 

0.22 

0.44 

0.66 

0.87 

0.18 

0.37 

0.56 

0.75 

RIVETED  PLATE  AND  BOX   GIRDERS.         641 

TABLE   II.— SHEARING  VALUE    OF    WEB-PLATES    IN 
POUNDS. 

Wrought  Steel.     Gross  Area.     Unit  Stress  7,000  Ibs. 


Depth  in 
inches. 

Thickness  in  inches. 

3/8 

7/16 

1/2 

9/16 

5/8 

3/4 

7/8 

28 
30 
32 
3F> 
10 
42 
10 
48 

73,500 
78,750 
84,000 
94,500 
105,000 
110,250 
120,750 
126,000 

85,750 
91,875 
98,000 
110,250 
122,500 
128,625 
140,875 
147,000 

98,000 
105,000 
112,000 
12o,000 
140,000 
147  ,000 
161,000 
168,000 

110,250 
118,125 
126,000 
141,750 
157,500 
165,375 
181,125 
189,000 

122,500 
131,250 
140,000 
157,500 
175,000 
183,750 
201,250 
210,000 

147,000 
157,5uO 
168,000 
189,000 
210,000 
220,500 
241,500 
252,000 

171,500 
183,750 
196,000 
220,500 
245,000 
257  ,250 
281,750 
294,000 

Deduct  for  one  3<±-inch  rivet. 

2,240 

2,660 

3,010 

3,430 

3,850 

4,620 

5,390 

Deduct  for  one  7/s-inch  rivet. 

2,625 

3,080 

3,500 

3,920 

4,375 

5,250 

6,125 

EXAMPLE. — What  is  the  safe  shearing  value  of  a  36" 
web-plate  \yith  seven  f-inch  rivets  in  stiffeners? 

Answer. — Gross  shearing  value  =94,500  Ibs. 
Deduct  for  7  rivets  7X2,240     =15,680  " 


Safe  resistance 


=  78,820  Ibs. 


642         RIVETED  PLATE   AND  BOX  GIRDERS. 


TABLE  III.— SAFE  BUCKLING  VALUE  OF  WEB-PLATES 
IN  POUNDS  PER  SQUARE  INCH. 

Calculated  by  formula  p=     1000J,    . 

1+  3000*2 
d  =  depth  in  inches,     t  =  thickness  in  inches. 


£  • 

Thickness  in  inches. 

£§ 

3/8 

7/16 

1/2 

9/16 

5/8 

3/4 

7/8 

28 

3,498 

4,228 

4,890 

5,476 

5,932 

30 

3,192 

3,896 

4,546 

5,133 

5,656 

6,522 

32 

2,889 

3,624 

4,228 

4,787 

5,339 

6,226 

6,920 

36 

2,456 

3,069 

3,666 

4,229 

4,748 

5,656 

6,392 

40 

2,087 

2,696 

3,191 

3,724 

4,228 

5,133 

5,882 

42 

1,930 

2,455 

2,983 

3,498 

3,992 

4,889 

5,649 

48 

1,548 

1,994 

2,543 

2,918 

3,371 

4,228 

4,992 

TOTAL   RESISTANCE    FOR    PLATES   WITH   TWO    f  "   RIVETS. 


Depth  in 
inches. 

Thickness  in  inches. 

3/8 

34,450 

33,830 
31  ,560 
29,140 
26,860 

7/16 

1/2 

9/16 

5/8 

97,340 
99,880 
101,750 
100,440 
97,450 

3/4 

138,200 
145,300 
147,600 
146,670 

7/8 

191,570 
198,960 
202,000 

28 
30 
36 
42 
48 

48,580 
48,150 
46,000 
43,230 
40,360 

64,200 
64,230 
62,800 
60,040 
58,820 

80,880 
81,560 
81,500 
79,190 
75,920 

TOTAL   RESISTANCE    TOR    PLATES    WITH   TWO    }"   RIVETS. 


J>J 

•SJi 

Thickness  in  inches. 

a  « 
&* 

3/8 

7/16 

1/2 

9/16 

5/8 

3/4 

7/8 

28 

34,100 

48,110 

63,570 

80,100 

96,390 

30 

33,510 

47,720 

63,640 

80,840 

98,980 

136,960 

b6 

31,310 

45,660 

62,320 

80,900 

100,690 

144,230 

190,170 

•*2 

*8 

°8,950 
26,700 

42,960 
40,140 

59,660 
58,490 

78,700 
75,520 

99,800 
96.910 

146,690 
145,860 

197.710 
200,93D 

RIVETED  PLATE  AND   BOX   GIRDERS.         643 


Tables  of  Riveted  Steel  Plate  and  Box  Girders. 

The  tables  on  pages  644-647,  giving  the  greatest  safe  dis- 
tributed load  that  should  be  imposed  on  the  girders  were  com- 
puted by  the  author  in  accordance  with  formula  (la),  using 
13,000  Ibs.  fibre  strain  and  deducting  for  two  f-inch  holes  (for 
f-inch  rivets)  in  flange-plates  and  angles. 

From  the  safe  load  given  by  the  formula  the  weight  of  the  girder 
between  supports  has  been  subtracted. 

The  sizes  given  are  those  most  commonly  found  in  buildings. 

The  weight  per  foot  should  be  considered  as^a  close  approxi- 
mation only;  it  is  intended  to  include  rivets  and  stiffeners, 
where  required. 

These  tables  should  be  used  only  for  determining  the  size  of 
girder  and  thickness  of  the  plates  and  angles.  Rivet  spacing 
should  be  determined  in  each  case  by  the  rules  previously  given, 
and  also  the  number  and  position  of  stiffeners.  For  distributed 
loads  below  the  heavy  cross-lines  stiffeners  will  not  be  required. 
It  should,  however,  be  remembered  that  stiffeners  are  always 
required  at  the  ends  of  the  girders,  as  shown  in  Figs.  15  and  18. 

These  tables  may  also  be  used  to  serve  as  a  check  on  special 
calculations  for  other  girders.  //  more  than  two  rivet-holes  occur 
in  any  given  cross-section  of  the  bottom  flange,  then  the  safe 
load  must  be  decreased  accordingly. 

The  loads  given  in  the  second  column  of  the  tables  are  for  the 
least  thickness  of  flange -plates  that  should  be  used.  This  thick- 
ness may  be  increased  as  required  to  give  the  desired  strength  to 
the  girder,  thus :  If  we  wish  to  carry  a  distributed  load  of  47 
tons,  with  a  span  of  35  feet,  with  a  girder  of  the  dimensions  given 
for  girder  A,  we  must  increase  the  thickness  of  the  flange-plates 
sufficient  to  take  difference  between  47  and  38.12  tons  or  8.88 
tons.  This  will  require  an  increase  of  -f^  or  J  inch  in  both  top 
and  bottom  flange. 

It  is  not  desirable  to  use  girders  of  these  dimensions  for  greater 
spans  than  those  given  in  the  table 

The  tables  on  pages  648-650  are  from  the  manual  of  the 
Passaic  Rolling  Mill  Co.,  prepared  by  Geo.  H.  Blakeley,  O.E. 
It  should  l)e  noted  that  they  are  based  on  a  fibre  stress  of  15,000 
Ibs.  per  sq.  inch,  and  that  they  include  weight  of  girders. 


644         RIVETED  PLATE  AND   BOX  GIRDERS. 


STEEL  PLATE  GIRDERS. 
SAFE  LOADS  IN  TONS  UNIFORMLY  DISTRIBUTED. 

See  explanation,  page  643. 


»! 

_r> 

"Crr» 

K 

r\ 

7      ll-fl 

>! 

^1 

*-**-- 

•W-jjjJJ 

Afli 

B  |||;l 

d 

=S= 

Lex 
—  -CT- 

I  1} 

fi 

J 

-o  — 

\ 

li  r>> 

CT- 

L       fcfc^l 

Safe 

iTicrease  in 
safe  load  for 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

Span 
feet 

in 

applied 
load,  in 

Vic"  increase 
in  thickness 

applied 
load,  in 

Vie"  increase 
in  thickness 

tons. 

of  flange- 

tons. 

of  flange- 

plates. 

plates. 

20 

69.80 

4.16 

20 

76.81 

4.57 

21 

66.33 

3.96 

21 

73.00 

4.36 

22 

63  .  17 

3.78 

22 

69.52 

4.16 

23 

24 

60  .  27 

57.82 

3.61 
3.46 

23 
24 

66.34 
63.42 

3.98 
3.81 

25 

55.16 

3.33 

25 

60.72 

6  .  66 

26 

52.90 

3.20 

26 

58.22 

3.52 

27 

50.79 

3.08 

27 

55.91 

3.39 

28 

4£ 

S.83 

2.97 

28 

>.75 

3.27 

29 

4' 

r.oo 

2.87 

29 

51.74 

3.15 

30 

4. 

5.28 

2.77 

30 

4£ 

).86 

3.05 

31 

43  .  68 

2.68 

31 

48.09 

2.95 

32 

42.17 

2.60 

32 

46.43 

2.86 

33 

4( 

).74 

2.52 

33 

4^ 

1.86 

2.77 

34 

39.40 

2.44 

34 

43.38 

2.69 

35 

3* 

5.12 

2.38 

35 

41 

98 

2.61 

36 

36.92 

2.31 

36 

40.66 

2.54 

37 

3, 

5.77 

2.25 

37 

).12 

2.46 

38 

34.69 

2.19 

38 

3* 

5.20 

2.41 

39 

3,' 

5.66 

2.13 

39 

37 

'.06 

2.35 

40 

32.66 

2.08 

40 

35.97 

2  29 

Max.  load  for  Y<j'  web,  86.94  tons. 

Max.  load  for 

H"  web,  94.  43  tons. 

Loads  above  heavy  cross -line  require  stiffeners. 


RIVETED   PLATE   AND   BOX   GIRDERS. 


645 


STEEL  PLATE   GIRDERS. 
SAFE  LOADS  IN  TONS  UNIFORMLY  DISTRIBUTED. 

See  explanation,  page  643. 


«c 

d3= 

i 

-—  Q- 

r  M 

*£ 

_o_ 

-Cn- 

n 

rncr- 
1 

?        Js|4 

a?1  f^ 

rfsj 

4  tCo" 

^    !^M  §          ' 

C     ^xf 

D   ,T<8x 

S?5805N  & 

V'v     ^       A 

. 

x*^5o-*» 

•^x^'fcjo 

c 

L 

b*x[f> 

JJ 

,             ^v  ^'53 

t£ 

U     "^ 

•3.               CO  <M  v    '<D 

t* 

u   "    u- 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

applied 
load,  in 

V\Q"  increase 
in  thickness 

applied 
load,  in 

^Q"  increase 
in  thickness 

tons. 

of  flange- 

tons. 

of  flange- 

plates. 

plates. 

20 

83. 

88 

4.99 

24 

81. 

02 

4.85 

24 

69. 

28 

4.16 

26 

74. 

45 

4.48 

26 

63. 

63 

3.84 

28 

68. 

78 

4.16 

28 
30 
31 

,>8. 
54. 
52. 

76 
52 
60 

3  .  56 
3.33 
3.22 

30 
31 
32 

63. 
61. 
59. 

85 
61 
51 

3.88 
3.75 
3  .  64 

32 

50. 

78 

3.12 

33 

57. 

53 

;-j    5,-j 

33 

49. 

08 

3.02 

34 

55. 

66 

3i42 

34 

47. 

48 

2.93 

35 

53. 

89 

3.32 

35 

45. 

95 

2.85 

36 

52. 

21 

3.23 

36 

44. 

51 

2.77 

37 

50. 

63 

3.15 

37 

43. 

14 

2.70 

38 

49. 

11 

3.06 

38 

41. 

84 

2.63 

39 

47. 

68 

2.98 

39 

40. 

59 

2.56 

40 

46. 

31 

2.91 

40 

39. 

42 

2.49 

41 

45. 

00 

2.84 

41 

38. 

29 

2.43 

42 

43. 

75 

2.77 

42 

37. 

21 

2  37 

44 

41. 

41 

2.64 

44 

35. 

19 

2.27 

46 

39. 

26 

2.53 

46 

33. 

34 

2.17 

48 

37. 

27 

2.42 

48 

31. 

83 

2.08 

50 

35. 

43 

2.33 

50 

30. 

02 

1.99 

55 

31. 

35 

2.11 

Max.  load  for 

1A"  web,  104  tons. 

Max. 

load  for 

Vz'  web,  122  tons. 

Max.  load  for  %Q"  web,  117  tons. 

Max. 

load  for 

Y§'  web,  152  tons 

Loads  above  heavy  cross-line  require  stiffeners. 


646         RIVETED  PLATE  AND  BOX  GIRDERS. 

STEEL  BOX  GIRDERS. 
SAFE  LOADS  IN  TONS  UNIFORMLY  DISTRIBUTED. 

See  explanation,  page  643. 


1 

=g== 

r== 

=^ 

'  ill 

c 

^ 

)       < 

—  C,  

'   ill 

c 

=^} 
—  <^  — 

c 

I 

—  o-^ 

.  it 

t 

c 
—v  — 

c 

k 

—  CT— 

^°°  a 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

applied 
load,  in 

y\%"  increase 
in  thickness 

applied 
load,  in 

VIQ"  increase 
in  thickness 

tons. 

of  flange- 

tons. 

of  flange- 

plates. 

plates. 

20 

69.60 

5.78 

20 

83  .  56 

6.94 

21 

06.13 

5.51 

24 

68.90 

5.78 

22 

62.95 

5.26 

2 

3 

63.21 

5  .  34 

23 

60.04 

5.03 

28 

58.31 

4  .  9G 

9 

5 

7  .51 

3 

4.82 

3( 

) 

54 

.04 

4.62 

25 

54.91 

4.63 

31 

52.10 

4  .  48 

26 

52  .  64 

4.45 

32 

50  .  27 

4  .  34 

27 

5 

3.5: 

I 

4.28 

3, 

3 

48 

.55 

4  20 

28 

48  .  55 

4.13 

34 

46.93 

4  .  08 

2< 

) 

4 

3.7( 

} 

3.99 

3 

3 

45 

.39 

3.96 

30 

44.98 

3.85 

36 

43 

.93 

3.85 

31 

43  .  36 

3.73 

37 

42  .  55 

3.75 

35 

I 

4 

1.8 

\ 

3.61 

3 

* 

41 

.21 

3  .  65 

33 

40  .  40 

3  .  50 

39 

39.97 

3  .  56 

3- 

t 

3 

9.0 

5 

3.40 

4 

3 

3£ 

,.78 

3.47 

35 

37.76 

3  .  30 

41 

37 

.63 

3.38 

36 

36.55 

3.21 

42 

36  .  54 

3  .  30 

1 

3 

5.3 

3 

3.12 

4 

1 

3^ 

L4f 

3.15 

38 

34  .  30 

3.04 

46 

32.60 

3  02 

3 

) 

3 

3.2 

2.96 

4 

8 

3] 

L.Of 

2.89 

40 

32.2 

5 

2.89 

50 

29.22 

2.77 

Max.  load  for  ?  £ 

'  webs,  130  tons. 

Max.  load  for  ?i 

'  webs,  157  tons. 

Loads  above  heavy  cross-line  require  stiffeners. 


RIVETED  PLATE  AND  BOX   GIRDERS. 

STEEL  BOX  GIRDERS. 
SAFE  LOADS  IN  TONS  UNIFORMLY  DISTRIBUTED. 

See  explanation,  page  643. 


647 


r-^- 

JJus 

c 

•^                      n 
"^r\||          li  iTcr- 

f      lid 

In 

Cj1^  Cr-H 

• 

lift 

SI»S 

«  l|x| 

H  H?t 

*= 

)      \\\^ 

•v 

•  S| 

1 

w    c 

-*=>  cr— 

,   li 

Safe 

Increase  in 
safe  load  for 

Span  in 
feet. 

Safe 

Increase  in 
safe  load  for 

Span 
feet 

m 

applied 
load,  in 

^ie"  increase 
in  thickness 

applied 
load,  in 

^ie"  increase 
in  thickness 

tons. 

of  flange- 

tons 

of  flange- 

plates. 

plates. 

20 

93. 

75 

7.41 

20 

120.49 

8.89 

21 

89. 

08 

7.06 

2 

4 

99.5 

1 

7.41 

22 

84. 

83 

6.73 

26 

91.43 

6.84 

23 

80. 

93 

6.44 

2 

8 

84.4 

5 

6.35 

24 

77. 

35 

6.17 

30 

78.36 

5.92 

25 

74. 

05 

5.95 

3 

1 

75.6 

3 

5.73 

26 

70. 

99 

5.70 

32 

73.00 

5.55 

97 

68. 

16 

5.49 

3 

3 

70.5 

5.39 

28 

65. 

51 

5.29 

34 

68.2 

5.23 

29 
30 
31 
32 

60.' 
58. 
56. 

05 
73 
56 
53 

o.ll 
4.94 
4.78 
4.63 

35 
36 
37 
38 

66  .  0V 
64.00 
62.03 
60.18 

5.08 
4.94 
4.80 

4.68 

33 

54. 

60 

4.49 

39 

58  .  40 

4.56 

34 

52. 

80 

4.36 

40 

56.70 

4.44 

35 

51. 

07 

4.23 

4 

1 

55.0 

3 

4.34 

36 

49. 

44 

4.11 

42 

53  .  54 

4.23 

37 

47. 

90 

4.00 

4 

4 

50.6 

5 

4.04 

38 

46. 

43 

3.90 

46 

47.98 

3.86 

39 

45. 

03 

3.80 

4 

8 

45.5 

2 

3.70 

40 

43. 

69 

3.70 

5 

0 

43  .  24 

3.55 

Max. 

Load  for  % 

j"  webs,  130  tons. 

Max.  load  for  % 

'  webs,  157  tons. 

Loads  above  heavy  cross-line  require  stiffeners. 


648         RIVETED   PLATE  AND  BOX  GIRDERS. 


STEEL  PLATE  GIRDERS. 

PASSAIC    ROLLING    MILL    CO. 

SAFE  LOADS  IN  TONS  OF  2,000  LBS.    UNIFORMLY  DISTRIBUTED. 


No  stiffeners  required 

except  at  ends,  over 

supports  only. 


Girders  equivalent  to 
a  24"  I  beam. 


Web  

24") 

<%" 

26": 

$r 

28": 

<w 

30" 

*'4'' 

Angles  

5    X3.. 

X,2 

X    A 

Xi, 

6    X3A 

X/8 

5    X3 

\/8 

-    ^ 

-  ^ 

v     ^ 

-  ^ 

c 
_o 

?I4 

1 

?•!•§ 

c 

5 

?!! 

QQ 

c 

O 

111 

Span,  centres 

T3 

*2  ^  S 

T3 

«2  c  § 

«H  £  § 

*£  c  § 

of  bearings, 

c3 

*  $*o 

08 

0    ^q-* 

m 

§"            «4H 

s 

§"'          «41 

feet. 

J2 

r2 

03    Jg    ° 

^ 

C 

0 

C 

M 

c3 
QQ 

II  1 

0> 

o  ^  <i> 

i 

II1 

<£ 

K 

OQ 

||    1 

20 

47.2 

5.3 

46.5 

5.8 

45.1 

6.2 

47.7 

6.4 

21 

44.9 

5.0 

44.3 

5.5 

42.9 

5.9 

45.5 

6.1 

22 

42.9 

4.8 

42.3 

5.2 

41.0 

5.7 

43.4 

5.8 

23 

41.0 

4.6 

40.4 

5.0 

39.2 

5.4 

41.5 

5.5 

24 

39.3 

4.4 

38.8 

4.8 

37.6 

5.2 

39.8 

5.3 

25 

37.7 

4.2 

37.2 

4.6 

36.1 

5.0 

38.2 

5.1 

26 

36.3 

4.1 

35.8 

4.4 

34.7 

4.8 

36.7 

4.9 

27 

34.9 

3.9 

34.4 

4.3 

33.4 

4.6 

35.4 

4.7 

28 

33.7 

3.8 

33.2 

4.1 

32.2 

4.5 

34.1 

4.5 

29 

32  .  5 

3.6 

32.1 

4.0 

31  .  1 

4.3 

32.9 

4.4 

30 

31,4 

3.5 

31.0 

3.8 

30.0 

4.2 

31.8 

4.2 

31 

30.4 

3.4 

30.0 

3.7 

29.1 

4.0 

30.8 

4.1 

32 

29.4 

3.3 

29.1 

3.6 

28.2 

3.9 

29.8 

4.0 

33 

28.6 

3.2 

28.2 

3.5 

27.3 

3.8 

28.9 

3.9 

34 

27.7 

3.1 

27.4 

3.4 

26.5 

3.7 

28.1 

3.7 

35 

26.9 

3.0 

26.6 

3.3 

25.8 

3.6 

27.3 

3.6 

36 

26.2 

2.9 

25.8 

3.2 

25.0 

3.5 

26.5 

3.5 

37 

25.5 

2.8 

25.1 

3.1 

24.4 

34 

25.8 

3.4 

38 

24.8 

2.8 

24.5 

3.0 

23.7 

3.3 

25.1 

3.3 

39 

04  2 

2.7 

23.8 

2.9 

23.1 

3.2 

24.5 

3.3 

40 

23.6 

2.6 

23.3 

2.9 

22.5 

3.1 

23.9 

3.2 

Weight  per 
foot,  Ibs. 

88 

7.2 

84 

7.2 

79 

7.2 

79 

6.8 

Safe  loads  given  include  weight  of  girder. 

Weights  of  girders  given  include  weight  of  rivet  heads,  but  not  stif- 
feners. 

Maximum  fibre  strain,  15,000  Ibs.  per  square  inch  of  net  area,  holes  for 
%"  rivets  being  deducted. 


RIVETED  PLATE  AND  BOX   GIRDERS. 
STEEL  PLATE  GIRDERS. 


649 


PASSAIC    ROLLING    MILL    CO. 


SAFE  LOADS  IN  TONS  OF  2,000  LBS.  UNIFORMLY  DISTRIBUTED. 


No  stiffeners  required 

except  at  ends,  over 

supports  only. 


Girders  equivalent  to 
two  24"  I  beams. 


Web 

24"X9/i6" 

26"X9/i6// 

28"  X  1A" 

30"  X  1A" 

\ngles 

5"  X  5"  X  V<>" 

5"X5"X7/iG" 

5"  X  5"  X  W 

5"  X  5"  X  3/s" 

Plates.  . 

12"  X  Vf' 

12"  X  W 

12"  XM" 

12"X3xi" 

. 

^ 

^ 

CO 

^ 

CO 

^•4 

c 

a 

C 

C 

3 

5-1  ^  ~C3 

0 

iT+a  •*•* 

c 

'»-la"oS 

7,  -5  tg 

Span,  centres 

•^.a  a 

1-3" 

•2  .S3, 

J 

^.S'E 

- 

«S  53, 

of  bearings, 

cs3 

I 

c3 

P     014-c 

ft;  «J**-" 

feet. 

,2 

^  o3  ^ 

sS  c§  ° 

r2 

Co    r§    ° 

0 

OJ    c§    ° 

O 

o 

L   &  cr 

a) 

S  g  * 

Q/ 

£  £  * 

1 

si* 

a 

C  G  fl 

c3 
02 

1 

|JS 

20 

90.8 

3  .  6 

93.6 

3.9 

93.6 

4.3 

91.7 

4.6 

21 

86.5 

3.4 

89.1 

3.7 

89.1 

4.1 

87.3 

4.3 

22 

82.5 

3.3 

85.1 

3.6 

85.0 

3.9 

83.4 

4.1 

23 

78.9 

3.1 

81.3 

3.4 

81.3 

3.7 

79.7 

3.9 

24 

75.6 

3.0 

78.0 

3.3 

78.0 

3.6 

76.4 

3.8 

25 

72.6 

2.9 

74.8 

3.1 

74.8 

3.4 

73.3 

3.6 

26 

69.8 

2.8 

72.0 

3.0 

72.0 

3.3 

70.5 

3.5 

27 

67.2 

2.7 

69.3 

2.9 

69.3 

3.2 

67.9 

3.4 

28 

64.8 

2.6 

66.8 

2.8 

66.8 

3.1 

65.5 

3.3 

29 

62.6 

2.5 

64  .  5 

2.7 

64.5 

3.0 

63.2 

3.1 

30 

60.5 

2.4 

62.4 

2.6 

62.4 

2.9 

(H.I 

3.0 

31 

58.6 

2.3 

60.4 

2.5 

60.4 

2.8 

59.2 

2.9 

32 

56.7 

2.2 

58.5 

2.5 

58  .  f> 

2.7 

57.3 

2.8 

33 

55.0 

2.2 

56.7 

2.4 

56.7 

2.6 

55  .  6 

2.8 

34 

53.4 

2.1 

55.0 

2.3 

55  .  0 

2.5 

53.  » 

2.7 

35 

51.9 

2.0 

53.5 

2.3 

53.5 

2.4 

52.4 

2.6 

36 

50.4 

2.0 

52.0 

2.2 

52.0 

2.4 

50.9 

2.5 

37 

49.1 

1.9 

50.6 

2.1 

50  .  6 

2.3 

49.6 

2.5 

38 

47.8 

1.9 

49  2 

2.1 

49.2 

2.3 

48.3 

2.4 

39 

46.6 

1.8 

48.0 

2.0 

48.  0 

2.2 

47.0 

2.3 

40 

45.4 

1.8 

46.8 

2.0 

46.8 

2.1 

45.8 

2.3 

Weight  per 
foot,  Ibs. 

158 

5.1 

153 

5.1 

143 

5.1 

136 

5.1 

Safe  loads  given  include  weight  of  girder. 

Weights  of  girders  given  include  weight  of  rivet  heads,  but  not  stif- 
feners. 

Maximum  fibre  strain,  15,000  Ibs.  per  square  inch  of  net  area,  holes  for 
%"  rivets  being  deducted. 


650 


RIVETED  PLATE  AND   BOX   GIRDERS. 


STEEL  BOX  GIRDERS. 

PASSAIC    ROLLING    MILL    CO. 

SAFE  LOADS  IN  TONS  or  2,000  LBS.  UNIFORMLY  DISTRIBUTED. 


No  stiffeners  required 

except  at  ends,  over 

supports  only. 


Girders  equivalent  to 
two  24"  I  beams. 


Webs'.  

24"  XW 

26"  XH" 

28"  XM" 

30"X<K" 

Angle*  

5"  x  3"  x  y>" 

5"  X  3"  X  Vie" 

5"X3"xm" 

5"  X  3"  X  *<<" 

Plates  

14"X%6" 

14"X^" 

14"  XW 

14"  XH" 

VM  v. 

V®  v 

^ 

n 

J5J3  m 

2 

| 

a 

g 

o 

f-i  "5  "aS 

o 

•^  -*- 

Y/S  •*•* 

o 

v/5  IS 

Span,  centres 

*^ 

oc^ 

. 

•s  si 

. 

£  c^ 

• 

«3  C"E 

of  bearings, 

<rJ 

"2 

a/  a>««-i 

.    c3 

a>  otM 

^ 

OJ     fl)«4-l 

feet. 

J| 

0) 

<u  <S  * 

JD 
0) 

li? 

^0 

a> 

III 

to 

HH  S 

to 

3.S 

to 

H^.S 

i 

^5.2 

20 

93.8 

4.3 

93  .  5 

•  4.7 

92.9 

5.1 

95.6 

5.4 

21 

89.3 

4.1 

89.0 

4.5 

88.5 

4.8 

91.1 

5.2 

22 

85.3 

3.9 

85.0 

4.3 

84  .  5 

4.6 

86.9 

4.9 

23 

81.6 

3.8 

81.3 

4.1 

SO.  8 

4.4 

83.2 

4.7 

24 

78.2 

3.6 

77.9 

3.9 

77.4 

4.2 

79.7 

4.5 

25 

75.0 

3.5 

74.8 

3.8 

74.3 

4.1 

76.5 

4.3 

26 

72.2 

-3.3 

71.9 

3.6 

71.5 

3.9 

73.6 

4.2 

27 

69.5 

3.2 

69.2 

3.5 

68.8 

3.8 

70.8 

4.0 

28 

67.1 

3.1 

66.8 

3.4 

66.3 

3.6 

68.3 

3.9 

29 

64.7 

3.0 

64.4 

3.2 

64.0 

3.5 

66.0 

3.7 

30 

62.5 

2.9 

62.3 

3.1 

61.9 

3.4 

63.8 

3.6 

31 

60.5 

2.8 

60.3 

3.0 

60.0 

3.3 

61.7 

3.5 

32 

58.6 

2.7 

58.4 

2.9 

58  .  1 

3.2 

59.8 

3.4 

33 

56.9 

2.6 

56.6 

2.8 

56.3 

3.1 

58.0 

3.3 

34 

55.2 

2.5 

55.0 

2  7 

54.6 

3.0 

56  .  3 

3.2 

35 

53.6 

2.5 

53.4 

2.7 

53.1 

2.9 

54.7 

3.1 

36 

52.1 

2.4 

51.9 

2.6 

51.6 

2.8 

53.1 

3.0 

37 

50.7 

2.3 

50.5 

2.5 

50.2 

2.7 

51.7 

2.9 

38 

49.4 

2.3 

49.2 

2  5 

48.9 

2.7 

50  .  3 

2.9 

39 

48.1 

2.2 

47.9 

2.4 

47.6 

2.6 

49.0 

2.8 

40 

46.9 

2.2 

46.7 

2.4 

46.4 

2.6 

48.0 

2.8 

Weight  per 
foot,  Ibs. 

174 

6.0 

166 

6.0 

159 

6.0 

158 

6.0 

Safe  loads  given  include  weight  of  girder. 

Weights  of  girders  given  include  weight  of  rivet  heads,  but  not  stif- 

Maximum  fibre  strain,  15,000  Ibs.  per  square  inch  of  net  area,  holes  for 
%"  rivets  being  deducted 


WOODEN  FLOORS.  651 


CHAPTER  XXI. 

STRENGTH  AND  STIFFNESS  OF  WOODEN 
FLOORS. 

Two  problems  present  themselves  under  this  head;  first,  to 
proportion  the  beams  and  girders  forming  the  framework  of  the 
floor  to  the  greatest  load  likely  to  come  upon  it ;  and  second,  to 
determine  the  maximum  safe  load  for  a  floor  already  built. 

The  former  of  these  problems  is  the  one  with  which  architects 
and  builders  more  commonly  have  to  deal,  and  will  therefore  be 
considered  first. 

Layout  of  the  Floor  Framing. — Before  any  calcula- 
tions can  be  made  for  the  size  of  the  timbers  it  will  be  necessary 
to  know  the  span  of  the  joists,  and,  if  there  are  openings  in  the 
floor,  or  the  floor-joists  have  to  support  longitudinal  partitions, 
a  framing  plan  should  be  made,  showing  the  floor  area  that  will 
be  supported  by  each  beam,  and  also  the  position  of  partitions 
or  special  loads.  If  the  floor  is  to  be  supported  by  posts  and 
girders  the  position  of  these  should  also  be  accurately  indicated 
on  the  framing  plan.  For  a  detailed  description  of  the  manner 
of  framing  wooden  floors  the  reader  is  referred  to  Part  II,  of 
"Building  Construction  and  Superintendence." 

Where  the  floor-beams  are  supported  entirely  by  walls  or  par- 
titions, the  span  of  the  beams  will  of  course  be  fixed  by  the  plan 
of  the  building.  When  the  distance  between  walls  and  parti- 
tions is  too  great  for  a  single  span,  there  may  be  a  question  as  to 
the  best  location  of  the  posts  and  girders. 

When  planning  a  building  in  which  wooden  floor-beams  are  to 
be  used,  it  is  important  to  keep  in  mind  how  the  floors  are  to  be 
framed,  and  particularly  the  span.  Whenever  practicable  the 
span  of  wooden  beams  should  be  kept  under  25  feet.  When  the 
distance  between  the  supporting  walls  exceeds  30  feet,  girders 
should  be  placed  so  that  the  maximum  span  of  the  joists  will  not 
exceed  21  feet  for  light  buildings  or  16  to  18  feet  for  warehouses. 

In  school  buildings  it  is  desirable  to  have  the  rooms  at  least  27 


652  WOODEN  FLOORS. 

feet  wide,  and  hence  in  this  class  of  buildings  the  Joists  usually 
have  a  span  of  from  27  to  30  feet.  For  a  span  of  30  feet,  however, 
16-iuch  joists  should  be  used,  and  as  these  are  expensive,  and 
often  difficult  to  obtain,  it  is  much  better  and  more  economical 
to  make  the  schoolrooms  27  X  32  or  34  feet,  than  to  make  them 
30  feet  square.  In  the  opinion  of  the  writer  a  schoolroom  27 
feet  wide  by  32  to  34  feet  long,  with  windows  on  the  long  side  of 
the  room  only,  is  the  most  economical  and  satisfactory,  as  it 
permits  of  using  3"Xl4"  joists  28  feet  long,  and  also  gives  the 
most  satisfactory  lighting. 

When  floor-beams  are  supported  by  a  girder  placed  so  that  a 
24-  or  26-foot  beam  will  reach  over  the  two  spans,  it  is  always 
better  to  have  the  joists  continuous  over  the  girder,  as  it  makes 
a  much  stiffer  floor,  although  the  ultimate  strength  is  not  in- 
creased (see  Chapter  XIX.). 

Having  decided  on  the  arrangement  of  the  joists,  and  drawn 
a  framing  plan  showing  the  span  and  location  of  all  special 
timbers,  the  next  step  will  be  to  decide  upon  the  loads  for  which 
the  joist  and  timbers  shall  be  proportioned. 

Floor  loads  are  made  up  of  two  factors,  first  the  weight  of 
materials  composing  the  floor  (and  ceiling  below,  if  there  is  one) ; 
and  second,  an  allowance  for  the  load  liable  to  come  upon  the 
floor.  The  first  is  commonly  designated  as  the  "dead  load,"  and 
the  second  as  the  "live  load."  When  the  "safe  load"  for  a  floor 
is  spoken  of  the  live  load  is  generally  meant. 

Weight  of  Wooden  Floor  Construction. — Wooden 
floors  usually  consist  of  beams,  commonly  called  "joists,"  or 
"floor-joists,"  one  or  two  thicknesses  of  flooring  boards,  and,  in  a 
finished  building,  of  a  ceiling  underneath  the  beams.  In  figuring 
the  weight  of  f-inch  flooring  boards  it  will  be  sufficiently  accurate 
to  estimate  the  weight  of  a  single  thickness  at  3  pounds  per  square 
foot.  The  joists  may  also  be  figured  at  3  pounds  per  foot,  board 
measure,  with  the  exception  of  hard  pine  and  oak  joists,  which 
should  be  figured  at  4  pounds  per  foot  board  measure.  The 
weight  of  the  joists  must  also  be  reduced  to  their  equivalent 
weight  per  square  foot  of  floor.  Thus  the  weight  of  a  2  X  12-inch 
joist  is  about  6  pounds  per  lineal  foot.  If  the  joists  are  spaced 
12  inches  on  centres,  this  will  be  equal  to  6  pounds  per  square  foot; 
but  if  the  joists  are  16  inches  on  centres  there  will  be  but  one 
lineal  foot  of  joist  to  every  1J  square  feot,  which  will  be  equiva- 
lent to  4J  pounds  per  square  foot,  and  if  they  are  20  inches  on 
Centres,  the  weight  will  be  equal  to  3J  pounds  per  square  foot; 


WOODEN  FLOORS. 


653 


spaced  24  inches  on  centres,  the  weight  will  be  3  pounds  per 
square  foot. 

The  weight  of  a  lath-and-plaster  ceiling  should  be  taken  at 
10  pounds  per  square  foot,  and  of  a  f-inch  wood  ceiling  at  2J 
pounds  per  square  foot.  Corrugated  iron  ceiling  weighs  about 
1  pound  per  square  foot.  For  stamped  steel  ceilings  2  pounds 
per  square  foot  will  cover  the  weight  of  the  metal  and  furring. 

The  following  table,  giving  the  weight  of  joists,  will  be  found 
convenient  in  figuring  the  weight  of  floors: 

TABLE  I.— WEIGHT    OF  FLOOR-JOISTS   PER  SQUARE 
FOOT   OF   FLOOR. 


Spruce,  hemlock,  white 
pine. 

Hard  pine  or  oak. 

Size  of 
joists  in 
inches. 

Spacing  in  inches,  centre 
to  centre. 

Spacing  in  inches,  centre 
to  centre. 

12 

16 

12 

16 

Pounds. 

Pounds. 

Pounds. 

Pounds. 

2XG.  ... 

3 

2i 

4 

3 

2X8  

4 

3 

&J 

4 

3X8  

6 

4i 

8 

6 

2X10.... 

5 

3} 

6f 

5 

3X10.... 

7J 

5i 

10 

7J 

2X12.... 

6 

4* 

8 

6 

3X12.... 

9 

6J 

12 

9 

2X14.... 

7 

5i 

0i 

7 

3X14.... 

10i 

Si 

14 

10J 

Weight  of  Crowds. — Prof.  L.  J.  Johnson,  of  Harvard 
Univ.,  reports  in  the  Eng.  News  of  Apr.  14,  1904,  results  of 
some  tests  to  ascertain  the  weight  of  crowds  (of  men),  in  which 
he  obtained  weights  of  134.2,  143.9,  148.1,  and  156.9  Ibs.  per 
sq.  ft.  The  last  weight  was  obtained  by  packing  67  men  in  a 
room  about  ll'X6'.  Prof.  Johnson  also  found  that  with  50 
men  in  the  room,  giving  a  weight  of  122  Ibs.  per  sq.  ft.,  the  crowd 
was  compacted  "so  that  a  man  could  elbow  his  way  through 
it  only  with  perseverance  and  determined  effort." 

Superimposed  Loads.— There  is  much  difference  of 
opinion  as  to  what  allowance  should  be  made  for  the  live  load. 
Table  II.  shows  the  minimum  allowance  for  live  loads  for  dif- 
ferent classes  of  buildings,  as  fixed  by  the  building  laws  of  the 
cities  mentioned:  . 


654 


WOODEN   FLOORS. 


TABLE  II.— MINIMUM  SAFE  SUPERIMPOSED  LOADS 
FOR  FLOORS  REQUIRED  BY  VARIOUS  BUILDING 
LAWS. 


Class  of  buildings. 

Minimum  live  load  per  square  foot 
of  floor. 

£  . 
tt^ 

Q»d 
11 

ffi 

Chicago, 
1895. 

£06 

r<O5 

goo 

NewYork, 
1899. 

'5  . 

40 

70 
70 
100 
120 

50 

50 
100 
150 
250 

70 

70 
70 
70 
150§ 

40 

50f 
70 
80  J 
150§ 

60 

60 
75* 
90 
120§ 

70 

70 
70* 
120t 
150§ 

Hotels,    tenements,    and     lodging- 

Offices           .                   

Buildings  for  public  assembly  
Stores,  warehouses,  and  mfg.  bldgs. 

*  First  floor,  150  Ibs. 
t  Also  schoolhouses. 


J  With  fixed  desks. 
§  And  upwards. 


It  is  the  opinion  of  the  author  that  the  following  allowances 
for  floor  loads,  taken  in  connection  with  the  values  given  for  the 
safe  strength  of  beams,  will  provide  absolute  safety  with  proper 
allowance  for  economy. 

For  dwellings,  sleeping  and  lodging  rooms 40  Ibs. 

For  schoolrooms 50  " 

For  offices  (upper  stories) 60  " 

.For  offices  (first  story) 80  " 

For  stables  and  carriage-houses 65  " 

For  banking-rooms,  churches,  and  theatres 80  '* 

For  assembly  halls,  dancing  halls,  and  the  corridors  of  all 

public  buildings,  including  hotels 120  " 

For  drill-rooms 150  "• 

Floors  for  ordinary  stores,  light  manufacturing  and  light  stor- 
age should  be  computed  for  not  less  than  120  pounds  per  square 
foot,  and  to  sustain  a  concentrated  load  at  any  point  of  4,000  Ibs. 

It  is  rarely,  if  ever,  that  the  floors  of  a  dwelling,  tenement,  or 
lodging-house,  or  the  rooms  in  a  hotel,  are  loaded  to  more  than 
twenty  pounds  per  square  foot,  for  the  entire  area,  and  a  mini- 
mum load  of  40  pounds  should  provide  for  all  possible  con- 
tingencies. 

The  floors  of  offices  are  as  a  rule  not  more  heavily  loaded  than 
dwellings,  but  the  possibilities  for  increased  loads,  in  the  way  of 
safes  and  heavy  furniture,  and  possibly  of  a  more  compact  crowd 
of  people,  are  greater,  so  that  the  minimum  floor  load  for  offices 
should  be  somewhat  Increased.  Some  years  ago  Messrs.  Blackall 


WOODEN   FLOORS.  655 

&  Everett,  of  Boston,  found  that  the  average  live  load  in  210 
offices,  in  three  prominent  office  buildings  in  that  city,  was  be- 
tween 16  and  17  pounds,  while  the  average  load  for  the  10 
heaviest  offices  was  33.3  pounds.  As  such  loads,  however,  are 
not  usually  evenly  distributed,  some  portions  of  the  floor  being 
generally  much  more  heavily  loaded  than  the  others,  it  would 
not  appear  to  be  safe  to  use  the  average  above  determined  for 
determining  the  strength  of  floor-beams  and  arches,  although  it 
would  probably  answer  for  the  columns.  There  seems  to  be 
considerable  difference  of  opinion  among  the  leading  architects 
and  structural  engineers  as  to  just  what  allowance  should  be 
made  for  office  floors.  In  the  Mills  Building  in  San  Francisco 
the  live  loads  were  assumed  at  40  pounds  per  square  foot  for  all 
floors  above  the  first;  in  the  Venetian  Building,  Chicago,  the 
second,  third,  and  fourth  floors  were  calculated  for  60  pounds, 
and  the  upper  floors  for  35  pounds  live  load  per  square  foot, 
while  in  the  Old  Colony  and  Fort  Dearborn  Buildings  in  Chicago 
the  live  loads  on  the  floor-beams  were  assumed  at  70  pounds 
in  accordance  with  the  building  ordinance. 

An  allowance  of  120  Ibs.  per  square  foot  for  the  live  load  in 
churches,  theatres,  and  schoolhouses  is,  in  the  opinion  of  the 
author,  much  greater  than  the  actual  conditions  require. 

The  average  size  of  a  schoolroom  is  about  28X32  feet,  and 
such  a  room  usually  contains  seats  for  fifty-six  scholars  and  the 
teacher.  Assuming  the  average  weight  of  each  scholar  at  120 
pounds,  we  have  for  the  average  live  load,  including  ten  visiting 
adults  and  the  desks  and  furniture,  13  pounds  per  square  foot. 
Even  supposing  that  the.  scholars  of  two  rooms  were  united  for 
some  special  occasion,  we  would  have  but  21  pounds  per  square 
foot,  and  this  is  as  great  a  load  as  it  is  possible  to  imagine  in  such 
a  room,  as  the  fixed  desks  prevent  the  crowding  together  of  the 
scholars  except  at  the  sides  of  the  room.  From  this  reasoning, 
therefore,  a  minimum  load  for  the  schoolrooms  of  50  pounds  per 
square  foot  would  appear  abundant. 

As  a  matter  of  fact,  3  X  14-inch  Georgia  pine  beams,  16  inches 
on  centres  and  28  feet  span,  have  been  used  for  schoolroom 
floors  for  years,  and  no  practical  person  would  doubt  their  safety, 
but  such  beams,  if  calculated  by  the  formula  for  stiffness  as 
hereinafter  recommended,  would  only  support  a  live  load  of 
56  pounds. 

The  minimum  floor  space  allotted  to  a  single  seat  in  theatres 
is  4  square  feet,  while  the  average  is  about  5  square  feet.  As- 


656  WOODEN   FLOORS. 

suming  the  weight  of  an  opera-chair  at  35  pounds  and  of  the 
average  adult  at  140  pounds  (a  liberal  allowance),  we  have  an 
average  of  44  pounds  per  square  foot  of  floor.  A  minimum  of 
80  pounds  would  therefore  seem  to  provide  for  any  possible 
crowding  during  a  panic  except  in  corridors.  On  the  other  hand 
it  has  been  shown  *  that  a  crowd  of  able-bodied  men  may  pro- 
duce a  load  of  about  120  pounds  per  square  foot,  and  this 
should  be  the  minimum  for  assembly  halls,  without  fixed  desks, 
and  also  for  the  corridors  of  all  public  buildings.  For  armories 
the  minimum  load  should  be  increased  on  account  of  the'  vibra- 
tion produced. 

The  average  floor ^oads  for  stores  has  also  been  greatly  over- 
estimated. Mr.  W.  L.  B.  Jenney  found  that  the  average  load 
on  the  floors  of  the  wholesale  warehouse  of  Marshall  Field  &  Co., 
in  Chicago,  was  but  50  pounds  per  square  foot,  and  very  few 
retail  stores  will  average  over  80  pounds.  An  allowance  of  120 
pounds  is  sufficient  for  any  ordinary  retail  store,  with  the  possible 
exception  of  hardware  stores. 

Warehouses,  on  the  other  hand,  may  be  very  heavily  loaded, 
and  the  floors  in  buildings  intended  for  the  storage  of  merchan- 
dise should  be  proportioned  to  the  especial  class  of  goods  which 
they  are  designed  to  support. 

The  following  table,  originally  compiled  by  Mr.  C.  J.  H.  Wood- 
bury,!  and  to  y/hich  some  additions  have  been  made  by  the 
Insurance  Engineering  Experiment  Station  and  by  the  author, 
will  be  found  of  assistance  in  deciding  upon  the  live  load  to  be 
assumed  for  warehouse  floors.  The  weights  per  square  foot  are 
for  single  packages.  If  the  goods  are  piled  two  or  more  cases 
high,  the  weight  per  square  foot  of  floor  will  of  course  be  increased 
accordingly.  In  fact,  the  height  to  which  the  goods  are  liable 
to  be  piled  is  a  very  important  consideration  in  fixing  upon  the 
floor  load. 

In  the  following  table  "the  measurements  were  always  taken 
to  the  outside  of  case  or  package,  and  gross  weights  of  such 
packages  are  given." 

To  find  the  size  of  joists,  beams,  and  girders 
required  for  any  particular  building. — As  already 
explained,  the  first  step  should  be  to  make  a  framing  plan  of  the 
floors  or  enough  of  it  to  show  any  special  framjng  and  the  span 

*  See  "  Weight  of  Crowds,"  p.  653. 
t  The  Fire  Protection  of  Mills,  p.  118. 


WOODEN  FLOORS.  657 

TABLE  III.— WEIGHTS  OF  MERCHANDISE. 


Material.     ' 

Measurements. 

Weights. 

WOOL. 
Bale  Ei/st  India   .                 ...<,... 

Floor 
space. 
3.0 
5.8 
7  0 

Cubic 
feet. 
12.0 
26.0 
34.0 
33.0 
33.0 
30.0 

12.7 
15.2 
22.0 
28.0 
21.0 
35.0 
14.0 

44.2 
21.6 
11.0 
7.2 
9.9 
10.5 
10.9 
34.7 
17.0 

12.5 
2.3 
10.1 
11.4 
19.0 
9.3 
13.4 
8.8 

5.3 

39.5 
40.0 
30.0 
34.0 
65.0 
30.0 
11.1 

Gross. 

340 
385 
1000 
482 
550 
200 

220 
330 
460 
550 
350 
450 
250 

515 
550 
263 
254 
300 
450 
280 
700 
400 

300 
75 
235 
330 
295 
175 
420 
325 

130 
100 

910 
715 
442 
507 
450 
600 
400 

Per 

sq.  ft. 
113 
66 
143 

70 
73 
40 

40 
46 
84 
52 
48 
44 
63 

64 
134 
66 
110 
125 
172 
88 
81 
75 

72 
68 
65 
69 
41 
44 
93 
99 

70 

107 
78 
59 
68 
28 
80 
143 

Per 
cu.  ft. 
28 
15 
29 
15 
17 
7 
5 

17 
22 
21 
20 
16 
13 
18 

12 
25 
24 
35 

30 
43 
26 
20 
24 

24 
33 
23 
30 
16 
19 
31 
37 
11 
30 
24 

23 

18 
15 
15 
7 
20 
36 

50 
69 
38 
33 
59 
64 
10 
37 

"     Australia                 

44     South  America                     .  .  . 

"     Oregon      .            

6.9 
7.5 

5.0 

5.5 
7.1 
5.5 
10.5 
7.3 
10.3 
4.0 

8.1 
4.1 
4.0 
2.3 
2.4 
2.6 
3.2 
8.7 
5.3 

4.0 
1.1 
3.6 
4.8 
7.2 
4.0 
4.5 
3.3 

1.4 

8.5 
9.2 
7.6 

7  5 

"     California  

Bag  wool                        

Stack  of  scoured  wool     .           ...... 

WOOLLEN  GOODS. 
Case  flannels             .      

"     flannels  heavy                     ... 

"     dress  goods        

"     cassimeres 

"     underwear   

"     blankets 

"     horse  -blankets  °  .  .  

COTTON,  ETC. 
Bale                               

"     compressed 

"     American  Cotton  Co  

"     Planters'  Compressed  Co.  .  .  . 

"     jute                   

"     iute  lashings                         . 

"     manila                       

"     sisal  

COTTON  GOODS. 
Bale  unbleached  jeans  

Bale  brown  sheetings  

Case  bleached  sheetings      . 

"     quilts                 

Bale  print  cloth 

Case  prints           

Bale  tickings 

Skeins  cotton  yarn  

Jute  bagging                

RAGS  IN  BALES. 

W^hite  cotton        .          

16.0 
7.5 

2.8 

PAPER. 
Calendered  book          

Supercalendered  book     . 

Newspaper      

Straw  board 

Writing 

Wrapping.  .  ,  

Manila 

658  WOODEN  FLOORS. 

TABLE  III.— WEIGHTS  OF  MERCHANDISE  (continued). 


Material. 

Measurements. 

Weights. 

GRAIN.* 
Wheat  in  bags  „  

Floor 
space 
4.2 

4.1 
3.1 
3.6 
3.7 
3.3 
5.0 
1.75 
1.75 
1.75 
1.75 

11.8 
10.8 
3.0 
4.0 
1.6 
4.3 
3.0 
3.0 
1.06 
3  6 

Cubic 
feet 

4.2 

5.4 
7.1 
3.6 
5.9 
3.6 
20.0 
5.25 
5.25 
5.25 
5.25 

39.2 
29.2 
9.0 
3.3 
4.1 
6.8 
10.5 
10.5 
.8 
4  5 

Gross. 
165 

218 
218 
112 
218 
96 
284 
125 
100 
150 
100 

1200 
1800 
385 
150 
160 
600 
250 
350 
55 
225 
325 
400 
325 
430 
422 

139 

1600 
600 
190 
300 
400 
700 
200 

317 
340 

Per 

sq.  ft. 
39 

53 
70 
31 
59 
29 
57 
72 
57 
86 
57 

102 
167 
128 
38 
100 
140 
83 
117 
52 
63 
86 
105 
.88 
143 
98 

99 

162 
52 
26 
27 
67 
117 
22 

106 
113 

Per 
cu.  ft. 
39 
44 
39 
41 
40 
31 
31 
37 
27 
14 
24 
19 
29 
19 
4 

31 
62 

43 
45 
39 
88 
23 
33 
70 
50 
59 
73 
53 
48 
34 
42 

278 
60 
40 
14 
16 
18 
13 
23 
16 
17 
42 
45 
30 

in  bulk  

44  .              mean   . 

Barrels  flour  on  side.  „  „  .    . 

on  end  

Corn  in  bags.  ... 

Cornmeal  in  barrels  

Oats  in  bags  

Bale  of  hay  

Hay,  Dederick  compressed  

Straw         " 

Tow                                            

Excelsior  "                  **           
Hay,  loose.  .  . 

DYESTUFFS,  ETC. 
Hogshead  bleaching  powder  

soda  ash  

Box  indigo  

4     cutch.  .  .  . 

4     sumac  

Caustic  soda  in  iron  drum  

Barrel  starch 

pearl  alum    

Box  extract  logwood  

Barrel  lime  

cement,  American  

3.8 
3.8 
3.7 
3.0 
4.3 

2.7 

9.9 

13.4 
7.3 
11.2 
6.0 
6.0 
12.6 

3.0 
3.0 

5.5 
5.5 
6.1 
9.0 
12.3 

0.5 

39.6 
42.5 
12.2 
16.7 
30.0 
30.0 
8.9 

7.5 
7.5 

English  

plaster  

rosin  

44       lard  oil  

Rope  ... 

MISCELLANEOUS. 
Box  tin  

4     glass                 

Crate  crockery  

Bale  leather      

4     raw  hides.  

compressed  

Pile  sole  leather                  .  .           .    . 

Barrel  granulated  sugar  

Cheese.  .   .        .            

and  floor  area  supported  by  the  different  beams  and  girders.  The 
second  step  is  to  determine  approximately  the  weight  of  the  floor 
and  ceiling,  and  decide  upon  what  superimposed  load  (per 
square  foot)  the  floor  shall  be  proportioned  to  carry. 

Having  done  this,  the  next    step  will    be  to  compute  the 
required  dimensions  of  the  common  floor  joists. 

*  For  pressure  of  grain  in  deep  bins,  see  Engineering  News  of  March  1Q, 
1904,  pp.  224  and  336,  aiao  of  Dec.  15, 1904. 


WOODEN  FLOORS.  659 

For  most  buildings  the  size  of  floor  joist  required  can  be 
readily  determined  by  reference  to  Tables  VI.-X.  of  this  chapter. 

For  other  floor  loads  the  size  of  the  common  joists  may  be 
computed  as  follows :  Compute  the  load  to  be  supported  by  a  single 
joist  and  then,  by  the  rules  or  tables  in  Chapter  XVL  or  XVIII. , 
determine  the  dimensions  of  the  joists  to  support  the  load.  (See 
Example  1.) 

For  the  floors  of  all  buildings  except  stores  and  warehouses 
the  author  recommends  that  the  size  of  the  common  joists  be 
determined  by  the  rules  or  tables  in  Chapter  XVIII.  For 
stores  and  warehouses  the  size  of  the  joists  may  be  proportioned 
by  the  formulas  for  strength,  Chapter  XVI. 

The  dimensions  of  all  special  beams,  such  as  headers,  trimmers, 
beams  supporting  partitions,  and  also  of  the  girders,  should  be 
found  in  the  same  way,  viz.,  by  computing  the  maximum  load 
which  the  beam  may  have  to  support,  and  then  the  dimensions 
of  a  beam  that  will  sustain  the  load  with  safety. 

The  manner  of  making  the  computations  can  be  best  ex- 
plained by  means  of  examples. 

EXAMPLE  1. — The  simplest  floor  framing  is  that  shown  in 
Fig.  1;  in  which  all  of  the  joists  are  of  the  same  span  and  sustain 


Fig.  I. 

Plan  of  Floor  Beams. 

equal  floor  areas.  In  such  a  floor,  the  floor  area  supported  by 
each  joist  is  equal  to  the  span  L  multiplied  by  the  spacing  S 
(in  feet). 

The  load  on  each  joist  is  equal  to  the  floor  area  multiplied  by 
the  sum  of  the  dead  and  superimposed  loads.  .To  show  the 
application  of  the  above  rules  and  directions  we  will  assume  that 
Fig  1  represents  the  framing  of  a  floor  in  a  dwelling- or  lodging- 


660  WOODEN  FLOORS. 

house,  that  I/  =  18  ft.,  £  =  16  ins.  or  1J  ft.,  and  that  the  timber  is 
to  be  common  white  pine.  The  joists  are  to  sustain  a  plastered 
ceiling  and  a  double  floor  of  |-inch  boards.  What  should  be  the 
size  of  the  joists? 

Ans.  The  floor  area  supported  by  each  joist  will  be  1JX18, 
or  24  sq.  feet.  As  the  joists  will  probably  have  to  be  at  least 
2"X12",  their  weight  will  be  about  4}  Ibs.  per  square  foot  (see 
Table  I.).  The  plastered  ceiling  will  weigh  about  10  Ibs.  and 
the  flooring  6  Ibs.,  making  the  total  weight  of  the  floor  20}  Ibs. 
per  sq.  ft.  For  the  superimposed  load  we  should  allow  40  Ibs. 
(see  p.  654).  The  load  on  a  single  joist  will  therefore  be  60} 
Ibs.  X 24  sq.  ft.,  or  1452  Ibs. 

From  Table  V.,  Chapter  XVIII.,  we  find  that  the  maximum 
load  for  a  1 X 12  beam  of  18  ft.  span  is  700  Ibs.,  hence  to  support 
1452  Ibs.  will  require  LI  breadth  equal  to  1452 ~ 700  or  2^  ins. 
Therefore,  to  comply  with  the  requirements  for  stiffness,  the 
joists  should  be  2TV'X12". 

If  we  do  not  mind  the  deflection  we  can  use  the  table  for 
strength  (Table  VII.,  Chapter  XVI.),  which  gives  960  Ibs.  for  the 
safe  load  of  a  1X12  beam,  and  dividing  1452  by  960  we  have 
1.51  for  the  required  breadth  of  the  beam;  therefore  a  lf"X  12" 
joist  will  be  strong  enough,  but  would  bend  more  than  is  desirable 
where  the  ceiling  is  to  be  plastered.  Joists  full  2"X  12",  spaced 
16  ins.  on  centres,  would  answer  in  this  case,  but  if  they  come 
J  in.  scant  in  one  or  both  dimensions  they  should  be  spaced  only 
12  ins.  on  centres.  From  Table  VI.  we  see  that  the  maximum 
span  for  2"X12"  joists,  spaced  16  ins.  on  centres,  in  dwellings 
is  given  as  17'  3". 

EXAMPLE  2. — Fig.  2  shows  a  partial  section  of  a  dwelling,  in 
which  the  second -floor  joists  support  a  plastered  partition  which 
also  supports  an  attic  floor.  What  should  be  the  size  of  the 
second-floor  joists  to  meet  the  requirements  of  strength,  the 
timber  to  be  Eastern  spruce? 

NOTE. — As  the  effect  of  a  concentrated  load  in  producing 
deflection,  compared  with  a  distributed  load,  is  not  as  great  as 
the  comparative  effect  to  produce  rupture,  whenever  beams  have 
a  considerable  concentrated  load  they  may  be  calculated  by  the 
formula  or  tables  for  strength  only.  jgp  " 

Ans.  The  first  step  will  be  to  determinerthe  load  on  a  single 
floor  joist.  We  will  assume  that  the  joists  are  to  be  2"X  10", 
12  ins.  on  centres,  that  both  the  first-  and  second-story  ceilings 
are  to  be  plastered,  and  that  only  single  flooring  will  be  used  in 


WOODEN   FLOORS. 


661 


the  second  story  and  attic.  We  will  assume  that  the  attic  joists 
are  to  be  2"X8",  16  ins.  centre  to  centre,  and  that  the  width  of 
floor  supported  by  the  partition  is  10  ft. 

The  second-floor  area  supported  by  a  single  joist  will  be  12"X 
15  ft.,  or  15  sq.  feet.  The  weight  of  the  floor  joists  per  sq.  ft. 
will  be  5  Ibs.,  of  the  plastered  ceiling  10  Ibs.,  and  of  the  flooring 
3  Ibs.,  making  the  dead  load  per  sq.  ft.  18  Ibs.  For  the  live 
or  superimposed  load  we  should  allow  40  Ibs.,  hence  the  load 


'—  '3  9  - 


Second  Story 


15- 


Fig.  2. 

Section. 


per  sq.  ft.  on  the  second-floor  joists  due  to  the  second  floor  and 
its  load  will  be  58  Ibs.  As  the  floor  area  is  15  sq.  ft.  the  load  from 
the  second  floor  will  be  15X58  or  871  Ibs.  We  must  now  find 
what  will  be  the  load  from  the  partition  and  attic  floor.  The 
attic  floor  and  ceiliipg  will  weigh  about  16  Ibs.  per  sq.  ft.,  and  24 
Ibs.  will  be  a  sufficient  allowance  for  the  live  load.  The  weight 
per  lineal  foot  on  the  partition  will  therefore  be  400  Ibs.  A 
partition  of  2X4  studding  lathed  and  plastered  both  sides  will 
weigh  about  20  Ibs.  per  sq.  ft. ;  hence  the  partition  itself  will 


662  WOODEN  FLOORS. 

weigh  180  Ibs.  per  lineal  ft.  The  partition  and  attic  floor  will 
therefore  bring  a  load  of  580  Ibs.  on  each  second -floor  joist, 
concentrated  at  a  point  one-fourth  of  the  span  from  the  inner  end 
of  the  joist.  To  combine  this  concentrated  load  with  the  load 
from  second  floor,  we  must  multiply  the  concentrated  load  by 
1.5  (see  page  565),  which  gives  an  equivalent  distributed  load 
of  870  Ibs.  Adding  this  to  the  second -floor  load  we  have  1740 
Ibs.  as  the  total  load  for  which  each  joist  should  be  proportioned. 
From  Table  VI.,  Chapter  XVI.,  we  find  that  the  safe  load  for  a 
1X10  spruce  beam  of  15  ft.  span  is  933  Ibs.;  hence  the  breadth 
of  the  joists  should  be  equal  to  1740-^933  or  If  ins.  If  the 
joists  were  spaced  16  ins.  on  centres  the  load  on  a  single  joist 
would  be  increased  one-third,  or  to  2320  Ibs.,  which  would  require 
a  1}"X12"  joist. 

EXAMPLE  3. — To  determine  the  size  of  the  girder  and  floor 
timbers  in  the  floor  shown  in  Fig.  3,  all  of  the  timbers  being  of 
Texas  yellow  pine,  and  the  floor  above  being  supported  by  posts 
and  girders  in  the  same  way.  The  building  is  intended  for 
lodging  purposes,  and  the  height  of  the  story  is  10  feet.  There 
is  to  be  a  double  floor  and  the  ceilings  and  partitions  are  to  be 
plastered.  The  floor  joists  will  be  spaced  16  ins.  centre  to 
centre. 

Ans.  We  wrill  first  determine  the  size  of  the  common  joists 
at  A,  calling  the  span  24  ft. 

The  floor  area  supported  by  a  single  joist  will  be  24X1J,  or 
32  sq.  ft. 

As  it  will  probably  require  2"X  14"  joists,  we  will  allow  7  Ibs. 
per  sq.  ft.  for  the  weight  of  joists  and  bridging,  10  Ibs.  for  the 
ceiling,  and  6  Ibs.  for  the  flooring,  making  23  Ibs.  per  sq.  ft  for  the 
dead  load.  For  the  live  load  we  will  allow  40  Ibs.  The  load  for 
which  the  joists  should  be  proportioned  will  therefore  be  32X63, 
or  2016  Ibs.  As  the  stiffness  of  Texas  pine  is  nearly  the  same  as 
that  of  Georgia  yellow  pine,  we  may  use  Table  II.,  Chapter  XVIII., 
to  find  the  maximum  load  for  a  1"X14"  beam  of  24  ft.  span. 
The  load  given  in  the  table  is  1042  Ibs.,  hence  the  thickness  of  the 
joists  must  equal  2016  -f- 1042  or  2  ins.  Therefore  2"X  14"  joists, 
16  ins.  on  centres  should  be  used,  but  they  should  run  full  2  ins. 
thick. 

The  joists  at  B  have  to  support  a  partition,  but  as  the 
span  is  much  less,  and  the  partition  is  quite  near  the  end  of 
the  joists,  it  will  be  safe  to  make  them  of  the  same  size  aa 
at  A. 


WOODEN   FLOORS. 


663 


The  joists  at  C  have  the  same  floor  load  to  support  as  at  A, 
and  in  addition  the  weight  of  the  partition,  which  is  concentrated 
one-third  of  the  span  from  one  support.  As  the  partition  is  10 
ft.  high,  13 J  sq.  ft:  of  partition  will  be  supported  by  each  joist 


-Girder  G   under 


IF- 


j— Column 


*— Girder 
G' 


60-- 


\Partition 


Fig.  3. 

Plan  of  Floor  Framing  showing  Partitions  Above. 

(the  joists  being  16  ins.  on  centres).  Assuming  20  Ibs.  per  sq. 
ft.  as  the  weight  of  the  partition,  we  have  267  Ibs.  as  the  weight 
from  the  partition  to  be  borne  by  each  joist.  To  reduce  this  to 


664  WOODEN  FLOORS. 

an  equivalent  distributed  load,  we  should  multiply  by  1.78, 
which  gives  468  Ibs.  The  joist  at  C,  therefore,  should  be  pro- 
portioned to  a  uniformly  distributed  load  of  2016+468  or  2484 
Ibs.,  which  will  require  a  14-inch  joist  2.4  ins.  thick,  or  say 
2JX14. 

Header. — We  will  next  determine  the  required  breadth 
for  the  header  H,  the  depth  being  necessarily  14  ins.  (the  same 
as  for  the  joists). 

The  header  is  14  ft.  long  and  must  support  the  floor  half  way 
to  the  wall,  or  a  floor  area  of  14X9,  or  126  sq.  ft.  Multiplying 
this  area  by  63,  the  weight  per  square  foot,  we  have  7938  Ibs.  as 
the  total  floor  load  to  be  supported,  to  which  must  be  added  a 
certain  percentage  of  the  partition.  The  portion  of  the  partition 
supported  by  the  header  is  12'-8"  long  (14'-0"— l'-4')  10'  high 
and  will  weigh  about  20  Ibs.  per  square  foot,  or  a  total  of  2532 
Ibs.  As  the  partition  is  one-ninth  of  the  span  from  the  header, 
eight-ninths  of  its  weight  will  be  supported  by  the  header  and 
one-ninth  by  the  wall.  Eight-ninths  of  2532  is  2251  Ibs.,  which 
added  to  the  floor  load  makes  a  total  load  for  the  header  of  10,188 
Ibs.  From  Table  IV.,  Chapter  XVI.,  we  find  that  the  safe  load 
for  a  1"X  14"  beam  of  Texas  pine,  14  ft.  span  is  2520  Ibs.,  hence 
it  will  require  a  breadth  of  4  ins.  to  support  10,630  Ibs.  If  the 
tail  beams  are  framed  into  the  header,  additional  thickness 
should  be  given  to  the  header  to  allow  for  the  weakening  effects 
of  the  framing,  so  that  the  header  should  be  at  least  5"X  14". 

Trimmers. — We  will  next  consider  the  trimmer  T.  This 
beam  has  four  loads:  A  distributed  floor  load;  a  distributed 
load  from  the  partition  above;  one-half  the  load  on  the  header 
H,  and  a  small  direct  load  from  the  longitudinal  partition.  The 
strip  of  floor  supported  by  the  trimmer  will  be  about  12  ins.  wide 
and  24  ft.  long,  and  will  weigh  1512  Ibs. 

The  partition  above  will  weigh  10  X  24  X  20,  or  4800  Ibs.  One- 
half  of  the  load  on  H  is  5094  Ibs.  As  this  is  concentrated  one- 
fourth  of  the  span  from  the  support,  we  must  multiply  it  by  1.5 
to  obtain  the  equivalent  distributed  load,  which  gives  7641  Ibs. 
About  8  inches  of  the  longitudinal  partition  must  be  supported 
by  the  trimmer,  and  this  will  weigh  133  Ibs.  As  it  is  concen- 
trated one-third  of  the  span  from  the  support,  we  must  multiply 
by  1.78  to  obtain  the  equivalent  distributed  load — which  gives 
236  Ibs. 

The  total  load  for  which  the  trimmer  must  be  computed  will 
therefore  be: 


WOODEN   FLOORS.  665 

From  the  floor 1512 

From  the  partition  above 4800 

From  the  header 7641 

From  the  longitudinal  partition 236 


Total.... 14,189 

The  trimmer  should  be  of  the  same  depth  as  the  joists,  14  ins. 
From  Table  IV.,  Chapter  XVI.,  we  find  that  a  1X14  in.  Texas 
pine  beam  of  24  ft.  span  will  safely  support  1470  Ibs. ;  hence  the 
breadth  of  the  trimmer  must  =  14,189 -^1470  =9.5  ins.,  and  the 
header  should  be  hung  in  a  stirrup  or  joist  hanger.  The  load  on 
the  trimmer  R  will  be  the  same  as  on  the  trimmer  T,  except  for 
the  cross  partition.  Deducting  the  weight  of  this  partition,  we 
have  9389  pounds  for  the  equivalent  distributed  load  on  R, 
which  will  require  a  breadth  =9389-^1470  =6. 4  ins. 

Girders. — The  floor  area  supported  by  girder  G  is  equal 
to  12 X  24  ft.,  or  288  square  feet.  As  a  general  rule,  it  will  be  safe 
in  estimating  the  live  load  on  girders  to  take  only  85  per  cent, 
of  the  load  assumed  for  the  floor  beams,  because  there  will 
always  be  some  portion  of  the  floor  supported  by  the  girder  that 
is  not  loaded,  and  probably  other  portions  that  will  not  be  loaded 
up  to  the  assumed  load.  85  per  cent,  of  40  pounds  is  34  pounds. 
The  dead  load  of  the  floor  and  ceiling  will  be  about  23  Ibs.,  and 
the  girder  itself  will  weigh  at  least  1  pound  per  sq.  ft.  of  floor 
more,  so  that  we  will  use  58  Ibs.  per  square  ft.  for  the  total  floor 
load  on  girders.  As  girder  G  supports  288  sq.  ft.,  this  will  be 
equivalent  to  16,704  Ibs.  The  girder  also  supports  a  partition, 
9'  high  above,  which  will  weigh  12  X  9X  20  =  2160  Ibs.  The  total 
load  for  which  the  girder  should  be  proportioned  is  therefore 
18,864  Ibs.  Assuming  12  ins.  for  the  depth  of  the  girder,  we  find 
from  Table  IV.,  Chapter  XVI.,  that  the  safe  load  for  a  1+ 12  beam 
of  12  ft.  span  is  2160  Ibs.,  hence  the  breadth  of  the  girder  should 
be  18,864-2160=9  ins. 

The  girder  G'  supports  a  floor  area  at  the  left  of  12X12  =  144 
sq.  ft.,  which  represents  a  distributed  load  of  8352  Ibs.  On  the 
right  side  of  the  girder  there  is  a  strip  of  floor  40  ins.  wide  by  12 
ft.  long  (8  ins.  of  the  floor  being  included  in  the  load  on  T)  which 
will  weigh  2320  Ibs.  This  may  be  considered  as  a  concentrated 
load  applied  20  ins.  or  one-seventh  of  the  span  from  the  end  of 
the  girder,  in  which  case  the  effect  of  the  load  is  practically  the 
same  as  if  the  load  were  distributed. 


666  WOODEN   FLOORS. 

The  load  coming  upon  the  girder  from  T  will  equal  one-half 
'01  the  actual  distributed  load  on  T,  plus  |  (J  of  f)  of  the  load 
on//. 

The  load  on  //  we  found  to  be  10,188  Ibs.,  and  three-eighths  is 
3820  Ibs.  The  actual  distributed  load  on  T  we  found  to  be 
6312  Ibs.,  and  one-half  of  this  is  3156  Ibs.  Hence  the  trimmer 
T  transmits  a  load  of  6976  Ibs.  to  the  girder,  which  must 
be  considered  as  a  concentrated  load  applied  at  one-third  of 
the  span  from  the  support,  and  hence  we  must  multiply  it 
by  1.78  to  obtain  the  equivalent  distributed  load,  which  gives 
12,417  Ibs. 

The  load  for  which  the  girder  Gf  should  be  computed  will  there- 
fore be 

From  the  floor  at  the  left 8,352  Ibs. 

From  the  floor  at  the  right 2,320   " 

From  the  trimmer  T 12,417   " 

From  the  partition  above 2,160  " 

Total 25,249   " 


This  will  require  a  beam  11.7  ins.  wide.  For  this  floor,  there- 
fore, we  will  require  a  10"X  12"  girder  at  G,  a  12"X  12"  at  G't  a 
9"X  14"  beam  for  the  trimmer  T,  6J"X  14"  for  R,  5"X  14"  for 
//,  and  2"  X 14"  joists  at  A  and  B,  and  2i"X  14"  joists  at  C.  This 
example  illustrates  nearly  all  of  the  computations  that  are  re- 
quired to  determine  the  size  of  the  joists  and  special  beams  in 
any  ordinary  floor  construction. 

The  method  of  computation  is  the  same  for  any  floor  load,  the 
only  difference  being  that  the  greater  the  live  load  assumed  the 
greater  will  be  the  loads  for  which  the  beams  must  be  propor- 
tioned. 

As  will  be  seen,  the  most  laborious  computations  are  those  for 
beams  which  receive  loads  from  different  sources,  and  it  will  gen- 
erally be  found  that  the  weakest  portions  of  any  particular  floor 
are  the  headers,  trimmers,  and  girders,  and  the  beams  which  sup- 
port partitions. 

Strength  of  Mill  Floors. — The  beams  and  girders  for  mill 
floors  should  be  computed  by  the  same  process  as  exemplified  in 
the  foregoing  examples,  viz.,  first  determining  the  load  on  the 
beam  and  then  the  size  of  timber  required  to  support  it. 


WOODEN  FLOORS.  667 

Required    Thickness    of   Plank    Flooring.  —  The 

thickness  of  the  plank  flooring  in  mill  construction  may  be  deter- 
mined by  formulas  (a)  and  (b),  following: 


Thickness  of  plank  in  ins.   )  _  .  /  weight  per  sq.  ft.  XL2  . 

required  for  strength       \~V  24  X  A 

Thickness  of  plank  in  ins.   )  =    y  weight  per  sq.  ft.  X£r 
required  for  stiffness        )       V  '  19.2X^i 

L  denotes  span  in  feet,  centre  to  centre  of  beams,  A  the  con- 
stants for  strength,  p.  5G7,  and  ei  the  constant  for  stiffness 
(p.  595). 

When  the  planks  are  connected  by  f-in.  splines,  and  extend 
over  two  spans,  formula  (a)  may  be  used.  If  the  planks  are  in 
single  lengths  from  beam  to  beam,  or  are  not  splined,  then 
formula  (b)  should  be  used. 

Table  IV.  shows  the  safe  loads  for  plank  flooring  of  different 
thicknesses  and  spans,  as  derived  from  the  formulas  for  strength 
and  stiffness,  the  plain  figures  denoting  the  loads  given  by  the 
formula  for  strength  and  the  figures  in  italics  those  given  by  the 
formula  for  stiffness. 

The  span  is  supposed  to  be  measured  from  centre  to  centre  of 
beams.  The  plain  figures  should  be  considered  safe  only  for 
splined  floors  and  where  the  planks  are  continuous  over  at  least 
two  spans.  If  the  thickness  of  the  plank  falls  short  one-fourth  or 
even  one-eighth  inch  from  the  dimensions  given,  the  safe  loads 
must  be  materially  reduced. 

Tables  for  the  Maximum  Span  of  Floor  Joists.  — 
As  the  timbers  commonly  used  for  floor  joists  are  sawn  to  regular 
sizes,  and  are  usually  spaced  either  12  or  16  ins.  centre  to  centre 
it  is  practicable  to  show  by  means  of  tables  the  size  of  joist 
required  to  support  a  given  load  with  a  given  span  and  spacing. 
After  having  computed  various  tables  the  author  has  found  that 
tables  giving  the  maximum  safe  span  are  the  most  convenient  for 
general  use,  and  the  following  tables  have  accordingly  been  pre- 
pared, which  show  at  a  glance  the  maximum  span  for  which  dif- 
ferent sizes  of  floor  and  ceiling  joists  should  be  used  for  different 
loads  and  spacings;  it  is  believed  that  they  will  be  found  appli- 
cable to  most  buildings  in  which  wooden  floor  joists  are  used. 

By  knowing  the  size  of  the  room  to  be  covered  and  the  purpose 
for  which  it  is  to  be  used,  the  size  of  joist  required  can  be  told  at  a 


668 


WOODEN   FLOOtiS. 


TABLE     IV.— -SAFE    LIVE    LOAD    IN     POUNDS    PER 
SQUARE   FOOT  FOR  PLANK   FLOORING.* 

(See  explanation  on  preceding  page.) 
LONG-LEAF   YELLOW   PINE. 


Thickness  of 

Distance  between  centres  of  floor  beams  in  feet. 

plank  in  ins. 

4 

5 

6 

7 

8 

9 

'  10 

11 

12 

j 

515 

325 

222 

160 

120 

92 

72 

•*-/8      » 

255 

126 

68 

35 

21 

11 

5 

O3/ 

831 

527 

362 

262 

197 

153 

121 

97 

80 

^/S      -\ 

536 

268 

14^ 

55 

24 

6 

O3X 

1118 

710 

488 

354 

267 

208 

165 

134 

110 

4^4     •< 

535 

421 

237 

144 

91 

55 

35 

25 

15 

„,, 

1158 

798 

582 

442 

345 

276 

225 

186 

&72       ^ 

554 

504 

310 

202 

136 

67 

47 

4       J 

1046 

763 

580 

454 

364 

296 

246 

4       1 

755 

470 

305 

210 

145 

77 

5      J 

1200 

913 

716 

576 

471 

392 

1 

.934 

618 

427 

304 

223 

166 

6       J 

1322 

1038 

836 

686 

572 

1 

1051 

751 

540 

355 

300 

OREGON   PINE    OR   SHORT-LEAF  YELLOW  PINE. 


Distance  centre  to  centre  of  floor  beams  in  feet. 

Thickness  of 

plank  in  ins. 

4 

5 

6 

7 

8 

9 

10 

11 

12 

7      ^ 

462 

291 

199 

143 

106 

81 

64 

•1/8      j 

205 

55 

52 

25 

15 

7 

j 

747 

473 

324 

234 

176 

136 

107 

*/»      "j 

425 

21  '2 

1/7 

65 

41 

25 

14 

1005 

637 

438 

317 

239 

185 

1  17 

119 

97 

*-/4       j 

670 

335 

157 

112 

65 

44 

28 

77 

5 

t  '     i 

1040 

717 

522 

395 

308 

246 

*^oo 

165 

=3/2       "j 

706 

401 

246 

1  59 

106 

72 

*~50 

34 

A 

1362 

940 

685 

520 

406 

325 

265 

220 

4         1 

1061 

606 

374 

244 

165 

115 

51 

55 

K          j 

1476 

1078 

819 

642 

516 

422 

351 

5          1 

745 

451 

240 

174 

125 

A          j 

1560 

1187 

932 

749 

614 

512 

6          1 

1302 

557 

425 

314 

236 

*  Weight  of  ceiling,  if  any,  to  be  deducted. 


WOODEN  FLOORS. 


669 


TABLE    IV.— SAFE    LIVE    LOAD    IN    POUNDS     PER 
SQUARE    FOOT   FOR   PLANK   FLOORING  * 

(continued). 

(See  explanation  on  page  667.) 
SPRUCE. 


Distance  between  centres  of  floor  beams  in  feet. 

Thickness  of 

plank  in  ins. 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 

360 

227 

155 

111 

83 

64 

50 

1/8      j 

755 

92 

49 

25 

3 

j 

581 

368 

252 

182 

137 

105 

83 

67 

54 

<2/§      -j 

357 

194 

705 

54 

39 

24 

75 

2M 

782 
572 

493 

307 

341 

773 

247 
704 

186 
55 

144 

42 

115 
23 

93 

75 

76 

1 

1228 

781 

548 

391 

298 

231 

184 

150 

124 

1 

7274 

544 

357 

225 

745 

98 

55 

47 

33 

A         3 

1060 

731 

533 

405 

317 

253 

207 

171 

4     1 

968 

554 

343 

753 

705 

77 

*      3 

1148 

839 

638 

500 

402 

329 

273 

5    1 

7053 

552 

450 

377 

272 

162 

120 

ft    j 

1213 

924 

725 

583 

478 

400 

6   1 

7755 

755 

545 

354 

250 

220 

WHITE    PINE. 


Distance  between  centres  of  floor  beams  in  feet. 

Thickness  of 

plank  in  ins. 

4 

5 

6 

7 

8 

9 

10 

11 

12 

7X       3 

307 

193 

131 

94 

70 

53 

41 

1x8       "j 

753 

74 

35 

27 

77 

5 

| 

496 

314 

114 

1  54 

116 

89 

70 

56 

2%     -j 

3/3 

757 

55 

50 

40 

75 

70 

i 

668 

424 

290 

210 

158 

122 

97 

78 

63 

2^     •< 

455 

245 

735 

53 

52 

33 

20 

1 

1088 

691 

476 

316 

261 

203 

162 

131 

,  108 

3/2      -j 

7047 

525 

255 

753 

7/5 

75 

53 

35 

25 

A     3 

906 

625 

455 

345 

269 

215 

175 

145 

4     1 

757 

457 

275 

757 

723 

50 

43 

5   i 

982 

716 

544 

426 

342 

283 

232 

5    I 

553 

555 

355 

257 

775 

725 

55 

fi        j 

1419 

1037 

789 

619 

497 

407 

339 

1 

7553 

570 

543 

445 

375 

234 

775 

*  Weight  of  ceiling,  if  any,  to  be  deducted. 


670  WOODEN  FLOORS. 

glance.  Incidentally  the  tables  also  show  which  kind  of  wood 
will  be  most  economical. 

If,  owing  to  the  room  being  irregular  in  shape,  the  joists  must 
be  of  different  lengths,  the  spacing  or  thickness  of  the  joists  may 
be  varied,  so  that  the  same  depth  may  be  used  throughout. 

The  only  precautions  to  be  exercised  in  using  these  tables  are  in 
regard  to  the  superimposed  load  and  the  actual  size  of  the  timbers. 

The  total  loads  for  which"  the  maximum  spans  have  been  com- 
puted are  given  at  the  head  of  each  table.  The  actual  weight  of 
the  floor  (beams,  flooring,  plastering,  and  deafening,  if  any) 
subtracted  from  the  total  load  will  give  the  superimposed  load, 
i.e.,  the  load  which  the  floor  is  expected  to  carry. 

If  the  joists  do  not  run  full  to  dimensions,  the  span  or  spacing 
must  be  reduced  from  that  given  in  the  tables,  and  as  in  certain 
localities  the  stock  sizes  of  joists  often  run  from  J  inch  to  f  inch 
scant  of  the  nominal  dimensions,  this  fact  should  always  be 
taken  into  account  when  determining  upon  the  size  of  joists. 
In  this  connection  it  will  be  convenient  to  remember  that  a 
2-inch  joist  spaced  16  ins.  c.  to  c.  has  the  same  strength  as  a  1 J- 
inch  joist  12  ins.  centre  to  centre. 

A  reduction  should  also  be  made  for  any  cutting  of  the  joists 
that  may  be  required. 

No  allowance  has  been  made  for  partitions,  and  when  they  are 
to  be  supported  by  the  floor  joists  additional  joists  should  be  used 
or  the  span  reduced  according  to  the  relative  direction  or  position 
of  the  partition  and  joists. 

Tables  V.  to  IX.  inclusive,  were  computed  by  the  formula  for 
stiffness,  on  the  assumption  that  the  deflection  should  not  exceed 
3*0  of  an  inch  per  foot  of  span.  Tables  X.  and  XI.  were  computed 
by  the  formula  for  strength. 

The  spans  given  in  these  tables  come  within  the  requirements 
of  the  Buffalo  and  Denver  building  laws,  and  Tables  V.,  VII., 
VIII.,  IX.,  and  X.  comply  with  the  Chicago  law  and  very 
nearly  with  the  New  York  law,  but  to  comply  with  the  Boston 
law  a  reduction  of  about  one-sixth  must  be  made  from  the  spans 
given. 

By  Georgia  pine  is  meant  the  long-leaf  yellow  or  hard  pine. 


WOODEN   FLOORS. 


671 


TABLE  V.— MAXIMUM  SPAN  FOR  CEILING  JOISTS. 

Total  load,  20  pounds  per  square  foot. 


Size  of 
Joist. 

Dist.  on 
Centres. 

Hemlock 

White 
Pine. 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas 
Pine. 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

2X4 

12 

9       3 

9       5 

10          1 

10         5 

11       2 

2X4 

16 

8       5 

8       6 

9         1 

9         5 

10       1 

2X6 

12 

14       0 

14        1 

15          1 

15         7 

16       8 

2X6 

16 

12       8 

12     10 

13         8 

14         2 

15       2 

2X8 

12 

18       8 

18     10 

20          1 

20         9 

22       4 

2X8 

16 

17       0 

17       2 

18         4 

18       11 

20       5 

2X8 

20 

15       9 

15     10 

17         0 

17         6 

18     10 

Total  load,  24  pounds  per  square  foot. 

2X10 

12 

22       0 

22       2 

23         8 

24         5 

26       4 

2X10 

16 

20       0 

20       2 

21         7 

22         3 

23     10 

2X10 

20 

18       6 

18       8 

20         0 

20         7 

22       2 

2X12 

12 

26       5 

26       8 

28         5 

29         4 

31       7 

2X12 

16 

24       0 

24       2 

25       10 

26         8 

28       8 

2X12 

20 

22       3 

22       5 

24         0 

24         8 

26       8 

See  remarks,  page  670. 


TABLE  VI.— MAXIMUM  SPAN  FOR  FLOOR  JOISTS. 

DWELLINGS,    TENEMENTS,    AND    GRAMMAR-SCHOOL    ROOMS    WITH 

FIXED    DESKS. 
Total  load,  60  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 
Centres. 

Hemlock 

White 
Pine. 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas 
Pine. 

Georgia 
Pine. 

Ins. 

Ft.    Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

2X6 

12 

9       9 

9     10 

10         5 

10       10 

11       7 

2X6 

16 

8       9 

8     10 

9         6 

9       10 

10       6 

3X6 

12 

11       1 

11       2 

12         0 

12         5 

13       4 

3X6 

16 

10       1 

10       2 

10       10 

11          2 

12       1 

2X8 

12 

12     11 

13       1 

13        11 

14         5 

15       6 

2X8 

16 

11       9 

11     10 

12         8 

13         1 

14       1 

3X8 

12 

14       9 

14     11 

16         0 

16         6 

17       8 

3X8 

16 

13       6 

13       7 

14          6 

15         0 

16       2 

2X10 

12 

16       2 

16       4 

17          5 

18         0 

19       4 

2X10 

16 

14       9 

14     10 

15         9 

16         4 

17       7 

Total  load,  66  pounds  per  square  foot. 

3X10 

12 

18       0 

18       1 

19         3 

20         0 

21       6 

3X10 

16 

16       3 

16       5 

17         7 

18         2 

19      6 

2X12 

12 

18     10 

19       0 

20         3 

20       10 

22       6 

2X12 

16 

17        2 

17       3 

18         4 

19         0 

20       6 

3X12 

12 

21       6 

21       8 

23          2 

24         0 

25       9 

3X12 

16 

19       7 

19       8 

21          1 

21          9 

23       5 

2X14 

12 

22       0 

22        2 

23         8 

24         4 

26       3 

2X14 

16 

20       0 

20        1 

21          6 

22         2 

23     10 

2^X14 

12 

23       8 

23     10 

25          6 

26          3 

28       3 

24-X14 

16 

21       6 

21       8 

23          2 

23       10 

25       8 

3X14 

12 

25       4 

25        4 

27          1 

28         0 

30       1 

3X14 

16 

23       0 

23        0 

24         7 

25         4 

27       4 

672 


WOODEN   FLOORS. 


TABLE  VII.— MAXIMUM  SPAN   FOR  FLOOR  JOISTS. 

OFFICE    BUILDINGS. 
Total  load,  93  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 
Centres. 

White  Pine 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas  Pine 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

3X8 

12 

12     10 

13       9 

14       2 

15       4 

3X8 

16 

11       8 

12       6 

12     10 

13     10 

2X10 

12 

14       1 

15       1 

15       6 

16       7 

2X10 

16 

12       9 

13       8 

14       1 

15       2 

3X10 

12 

16       1 

17       3 

17       9 

19       2 

3X10 

16 

14       8 

15       8 

16       2 

17       5 

2X12 

12 

16     10 

18       1 

18       8 

20       1 

2X12 

16 

15       4 

16       5 

17       0 

18       3 

Total  load,  96  pounds  per  square  foot. 

3X12 

12 

19       2 

20       6 

21       2 

22       9 

3X12 

16 

17       5 

18       7 

19       3 

20       8 

2X14 

12 

19       6 

20     10 

21       7 

23       2 

2X14 

16 

17       9 

19       0 

19       7 

21       2 

2^X14 

12 

21        1 

22       6 

23       2 

25       0 

2^X14 

16 

19       2 

20       4 

21       2 

22       8 

3X14 

12 

22       4 

23     10 

24       8 

27       7 

3X14 

16 

20       4 

21       8 

22       5 

24       1 

See  remarks,  page  670. 


TABLE  VIII.— MAXIMUM    SPAN    FOR    FLOOR  JOISTS. 

CHURCHES    AND   THEATRES    WITH   FIXED   SEATS. 
Total  load,  102  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 
Centres. 

White  Pine 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas  Pine 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

3X8 

12 

12       6 

13       4 

13       9 

14     10 

3X8 

16 

11       4 

12       2 

12       6 

13       6 

2X10 

12 

13       7 

14       7 

15       1 

16       2 

2X10 

16 

12       4 

13       3 

13       8 

14       9 

3X10 

12 

15       8 

16       9 

17       3 

18       7 

3X10 

16 

14       2 

15       2 

15       8 

16     10 

2X12 

12 

16       5 

17       7 

18       1 

19       6 

2X12 

16 

14     10 

15   n 

16       5 

17       8 

Total  load,  105  pounds  per  square  foot. 

3X12 

12 

18       7 

19     11 

20       6 

22       1 

3X12 

16 

16     10 

18       1 

18       7 

20       1 

2X14 

12 

19       0 

20       3 

20     10 

22       6 

2X14 

16 

17       3 

18       5 

19       0 

20       6 

2^X14 

12 

20       4 

21       9 

22       6 

24       3 

2^X14 

16 

18       7 

19     10 

20       6 

22       1 

3X14 

12 

21       8 

23       2 

23     10 

25       9 

3X14 

16 

19       8 

21        1 

21       9 

23       4 

WOODEN   FLOORS.  673 

TABLE  IX.— MAXIMUM    SPAN    FOR    FLOOR    JOISTS. 

ASSEMBLY   HALLS   AND    CORRIDORS. 
Total  load,  123  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 

Centres. 

White  Pine 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas  Pine 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.    Ins. 

3X8 

12 

11       7 

12       7 

13       0 

14       0 

3X8 

16 

10       8 

11       4 

11       9 

12       8 

2X10 

12 

12     10 

13       9 

14       2 

15       2 

2X10 

16 

11       7 

12       6  . 

12     10 

13     10 

3X10 

12 

14       8 

15       8 

16       2 

17       5 

3X10 

16 

13       4 

14       3 

14       9 

15     10 

2X12 

12 

15       4 

16       6 

17       0 

18       3 

2X12 

16 

14       0     1     15       0 

15       5 

16       7 

Total  load,  126  pounds  per  square  foot. 

3X12 

12 

17       6 

18       8 

19       3 

20       9 

3X12 

16 

15     10 

17       0 

17       7 

18     11 

2X14 

12 

17     10 

19       1 

19       8 

21        2 

2X14 

16 

16       2 

17        4 

17     11 

19       3 

2^X14 

12 

19       3 

20       6 

21       2 

22       9 

2^X14 

16 

17       6 

18       8 

19       3 

20       9 

3  X14 

12 

20       5 

21       9 

22       6 

24       3 

3X14 

16 

18       7 

19     10 

20       6 

22       1 

See  remarks,  page  670. 


TABLE  X.— MAXIMUM  SPAN  FOR  FLOOR  JOISTS. 

RETAIL   STORES. 
Total  load,  174  pounds  per  square  foot. 


Size  of 

Joists. 

Dist.  on 
Centres. 

White 
Pine. 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas  Pine. 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.     Ins. 

Ft.  Ins. 

Ft.  Ins. 

3X8 

12 

11       6 

12       5 

14       1 

14       9 

3X8 

16 

9     11 

10       2 

12       2 

12       9 

2X10 

12 

11       8 

12       8 

14       5 

15       1 

2X10 

16 

10       2 

10     11 

12       5 

13       1 

3X10 

12 

14       4 

15       6 

17       7 

18       7 

3X10 

16 

12       5 

13       5 

15       2 

16       0 

2X12 

12 

14       1 

15       2 

17       2 

18       2 

2X12 

16 

12       2 

13       1 

14     11 

15       8 

Total  load,  177  pounds  per  square  foot. 

3X12 

12 

17            2 

18           5 

20          11 

22            1 

3X12 

16 

1  !          10 

16            0 

18           2 

T5       i 

2X14 

12 

1  0            3 

17           7 

19         11 

21            1 

2X14 

16 

14            2 

15            2 

17           3 

18           2 

2^X14 

12 

18            2 

19           7 

22            3 

23           6 

2^X14 

16 

15           9 

17            0 

19           3 

20           4 

3X14 

12 

19         11 

21            6 

24           5 

25           8 

3X14 

16 

17           3 

18           7 

21            2 

22           3 

674 


WOODEN  FLOORS. 


TABLE  XI.— MAXIMUM  SPAN  FOR  RAFTERS. 

A.    SHINGLED  ROOFS    NOT   PLASTERED.* 
Total  load,  48  pounds  per  square  foot 


Size  of 
Joists. 

Dist.  on 
Centre. 

Hemlock 

White 
Pine. 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas 
Pine. 

Georgia 
Pine. 

Ins. 

Ft    Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

2X4 

16 

7       4 

7       9 

8         4 

9         6 

10     10 

2X4 

20 

6       7 

6     10 

7         6 

8         6 

8     10 

2X6 

16 

11        1 

11       7 

12         6 

14         2 

15       0 

2X6 

20 

9     11 

10       4 

11          2 

12         8 

13       4 

3X6 

16 

13      7 

14       2 

15         3 

17         5 

18       3 

3X6 

20 

12       2 

12       8 

13         8 

15         7 

16       4 

2X8 

16 

14       9 

15       6 

16         8 

18       11 

20       0 

2X8 

20 

13       3 

13     10 

14       11 

16       11 

17      10 

2X8 

24 

12        1 

12       7 

13         7 

15         6 

16       3 

2X10 

16 

18       6 

19       3 

20       10 

23         8 

25       0 

2X10 

20 

16       7 

17        3 

18         8 

21          2 

22       3 

2X10 

24 

15        1 

15       9 

17         0 

19          3 

20       4 

B.     SLATE    ROOFS    NOT    PLASTERED,    OR    SHINGLE    ROOFS 
PLASTERED.* 

Total  load,  57  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 
Centres. 

Hemlock 

White 
Pine. 

Spruce. 

Oregon 
Pine, 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

2X4 

16 

6       9 

7       1 

7         7 

8         8 

9       2 

2X4 

20 

6       0 

6       4 

6         9 

7         9 

8       2 

2X6 

16 

10       2 

10       7 

11         6 

13         0 

13       8 

2X6 

20 

9       1 

9       6 

10         2 

11         7 

12       3 

3X6 

16 

12       6 

13       0 

14         1 

15       11 

16       9 

3X6 

20 

11        1 

11       8 

12         7 

14         3 

15       0 

2X8 

16 

13       7 

14       2 

15         3 

17         4 

18       3 

2X8 

20 

12       2 

12       8 

13         8 

15         6 

16       4 

2X8 

24 

11        1 

11       7 

12         6 

14         2 

14     11 

3X8 

16 

16       7 

17       4 

18         9 

21         3 

22       5 

3X8 

20 

14     10 

15       6 

16         9 

19         0 

20       1 

3X8 

24 

13       7 

14       2 

15         3 

17         4 

18       4 

2X10 

16 

17       0 

17       8 

19         2 

21         7 

22     10 

2X10 

20 

15       2 

15     10 

17          1 

19         4 

20       6 

2X10 

24 

13     10 

14       6 

15         7 

17         8 

18       8 

*  These  tables  allow  for  a  snowfall  of  2  feet.  In  the  Southern  States  the 
spans  in  section  A  will  be  safe  for  slate  or  gravel  roofs,  if  the  joists  are  full 
to  dimensions. 


WOODEN  FLOORS. 


B75 


TABLE  XL— MAXIMUM  SPAN  FOR  RAFTERS  (continued). 

C.    SLATE    ROOFS    PLASTERED,    OR    GRAVEL   ROOFS   NOT 

PLASTERED.* 
Total  load,  66  pounds  per  square  foot. 


Size  of 
Joists. 

Dist.  on 
Centres. 

Hemlock 

White 
Pine. 

Spruce  or 
Norway 
Pine. 

Oregon  or 
Texas 
Pine. 

Georgia 
Pine. 

Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ft.  Ins. 

2X6 

16 

9       5 

9     10 

10         8 

12          1 

12       9 

2X6 

20 

8       6 

8     10 

9         6 

10         9 

11       5 

3X6 

16 

11       7 

12       1 

13          1 

14       10 

15       7 

3X6 

20 

10      4 

10     10 

11         8 

13         3 

14       0 

2X8 

16 

12      7 

13       2 

14         2 

16         2 

17       0 

2XC 

20 

11       3 

11       9 

12         9 

14         5 

15       2 

2X8 

24 

10      3 

10       9 

11        7 

13         2 

13     10 

3X8 

16 

15       5 

16       1 

17         5 

19         9 

20     10 

3X8 

20 

13       9 

14       5 

15         3 

17         8 

18       8 

3X8 

24 

12       7 

13       2 

14         2 

16         2 

17       0 

2X10 

16 

15       9 

16       6 

17         9 

20         2 

21       3 

2X10 

20 

14       1 

14      8 

15       11 

18         0 

19       0 

2X10 

24 

12     10 

13       5 

14         6 

16        6 

17       5 

2X12 

16 

18     10 

19       9 

21         4 

24         2 

25       6 

2X12 

20 

16     10 

17       8 

19         1 

21         8 

22     10 

2X12 

24 

15       5 

16       1 

17         5 

19         9 

20     10 

*  These  tables  are  intended  for  climates  where  a  snowfall  of  2  feet  may  be 
expected.  In  the  Southern  States,  where  there  is  no  snow  to  speak  of,  the 
spans  in  the  first  sections  will  be  safe  for  slate  or  gravel  roofs  if  the  joists  are 
sawn  full  to  dimensions. 

To  Determine  the  Strength  of  an  Existing  Floor. 

—When  a  building  is  leased  for  mercantile  or  manufacturing 
purposes  the  tenant  will  generally  desire  to  know  the  greatest 
load  which  it  will  be  safe  to  put  upon  the  floors,  and  some  build- 
ing laws  require  that  the  safe  load  for  the  floors  in  certain  classes 
of  buildings  shall  be  computed  and  posted  in  a  conspicuous 
place  in  each  story.  It  is  therefore  important  that  every  architect 
should  know  how  to  compute  the  safe  strength  of  any  existing 
floor. 

The  problem  is  practically  the  reverse  of  that  of  proportioning 
a  floor  to  a  given  load. 

In  speaking  of  the  strength  of  a  floor  a  distinction  should  be 
made  between  the  safe  strength  and  the  safe  load.  The  "safe 
strength "  should  mean  the  maximum  safe  load  for  the  beams, 
including  the  weight  of  the  construction,  flooring,  and  ceiling, 
while  the  "safe  load"  refers  to  the  maximum  load  which  may 
safely  be  placed  upon  the  floor.  The  safe  load  is  found  by  first 
computing  the  safe  strength  and  then  subtracting  the  weight 
of  the  materials  forming  the  floor,  including  the  ceiling  below? 


676 


WOODEN  FLOORS. 


if  there  is  one.  The  most  convenient  measurement  for  either 
the  "safe  strength  "  or  the  "safe  load  "  of  a  floor  is  in  pounds  per 
square  foot. 

The  following  example  will  serve  to  show  the  process  of 
determining  the  safe  load  for  an  ordinary  warehouse  floor. 

EXAMPLE  4. — What  is  the  safe  load  per  square  foot  for  a  floor 
framed  as  shown  in  Fig.  4,  all  of  the  timber  being  Eastern  spruce, 


Load  from  Stairs 
1800  Ibs. 

Fig.  4 

the  beams  being  covered  with  two  thicknesses  of  |-inch  flooring 
and  having  a  corrugated  iron  ceiling  below  ? 

The  first  step  will  be  to  find  the  safe  strength  of  the  22-ft.  joists. 
As  this  is  a  warehouse  floor  we  will  use  the  tables  for  strength 
entirely.  From  Table  VI. ,  Chapter  XVI.;  we  find  the  safe  strength 
of  a  1X14  spruce  beam  of  22  ft.  span  to  be  1,247  Ibs.,  hence  the 
strength  of  a  2i"X  14"  beam  will  be  2$X  1,247,  or  3,117  Ibs.  As 
the  joists  are  16  ins.  on  centres,  each  joist  supports  a  floor  area 
of  1 JX22  ft.  =  29J  sq.  ft.  The  safe  strength  per  square  foot  of  this 
portion  of  the  floor  will  therefore  be  3,117-^29.3  or,  106  Ibs.  The 
weight  of  the  floor  per  square  foot  will  be  about  6|  Ibs.  for  the 
joists,  6  Ibs.  for  the  flooring,  and  1  Ib.  for  the  corrugated  iron 
ceiling,  or,  say  14  Ibs.  in  all.  Therefore  the  safe  load  per  square 
foot  for  the  22-ft.  joists  will  be  106-14,  or  92  Ibs. 

We  will  next  find  the  safe  load  for  the  4X14  headers  at  each  side 


WOODEN  FLOORS.  677 

of  the  stair  well.  As  the  tail  beams  are  framed  into  the  headers, 
we  should  deduct  one  inch  from  the  thickness  of  the  beam  for 
the  loss  of  strength  in  framing,  leaving  3"X  14"  for  the  effective 
dimensions  of  the  headers.  From  Table  VI.  ,  Chapter  XVI.,  we 
find  the  safe  strength  of  a  1  X  14,  12-ft.  span  to  be  2,286  Ibs. 
Hence  the  strength  of  the  3X  14  will  be  6,858  Ibs.  The  floor  area 
supported  by  each  header  is  4iXl2  ft.  =54  sq.  ft.;  hence  the 
safe  strength  of  the  header  per  square  foot  of  floor  =  6,  858  -f-  54  = 
127  Ibs.  Deducting  the  weight  of  the  floor  per  sq.  ft.  14  Ibs., 
we  have  113  Ibs.  per  sq.  ft.  for  the  safe  load. 

Strength  of  Trimmer  A.  —  Trimmer  A  supports  about  the 
same  amount  of  flooring  as  one  of  the  common  joists,  and  also 
the  ends  of  the  headers.  Deducting  2J  ins.,  the  thicknesses  of 
the  common  joists,  we  have  a  5"X14"  beam  left  to  support 
the  headers.  As  the  headers  are  supported  in  iron  stirrups  no 
deduction  in  strength  need  be  made  for  framing. 

To  find  the  safe  strength  of  a  beam  loaded  with  two  concen- 
trated loads,  equally  distant  from  the  supports,  we  must  use 
formula  14,  Chapter  XVI.  In  this  case  ra=8'  10"  or  8f,  and 
A  =70. 

T  •      4.U    t         i        t    i     A  t;  '  •'  i     5X196X70 

Applying  the  formula  safe  load  at  each  point  = 


1,942  Ibs.  The  floor  area  supported  by  one  stirrup  is  equal  to 
one-half  of  the  area  supported  by  the  header,  or  27  sq.  ft.  ;  hence 
the  safe  strength  per  square  foot  of  the  5X  14  header  is  1,942-^-27, 
or  72  Ibs.,  and  deducting  14  Ibs.  for  weight  of  the  floor,  we  have 
58  Ibs.  per  square  foot  as  the  safe  load  that  the  trimmer  will  sup- 
port on  the  floor  at  each  side  of  the  stairs.  Considering  that  the 
safe  load  for  the  2J  ins.  which  we  deducted  to  take  the  place  of  a 
common  joist  is  92  Ibs.,  we  might  place  the  safe  load  for  the  trim- 
mer at  an  average  of  92  and  58,  or  75  Ibs. 

Trimmer  B.  —  This  timber  has  to  support  the  same  floor 
loads  as  trimmer  A,  and  also  the  bottom  of  a  flight  of  stairs  for 
which  an  allowance  of  at  least  1,800  Ibs.  should  be  made. 

This  stair  load  being  practically  concentrated  at  the  centre  of 
the  trimmer  is  equivalent  to  a  distributed  load  of  3,600  Ibs.  As 
the  safe  load  for  a  IX  14-inch  joist  of  22  ft.  span  is  1,247  Ibs.,  it 
will  require  a  thickness  =3,  600-^1,  247,  or  2J  ins.,  to  support  the 
stairs,  leaving  7  J  ins.  to  support  the  floor  loads.  As  this  is  f  in. 
less  than  the  thickness  of  trimmer  A,  it  is  evident  that  the 
strength  of  the  floor  at  B  will  be  a  little  less  than  at  A,  but  as  it 
is  improbable  that  the  entire  floor  space  will  be  loaded  at  any 


678  WOODEN  FLOORS. 

given  time,  it  would  be  safe  to  rate  the  strength  of  the  floor  at 
each  side  of  the  stairway  at  75  Ibs.  per  square  foot,  live  load,  and 
beyond  the  stairway  at  92  Ibs. 

Partitions. — When  the  floor  supports  partitions  their  weight 
and  any  load  resting  upon  them  must  be  taken  into  account  in 
determining  the  safe  load  for  the  floor.  If  the  partition  runs  the 
same  way  as  the  joists,  then  only  the  joist  directly  under  the 
partition,  and  the  joists  at  each  side  will  be  affected;  but  if  the 
partition  runs  across  the  joists,  then  it  affects  the  safe  load  of  the 
entire  floor. 

EXAMPLE  5. — Suppose  that  the  22-ft.  joists  in  the  floor  shown 
by  Fig.  4  have  to  support  a  plastered  partition  12  ft.  high  run- 
ning across  the  joists  half-way  between  the  walls,  what  will  be 
the  safe  load  for  the  floor? 

Ans.  A  plastered  partition  with  2"X4"  or  2"X6"  studding 
16  ins.  on  centres  will  weigh  about  20  Ibs.  per  sq.  ft. ;  hence  a 
partition  12  ft.  high  will  weigh  240  Ibs.  per  lineal  foot.  As  the 
joists  are  16  ins.  on  centres,  each  joist  will  support  1J  lineal  ft. 
of  partition  weighing  320  Ibs.  As  this  load  is  concentrated  at  the 
centre  of  the  joists  it  is  equivalent  to  a  distributed  load  of  640 
Ibs.  In  Example  4,  we  found  the  safe  distributed  load  for  a 
2J"X14"  spruce  joist  of  22ft.  span  to  be  3,117.  Subtracting 
640  Ibs.  from  this  we  have  2,477  Ibs.,  which  may  be  used  for 
the  floor.  As  the  floor  area  supported  by  one  joist  is  29J-  sq.  ft., 
the  safe  strength  of  the  floor  per  sq.  ft.  will  be  2,477  -f-  29  J,  or 
84  Ibs.,  and  the  safe  load  70  Ibs.  Hence  the  partition  decreases 
the  safe  load  by  22  Ibs.  per  square  foot. 

Whenever  the  upper-floor  joists  are  supported  by  a  partition 
carried  by  a  floor  below,  the  effect  of  the  partition  and  its  load 
upon  the  strength  of  the  lower  floor  should  be  very  care- 
fully computed. 

Bridging  of  Floor  Beams. — By  "bridging"  is  meant 
a  system  of  bracing  floor  beams,  either  by  means  of  small  struts, 
as  in  Fig.  5,  or  by  means  of  single  pieces  of  boards  set  at  right 
angles  to  the  joists,  and  fitting  in  between  them. 

The  effect  of  this  bracing  is  decidedly  beneficial  in  sustaining 
any  concentrated  weight  upon  a  floor;  but  it  does  not  materially 
strengthen  a  floor  to  resist  a  uniformly  distributed  load.  The 
bridging  also  stiffens  the  joists,  and  prevents  them  from  turning 
sideways  It  is  customary  to  insert  rows  of  cross-bridging 
at  from  every  five  to  eight  feet  in  the  length  of  the  beams; 
and  to  be  effective  thr-y  should  bo  in  straight  lines  along  the  floor, 


WOODEN  FLOORS. 


679 


so  that  each  strut  may  abut  directly  opposite,  those  adjacent  to 
it.     The  method  of  bridging  shown  in  Fig.  1,  and  known  as 
"cross-bridging, "is  considered 
to  be  by  far  the  best,  as  it  al- 
lows the  thrust  to  act  parallel 
to  the  axis  of   the   strut,  and 
not  across  the  grain,  as   must 
be  the  case  where  single  pieces 
of  board  are  used. 

The  bridging  should  be  of  1  \ 
inch  by  3-inch  stock,  for  joists 
2"X  Wand  under,  and  2"X3" 
stock  for  12"  and  14"  joists. 

Framing  of  Floor 
Beams. — In  dwellings,  tene- 
ment and  lodging  houses,  it 
is  a  common  practice  to  frame 

the  ends  of  the  tail  beams  into  Fig.  5 

the  headers,  and  very  often  the 

ends  of  the  headers  are  framed  into  the  trimmers.  For  light 
floors,  with  moderate  spans,  it  is  safe  to  frame  the  tail  beams  into 
a  header,  provided  the  latter  is  strong  enough  to  carry  the  load  and 
allow  1  inch  in  thickness  for  the  mortising.  Headers  carrying  not 


Fig.  6 

more  than  two  tail  beams  may  also  be  framed  into  the  trimmers, 
but    all   headers   six   feet   long   or   over    should    be   carried   in 


680 


WOODEN  FLOORS. 


joist  hangers  or  s-tirrups,  and  in  warehouses  and  all  firso-elas;? 
buildings  all  framing  should  be  done  by  means  of  joist  hangerc. 
As  to  the  best  shape  and  proportions  for  the  tenon  on  the  end 
of  the  tail  beam  or  header,  that  shown  by  Fig.  6  gives  probably 
as  large  a  proportion  of  the  strength  of  the  timbers  as  it  is  pos- 
sible to  utilize,  although  for  tail  beams  the  author  believes  that 
a  single  tenon  like  that  shown  in  Fig.  7  is  fully  as  strong,  especially 
when  the  header  is  built  up  of  two-inch  plank  spiked  together. 
In  either  case,  if  the  floor  is  loaded  to  its  full  strength,  the  tail 
beam  will  split  at  the  bottom  of  the  tenon  as  shown  in  Fig.  8. 


Rig.  7 


Fig.  8 


Stirrups  and  Joist  Hangers.  —  The  first  device  used 
for  framing  headers  to  trimmers  without  mortising  was  the 
wrought-iron  stirrup  shown  in  Fig.  9.  These  are  made  either 
single  or  double,  according  to  whether  one  or  two  beams  are  to 
be  supported.  To  prevent  the  floor  from  spreading  and  thus 
permitting  the  header  to  slip  out  of  the  stirrup  a  joint  bolt 
may  be  inserted,  as  shown  in  the  two  right-hand  illustrations 
of  Fig.  9. 

To  figure  the  strength  of  a  stirrup,  multiply  the  sectional  area 
of  the  iron  in  square  inches  by  12,000  Ibs. 

The  following  sizes  of  iron  should  in  general  be  used  for  the 
size  of  joist  to  be  supported: 


Section  of 
Stirrup. 


Size  of  Joist  or  Timber 
to  be  supported. 

2X  8to3X10 

4X10  to  4X.12  ...........................  }"X2J" 

6X12  to  3X14  ...........................  |"X3  " 

8X12  to  4X14  ...........................  J"X3J" 

6X14  ...................................  t"X4  " 

8X14  to  10X14  ..........................  |"X4  " 


WOODEN  FLOORS. 


681 


«Joist  Hangers. — Aside  from  the  matter  of  strength  there 
are  objections  to  the  use  of  stirrups,  in  that  if  the  timber  on 
which  they  rest  is  not  perfectly  dry,  the  stirrup  will  settle  by 
an  amount  equal  to  the  shrinkage  of  the  beam  on  which  it  rests, 


DOUBLE  STIRRUP 


SINGLE  STIRRUP  AND  JOINT  BOLT 


Fig.  9 

and  let  the  header  down  with  it ;  the  projection  of  the  iron  above 
the  top  of  the  timbers  necessitates  cutting  out  the  flooring,  and 
where  the  stirrups  are  exposed  they  do  not  present  a  neat 
appearance. 


Fig.  10 

Duplex  Joist  Hanger. 


Fig.  II 

Goetz  Joist  Hanger. 


Within  the  past  fifteen  years  several  patented  hangers  have 
been  placed  upon  the  market,  which  are  claimed  to  be  superior 


682  WOODEN  FLOORS. 

to  the  wrought-iron  stirrup.  The  first  of  these  in  point  of  time 
was  the  Duplex  hanger,  shown  in  Fig.  10.  This  was  quickly  fol- 
lowed by  the  Goetz  hanger,  shown  in  Fig.  11.  Both  styles  have 
been  extensively  used,  and  have  proven  perfectly  satisfactory. 
Both  are  made  in  sizes  to  fit  all  regular  sizes  of  joists  or  timbers, 
and  have  ample  strength  for  the  purpose  for  which  they  are 
intended.  As  shown  by  the  illustrations,  they  are  made  to  be 
inserted  in  round  holes  bored  in  the  side  of  the  carrying  timbers, 
at  or  a  little  above  the  centre  line.  With  these  hangers  the  effect 
of  shrinkage  is  reduced  one-half,  and  the  other  two  objections  to 
the  stirrup,  previously  mentioned,  are  overcome.  The  duplex 
hanger  has  ridges  on  the  inside  of  the  side  brackets  to  hold  the 
beam. 

When  the  timber  to  be  supported  exceeds  6  ins.  in  breadth, 
the  Duplex  hanger  is  made  in  two  parts,  and  is  bolted  to  both 
beams,  an  illustration  of  the  larger  size  hangers  being  given  in 
Chapter  XXII.  Fig.  12  shows  the  Duplex  I-beam  hanger  for 


Fig.  12 

Duplex  I-Beam  Hangers. 

framing  floor  joists  to  I-beams.  These  hangers  are  made  to 
exactly  fit  into  the  flange  of  the  I-beam,  they  have  a  rib  in 
bottom  of  hanger  §"  high,  which  serves  as  a  tie  when  the  joist 
is  placed  in  the  hanger,  and  they  provide  a  bearing  of  4J  inches 
for  the  joists.  These  hangers  are  made  to  carry  all  regular 
sizes  of  joists  from  2"X6"  up  to  6"X  16",  and  in  the  opinion  of 
the  author  offer  the  best  device  for  framing  wooden  joists  to 
I-beams  of  the  same  depth.  The  hangers  are  all  of  uniform 
height  and  a  f  "  hole  punched  6"  from  the  bottom  of  the  beam 
will  fit  any  of  them.  The  hangers  are  bolted  to  the  web  of  the 
I-beam. 

Fig.  13  shows  a  similar  hanger  made  to  support  the  wall  end 


WOODEN  FLOORS. 


683 


of  a  floor  joist.     The  writer  believes  this  to  be  much,  superior 
to  the  method  of  building  the  joist 
into  the  wall,  as  it  absolutely  pre- 
vents dry-rot,  and  permits  the  joist 
to   fall,    in    case    of    fire,    without 
throwing  the   wall.     It  also  gives £ 
the  weight  a  good  bearing  on  the 
wajl. 

Other  illustrations  of  wall  hang- 
ers are  given  in  Chapter  XXII. 

The  Van  Dorn  Hanger,  illus- 
trated by  Fig.  14,  is  essentially  a 
stirrup  forged  from  high-grade 
steel.  The  few  tests  that  have  been 


Fig.  13 

Duplex  Brick  Wall  Hanger. 


made  would  seem  to  indicate  that  it  possesses  a  little  more 
resistance  to  bending  than  the  ordinary  stirrup,  while  it  gives  a 
wider  bearing  for  the  joist,  and  presents  a  much  neater  appear- 
ance. 

Fig.  15  shows  the  same  hanger  riveted  to  a  bent  iron  plate,  to 
build  into  brick  walls. 

When  the  hanger  is  to  be  used  over  a  steel  beam  the  upper 
ends  are  bent  to  fit  over  the  flange  of  the  beam,  as  in  Fig.  16. 


Fig.  14 


Fig.  15 


Although  the  author  knows  of  no  test  of  the  strength  of  a  Van 
Dorn  I-beam  hanger,  it  would  seem  as  though  it  must  be  much 
stronger  than  the  pattern  made  for  wooden  beams,  on  account 


684 


WOODEN  FLOORS. 


of  the  clinch  over  the  flange  of  the  I-beam.    The  Van  Dora 
hangers  have  been  used  in  many  important  buildings. 


Fig.  16 


Rg.  u 

National  Hanger. 


Figs.  17  and  18  show  two  other  patented  joist  hangers  of  the 
Stirrup  type,  which  are  forged  from  plate  steel.  Both  of  these 

hangers  are  also  made 
for  building  into  brick 
walls,  and  to  go  over 
steel  beams.  The  na- 
tional hanger  is  a  par- 
ticularly good  one,  on 
account  of  the  flange 
on  top,  which  should 
help  to  a  considerable 
degree  in  distributing 
the  load  over  the  top 
of  the  beam.  The 
Fig.  18  larger  hangers  of  this 

Lane  Hanger.  style  have  holes  in  the 

top  for  large  spikes.     The  Lane  hanger  is  made  very  light. 

Comparative  Strength  of  Different  Styles  of  Joist 
Hangers, — Although  the  tests  that  have  been  made  to  deter- 
mine the  strength  of  different  hangers  are  few  in  number,  still 
enough  have  been  made  to  show  that  any  one  of  the  hangers 
described,  including  the  common  stirrup,  are  abundantly  strong 
for  any  single  floor  beam  not  exceeding  4"  X 14"  in  size.  It  is 
only  in  the  case  of  a  header  or  trimmer  which  supports  a  con- 
siderable floor  area  that  the  strength  need  be  considered  at  alL 


WOODEN  FLOORS. 


685 


From  tests  made  at  the  Massachusetts  Institute  of  Technology, 
and  later  at  St.  Louis,  it  would  appear  that  the  Duplex  hangers 
are  affected  the  least  of  any  under  extreme  loads.  A  two-part 
hanger,  carrying  a  10  X 14 
inch  girder,  sustained  a 
load  of  38,000  Ibs.  with- 
out injury  to  the  hanger 
itself.  A  similar  hanger 
held  until  loaded  to 
39,550  Ibs.,  when  one  side 
broke  off  short  under  the 
nipple  projecting  into  the 
timber,  the  condition  of 
the  hanger  after  failure 
being  shown  by  Fig.  19. 

A  common  stirrup  made 
from    f"X2J"    wrought  ;  Fi9-  l9 

iron  failed  under  a  load  of  13,750  Ibs.  by  bending  and  pulling 
over  the  header,  as  shown  in  Fig.  20.  A  6"  XI 2"  Van  Dorn 
hanger  "began  to  straighten  out  under  a  load  of  13,300  Ibs., 
and  failed  as  in  Fig.  21  at  a  load  of  18,750  Ibs."  * 

Single  hangers  of  the 
stirrup  type  do  not  break, 
but  fail  by  the  bending 
up  of  the  portion  which 
lays  over  the  top  of  the 
header,  as  in  Figs.  20  and 
21.  They  also  appear  to 
crush  the  wood  under 
them,  particularly  at  the 
edge,  to  a  very  much 
greater  degree  than  does 
the  spool  of  the  Duplex 
hanger. 

With   a  double  stirrup 
the  ultimate   strength   is 
measured  by  the  strength 
F'9«  20  of     the     iron.      Thus    a 

double  stirrup  made  of  f"X2J"  wrought  iron  was  loaded 
up  to  57,650  Ibs.  (28,825  Ibs.  on  each  side),  when  it  broke 


*  Chas.  E.  Fuller,  M.E.D.,  Dept.  M.I.T. 


686 


WOODEN  FLOORS. 


at  one  of  the  lower  corners.  A  single  stirrup  would  of  course 
be  just  as  strong  if  it  could  be  kept  from  bending.  In  actual 
construction  the  flooring  over  the  beams  would  to  some  degree 

prevent  the  top  of  a  stirrup 
from  springing  up.  The 
tests  that  have  been  made 
of  the  Duplex  hangers? 
show  conclusively  that 
where  only  a  single  hanger- 
is  used  the  holes  which  are 
bored  in  the  header  do  not 
affect  its  strength,  at  least 
when  the  load  is  within  the 
safe  limit,  and  a  test  made 
at  Baltimore,  Md.,  Aug.  24, 
190.4,  with  2//X12//  joists, 
spaced  12  ins.  on  centres 
and  suspended  by  duplex 
hangers  let  into  a  header 
formed  of  three  3"X12" 
j  oists ,  spiked  together , would 
seem  to  prove  that  even 
when  the  holes  are  12  ins. 
on  centres  they  do  not 

weaken  the  header.  The  only  record  of  the  failure  of  any  form 
of  hanger  when  in  actual  .use  in  a  building,  of  which  the  author  is 
aware,  is  that  of  a  case  in  Minneapolis,  where  a  portion  of  six 
floors  of  a  warehouse  fell,  on  Nov.  7,  1902,  through  the  failure  of 
a  wall  hanger  made  from  a  4"X2"Xi"  structural  steel  angle, 
sheared  and  bent  as  in  Fig.  17,  and  riveted  to.  a  bearing-plate 
8"X1G"X  i".  The  failure  was  due  to  the  crushing  of  the  outer 
edge  of  the  brickwork  under  the  hanger,  and  the  [consequent 
bending  up  of  the  top.  The  actual  load  on  the  hanger  was 
about  15,000  Ibs.  See  Engineering  News  of  Nov.  20,  1902. 


Fig.  21 


MILL  AND  WAREHOUSE  CONSTRUCTION.      687 


CHAPTER  XXII. 
MILL  AND  WAREHOUSE  CONSTRUCTION. 

Mill  Construction. — This  term  is  commonly  used  to  des- 
ignate a  method  of  construction  brought  about  largely  through 
the  influence  of  the  factory  mutual  insurance  companies  of  New 
England,  and  especially  through  the  efforts  of  Mr.  William  B. 
Whiting,  whose  mechanical  judgment,  experience,  and  skil)  as  a 
manufacturer  were  for  many  years  devoted  to  the  interests  of 
these  companies  and  to  the  improvement  of  factories  of  all 
kinds. 

The  extended  use  of  this  system,  and  the  improvements  that 
have  been  made  in  it  during  the  past  twenty  years,  is  probably 
due  more  to  the  influence  of  Mr.  Edward  Atkinson,  president 
of  the  Boston  Manufacturers  Mutual  Insurance  Co.  and  director 
of  the  Insurance  Engineering  Experiment  Station  at  Boston,  than 
to  that  of  any  other  individual. 

The  motive  of  mill  construction  is  to  reduce  the  fire  risk  to 
its  lowest  point,  without  going  to  the. expense  of  fire-proof  con- 
struction. The.  mill  construction  recommended  by  the  Factory 
Mutual  Companies  has  proved  to  be  so  safe  as  a  whole,  and 
such  factories  have  been  covered  by  mutual  insurance  at  so 
little  cost  as  to  render  it  wholly  inexpedient,  or  even  unneces- 
sary, for  the  owners  of  textile  factories  and  workshops  to  take 
any  other  method  into  consideration. 

The  entire  subject  of  Slow-burning  or  Mill  Construction,  as 
applied  to  factories,  is  most  admirably  described  and  illustrated 
in  Report  No.  5,  of  the  Insurance  Engineering  Station,  No.  31 
Milk  St.,  Boston,  Mass.,*  from  which  the  author  has  by  permis- 
sion taken  the  following  illustrations  and  descriptions. 

What  Mill  Construction  Is. 

[From  Report  No.  5  of  the  Insurance  Engineering  Station.] 
1.  Mill  construction  consists  in  so  disposing  the  timber  and 
plank  in  heavy  solid  masses  as  to  expose  the  least  number  of 

*  This  Report  may  be  procured  for  25  cents. 


688     MILL  AND  WAREHOUSE   CONSTRUCTION. 

corners  or  ignitable  projections  to  fire,  to  the  end  also  that 
when  fire  occurs  it  may  be  most  readily  reached  by  water  from 
sprinklers  or  hose. 

2.  It  consists  in  separating  every  floor  from  every  other  floor 
by  incombustible  stops, — by  automatic  hatchways,  by  encasing 
stairways  either  in  brick  or  other  incombustible  partitions, — 
so  that  a  fire  shall  be  retarded  in  passing  from  floor  to  floor  to 
the  utmost  that  is  consistent  with  the  use  of  wood  or  any  material 
in  construction  that  is  not  absolutely  fire-proof. 

3.  It  consists  in  guarding  the  ceilings  over  all  specially  haz- 
ardous stock  or  processes  with  fire-retardent  material  such  as 
plastering  laid  on  wire  lath  or  expanded  metal,  or  upon  wooden 
dovetailed  lath,  following  the  lines  of  the  ceiling  and  of  the 
timbers  without  any  interspaces  between  the   plastering  and 
the  wood;  or  else  in  protecting  ceilings  over  hazardous  places 
with  asbestos  air-cell  board,  sheet  metal,  Sackett  wall  board,  or 
other  fire-retardent. 

4.  It  consists  not  only  in  so  constructing  the  mill,  workshop, 
or  warehouse  that  fire  shall  pass  as  slowly  as  possible  "from  one 
part  of  the  building  to  another,  but  also  in  providing  all  suitable 
safeguards  against  fire. 

What  Mill  Construction  is  Not. 

1.  Mill   construction  does    not    consist  in  disposing   a  given 
quantity  of  materials  so  that  the  whole  interior  of  a  building 
becomes  a  series  of  wooden  cells,  being  pervaded  with  concealed 
spaces,  either  directly  connected  each  with  the  other  or  by 
cracks  through  which  fire  may  freely  pass  where  it  cannot  be 
reached  by  water. 

2.  It  does  not  consist  in  an  open-timber  construction  of  floors 
and  roof  resembling  mill  construction,  but  of  light  and  insuffi« 
cient  size  in  timbers  and  thin  planks,  without  fire-stops  or  fire- 
guards from  floor  to  floor. 

3.  It  does  not  consist  in  connecting  floor  with  floor  by  com- 
bustible wooden  stairways  encased  in  wood  less  than  two  inches 
thick. 

4.  It  does  not  consist  in  putting  in  very  numerous  divisions 
or  partitions  of  light  wood. 

5.  It  docs  not  consist  in  sheathing  brick  walls  with  wood,  espe- 
cially when  the  wood  is  set  off  from  the  wall  by  furring,  even 
if  there  are  stops  behind  the  furring. 


MILL  AND  WAREHOUSE  CONSTRUCTION.      689 

6.  It  does  not  consist  in  permitting  the  use  of  varnish  upon 
woodwork  over  which  a  fire  will  pass  rapidly. 

7.  It  does  not  consist  in  leaving  windows  exposed  to  adjacent 
buildings  unguarded  by  fire-shutters  or  wired  glass. 

8.  It  is  dangerous  to  paint,  varnish,  fill  or  encase  heavy  tim- 
bers and  thick  plank  as  they  are  customarily  delivered,  lest  what 
is  called  dry-rot  should  be  caused  for  lack  of  ventilation  or  oppor- 
tunity to  season. 

9.  It  does  not  consist  in  leaving  even  the  best-constructed 
building  in  which  dangerous  occupations  are  followed  without 
automatic  sprinklers,  and  without  a  complete  and  adequate 
equipment  of  pumps,  pipos,  and  hydrants. 

10.  It  does  not  consist  in  using  any  more  wood  in  finishing  the 
building  after  the  floors  and  roof  are  laid  than  is  absolutely 
necessary,  there  being  now  many  safe  methods  available  at  low 
cost  for  finishing  walls  and  constructing  partitions  with  slow- 
burning  or  incombustible  material. 

It  follows  that  if  plastering  is  to  be  put  upon  a  ceiling  follow- 
ing the  line  of  the  underside  of  the  floor  and  the  timber,  it  should 
be  plain  lime-mortar  plastering,  which  is  sufficiently  porous  to 
permit  seasoning.  The  addition  of  the  skim  coat  of  lime  putty 
is  hazardous,  especially  if  the  top  floor  is  laid  upon  resin-sized 
or  asphalt  paper.  This  rule  applies  to  almost  all  timber  as  now 
delivered. 

All  the  faults  above  recited  have  been  committed  in  buildings 
purporting  to  be  of  mill  construction,  and  all  form  a  part  of  the 
common  practice  in  "combustible  architecture." 

Standard  Mill  Construction. 

Fig.  1  shows  a  partial  cross-section  through  a  mill  of  the 
customary  or  standard  type  as  revised  to  Nov.,  1902. 

If  additional  stories  are  required  the  walls  may  be  increased 
in  thickness  according  to  the  number  of  stories  added,  after  a 
computation  of  the  loads  which  a  standard  factory  may  be 
called  upon  to  sustain. 

Fig.  2  shows  an  enlarged  view  of  the  exterior  of  two  bays, 
with  recessed  panels  between  the  piers.  Fig.  3  shows  the 
common  form  of  cast-iron  pintle,  which  serves  as  a  cap  for  the 
lower  column,  and  a  support  for  the  upper  column. 

These  illustrations  are  only  intended  to  give  general  directions 
for  slow-burning  or  mill  construction.  They  should  always  be 


690    MILL  AND  WAREHOUSE  CONSTRUCTION. 


adapted  to  the  special  conditions  of  each  site  and  of  each  art 
for  which  the  buildings  are  used. 

When  a  span  exceeds  twenty-two  feet  it  is  judicious  to  add 
to  the  support  by  hackmatack  or  iron  knees  projecting  from 
wall  and  posts.  These  knees  or  braces  are  not  deemed  neces- 
sary even  on  spans  of  twenty-five  feet  when  the  timbers 
are  of  ample  dimension.  They  have  sometimes  been  put  into 
old  mills  of  high  and  narrow  type  and  have  stopped  serious 
vibration  in  the  upper  stories.  If  used,  they  must  be  kept 
bolted  closely  to  timbers  and  posts,  and  care  should  be  taken 


S"  plank,  2  bays  in  length,  -^ 
Breaking  Joints  every  3  feet 


Roofing;-  4  ply,  Tar  and  Gravel,  or  Tin 


E=E 

; 

; 

"3*=acCTj»m:  r 

~~  V10"i  12  "Rafters 

s\}C  Top  floor.  Hard  wood. 
/    3  Thicknesses  of  Resin-sized  paper;x 
J       Each  layer  mopped  with  Tar.             \ 

^%"Wro't  Iron  Dogs 

—  8"x8'* 

^-3  "plank,  2  bays  In  length, 
/    Breaking  Joints  every  3  feet* 



„ 

^* 

> 

^-Cast  Iron  Wall  Plate 
~~22                                25  V 

^-Double  Floor  Beams  6"  x>  14" 

"s'o" 

^ 

: 

;- 
| 

Bays;-  About  8  feet 

-9"x9* 
Iron  Pintle  ^ 

0                         0                         °                         0                        °                         0 

0  )    ^ 

f                           If"                        H 

I 


Fig.  I 

Standard  Construction. 

that  the  load  on  each  side  should  be  practically  the  same.  They 
are  necessary  in  the  self-sustaining  frame  (Figs.  9  and  11).  In 
computing  the  size  of  the  timbers  in  ratio  to  the  working  load, 
regard  must  be  given  not  only  to  the  weight  which  is  to  be 
carried,  but  also  to  the  character  of  the  mechanism  which  is 
to  be  operated  upon  the  floor.  Beams  of  sufficient  strength  to 
support  the  weight  may  be  caused  to  vibrate  or  deflect  under 
the  action  of  the  machinery ;  therefore  the  two  factors  of  weight 
and  vibration  must  be  considered  in  determining  the  size  or 
depth  of  the  beams  that  may  be  made  use  of. 

"We  do  not  approve  what  has  sometimes  been  miscalled  mill 


MILL  AND  WAREHOUSE  CONSTRUCTION.      691 


Fig.  2 

Detail  of  Side  Walls. 


692      MILL  AND  WAREHOUSE  CONSTRUCTION. 

construction,  i.e.,  longitudinal  girders  resting  upon  posts  and 
supporting  floor-beams  spaced  four  feet,  more  or  less,  on  centres. 
This  mode  of  construction  not  only  adds  to  the  quantity  of  wood 
used,  but  the  disposal  of  the  timbers  obstructs  the  action  of 
sprinklers,  prevents  the  sweeping  of  a  hose  stream  from  one 
side  of  the  mill  to  the  other,  and  the  girders  also  obstruct  the 
most  important  light,  that  from  the  top  of  the  windows." 


Iron  Pintle,  Cap  and  Base, 
cast  in  one  piece. 


Fig,  3 

The  standard  plan  calls  for  but  one  thickness  of  boards  laid  over 
the  planks,  with  three  layers  of  resin-sized  paper  mopped  with 
tar  between.  In  the  best  mills  lately  built  a  board  flooring  has 
been  laid  diagonally  upon  the  plank,  over  that  a  top  floor  of 
birch  or  maple,  laid  lengthwise.  The  diagonal  floor  gives  great 
resistance  to  the  lateral  strain  or  vibration;  the  top  floor,  espe- 
cially in  alleyways,  can  be  more  easily  repaired  or  replaced 
when  worn.  This  intermediate  diagonal  flooring  is  well  worth 
the  additional  cost. 

The  following  notes,  pertaining  to  the  details  of  mill  construc- 
tion, are  the  result  of  many  years'  study  and  observation,  and 
should  be  carefully  noted  when  preparing  plans  and  specifications 
for  mill  construction. 

Timbers,  unless  known  to  be  absolutely  and  fully  seasoned, 
should  not  be  encased  in  any  kind  of  air-proof  plastering,  nor 
should  they  be  painted  with  oil-paints;  whitewash,  kalsomine, 
and  water-paints  may  be  used  as  they  are  porous.  Timbers  or 
plank  may  also  be  covered  in  with  common  lime  mortar  laid  on 
wire  lathing,  provided  no  skim  coat  of  lime  putty  is  added. 
Ordinary  plastering  unskimmed  is  sufficiently  porous  to  permit 
seasoning.  As  a  rule  timbers  may  be  left  unprotected,  except 
in  very  dangerous  places,  since  any  fire  which  will  seriously 
impair  and  destroy  a  heavy  timber  will  already  have  done  its 
work  upon  other  parts  of  the  structure. 


MILL  AND   WAREHOUSE  CONSTRUCTION.      693 

% 

In  many  instances  it  may  be  preferable  to  substitute  com- 
pound beams  for  single  timbers,  made  by  securing  two  or  more 
beams  or  thick  planks  side  by  side;  it  being  often  easier  to 
obtain  well-seasoned  lumber  in  smaller  dimensions;  such  com- 
pound beams,  of  which  the  parts  may  be  slightly  separated  by 
spaces  for  ventilation  when  put  together,  are  less  subject  to 
decay. 

Weaving  mills  can  be  made  more  rigid  and  more  capable  of 
resisting  the  vibration  caused  by  the  motion  of  looms  by  laying 
the  top  floor  across  the  plank  and  parallel  to  the  beams,  nails 
being  driven  in  diagonal  rows.  This  may  brace  the  floor  as 
firmly  as  diagonal  boarding,  and  it  avoids  the  increased  expense 
in  construction  and  repairs  which  ensues  from  the  adoption  of 
that  method. 

The  edges  of  the  floor  plank  should  be  kept  clear  of  the  faces 
of  the  brick  walls  by  about  half  an  inch,  in  order  to  obviate  the 
danger  of  cracking  the  walls,  which  sometimes  occurs  from  the 
swelling  of  the  plank  when  laid  close  against  them.  These  cracks 
must  be  covered  by  strips  or  battens  both  above  and  below. 

To  protect  the  contents  of  floors  below,  three  thicknesses  of 
tarred  paper  should  be  placed  between  the  floor  plank  and  top 
floor,  each  layer  to  be  mopped  with  tar,  asphalt,  or  similar 
material,  care  being  taken  to  break  all  joints. 

Basement  floors  can  be  laid  solid  upon  the  natural  soil  if  it 
is  dry,  or  upon  rock  or  cinder  filling,  by  covering  either  with  a 
suitable  layer  of  coal-tar  concrete.  Upon  this  concrete  place  an 
underfloor  of  two-inch  plank.  Then  lay  the  top  flooring  across 
the  plank,  and  nail  in  the  usual  manner.  Sills  under  the  plank 
are  not  thought  to  be  necessary  to  the  preservation  of  the 
floor.  If  extra  support  is  required  to  sustain  machinery  more 
firmly  than  it  can  be  upon  a  plank  and  board  floor,  independent 
foundations  of  masonry  are  generally  preferred.  Cement  con- 
cretes may  absorb  moisture  and  promote  the  decay  of  timber 
or  plank  laid  upon  them. 

In  view  of  the  difficulties  which  have  frequently  occurred  in 
preserving  basement  floors  of  the  ordinary  timber  construction 
for  lack  of  suitable  ventilation  underneath,  and  also  in  view  of 
the  rapid  decay  of  timber  and  plank  floors  in  bleacheries,  dye- 
works,  print-works,  and  the  like,  where  they  quickly  become 
saturated  with  moisture,  artificial  stone  floors  are  being  laid  in 
many  of  the  modern  plants. 

If  the  mill  is  to  be  heated  by  conveying  steam  through  pipes, 


694      MILL  AND   WAREHOUSE  CONSTRUCTION. 


MILL  AND  WAREHOUSE  CONSTRUCTION      695 


696     MILL   AND   WAREHOUSE  CONSTRUCTION. 

such  pipes  should  be  hung  overhead.  If  the  modern  method, 
which  is  probably  the  best  method,  of  conveying  the  heat 
through  ducts  in  the  plastered  walls  should  be  adopted,  provision 
will  be  made  thereto  in  the  construction  of  the  mill  wall. 

The  carrying  off  from  the  walls  of  about  one-half  a  roof 
corresponding  to  this  plan,  in  a  hurricane,  calls  attention  to 
the  necessity  of  tying,  binding,  or  bolting  the  timbers  of  the  roof 
to  the  walls  of  the  mill  in  a  safe  and  suitable  manner.  This  is 
the  common  practice,  but  the  necessity  is  sometimes  overlooked. 

Belt,  Stairway,  and  Elevator  Towers. 

Stairways  should  always  be  located  in  towers  or  sections 
of  the  building,  cut  off  by  incombustible  walls  from  all  the 
rooms  of  the  factory,  the  entrances  to  each  room  being  guarded 
with  standard  fire-doors. 

In  modern  practice  all  belts  or  ropes  which  may  be  used  for 
the  transmission  of  power  to  the  various  rooms  are  placed  in 
incombustible  vertical  belt  chambers,  from  which  the  power  is 
transmitted  by  shafts  through  the  walls  into  the  several  rooms 
of  the  factory.  There  should  be  no  unprotected  or  unguarded 
openings  in  the  inner  walls  of  this  belt  chamber. 

Elevator  shafts  and  belt  towers  or  chambers  should  be  guarded 
by  fire-doors  and  covered  overhead  by  skylights,  glazed  with 
thin  glass,  protected  underneath  with  wire  netting.  Hatchways 
outside  the  fire-proof  shafts  should  be  well  guarded  by  auto- 
matic or  self-closing  hatches,  both  to  stop  the  passage  of  fire 
and  to  assure  safety  to  persons.  The  most  important  feature 
in  what  is  called  slow-burning  construction  is  to  make  each 
and  every  floor  continuous,  avoiding  belt  holes  and  open  ways  to 
the  utmost  possible  extent,  so  that  a  fire  originating  in  any 
one  room  may  be  confined  to  that  room  or  story,  if  possible. 

Figs.  4  and  5  illustrate  a  partial  section  and  plan  of  a  cotton 
mill,  showing  belt,  stair,  and  elevator  towers  arranged  on  the 
above  principle.  It  should  be  noted  that  the  water-closets 
are  located  in  the  tower  rather  than  in  the  manufacturing 
rooms. 

The  boiler-house  should  be  located  beyond  the  engine-room, 
and  separated  from  the  latter  by  a  brick  wall  with  doorway 
protected  by  a  standard  automatic  fire-door. 


MILL  AND  WAREHOUSE  CONSTRUCTION.      697 


Standard  Storehouse  Construction. 

Figs.  6,  7,  and  8  represent  salient  points  in  design  for  a  mill 
storehouse  several  stories  in  height,  and  include  many  fea- 
tures found  useful  in  practice  for  convenience  in  operation 
and  also  securing  the  greatest  measure  of  resistance  to  fire. 


8x8 

2  Thicknesses  of  Resin-sized  paper  under 
Top  Flooring.  Floor  Plank,  2  bays  in  length, 
breaking  joints  every  3  feet. 


Fig.  6 

One-half  of  Transverse  Section, 

The  size  of  columns  and  beams  is  only  for  example,  differ- 
ing according  to  load  and  span,  the  drawings  not  being  intended 
to  take  the  place  of  the  services  of  any  mill  engineer,  but  rather 
to  assist  in  such  work.  It  is  important  that  the  floor  beams 
should  be  designed  to  sustain  the  greatest  load  ever  to  be 
placed  on  them,  and  the  stories  should  be  made  low  enough 
to  prevent  overloading,  and  also  to  prevent  bales  of  material 
from  being  piled  to  great  height,  the  preferable  method  being 
to  place  bales  on  end. 


698      MILL  AND  WAREHOUSE  CONSTRUCTION. 

These  floors,  with  beams  of  20  feet  span,  laid  8  feet  on  cen- 
tres, will  sustain  a  load  of  180  pounds  per  square  foot,  which 
is  as  much  as  would  be  required  for  raw  material  or  finished 
goods  of  a  textile  or  paper  mill.  The  heavy  drugs  and  dye- 
stuffs  would  be  placed  on  the  ground  floor. 

For  convenience,  as  well  as  to  separate  the  different  hazards 
of  raw  material  and  finished  goods,  the  building  may  be  di- 
vided into  sections  by  fire-walls  extending  through  the  roof. 

A  storehouse  one  story  in  height  is  recommended  in  prefer- 
ence to  this  design  whenever  there  is  sufficient  quantity  of 
level  land  at  disposal  for  this  purpose,  as  being  cheaper,  more 
convenient,  and,  when  separated  into  small  divisions  by  fire- 
walls, the  safest  method  of  storehouse  construction. 

The  floors  in  such  a  building  should  be  continuous,  without 
openings,  and  of  the  standard  slow-burning  construction — • 
a  type  which  has  not  yet  been  burned  through  by  any  fire 
starting  under  such  a  floor,  unless  there  have  been  openings 
in  the  floor.  To  reduce  water  damage  the  floors  are  not  level, 
but  have  a  camber  of  two  inches  in  the  middle  made  by  iron 
plates  inserted  under  the  columns  in  the  basement.  If  it 
should  become  desirable  to  use  the  building  for  any  purpose 
requiring  level  floors,  they  can  be  reduced  to  a  level  by  re- 
moving these  plates.  Inclined  iron  tubes,  with  a  light  swing- 
ing cap  on  the  outside,  laid  in  the  wall  at  the  level  of  the  floors, 
act  as  scuppers  for  the  purpose  of  removing  any  water. 

The  floor-beams  are  preferably  of  Southern  pine  bolted  to- 
gether  in  pairs,  leaving  about  one  inch  space  between  the 
beams.  At  the  columns  the  beams  are  joined  by  dogs  made 
of  three-fourths  inch  round  iron,  driven  in  at  the  top,  and  they 
are  anchored  to  the  walls  by  cast-iron  wall-plates,  to  which 
they  are  secured  by  means  of  a  rib  which  fits  into  a  groove 
crossing  the  underside  of  the  beam.  It  is  important  that 
there  should  be  a  small  space  at  each  side  and  at  the  end  of 
the  beam,  in  order  to  allow  free  ventilation,  for  the  purpose 
of  preventing  dry-rot.  The  Goetz  box-anchor  is  a  special  form 
of  wall-plate  which  is  especially  adapted  to  such  purposes. 

The  underfloor  is  made  of  spruce  plank,  generally  three 
inches  thick,  planed  on  the  underside,  and  grooved  at  the 
edges,  and  fitted  with  hardwood  splines.  These  plank  are 
two  bays  in  length,  breaking  joints  at  least  every  three  feet. 

The  floor  is  smoother  if  laid  across  the  line  of  plank,  and 
the  travelling  loads  moved  in  or  out  of  the  storehouse  are 


MILL   AND  WAREHOUSE  CONSTRUCTION.      699 

better  distributed  than  when  the  top  floor  is  laid  parallel  to 
the  plank.  To  protect  the  contents  of  floors  below,  three 
thicknesses  of  tarred  paper  should  be  placed  between  the  floor 
plank  and  top  floor,  each  layer  to  be  mopped  with  tar,  asphalt, 
or  similar  material,  care  being  taken  to  break  all  joints.  The 
floor  should  not  be  secured  to  the  walls,  but  a  narrow  strip 


Fig.  7 

Showing  Stairway  Tower  Inside  Walls  of  Building. 

laid  around  the  edges  of  the  floor  and  fastened  to  the  wall 
covers  any  openings  due  to  shrinkage. 

Floors  of  storehouses  may  have  a  slight  pitch  toward  the 
centre,  draining  in  the  same  method  as  the  roof  is  drained; 
or  if  the  other  type  of  roof  is  adopted,  the  floors  of  storehouses 
may  have  a  slight  pitch  from  centre  to  walls,  draining  through 
scupper-holes  indicated  in  Fig.  6.  Goods  raised  on  low  skids 
may  then  be  very  free  of  water  damage. 

The  columns  should  be  square  Southern  pine  or  oak,  with 
iron  cap,  pintle,  and  base,  preferably  cast  in  one  piece,  and 
secured  to  the  under  side  of  the  beam  by  six-inch  lag  screws. 
The  caps  should  be  large  enough  to  give  the  beams  ample 
bearing  surface. 

In  a  warm  storehouse  it  is  preferable  that  the  roof  should 
slope  towards  the  centre  one-ha/f  inch  to  the  foot,  and  that 
the  gutter  should  slope  towards  the  drain-pipe  one-twentieth 
of  an  inch  to  the  foot.  In  a  cold  storehouse  it  is  considered 
necessary  that  the  roof  should  slope  one-half  of  an  inch  towards 
the  walls  as  in  Fig.  1,  and  if  there  is  a  gutter,  the  conductors 
should  be  carried  outside  of  the  building. 

Access  to  the  various  stories  is  obtained  by  means  of  a  tower 


700     MILL   AND  WAREHOUSE  CONSTRUCTION. 

outside  the  main  building  and  extending  above  the  roof5  con 
taming  stairways,  elevator,  and  water-pipes.  At  each  story 
of  the  tower  open  galleries  communicate  to  the  rooms  on  that 
level.  A  doorway  from  the  upper  story  of  the  tower  affords 
a  ready  means  of  reaching  the  roof.  It  is  often  a  matter  of 
great  convenience  if  the  doorway  at  the  first  story  of  the  tower 
is  made  large  enough,  and  at  the  outside  grade,  so  that  a  wagon 
can  be  backed  directly  to  the  elevator.  It  is  unnecessary 
to  provide  these  elevators  with  automatic  hatches,  as  guard- 
gates  serve  every  purpose.  When  it  is  necessary  to  construct 
the  elevator  wells  and  stairway  within  the  lines  of  the  main 
building  it  is  best  to  arrange  it  as  in  Fig.  7.  The  omission 
of  the  outer  wall  prevents  the  way  becoming  a  flue. 

The  walls  extend  above  the  roof,  and  the  parapet  should 
be  laid  in  cement,  because  the  moisture  readily  absorbed  by 
brick  would  otherwise  pass  downward  and  render  walls  in  the 
top  story  damp.  In  some  instances  a  course  of  brick  dipped 
in  coal-tar  is  laid  above  the  roof  level. 


Storage  oLRaw  Material 


//////////\   Door  V///////////////////< 


Storage  of  G6"0© 


'////////////////////A  Door 


Open  Gallery                °                  Elevator  g  Open  Gallery 

at  each  story  F771  n OPIPa     WA  at  each  story 


Fig.  8 

Showing  Stairway  Tower  at  Side  of  Storehouse. 

In  addition  to  yard  hydrants  near  the  buildings  there  should 
be  a  six-inch  standpipe  in  the  tower,  the  supply  to  which 
should  be  controlled  by  an  out-of-door  Post  indicator  valve 
at  a  safe  distance  from  the  building,  with  two  2J"  hydrants 
and  hose  at  each  story,  and  at  the  top  story  of  the  tower,  the 
standpipe  branches  to  a  Morse  or  Phillips  monitor  nozzle  on 
the  roof,  if  there  are  any  adjacent  buildings  which  might  be 
reached  by  streams  from  this  position.  A  set  of  plugs  for  the 
roof  drain-pipes  will  allow  the  roof  to  be  covered  with  water 
in  case  the  property  is  endangered  by  sparks  from  burning 
buildings. 

Storehouses  should  be  provided  with  automatic  sprinklers. 


MILL  AND  WAREHOUSE  CONSTRUCTION.      701 

When  so  protected  the  water  can  be  shut  off  in  the  winter; 
or  if  an  air  system  be  adopted  it  may  be  applied  only  in  the 
winter;  water  being  kept  directly  upon  the  sprinklers  in  warm 
weather. 


Mill  Construction  with  Self-sustaining  Frame. 

Slope  of  roof,  one  in  twenty-four 


Double  floor  timbers,  6"x  15" 


Double  floor  timbers,  6"  x  15" 


'Rock  filling  covered  with  cement  concrete,  on  which  is  a  layer  of  Tar  or  Asphalt 

Fig.  9 

Partial  Transverse  Section,  Showing  Self-sustaining  Frame. 

Figs.  9,  10,  and  11  show  suggestions  for  mill  construction 
in  which  the  interior  framework  is  self-sustaining  and  inde- 
pendent of  the  walls,  except  that  the  outer  posts  serve  to  brace 
the  walls.  Regarding  this  construction  the  Boston  Manu- 
facturers Mutual  Fire  Insurance  Co.  says: 

"It  is  suggested  that  the  framework  of  a  factory  itself  should 
consist  of  two  parts,  first,  of  two  outer  lines  of  posts  pus: •••ing 
around  the  whole  building,  joined  and  braced  together  either 
with  hackmatack  knees,  angle  irons,  or  iron  cross-ties;  this 


?02     MILL  AND   WAREHOUSE  CONSTRUCTION. 

outer  framework  carrying  the  alleyways  to  be  so  constructed 
that  it  may  be  put  up  separately  from  the  outer  walls  and  also 
separately  from  the  inner  posts  and  floors  on  which  the  ma- 
chinery is  to  be  placed,  so  that  this  part  of  the  frame  bearing 
the  outer  alleyways  will  stand  alone. 

"Second,  The  interior  framework  and  the  floors  upon  which 
machinery  is  to  rest  may  be  adjusted  and  connected  with 
the  outer  lines  of  support  already  designated,  so  that  in  the 


Fig.  10 

Partial  Plan,  Showing  Locations  of  Posts  and  Staircase  Tower. 

event  of  the  burning  of  any  timber,  the  giving  away  of  any 
post,  or  accident  to  any  part  of  the  floor,  any  section  of  ma- 
chine-bearing floor  may  fall  out  without  bringing  a  severe 
strain  upon  the  outer  line  of  posts  or  upon  other  parts  of  the 
frame  of  the  mill. 

"The  self-sustaining  frame  being  established  and  covered  in, 
the  question  may  follow  rather  than  precede,  as  to  what  the 
material  of  the  outer  walls  should  consist  of.  In  very  many 
arts  it  is  important  that  the  outer  walls  should  consist  in  large 


MILL  AND   WAREHOUSE  CONSTRUCTION.      703 

measure  of  glass,  especially  since  the  adoption  of  double- 
glazed  windows  and  the  suggestion  of  ribbed  glass  for  glaz- 
ing has  solved  the  problem  of  the  transmission  of  light,  while 
the  double  glazing  in  the  same  sash  obstructs  the  passage  of 
heat  and  cold  in  a  very  effectual  way,  thus  avoiding  the  con- 
densation of  the  moisture  within. 

"These  windows  are  to  be  carried  to  the  under  side  of  the 
roof,  against  the  plate,  and  to  the  under  side  of  each  floor, 
close  to  the  ceiling,  therefore  the  only  remaining  part  of  the 
outer  wall  to  be  dealt  with  will  be  the  space  between  and  be- 
neath the  windows.  This  part  of  the  wall  may  be  built  of 
brick,  but  as  no  dependence  is  to  be  placed  upon  the  wall  for 
sustaining  the  building  itself,  the  walls  may  be  lighter  or 
thinner  than  the  common  practice. 

"It  being  premised  that  this  building  is  planned  for  a  de- 
tached position,  where  it  will  be  free  from  hazard  of  fire  from 
neighboring  buildings,  large  windows  may  be  put  in  which 
cannot  be  guarded  by  fire-shutters,  the  consideration  of  danger 
from  fire  being  only  given  to  the  interior  hazard.  Upon  such 
conditions  and  in  such  a  position  other  materials  than  brick 
may  be  considered  for  the  walls.  For  instance,  the  timbers 
may  be  so  disposed  as  to  show  upon  the  outside.  The  entire 
framework  for  the  window  to  be  placed  between  these  tim- 
bers may  then  be  constructed  so  that  it  can  be  brought  to  the 
factory  ready  to  be  put  into  its  place,  all  window-frames  being 
interchangeable.  This  structure-  may  then  be  protected  both 
inside  and  outside  with  incombustible  materials. 

"  Where  there  is  an  outside  hazard  the  windows  must  be  di- 
minished in  width,  with  an  equal  or  greater  area  of  wall  sur- 
face between,  in  or  upon  which  automatic  shutters  may  be 
placed  for  closing  up  the  windows  against  fire.  In  such  posi- 
tions the  outer  wall  can  only  safely  consist  of  brick  of  such 
thickness  as  may  be  suitable  to  each  case."* 

Fig.  11  shows  a  detail  of  outside  wall  consisting  principally 
of  windows,  the  frames  filling  the  entire  width  between  the 
posts.  The  outside  of  the  posts  and  the  spaces  under  the 
windows  may  be  covered  with  plank,  and  then  with  metal 
or  sheathing  lath  and  rough  plaster;  the  entire  wall  being 
carried  by  the  posts.  In  this  mill  there  is  but  a  single  line 
of  outer  posts,  i.e.,  no  alley. 

*  Hollow  concrete  wajls  should  be  even  better  than  brick. — Author. 


704      MILL   AND   WAREHOUSE  CONSTRUCTION. 


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Fig.  II 

Outside  Walls  of  Wood  and  Plaster  Supported  by  the  Frame. 


Example    of    One-story    Slow-burning     Machine- 
shop, 

"COVERING  IMPROVEMENTS  WHICH  HAVE  BEEN  DEVELOPED  BY 
EXPERIENCE  IN  THE  CONSTRUCTION  AND  USE  OF  ONE-STORY 
FACTORY  BUILDINGS  UP  TO  THE  PRESENT  DATE."  * 

For  workshops   on   cheap,   level  land,   especially  where   the 
stock  is  heavy,   one-story  buildings  have  proved  to    be  more 

*  Edward  Atkinson,  President.     November,  1902. 


MILL  AND  WAREHOUSE  CONSTRUCTION.       705 


706      MILL  AND  WAREHOUSE  CONSTRUCTION. 

economical  in  cost  of  floor  area,  supervision,  moving  stock  in 
process  of  manufacture,  and  repairs  to  machinery — many 
kinds  of  which  can  be  run  at  greater  speeds  than  when  in  high 
buildings. 

Such  buildings  are  readily  warmed  and  ventilated,  and 
heavy  plank  roofs  are  free  from  condensation  in  cold  weather; 
the  large  window  area  reduces  the  hours  of  artificial  illumi- 
nation. 

Forced  circulation  of  heated  air  is  a  very  desirable  method 
of  heating  a  mill,  being  economical  as  to  maintenance  and 
repairs,  and  thoroughly  under  control.  Overhead  steam- 
pipes  are  very  satisfactory,  if  used  in  the  ratio  of  one  foot  of 
IJ-inch  pipe  to  70  cubic  feet  of  air. 

Floors.  —  Floors  over  an  air  space  or  on  cement  are  sub- 
ject to  dry-rot.  Asphalt  or  coal-tar  concrete  is  softened  by 
oil,  and  the  dust  will  wear  machinery,  unless  covered  by  floor- 
ing. Floors  made  by  laying  sleepers  on  six  inches  of  pebbles, 
tarred  when  hot,  then  two  inches  tarred  sand  flush  to  top  of 
sleepers  and  covered  by  double  flooring,  have  remained  sound 
since  1865;  but  double  flooring  at  right  angles  can  be  laid 
on  the  concrete  without  the  use  of  sleepers,  and  nailed  together. 
It  is  usually  preferable  to  secure  nailing  strips  to  stakes  four 
feet  apart  each  way  and  driven  to  grade,  concrete  flush  to 
top  of  strips,  and  lay  single  1^-inch  flooring. 

Walls. — Piers  reaching  to  roof  timbers,  and  light  walls  to 
window-sills  are  finished  with  slope  on  inside.  To  increase 
the  window  area  over  that  shown  in  the  elevation,  the  brick 
piers  between  the  windows  may  be  narrowed  and  made  thicker 
so  as  to  give  the  requisite  strength,  leaving  more  space  for 
light.  Large  windows  are  placed  high,  and  the  sashes  sepa- 
rated by  a  mullion.  Lower  sashes  should  be  stationary  and 
glazed  with  ribbed  glass,  with  transom  sash  or  window  venti- 
lators above.  If  the  light  is  too  strong,  apply  to  glass  white 
zinc  and  turpentine. 

Monitors  may  well  be  glazed  with  ribbed  glass. 

Columns. — Wooden  mill  columns,  Southern  pine  or  oak, 
safely  sustain  loads  of  600  pounds  per  square  inch;  a  square 
column  is  stronger  than  a  round  one  of  the  same  diameter. 
They  should  have  a  IJ-inch  core  bored  from  end  to  end, 
and  two  half-inch  holes  through  the  column  near  to  each 
end. 

The  columns  should  be  securely  held  at  each  end,  the  base 


MILL  AND  WAREHOUSE  CONSTRUCTION.      707 

resting  on  iron  plates  projecting  above  the  floor  level,  and 
the  caps  at  the  top  bolted  to  the  roof  beams. 

Roofs. — Double  or  solid  timbers  of  Southern  pine  sup- 
port the  roof  plank,  and  the  ends  pass  through  the  wall,  and 
are  finished  as  brackets  to  the  cornice;  or  another  plan  often 
adopted  is  to  make  a  projecting  brick  cornice  covering  the 
ends  of  the  roof  timbers,  thus  avoiding  the  exposure  to  an 
outside  fire.  The  beams  are  anchored  to  plates  in  the  walls 
by  means  of  tongues  which  project  into  grooves  across  the 
lower  side  of  the  beams.  Beams  should  not  be  painted  or 
varnished  until  thoroughly  seasoned. 

The  roof  plank  should  be  two  bays  in  length,  breaking  joints 
every  three  feet.  There  is  no  need  of  gutters,  but  a  concrete 
walk  at  the  ground  level,  sloping  toward  drains,  will  take  the 
water  from  the  roof.  Do  not  drive  nails  upward  into  the  roof 
plank,  as  moisture  will  condense  and  drop  from  the  heads. 

Monitors  must  be  of  solid  construction. 

The  roof  should  be  tied  by  binding  or  bolting  the  timbers 
of  the  roof  to  the  walls  of  the  mill  in  a  safe  and  suitable  man- 
ner. This  is  the  common  practice,  but  the  necessity  is  some- 
times overlooked. 

The  saw-tooth  roof  is  taking  the  place  of  the  monitor  in 
weaving  and  other  buildings.  We  do  not  supply  any  plan 
for  this  type  because  it  requires,  in  each  case,  the  service  of 
a  competent  mill  engineer  and  constructor  to  plan  the  roof 
so  as  to  meet  special  conditions,  and  to  supervise  the  work. 

Roofing'  Material. — Mill  roofs  are  almost  always  flat, 
as  shown  in  the  foregoing  specifications,  and  are  most  com- 
monly covered  with  coal-tar,  pitch,  and  gravel,  although  as- 
phaltic  compositions  are  often  used  and  occasionally  tin  roof- 
ing is  used.  Cotton  duck  or  canvas  has  been  used  for  cover- 
ing mill  roofs  to  some  extent,  but  does  not  appear  to  have 
proved  very  satisfactory,  except  on  small  buildings  and  for 
covering  platforms,  etc.  Canvas  roofing  will  stand  harder 
usage  than  any  of  the  materials  above  mentioned,  as  is  shown 
by  its  continued  •  use  on  the  decks  of  vessels  and  steamers. 
Duck  or  canvas  for  roofing  purposes  should  be  what  is  termed 
"12  ounce,"  weighing  16  ounces  to  the  square  yard.  It  should 
be  tightly  stretched,  and  tacked  with  seventeen-ounce  tinned 
carpet-tacks,  the  edges  being  lapped  about  an  inch.  If  the 
roof  planks  are  rough,  or  not  of  an  even  thickness,  a  layer  of 
heavy  roofing  paper  should  be  laid  before  the  duck  is  put  down. 


708      MILL  AND  WAREHOUSE  CONSTRUCTION. 

After  the  duck  is  laid,  it  should  be  thoroughly  wet,  and  then 
painted  with  white  lead  and  boiled  linseed-oil  before  it  becomes 
dry;  which  makes  it  water  proof.  To  protect  from  fire,  give 
it  two  more  coats  of  white  lead,  and  over  this  a  coat  of  iron- 
clad paint.  Instead  of  the  four  coats  of  white  lead  and  oil, 
the  duck  may  be  saturated  with  a  hot  application  of  pine- tar 
thinned  with  boiled  linseed-oil.  This  has  been  found  to  work 
perfectly.  The  iron-clad  paint  should  be  applied,  which- 
ever method  is  used. 

Partitions. — Partitions  used  for  dividing  a  mill  into 
sections  should  be  built  of  brick,  concrete  or  porous  terra-cotta 
tiling.  Where  a  room  is  to  be  partitioned  off  the  partitions 
may  be  built  of  two-inch  tongued  and  grooved  plank  set  ver- 
tically (so  as  to  form  a  solid  partition),  and  plastered  both 
sides,  either  on  wire,  or  on  dovetailed  sheathing  lath.  Such 
partitions  have  been  found  to  work  well  after  a  trial  of  twelve 
years,  and  offer  effectual  resistance  to  fire. 

Two-inch  solid  partitions  of  plaster  on  metal  lath  wired 
to  light  iron  studs  may  also  be  used. 

Mill  Doors  and  Shutters  should  be  built  of  two  thick- 
nesses of  inch  boards  covered  on  all  sides  with  tin,  as  described 
in  Chapter  XXIII. 

For  information  relating  to  appliances  for  the  fire  protec- 
tion of  mills,  the  reader  is  referred  to  the  Insurance  Engineer- 
ing Station,  Boston. 

Patented  Systems  of  Mill  Construction. 

Mr.  Chas.  A.  M.  Praray,  Mill  Engineer  of  Providence,  R.  I., 
has  patented  a  system  of  mill  construction  which  he  has  desig- 
nated as  the  "Praray  Improved  Construction."  The  special 
points  in  which  this  system  differs  from  the  regular  mill  con- 
struction are,  the  construction  of  the  walls,  the  shape  of  the 
post  caps,  and  the  supporting  of  the  floors  and  roof,  independ- 
ent of  the  walls. 

The  walls  are  built  as  a  continuous  series  of  bay  windows, 
with  a  hollow  brick  pier  between,  and  with  a  supporting  col- 
umn in  the  centre  of  each  bay.  Fig.  13  shows  a  plan  of  one 
bay  and  of  the  column  supporting  the  floor,  while  Fig.  14 
shows  a  vertical  section  through  the  same.  Fig.  15  shows 
a  detail  of  the  post  and  girder  connection.  The  posts  are 
cut  down  to  a  square  where  they  pass  through  the  girder 


MILL  AND  WAREHOUSE   CONSTRUCTION,      702 


Fig.  13 
Plan  of  One  Bay. 


Fig.  14 

Vertical  Sect. ion  through 
One  Bay. 


710      MILL   AND   WAREHOUSE  CONSTRUCTION. 


PLAN 


and  are  dog-bolted  to  the  girders.  The  advantages  claimed 
for  this  construction  are  a  saving  of  about  33  per  cent,  in  brick- 
work, with  an  increase  in  light_ 
ing  of  about  33  per  cent.,  and 
also  a  saving  of  10  per  cent,  in 
the  height  of  the  building,  and 
a  consequent  saving  in  heat- 
ing. The  hollow  piers  between 
the  bays  can  be  used  as  air  ducts 
for  heating  and  ventilating. 
Five  large  cotton  mills  have 
been  erected  in  the  Southern 
States  on  this  system  of  con- 
struction, which  appear  to  verify 
the  claims  of  the  inventor. 

Architects  or  owners  can  make 
use  of  this  system  by  paying  a 
royalty  to  Mr.  Praray,  which 
will  also  include  many  practical 


Fig.  15 

Detail  of  Beam  and  Column  Con- 
nections for  Intermediate  Sup- 
ports in  all  Stories. 


suggestions  as  to  the  carrying 
out  of  the  system. 

Mr.  S.  E.  Loring,  Consulting  Architect  of  Syracuse,  N.  Y., 
and  one  of  the  first  in  this  country  to  advocate  the  use  of  por- 
ous terra-cotta  for  fire-proofing,  has  also  patented  a  system 
of  slow-burning  construction,  which  is  a  form  of  skeleton  con- 
struction executed  in  wood  instead  of  steel.  The  interior 
construction  is  made  entirely  self-supporting,  so  that  the  walls 
carry  nothing  but  their  own  weight,  and  may  consequently 
be  made  very  thin,  or  of  wood  veneered  with  brick.  Both 
the  columns  and  the  girders  are  built  up  of  2-inch  plank;  the 
planks  of  the  columns  break  joint  so  that  the  column  is  con- 
tinuous from  foundation  to  roof,  and  the  horizontal  and  ver- 
tical members  are  joined  so  as  to  make  the  entire  skeleton 
one  piece  of  framework,  and  consequently  very  rigid.  The 
construction  is  rendered  slow-burning  by  the  size  of  the  struc- 
tural members,  and  by  interlinings  of  felt,  asbestos,  or  equiva- 
lent fire-resisting  materials,  and  also  by  the  use  of  fire-proof 
paints,  tiles,  metal  sheathings,  etc. 

A  large  four-story  factory,  at  Nashville,  Tenn.,  for  the  Na- 
tional Casket  Co.,  was  built  in  the  fall  of  1902,  on  this  principle 
of  construction,  and  there  are  several  examples  of  it  in  New 
York  State,  Mr.  Loring  claims  that  the  New  England  Fire 


MILL  AND   WAREHOUSE  CONSTRUCTION.          1 

Insurance  Companies  have  granted  steel  structure  ratings  to 
all  buildings  erected  on  this  principle. 


Mill  Construction  as  applied  to  Warehouses. 

The  features  of  bad  construction  mentioned  on  page  688,  are  as 
objectionable  in  warehouses  as  in  factories,  while  the  con- 
struction advocated  in  mills  may  be  used  with  almost  equal 
advantage  in  the  erection  of  warehouses,  although  as  the  latter 
are  usually  erected  in  the  more  thickly  settled  portions  of  a 
city,  they  are  more  subject  to  the  dangers  of  a  conflagration, 
and  it  should  be  understood  that  even  the  best  slow-burning 
construction  will  stand  but  a  short  time  after  a  fire  has  obtained 
a  good  headway. 

The  main  object  of  mill,  or  as  it  is  often  called,  "slow-burn- 
ing" construction,  being  to  prevent  a  fire  from  readily  getting 
started,  or  from  spreading  in  concealed  spaces. 

In  applying  the  principles  of  mill  construction  to  warehouses, 
therefore  the  general  principle  of  using  large  timbers  placed 
as  far  apart  as  the  loads  will  permit,  and  of  avoiding  all  con- 
cealed spaces,  should  be  constantly  kept  in  mind. 

Warehouse  floors,  however,  are  generally  required  to  sus- 
tain heavier  loads  than  are  found  in  woollen  and  cotton  mills 
and  hence  require  heavier  construction.  While  warehouse  floors 
are  quite  often  built  with  transverse  girders,  eight  or  ten  feet 
apart,  with  the  space  between  spanned  by  flooring  from  four- 
to  six  inches  thick,  the  more  common  method  of  construc- 
tion is  to  use  one  or  more  lines  of  longitudinal  girders,  sup- 
porting floor  beams  spaced  from  two  to  four  feet  apart.  Where 
very  heavy  loads  are  to  be  supported  this  is  generally  the 
more  economical  construction,  as  it  requires  only  a  2-inch 
underfloor,  while  it  is  just  about  as  slow-burning. 

Steel  and  Iron  not  as  Desirable  as  Wood. — Wher- 
ever wooden  joists  and  flooring  are  to  be  used,  it  is  more  de- 
sirable from  the  point  of  safety  from  fire  to  use  wood  for  the 
posts  and  girders  also,  than  to  use  iron  or  steel  for  these  por- 
tions of  the  building,  for  the  reason  that  steel  beams  will  warp 
and  twist  and  pull  down  the  building  several  minutes  before 
the  wooden  beams  will  be  burnt  to  the  breaking  point,  .i.e, 
provided  the  wooden  beams  have  a  sectional  area  of  at  least 
72  square  inches  and  are  spaced  4  feet  or  more  from  centres. 


712      MILL   AND  WAREHOUSE   CONSTRUCTION. 

Cast-iron  columns  will  also  generally  fail  in  a  fire  sooner  than 
wooden  posts. 

By  using  Oregon  fir,  or  long-leaf  Southern  pine  for  the 
posts  arid  girders  and  placing  the  posts  close  enough  together, 
it  is  practicable  to  obtain  sufficient  strength  for  a  five-story 
building  with  a  live  load  of  300  pounds  per  square  foot. 

If  it  is  thought  necessary  to  place  the  posts  so  that  the  span 
of  the  girders  will  be  more  than  12  feet,  then  it  will  be  necessary 
co  use  steel  beams  for  the  girders,  but  to  obtain  slow-burning 
construction,  all  steel  and  also  all  cast-iron  columns  should 
be  protected  to  some  degree  from  the  heat. 

Fire-proofing  of  Steel  and  Iron  for  Slow-burning 
Construction. — Absolute  fire  protection  of  the  steel  and  iron  is 
hardly  warranted  in  a  building  in  which  the  larger  portion 
of  the  construction  is  of  wood,  but  sufficient  protection  should 
be  given  that  the  girders  and  columns  will  stand  at  least  until 
the  floor  timbers  have  fallen.  Such  protection  for  steel  beam 
girders  can  be  most  economically  obtained  by  first  enclosing 
the  girder  with  wood,  then  furring  with  f"Xj"  corrugated 
band  iron,  and  then  covering  with  metal  lath  and  plaster.  The 
furring  can  be  secured  to  the  wood  by  a  few  staples,  and  the 
metal  lath  by  nails  or  staples  according  to  the  kind  of  lath- 
ing that  is  used.  Sheathing  lath  may  also  be  used  in  place  of 
the  metal  furring. 


Fig.  16 

Fig.  16  shows  a  20"  steel  beam  girder  protected  in  this  way, 
the  floor  beams  being  6"  XI 2"  supported  on  malleable  iron 
brackets  bolted  to  the  I-beam.  Such  a  covering  would  un- 
doubtedly protect  the  steel  until  the  floor  beams  had  dropped, 
and  it  is  hardly  to  be  expected  that  the  columns  and  girders 
would  stand  after  all  of  the  floors  had  fallen. 


MILL  AND  WAREHOUSE  CONSTRUCTION.      713 

The  columns  can  be  protected  by  metal  furring  and  metal  lath 
and  plaster  as  shown  in  Fig.  17.     For.  round  cast-iron  columns, 


/Space 


Fig.  17 

Berger's   economy  stud,   see   Chapter  XXIII,   is   probably  the 

cheapest  form  of  furring  that  can   be  employed,  as  it  is  easily 

applied  and  the  lathing  does  not  have  to  be  wired  to  the  furring. 

Connection    of   Floor   Beams   and    Girders. — To 

render  the  construction  slow-burning,  and  particularly  the 
girders,  it  is  important  that  there  be  no  hollow  space  between 
the  top  of  the  girders,  and  the  flooring,  or  that  the  tops  of  the 
floor  beams  shall  be  flush  with  the  top  of  the  girder.  This, 
of  course,  necessitates  framing  of  the  floor  beams  to  the  girder. 


Fig.  18 

For  heavy  construction  the  only  kind  of  framing  that  is  per- 
missible, is  by  means  of  some  form  of  joist  hanger.  The  various 
forms  of  joist  hangers  now  in  the  market  have  been  illustrated 
and  commented  on  in  Chapter  XXI.  When  the  floor  beams 
are  G"X12"  or  larger,  and  the  girders  are  of  wood,  the  author 


714      MILL   AND  WAREHOUSE  CONSTRUCTION. 

would  give  the  preference  to  the  Duplex  hanger  shown  in 
Fig.  18.  If  the  girder  is  of  steel,  the  Van  Dorn  or  National 
double  hanger  will  probably  be  more  satisfactory,  as  these 
hangers  can  be  used  with  any  depth  of  beam  and  girder,  or 
special  malleable  iron  brackets  may  be  riveted  to  the  web 
of  the  girder,  as  in  Fig.  16. 


Fig.  19 

Fig.  19  shows  a  floor  framed  with  Van  Dorn  hangers  and 
post  caps.  The  same  principle  of  construction  is  applicable 
to  larger  joists  spaced  further  apart. 

Wall  Supports  and  Anchors  for  Joists  and 
Girders. — In  a  warehouse  intended  tc  be  constructed  on  the 
slow-burning  principle,  the  floor  beams  and  girders  should  be 
anchored  to,  and  supported  by  the  walls  in  such  a  way  that 
in  case  the  beams  are  burnt  through,  the  ends  may  fall  with- 
out injuring  the  wall,  and  where  large  timbers  are  used,  pro- 
vision should  be  made  against  the  possibility  of  dry-rot. 

The  method  of  supporting  the  beams  in  "Mill  Construction," 
as  originally  developed  in  the  New  England  Mills,  is  shown  by 
Fig.  20.  This  fulfilled  the  requirements  above  mentioned, 
but  it  weakened  the  wall  to  some  extent. 

The  Goetz  box  anchors  shown  by  Figs.  21,  22,  and  23,  are  a 
decided  improvement  upon  the  anchor  shown  in  Fig.  20  as 
they  afford  all  of  the  advantages  of  the  latter  while  they  do 
not  weaken  the  wall,  unless  the  floor  beams  are  very  wide. 

These  anchors  are  made  wedge-shaped  so  that  it  is  impossible 
to  pull  them  out  of  the  wall,  and  the  more  weight  there  is  upon 


MILL   AND  WAREHOUSE   CONSTRUCTION.      715 

the  beam,  the  greater  will  be  the  bondage  that  holds  beam  tc 
box  and  box  to  wall. 

In  case  of  fire  or  accident,  the   joist  can   burn  through  or 
break,  and  in  falling  they  free  the   anchorage   and  leave   the 


Fig.  20 

wall  standing,  not  even  weakened  by  the  space  left  in  the  wall, 
because  the  anchor  remains,  and  the  crushing  strength  of  this 


Fig.  21 


Fig.  22 


cast- iron  box  is  much  greater  than  that  of  the  wall.  No  break 
or  breach  is  made  in  the  wall,  and  the  anchor  that  remains, 
securely  held,  forms  a  space  for  the  easy  replacement  of  joist. 
The  anchor  provides  a  perfect  and  secure  foundation  for  each 


716      MILL  AND  WAREHOUSE  CONSTRUCTION. 

joist.     Fire   from  a  defective   flue   cannot   ignite   a  joist  end, 
because  it  is  protected  by  a  ventilated  cast-iron  box. 

The  boxes,  or  anchors,  also  have  air  spaces  in  the  sides,  J  inch 
wide,  which  permit  a  circulation  of  air  around  the  ends  of  the 
joist,  effectually  preventing  dry-rot  in  the  ends  of  the  timbers. 


Fig.  23 

If  timber  is  wet  or  unseasoned  it  will  have  a  chance  to  dry 
out  after  it  is  put  in  the  building. 

The  average  weight  of  a  box  like  Fig.  22  for  2X12  joists 
is  10  pounds. 

Another  device  for  obtaining  the  same  results  in  a  different 


Fig.  24 

Duplex  Wall  Hanger. 

way,  is  the  wall  hanger,  of  which  two  patterns  are  shown  in 
Chapter  XXI.  Figs.  24  and  25  show  Duplex  wall  hangers 
for  large  timbers.  The  hanger  shown  in  Fig.  25  is  made  extra 


MILL   AND   WAREHOUSE  CONSTRUCTION.      717 

heavy  and  is  provided  with  a  plate  which  has  eight  inches 
bearing  on  the  wall,  and  the  bearing  of  the  timbers  on  the 
hanger  is  also  eight  inches. 

For  beams  not  exceeding  ten  inches  in  breadth  there  is  prob- 
ably little  choice  between  the  box  anchor,  Fig.  23,  and  the 
wall  hangers,  Figs.  24  and  25,  except  perhaps  in  the  price 
and  appearance.  When  the  wall  hanger  is  used,  no  hole  is 
left  in  the  wall,  and  a  saving  of  six  inches  in  the  length  of  the 
beams  is  effected,  which  in  some  cases  would  be  a  consideration. 


Fig.  25 
Extra  Heavy  Duplex  Hanger. 

For  girders  12"X14"  and  upwards  the  author  believes  the 
hanger  shown  by  Fig.  25  to  be  preferable  to  the  box  anchor. 
Wall  hangers  made  from  stirrups  should  not  be  used  for  heavy 
beams.  Any  one  of  these  anchors  or  hangers  is  obviously 
greatly  superior  to  the  ordinary  method  of  anchoring  beams 
or  girders  to  walls,  and  the  use  of  such  anchors  will  un- 
doubtedly save  much  loss  by  the  falling  of  the  walls,  which  are 
almost  invariably  pulled  down  by  the  ordinary  iron  anchors 
when  the  beams  fall. 

A  reduction  in  the  rate  of  premiums  for  fire  insurance  can  be 
obtained  when  these  anchors  or  hangers  are  used. 

Weakness  of  Wrought  Iron  Stirrups  when  Ex- 
posed to  Fire. — Referring  to  this  subject,  Prof.  J.  B.  John- 
son, of  Washington  University,  says : 

"The  recent  fire  tests  of  steel  stirrups  and  brick  walls  which 
were  made  under  my  supervision  in  this  city  (St.  Louis)  show 


713      MILL  AND  WAREHOUSE   CONSTRUCTION. 

very  conclusively  that  unprotected  stirrups  are  extremely 
dangerous.  These  stirrups  become  red  hot  in  a  few  minutes 
and  then  rapidly  char  and  burn  away  the  ends  of  the  beam,  and 
also  bend  down  so  that  in  from  twenty  to  thirty  minutes  after 
the  fire  reaches  the  stirrups  the  beam  is  dropped  right  out  of 
the  twisted  steel  by  the  straightening  out  of  this  bend  or  twist." 

The  Duplex  hangers  possess  an  advantage  over  steel  stir- 
rups, in  that  being  of  malleable  iron  they  are  not  as  quickly 
affected  by  heat,  there  are  no  twists  or  bends  to  straighten, 
and  the  bearing  in  the  trimmer  or  header  is  to  a  great  degree 
protected  by  the  form  of  construction. 

During  the  severe  fire  at  Paterson,  N.  J.,  Feb.  9,  1902,  some 
Duplex  wall  hangers  were  subjected  to  a  most  severe  test 
without  apparent  injury. 

It  is  undoubtedly  desirable  that  all  structural  iron  should 
be  protected  from  fire,  but  it  is  almost  impracticable  to  effect- 
ively protect  the  stirrups  used  in  connection  with  wooden 
beams  without  going  to  a  greater  expense  than  the  character 
of  the  construction  will  warrant. 

Post  and  Girder  Connections. — Whenever  a  building 
is  constructed  with  wooden  posts  extending  through  several 
stories,  the  upper  posts  should  always  rest  on  top  of  an  iron  cap 
plate,  fitted  over  the  post  below,  as  in  Figs.  19  and  29,  and 
never  on  the  girder  or  even  on  a  wooden  bolster.  A  bolster 
would  not  be  so  objectionable  but  for  the  fact  that  the  pressure 
under  the  post  will  generally  be  sufficient  to  crush  the  fibres 
of  any  kind  of  wood.  Then,  too,  there  would  always  be  some 
settlement  due  from  shrinkage.  As  posts  are  used  expressly 
for  the  support  of  beams  or  girders,  the  iron  caps  must  of  course 
extend  sufficiently  beyond  the  upper  post  to  afford  ample 
bearing  for  the  end  of  the  girderu  This  bearing  in  square 
inches  should  be  at  least  equal  to  one-half  the  load  on  the 
girder  divided  by  the  safe  resistance  of  the  wood  to  crushing 
across  the  grain,  as  given  on  page  414.  For  example,  a  12"X  14" 
yellow  pine  girder  is  designed  to  support  a  possible  load  of 
38,000  pounds,  what  bearing  should  it  have  at  the  ends? 

Ans.  The  safe  resistance  of  yellow  pine  to  crushing  across 
the  grain  is  given  at  500  pounds.  One-half  of  the  load  on 
the  girder  is  19,000  pounds,  hence  the  bearing  area  should  be 
19,000-^500  or  38  square  inches.  As  the  breadth  of  the  beam 
is  12  inches  this  would  require  a  bearing  lengthways  of  the 
girder  of  3J  inches.  A  bearing  of  4  or  5  inches,  however, 


MILL   AND  WAREHOUSE  CONSTRUCTION.      719 


will  be  still  better,  but  in  no  case  should  the  bearing  be  less 
than  that  required  by  the  above  rule. 

Forms  of  Post  Caps. — A  very   common  form  of  post 
cap  is  shown  by  Fig.  26,  the  dimensions  ^ 

given  being  for  a  10  X 10  post.  Fig.  27 
shows  a  similar  cap  for  a  round  post. 
These  caps  fulfill  all  requirements  for 
strength  and  permit  of  the  use  of  a 
girder  wider  than  the  post.  When 
the  girders  and  joists  are  in  place, 
and  especially  when  the  building  is 
occupied,  there  is  no  danger  of  the 
girders  or  posts  slipping  on  the  plate — 
in  fact  it  would  require  a  great  force  to  move  them.  The 


Fig.  26 

Common  Cast-iron  Post  Cap. 


Fig.  27 

girders  should  be  tied  together  longitudinally  by  iron  straps 
spiked  to  their  sides. 


Fig.  28 

Goetz  Post  Cap. 

Many   persons,    however,    consider   it   important   that   in   a 
building  of   slow-burning  construction  the  posts  shall  be  tied 


720     MILL  AND  WAREHOUSE  CONSTRUCTION. 

together  in  vertical  lines,  and  the  girders  secured  in  such  a 
way  that  they  will  be  self -releasing  without  pulling  down  the 
posts.  Figs.  28  and  29  show  two  post  caps  which  fulfill  these 
requirements. 


Fig.  29 
Duvinage  Cap. 


With  these  caps,  the  ends  of  the  girders  are  not  fastened 
by  bolts  or  spikes,  but  are  held  in  place  and  tied  longitudinally 
by  means  of  the  lug  L  on  the  Goetz  cap,  and  by  the  pins  on 
the  Duvinage  cap,  so  that  in  case  the  girder  is  burned  to  the 
breaking  point,  it  can  fall  without  pulling  on  the  post.  Pro- 
vision is  also  made  for  bolting  the  cap  to  the  upper  post.  The 
author  doubts  very  much,  however, 
if  posts  bolted  together  in  this  way 
would  stand  after  the  girders  had 
fallen,  as  the  planking  would  be 
likely  to  pull  the  posts  over,  even 
if  they  did  not  burn  as  quickly  as 
the  beams.  Both  of  the  caps  shown 
by  Figs.  28  and  29  are  patented 
and  can  not  be  used  without  pay- 
ing a  small  royalty  to  the  patentees.  A  cap  like  that  shown 


Fig,  30 


MILL  AND  WAREHOUSE  CONSTRUCTION.      721 

by  Fig.  30  without  the  lugs  or  pins  can  be  made  at  any  foundry 
without  infringing  on  the  patents. 

Figs.  31  and  32  show  different  styles  of  steel  caps  that  are 
largely  taking  the   place   of  the   cast-iron  cap.      The   Duplex 


Fig.  31 

Van  Dorn  Post  Caps. 

post  caps  are  also  made  so  as  to  permit  of  the  extension  of  the 
post  for  two  stories,  thereby  giving  an  extremely  strong  and 


Fig.  32 

Duplex  Four-way  Post  Cap. 

stiff  connection.     The  tests  that  have  been  made  of  the  Duplex 
post  caps  show  that  they  possess  great  strength. 


722      MILL  AND  WAREHOUSE  CONSTRUCTION. 

There  is  an  objection  to  the  use  of  four-way  post  caps  where 
the  girders  are  of  wTood,  in  that  the  floor  beams  that  are  hung 
from  the  girders  will  drop  by  an  amount  equal  to  the  shrinkage 
in  the  girder,  if  the  beams  are  hung  in  stirrups,  or  by  one-half 
this  amount  if  hung  in  Duplex  hangers,  while  the  beams  sup- 
ported on  the  post  cap  can  not  drop  at  all,  consequently  the 
floor  will  be  higher  over  the  beam  supported  by  the  posts, 
than  over  the  intermediate  beams.  In  one  building  where 
deep  beams  were  used,  this  unevenness  in  the  floor  amounted  to 
nearly  an  inch  and  was  very  noticeable.  Wherever  wooden 
girders  are  used  it  is  therefore  much  better  construction  to 
support  all  of  the  floor  beams  from  the  girders,  then  the  effect 
of  shrinkage  will  be  uniform.  With  steel  girders  there  is  no 
shrinkage,  and  a  beam  may  be  placed  opposite  the  posts  with 
advantage. 

Mill  Construction  with  Concrete  Flooring-. — 
Fig.  33  shows  a  modification  of  mill  or  slow-burning  construc- 


Fig.  33 

tion  advocated  by  the  Hinchman-Renton  Fire-proofing  Co  for 
buildings  in  which  first-class  fire-proof  construction  cannot 
be  afforded.  It  differs  from  the  standard  slow-burning  con- 
struction only  in  the  substitution  of  reinforced  cinder  concrete 


MILL  AND   WAREHOUSE   CONSTRUCTION.      7->3 

for  the  usual  2  or  3-inch  plank  between  the  beams.  While 
this  construction  has  never  been  tested  by  a  fire,  it  appeals  to 
the  author  as  an  improvement  upon  the  standard  wooden  con- 
struction, in  that  there  is  less  wood  to  burn,  while  none  whatever 
(except  the  finished  flooring)  is  exposed,  and  it  is  more  sound 
proof  and  more  decorative  than  a  floor  ceiling  without  the 
plaster.  Were  it  not  for  the  element  of  shrinkage  which  can 
never  be  entirely  overcome  where  wood  is  used  for  floor  beams, 
the  author  believes  that  this  floor  would  stand  fire  fully  as 
long  as  many  so  called  fire-proof  floors  with  steel  joists.  This 
floor  can  also  be  finished  on  top  with  cement. 


Cost  of  Mills  and  Factories  Built  on  the  Slow- 
Burning-  Principle. 

The  cost  per  square  foot  of  total  floor  area  of  mills  and  factories 
in  the  year  1884  was,  according  to  Mr.  Edward  Atkinson,  as 
follows : 

Mill  with  three  stories  for  machinery,  and  a  base- 
ment for  miscellaneous  purposes 75  to  80  cts. 

Mill  with  two  stories  for  machinery,  and  no  base- 
ment    65  cts. 

Mill  with  one  story,  of  about  one  acre  of  floor,  with 

basement  for  heating  and  drainage  only about  85  cts. 

The  above  is  for  the  total  area  of  floors  in  the  building,  above 
the  basement.  These  figures,  while  perhaps  a  little  low  for 
present  prices,  are  a  fair  average  taken  through  a  number  of 
years. 

The  following  data  as  to  the  cost  of  mill  buildings  built  on 
the  "Praray  Improved  Construction"  and  also  of  mills  built 
on  the  modern  "  Slow- Burning  Method  of  Construction"  both 
in  the  East  and  South,  were  kindly  furnished  the  author  by 
Mr.  Praray. 

Mr.  Praray  also  says:  "The  cost  of  building  varies  according 
to  the  locality.  Lumber,  bricks,  and  labor  cost  50  per  cent, 
more  in  New  England  than  in  the  Carolinas,  and  therefore 
the  same  building  will  cost  much  less  in  the  South  than  in 
the  East." 

EXAMPLES. — The    Dixie    Cotton    Mills    at    La    Grange,    Ga., 


724     MILL  AND  WAREHOUSE  CONSTRUCTION. 

built  in  1895  and  1896  on  what  is  called  the  "Praray  Improved 
Construction." 

Total  floor  area  of  all  buildings  and  steam  plant,  87,100  square 
feet.  Cubical  contents  of  all  buildings,  including  the  Smoke 
Stack,  which  is  125  feet  high,  52"  core,  2,419,000  cubic  feet. 

Cost,  per  square  foot  floor  space,  43T6o3o  cents. 

The  Whitman  Cotton  Mills,  New  Bedford,  Mass.,  built  in 
1896  and  1897  on  Modern  Mill  Construction,  and  approved 
by  the  Mfrs.  Mutual  Ins.  Companies. 

Total  floor  area  of  all  buildings  and  steam  plant,  217,000 
feet.  Cubical  contents  of  all  buildings,  including  smoke  stack, 
which  is  200  feet  high,  10  feet  core,  is  6,494,000  cubic  feet. 

Cost  per  square  foot  floor  space,  81  ^Q  cents. 

The  Moorhead  Cotton  Mills,  Moorhead,  Miss.,  built  in 
1900  on  what  is  called  the  Modern  or  Slow-Burning  Construc- 
tion, and  higher  above  grade  than  is  usual  on  account  of  high- 
water  mark. 

Total  floor  area  of  all  buildings  and  steam  plant,  31,000  feet. 
Cubical  contents  of  all  buildings,  including  the  smoke  stack, 
which  is  125  feet  high,  48"  core,  532,640  cubic  feet. 

Cost  per  square  foot  floor  space,  82  cents. 

The  above  three  mills  were  built  for  cotton  mills,  and  are  all 
equipped  with  steam-power  plants. 

All  are  two-story  buildings.  It  will  be  noticed  that  the 
Mississippi  mill  cost  more  per  foot  floor  space  than  the  New 
England  mill. 

The  Georgia  or  Dixie  mill  cost  about  one-half  per  foot  floor 
space  of  the  two  other  mills. 

Five  other  mills  on  the  "Praray  Method"  have  been  built  in 
the  South,  and  the  cost  has  been  less  than  50  cents  per  foot- 
floor  space. 

Mills  built  throughout  the  New  England  States  cost  from 
75  cents  to  $1,10  per  square  foot  floor  surface 

Mills  built  in  the  Carolinas,  Georgia,  and  Alabama  average 
about  60  cents  per  square  foot  floor  surface. 

Mills  of  less  than  100,000  square  feet  floor  surface  will  cost 
from  80  cents  to  $1.25  per  foot. 

The  greater  amount  of  floor  space  will  enable  mills  to  be 
built  on  the  modern  methods  at  the  prices  named  above. 

Labor  in  the  South  is  much  cheaper  and  surely  33  per  cent, 
slower.  Lumber  and  materials  in  the  South  cost  about  50  per 
cent,  of  the  price  paid  in  New  England. 


MILL  AND  WAREHOUSE  CONSTRUCTION.      725 

A  mill  built  at  Taunton,  Mass.,  four  stories  high  with  a  floor 
area  the  same  as  the  Whitman  mills,  cost  96  cents  per  square 
foot  floor  space.  This  was  also  equipped  with  steam  power. 

The  cost  per  square  foot  of  floor  space  will  generally  be 
greater  for  a  small  mill  than  for  a  large  one  for  the  reason  that . 
a  small  mill  that  is  to  be  run  by  steam  power  has  to  build  boiler 
and  engine  house,  pump  house,  towers  for  tank  purposes,  etc., 
large  enough  for  doubling  the  size  of  the  mill  at  some  future 
time. 

The  mills  in  the  South  are  built  for  from  5,000  to  10,000 
spindles  to  start  with,  and  are  planned  to  add  that  amount  of 
spindles  at  some  future  time.  They  must  build  boiler  and 
engine  house,  belt- ways,  towers,  etc.,  to  accommodate  future 
extensions,  which  makes  the  first  cost  of  the  mill  come  very 
high,  and  very  often  places  the  mill  in  an  embarrassing  position. 

For  example,  the  Moorhead  Cotton  Mills,  Moorhead,  Miss., 
was  built  with  the  idea  of  adding  double  the  amount  of  spindles 
that  they  have  installed,  that  is  to  say,  the  power  house  and 
chimney  were  all  large  enough  for  the  future  extension,  making 
spare  room  in  the  boiler  house,  and  spare  room  in  the  engine 
house* 


CHAPTER  XXIII. 

FIRE-PROOFING    OF   BUILDINGS. 

By  RUDOLPH  P.  MILLER,  C.  E. 

Definitions. — The  term  "  fire-proof, "  while  now  quite 
well  understood  by  architects,  is  still  used  in  a  very  broad 
sense  by  the  public.  To  be  strictly  fire-proof,  a  building  must 
be  constructed  and  finished  entirely  with  incombustible  mate- 
rials, and  any  of  these  materials,  such  as  steel  or  iron,  which 
are  injuriously  affected  by  heat  or  streams  of  water  must  be 
efficiently  protected  by  other  materials  which  are  not  so  affected. 

This  precludes  the  use  of  wood,  whether  exposed  or  not  ex- 
posed, also  all  exposed  steel  or  iron,  common  glass,  and  most 
building  stones. 

It  is  safe  to  say  that  there  are  very  few  buildings  in  this 
country  that  are  absolutely  fire-praof — there  is  quite  a  large 
number,  however,  that  could  not  be  destroyed  by  fire,  and  in 
which  the  salvage  would  probably  amount  to  from  60  to  80 
per  cent.,  and  it  is  the  latter  class  which  is  generally  meant 
when  the  term  fire-proof  is  used. 

Incombustible  buildings,  and  buildings  having  wood  con- 
struction protected  to  a  greater  or  less  degree  from  the  flames, 
are  sometimes  advertised  as  fire-proof,  but  such  buildings 
should  be  considered  merely  as  slow-burning. 

To  build  absolutely  fire-proof  is  expensive — to  build  so  that 
the  building  can  be  merely  gutted  by  fire,  is  less  expensive,  and 
for  many  classes  of  buildings  cui  that  is  advisable. 

It  is  undoubtedly  the  duty  of  every  architect  to  be  well 
informed  concerning  the  fire-proof  qualities  of  all  materials  that 
enter  into  the  construction  and  finishing  of  buildings,  and  as 
to  the  best  use  of  these  materials — he  can  then  choose  his 
materials  and  use  them  to  such  an  extent  as  the  character  of 
the  building  and  the  interests  of  his  client  demand.  It  is  this 

726 


DEFINITIONS.  727 

information  that  this  chapter  is  intended  to  furnish  in  a  con- 
cise manner. 

Municipal  Definitions.  —  Municipal  definitions  as  to 
what  constitutes  "fire-proof  construction"  have  a  great  bear- 
ing on  the  construction  of  buildings  within  their  jurisdiction, 
and  those  of  the  two  largest  cities  are  therefore  quoted. 

Chicago  Definition. —  "The  term  fire-proof  construction 
shall  apply  to  all  buildings  in  which  all  parts  that  carry  weights 
or  resist  strains,  and  also  all  exterior  walls  and  all  interior 
wralls  and  all  interior  partitions  and  all  stairways  and  all  ele- 
vator enclosures  are  made  entirely  of  incombustible  material, 
and  in  which  all  metallic  structural  members  are  protected 
against  the  effects  of  fire  by  coverings  of  a  material  which  shall 
be  entirely  incombustible,  and  a  slow  heat  conductor,  and 
hereinafter  termed  ' fire-proof  material.'  Reinforced  concrete 
as  defined  in  this  ordinance  shall  be  considered  fire-proof  con- 
struction. 

"The  materials  which  shall  be  considered  as  filling  the  con- 
ditions of  fire-proof  covering  are:  First,  burned  brick;  second, 
tiles  of  burned  clay;  third,  approved  cement  concrete;  fourth, 
terra-cotta;  fifth,  approved  cinder  concrete." 

New  York  Definition. — Buildings  required  to  be  fire- 
proof shall  be  "constructed  with  walls  of  brick,  stone,  Port- 
land cement  concrete,  iron  or  steel,  in  which  wood  beams  or 
lintels  shall  not  be  placed,,  and  in  which  the  floors  and  roofs 
shall  be  of  materials  provided  for  in  Section  106  of  this  Code. 
The  stairs  and  staircase  landings  shall  be  built  entirely  of 
brick,  stone,  Portland  cement  concrete,  iron  or  steel.  No 
woodwork  or  other  inflammable  material  shall  be  used  in  any 
of  the  partitions,  furrings,  or  ceilings  in  any  such  fire-proof 
buildings,  excepting,  however,  that  when  the  height  of  the 
building  does  not  exceed  twelve  stories  nor  more  than  150 
feet,  the  doors  and  windows  and  their  frames,  the  trims,  the 
casings,  the  interior  finish  when  filled  solid  at  the  back  with 
fire-proof  material,  and  the  floor-boards  and  sleepers  directly 
thereunder,  may  be  of  wood,  but  the  space  between  the  sleepers 
shall  be  solidly  filled  with  fire-proof  materials  and  extend  up  to 
the^  underside  of  the  floor-boards. 

"When  the  height  of  a  fire-proof  building  exceeds  twelve 
stories,  or  more  than  150  feet,  the  floor  surfaces  shall  be  of 
stone  cement,  rock  asphalt,  tiling,  or  similar  incombustible 
material,  or  the  sleepers  and  floors  may  be  of  wood  treated  by 


728  FIRE-PROOFING   OF    BUILDINGS. 

some  process  approved  by  the  Board  of  Buildings,  to  render  the 
same  fireproof.  All  outside  window  frames  and  sash  shall  be 
of  metal,  or  of  wood  covered  with  metal.  The  inside  window- 
frames  and  sash,  doors,  trim,  and  other  interior  finish  may  be 
of  wood  covered  with  metal,  or  of  wood  treated  by  some  pro- 
cess approved  by  the  Board  of  Buildings  to  render  the  same 
fire-proof." 

Section  106  refers  to  fire-proof  floors.  These  may  be  con- 
structed of  brick,  tile,  cement  concrete,  and,  in  fact,  of  any 
material  that  will  successfully  pass  the  tests  prescribed  by  the 
Code.  Before  any  floor  construction  other  than  brick  or  tile 
will  be  passed  by  the  department,  however,  it  must  be  tested 
for  strength  and  fire  resistance  under  very  rigid  conditions, 
and  the  construction  must  stand  the  test  successfully.* 

When  Fire-proof  Construction  Should  be  Employed. 
— A  building  should  be  designed,  built,  and  finished  to  con- 
form to  the  purpose  for  which  it  is  to  be  used — a  building  that 
will  contain  but  little  inflammable  material,  and  that  not  of 
great  value — need  not  be  as  thoroughly  fire-proof  as  a  build- 
ing designed  for  the  storage  of  valuable  goods,  or  where  the 
safety  of  human  life  is  at  stake. 

The  height  of  a  building  is  an  important  factor  in  deter- 
mining whether  it  should  be  fire-proof  or  not.  The  ability  to 
cope  with  fire  in  a  building  increases  in  more  than  direct  pro- 
portion to  its  height.  The  area  covered  by  a  building  also  is 
important,  although  in  most  instances  interior  division  walls 
may  be  provided  which  practically  cut  up  a  building  into  a 
series  of  smaller  buildings. 

Some  of  the  limitations  placed  on  non-fire-proof  buildings 
by  various  municipal  laws  will  be  found  in  the  table  on  page 
729. 

Limiting  Areas  for  Non-fire-proof  Buildings. — 
New  York,    8,000  sq.  ft.  on  an  interior  lot. 


12,500    " 

(l    "   a  corner. 

22,000    " 

"  when  facing  three  streets. 

Chicago,f      9,000    " 

"  if  of  ordinary  joisted  construction. 

12,000    " 

"  if  of  slow-burning  construction. 

St.  Louis,      7,500    " 

(  i 

Boston,          5,000    " 

i  ( 

*  See  p.   745. 

f  Milwaukee  has  same  law. 


DEFINITIONS. 


729 


Cleveland,    Mill  Construction.* 

20,000  sq.  ft.  when  facing  streets  on  four  sides. 

15,000    "    "        "        "  "  "  three    " 

12,000    "    "        "        "  "  "  two      " 

9,000   "    "       "         "  "  "  one  side. 

5,000    "    "  on  any  lot  when  of  hazardous  occu- 
pancy. 

Ordinary  Construction: 

12,500  sq.  ft.  when  facing  streets  on  four  sides. 

10,000    "    "        "        "  "       "  three    " 

7,500    "    "        "        "  "       "  two      " 

5,000    "    "        "        "  "       "  one  side 

2,000    "    "  on  any  lot  when  of  hazardous  occu- 
pancy. 

LIMITING  HEIGHTS  FOR  NON-FIRE-PROOF  BUILDINGS 


City. 

All 
Build- 
ings. 

Hotels. 

Schools. 

Hospitals 
and 
Asylums. 

Residence 
Buildings. 

Buffalo   N   Y 

72ft. 

New  York   N   Y 

75ft 

35  ft 

35  ft. 

35  ft 

Kansas  City,  Mo  

75ft. 

St   Louis   Mo  

75ft 

1 

2  stories 
above 

2  stories 
above 

4  stories 
and 

Boston   Mass     

75  ft, 

1 

basement 

basement 

basement 
65  ft. 

Washington,  D.  C.     .  .  .  :  . 
New  Haven,  Ct  
Denver,  Col  
San  Francisco,  Cal  

75  ft. 
75ft. 
80ft. 
84ft. 

60ft. 
60ft. 

60  Yt.' 
3  stories 

"45  "ft."  ' 
3  stories 

60ft. 

Seattle   Wash 

85  ft 

3  stories 

3  stories 

Omaha  Neb 

90ft 

Chicago,  111  

Baltimore   Mrl 

100  ft. 
100  ft. 

3  stories 

2  stories  < 

5  stories 
and 
basement 

Milwaukee   Wis  

100  ft. 

Cleveland   O            

100  ft. 

New  Orleans,  La  
Newark   N   J 

52ft. 

52ft. 

3  stories 

Philadelphia   Pa 

4  stories 

Cost  of  Fire-proof  Construction.— Mr.  F.  W.  Fitz- 
patrick,  consulting  architect,  contributed  to  the  March,  June, 
and  July,  1903,  numbers  of  Fireproof  some  interesting  papers 
in  which  he  gives  the  comparative  cost  per  cubic  foot  of  a  large 
number  of  buildings  figured  for  both  fire-proof  and  ordinary 
construction.  These  figures  seem  to  indicate  that  fire-proof 
construction  for  office-buildings,  hotels,  etc.,  adds  from  9  to 


*  See  Chap.  XXII. 


730  FIRE-PROOFING  OF    BUILDINGS. 

13  per  cent  over  the  cost  of  ordinary  construction  with  wooden 
joists.  For  stores  and  warehouses  the  difference  will  often  be 
less  than  5  per  cent. 

See  also,  "Cost  of  Buildings  per  cubic  foot,"  Part  III. 

Divisions  of  the  Subject.— In  constructing  fire-proof 
buildings  it  is  necessary  to  consider: 

1.  Materials  to  be  used. 

2.  Form  of  construction. 

3.  Protecting  devices. 

4.  Extinguishing  appliances. 

This  arrangement  will  be  followed  in  the  discussion  of  the 
subject  in  this  chapter. 

Materials  of  Construction. 

All  materials  of  construction  are  more  or  less  injuriously 
affected  by  high  temperatures.  Furthermore,  an  incombustible 
material  is  not  necessarily  fire-resisting,  as,  for  instance,  steel. 
The  value  of  various  materials  in  fire-proof  construction  is 
indicated  in  the  following  paragraphs. 

Brickwork. — Common  brickwork,  when  of  a  good  quality, 
will  stand  exposure  to  fire  for  a  considerable  length  of  time, 
but  in  a  severe  conflagration  the  heated  side  of  the  wall  ex- 
pands, often  to  the  point  of  throwing  the  wall,  the  bricks  crack, 
shell,  and  are  sometimes  melted.  Experience  has  shown  that 
thick  walls  are  less  affected  by  heat  than  thin  walls,  and  that 
hard-burned  bricks  will  stand  better  than  soft  or  under-burned 
bricks.  In  buildings  which  are  to  contain  large  quantities  of 
inflammable  material  it  is  undoubtedly  better  to  line  the  walls 
with  porous  furring  tile  or  hollow  brick. 

In  the  Baltimore  and  San  Francisco  fires,  it  was  demon- 
strated that  for  outside  walls  brick  is  superior  as  a  fire-proof 
material  to  any  other  material  used  in  wall  construction. 

Stones. — Very  few  stones  will  successfully  stand  the  action 
of  severe  heat,  and  consequently  stone  should  be  used  very 
sparingly  in  fire-proof  buildings,  and  certain  stones  not  at  all. 

Granite  will  explode  and  fly  to'  pieces  or  disintegrate  into 
sand  when  exposed  to  flames. 

Limestones  and  Marbles  are  usually  ruined  if  not  totally 
destroyed  by  an  ordinary  fire.  They  are  the  least  desirable 
of  all  stones  to  use  in  a  fire-proof  building,  and  the  granites 
come  next. 


MATERIALS    OF    CONST-RUCTION.  731 

Sandstones  when  fine-grained  and  compact  will  sometimes 
stand  fire  without  serious  injury,  but  in  the  case  of  a  severe 
conflagration  are  generally  so  badly  affected  that  they  have  to 
be  replaced. 

Terra-cotta  is  made  from  clay  by  mixing  with  water  into 
a  plastic  mass,  shaping  the  same  into  the  form  and  shape  de- 
sired and  baking  at  high  temperature  in  kilns.  For  the  usual 
structural  form  the  shaping  is  generally  done  by  forcing  the 
plastic  mass  through  a  special  die  by  means  of  machinery. 
Ornamental  terra-cotta  must  generally  be  shaped  by  hand. 

Ornamental  Terra-cotta.  —  This  is  undoubtedly  the 
best  material  to  use  for  the  trimmings  of  a  building  that  is 
intended  to  be  absolutely  fire-proof,  and  especially  that  which 
has  a  glazed  surface.  " Terra-cotta  will  certainly  require  less 
reconstruction  after  severe  fire-and-water  tests  than  any 
building  material,  saving,  possibly,  the  best  qualities  of  fire- 
brick. "  * 

Structural  Terra-cotta.  —  Terra-cotta,  as  used  for 
floor  arches,  column  and  girder  protection,  and  for  building 
light  hollow  walls,  is  made  of  three  different  compositions, 
the  material  being  known  as  "Dense,"  "Porous,"  and  "Semi- 
porous,"  according  to  the  method  of  manufacture. 

Dense-Tiling  is  made  from  a  variety  of  clays.  Some  manu- 
facturers use  more  or  less  fire-clay,  and  combine  it  with  potter's 
clay,  plastic  clays,  or  tough  brick  clay.  It  is  very  dense,  and 
possesses  high  crushing  strength.  In  outer  walls  exposed  to 
the  weather  and  required  to  be  light,  it  is  very  desirable.  Some 
manufacturers  furnish  it  with  a  semi-glazed  surface  for  outer 
walls  of  buildings.  For  such  use  it  has  great  durability,  and 
effectually  stops  moisture.  In  using  dense  tiling  for  fire- 
proof filling,  care  should  be  taken  that  the  tiles  are  free  from 
cracks,  and  sound  and  hard  burnt. 

Porous  and  Semi-porous  Terra-cotta  is  made  by  mixing 
sawdust  with  the  clay,  the  sawdust  being  destroyed  by  the 
action  of  the  heat,  leaving  the  material  light  and  porous.  A 
small  proportion  of  fire-clay  mixed  with  the  plastic  clay  is 
desirable  but  not  essential.  The  proportion  of  sawdust  should 
be  from  25  to  35  per  cent,  according  to  the  toughness  of  the 
clay  used.  Care  is  required  in  manufacture  that  the  work  of 
mixing,  drying,  and  burning  be  thoroughly  done.  The  burning 

*  Freitag. 


732  FI^E-PROOFING    OF    BUILDINGS. 

should  be  done  in  down-draught  kilns  by  a  quick  process.  The 
product  should  be  compact,  tough,  and  hard,  ringing  when 
struck  with  metal.  Poorly  mixed,  pressed,  or  burned  tiles, 
or  tile  from  short  or  sandy  clays,  present  a  ragged,  soft, 
and  crumbly  appearance,  and  are  not  desirable.  When  prop- 
erly made,  porous  terra-cotta  will  not  crack  or  break  from 
unequal  heating,  or  from  being  suddenly  cooled  with  water 
when  in  a  heated  condition.  It  can  be  cut  with  a  saw  or  edge 
tools,  and  nails  or  screws  may  be  easily  driven  into  it  for  securing 
interior  finish,  slates,  tiles,  etc.  For  the  successful  resistance 
of  heat,  and  as  a  non-conductor  for  the  protection  of  other 
materials,  it  must  be  ranked  among  the  very  best. 

Semi-porous  Tiling.  —  This  material  was  introduced  by 
those  factories  which  use  pure  fire-clay  in  the  manufacture  of 
their  tile,  to  enable  them  to  compete  with  the  standard  porous 
material. 

During  the  process  of  grinding  the  clay  about  twenty  per 
cent  of  ground  coal  is  mixed  with  it.  This  coal  aids  in  the 
burning  of  the  material  and  also  makes  it  lighter  and  more  or 
less  porous.  Tiling  made  by  this  process  is  admitted  to  be  a 
much  better  fire-resistant  than  the  solid  or  dense  material. 

Mr.  E.  V.  Johnson  says:  "  Personally,  I  believe  that  good 
semi-porous  fire-clay  tile  is  fully  as  efficient  as  a  fire-resisting 
material  as  the  standard  makes  of  porous  terra-cotta." 

Strength  of  Terra-cotta. — In  a  series  of  tests  recently 
made  at  Columbia  University  for  the  building  authorities  of 
New  York  on  terra-cotta  blocks  taken  from  material  delivered 
in  the  open  market,  the  following  crushing  strength  was  de- 
veloped : 

Dense  tile  5820  Ibs.  per  square  inch  (an  average  of  10  tests). 

Semi-porous  terra-cotta  3292  Ibs.  per  square  inch  (an  average 
of  10  tests). 

The  inequality  in  strength  of  the  two  materials  can  be  over- 
come by  using  thicker  webs  and  shells  for  the  semi-porous  or 
porous  material. 

In  the  matter  of  weight,  porous  and  semi-porous  terra-cotta 
have  the  advantage  over  dense  tile.  It  has  already  been  pointed 
out  that  porous  terra-cotta  is  more  readily  cut  and  will  hold 
nails  or  other  fastenings  which  can  be  driven  into  it  without 
destroying  the  material. 

Dense  tiling, .  when  heated  and  cooled  by  water,  is  liable  to 
crack  from  the  sudden  contraction;  "  blocks  with  two  or  more 


MATERIALS    OF    CONSTRUCTION  733 

air-spaces  are  very  liable  to  have  the  outer  webs  destroyed 
under  this  action.  Even  if  not  cooled  with  water,  other  fires 
have  shown  that  hard-burned  terra-cotta  will  crack  and  fall 
to  pieces  under  severe  heat  alone."  * 

The  experience  of  the  recent  conflagrations  in  Baltimore  and 
San  Francisco  fully  bears  out  this  statement.  The  collapse  of 
the  floors  of  one  of  the  buildings  in  Baltimore  was  largely  due 
to  the  weakening  of  the  terra-cotta  arches  by  reason  of  the 
breaking  off  of  the  outer  shells. 

Porous  terra-cotta  is  non-heat-conducting  in  itself,  and  the 
best  qualities  will  usually  resist  fire  and  water  successfully, 
but  if  the  product  "is  not  burned  at  a  sufficiently  high  tem- 
perature to  consume  all  of  the  sawdust,  the  throwing  of  cold 
water  upon  the  heated  surfaces  will  cause  an  expansion  or 
disintegration  due  to  the  absorption  of  the  water  and  its  con- 
version into  steam." 

Porous  terra-cotta  absorbs  water  freely,  and  if  allowed  to 
freeze  when  wet  is  more  or  less  injured.  If  the  process  is  per- 
mitted to  continue,  the  blocks  become  so  weakened  as  to  make 
them  unsafe  for  use. 

Concrete. — Stone  concrete,  under  the  action  of  heat,  is 
affected  much  the  same  way  as  brickwork.  The  heated  surface 
expands  and,  as  the  concrete  is  a  very  poor  conductor,  the 
other  surface  remains  cool  and  either  cracks  or  causes  warping. 
The  heat  also  affects  the  strength  and  texture  of  the  concrete, 
causing  a  disintegration  of  the  concrete  to  a  depth  of  about 
one  inch.  Often  the  surface  spalls  off  with  more  or  less  of  a 
report.  If  water  is  applied  after  the  heat,  the  surface  is  washed 
away  to  the  depth  of  the  affected  part.  These  effects  vary 
somewhat  with  the  stone  used  in  the  aggregate.  Gravel  and 
granite,  on  account  of  difference  in  coefficient  of  expansion 
between  them  and  concrete,  are  likely  to  spall.  Limestone 
calcines  under  the  action  of  heat  and  is  especially  liable  to 
destruction  for  some  depth  by  the  water.  Trap-rock  is  the 
most  satisfactory  material  to  use,  from  the  fire-resisting  stand- 
point as  well  as  that  of  strength. 

If  there  is  no  application  of  water  after  the  fire  and  the  sur- 
face is  allowed  to  cool  off  gradually,  the  concrete  may  set  again 
and  become  hard.  It  is  not  well,  however,  to  rely  on  this. 

Slag    Concrete. — Blast-furnace    slag   has  been  used  as  the 

*  Freitag. 


734  FIRE-PROOFING    OF    BUILDINGS. 

aggregate  in  concrete,  with  very  satisfactory  results  both  as 
to  fire-resistance  and  strength. 

Cinder  Concrete. — Cinder  concrete,  because  of  its  porous 
character  and  the  nature  of  its  aggregate,  makes  a  most  ex- 
cellent fire-proofing  material.  Tests  and  the  experience  of 
recent  conflagrations  would  indicate  that  it  is  the  best.  Care 
must,  however,  be  taken  in  the  selection  of  the  cinders.  They 
must  be  clean  furnace  cinders,  free  from  particles  of  unburnt 
coal,  and  should  be  ground  by  machinery  before  mixing  for 
concrete. 

When  properly  selected  and  proportioned  cinder  will  produce 
good  concrete,  but  generally  a  very  ununiform  material  is 
obtained,  so  that  its  strength  is  variable  and  doubtful.  For 
this  reason  in  using  cinder  concrete  in  floor  construction  the 
working  loads  should  be  determined  from  load  tests  and  a 
high  factor  of  safety  should  be  used.  The  practice  in  New 
York  istotake  one-tenth  of  the  breaking  load  as  the  working  load. 

Corrosive  Action  of  Cinders. — When  cinder  concrete  is 
used  to  encase  steel,  either  as  a  protective  covering  or  as  a  part 
of  a  concrete  construction,  the  corrosive  effect  of  cinders  must 
be  guarded  against. 

A  discussion  of  this  subject  will  be  found  in  the  following 
chapter,  p.  SS2d. 

Mortars,  Plasters,  and  Plaster  of  Paris.  —  Mortar 
and  plaster  must  necessarily  enter  into  the  composition  of  all 
masonry  buildings,  whether  built  of  brick,  stone,  or  terra- 
cotta. That  ordinary  lime  mortar,  when  well  made,  will  endure 
for  unlimited  periods  of  time,  in  dry  situations,  has  been  proven 
by  actual  use. 

Hydraulic  cement  mortars  are  equally  durable  in  wet  or 
damp  places. 

For  laying  brick  or  tile  work  in  first-class  buildings,  cement 
and  sand  mortar  is  preferable  to  any  other,  and  cement  mixed 
with  lime  mortar  gives  greater  strength  than  lime  and  sand 
alone. 

Regarding  the  fire-proof  qualities  of  mortars  and  plaster 
compositions  there  has  been  much  controversy;  the  truth  of 
the  matter  seems  to  be  that  all  such  compositions  will  with- 
stand the  action  of  heat  up  to  a  certain  degree,  when  they  are 
affected  in  one  way  or  another  depending  not  only  upon  the 
composition  but  in  a  large  degree  upon  their  body,  and  upon 
the  way  in  which  they  are  used. 


MATERIALS    OF    CONSTRUCTION.  735 

Lime  mortar  for  walls  was  formerly  considered  as  the  most 
satisfactory,  so  far  as  fire-resistance  is  concerned,  but  since 
the  improvements  in  cement  manufacture,  cement  mortar  is 
generally  preferred. 

Lime  plaster,  applied  on  wire  lath,  will  withstand  a  high 
degree  of  heat  without  injury,  but  is  liable  to  be  washed  away 
in  places  by  streams  of  water. 

Hard  wall  plasters,  or  patent  plasters,  when  applied  to  brick 
work  or  metal  lath,  are  in  all  cases  equal  in  heat-resistance  to 
common  lime,  and  many  of  the  patent  plasters  will  stand  the 
combined  effects  of  fire  and  water  longer  than  the  common 
mortars. 

Plaster  of  Paris. — Compositions  of  plaster  of  Paris  and 
broken  bricks,  wood  chips,  or  sawdust  are  non-conductors  of 
heat  and  possess  fire-resisting  properties  of  considerable  magni- 
tude, and,  on  account  of  their  lightness  and  cheapness,  are 
used  to  quite  an  extent  in  fire-proof  or  semi-fire-proof  build- 
ings. 

In  France  such  compositions  have  been  used  for  generations 
for  forming  ceilings  between  beams,  and  its  durability  and  fire- 
proofing  qualities  are  there  unquestioned. 

Plaster-of-Paris  compositions  when  subjected  to  a  severe 
heat  are  softened  on  the  surface,  and  when  water  is  thrown 
upon  it  the  plaster  washes  away  to  some  extent. 

Asbestic  Plaster.  —  A  plaster  made  by  mixing  asbestic 
with  freshly  slacked  lime-putty  has  been  used  to  some  extent 
in  New  York  City.  Asbestic  is  made  from  a  serpentine  rock, 
mined  near  Montreal,  which  contains  a  large  proportion  of 
asbestos. 

''Claims  of  great  fire-resisting  properties  are  made  for  this 
material,  as  well  as  resistance  to  the  effects  of  water  during  fire  ; 
cracking  and  discoloration  due  to  the  percolation  of  water  or 
acids  are  also  claimed  to  be  avoided.  The  plaster  is  tough 
and  elastic,  and  it  will  receive  nails  without  chipping  or  crack- 
ing. The  weight  is  said  to  be  about  half  that  of  ordinary 
cement  mortar." 

Asbestic  was  subjected  to  a  severe  fire-and- water  test  in 
the  presence  of  the  officials  of  the  Supervising  Architect's  office 
at  Washington,  "and  the  plaster  did  not  crack  or  drop,  but 
remained  intact." 

"All  of  the  walls,  ceilings,  and  columns  of  the  appraiser's 
warehouse  in  New  York  City  were  covered  with  a  coat  of  asbestic 


736  FIRE-PROOFING  OF   BUILDINGS. 

applied  from  ^  to  J  of  an  inch  thick,  on  the  concrete  or  terra- 
cotta surfaces. 

"The  great  objection  to  the  use  of  this  material  lies  in  its 
slow  drying,  the  time  required  for  a  thorough  drying  out  being 
usually  very  long."  * 

Steel  and  Wrought  Iron. — Wrought  iron  and  steel  will 
expand,  bend  and  twist  under  a  moderate  degree  of  heat.  In- 
asmuch as  a  temperature  of  1700°  F.  is  not  unusual  in  fires, 
these  materails  should  not  be  used  in  fire-proof  construction 
without  proper  protection. 

Fire  tests  at  the  Continental  Iron  Works  in  1896  showed 
that  unprotected  •  steel  columns  under  load  began  to  fail  when 
the  temperature  had  reached  about  1100°  F.f  In  the  Balti- 
more and  San  Francisco  fires  there  were  many  instances  of 
failure  in  steel  columns  due  to  lack  of  or  to  insufficient  pro- 
tection. 

Cast  Iron. — "  As  the  result  of  tests  and  actual  experience 
in  conflagrations  it  may  be  stated  that  unprotected  cast  iron 
can  stand  practically  unharmed  up  to  temperatures  of  1300 
or  1500°  F.  while  carrying  very  heavy  loads  even  with 
frequent  applications  of  cold  water  while  the  metal  is  at  a  red 
heat."  *  In  the  tests  at  the  Continental  Iron  Works,  referred 
to  in  the  previous  paragraph,  a  temperature  of  nearly  1300°  F. 
was  reached  before  the  cast  iron  columns  began  to  fail. 

The  contents  of  most  mercantile  buildings,  when  burning 
freely,  would  probably  generate  a  heat  exceeding  at  times 
2000  degrees.  Consequently  cast-iron  columns,  when  un- 
protected, are  almost  sure  to  fail  in  such  a  fire  either  by  bending 
or  breaking. 

No  building  can  be  considered  fire-proof  in  which  unprotected 
iron  or  steel  columns  are  used,  but  in  many  classes  of  buildings 
unprotected  cast-iron  columns  might  safely  withstand  any 
heat  to  which  they  would  probably  be  exposed.  From  a  fire- 
resisting  point  of  view,  cast-iron  columns  are  unquestionably 
preferable  to  steel  columns  when  unprotected. 

Fire-proof  Wood. — To  meet  a  demand  for  an  incombusti- 
ble flooring  in  the  warships  of  the  U.  S.  Government,  and  the 
requirements  of  certain  provisions  of  the  New  York  Building 
Code,  an  attempt  has  been  made  to  produce  fire-proof  wood. 


*  Freitag. 

t  See  Engineering  News,  Aug.  6.  1896, 


MATERIALS    OF    CONSTRUCTION.  737 

The  processes  for  rendering  wood  fire-proof,  in  general,  con- 
sist in  impregnating  its  fibers  with  certain  chemicals.  After 
the  fire-proofing  process,  the  lumber  should  be  thoroughly 
kiln-dried  before  it  is  allowed  to  enter  into  construction.  The 
kiln-drying,  to  be  done  properly,  requires  several  weeks,  the 
actual  time  varying  in  accordance  with  the  thickness  of  the 
stock,  but  to  secure  a  first-class  job  in  fire-proofed  wood  it  is 
essential  that  the  stock  be  bone-dry. 

The  soft  woods  are  more  easily,  thoroughly  treated  than  the 
hard  woods,  the  resinous  woods  being  particularly  difficult 
to  handle. 

"The  treatment  of  the  wood  to  render  it  fire-proof  slightly 
raises  the  igniting- point  of  the  wood.  The  treated  wood  is 
harder  to  light  than  the  untreated  wood,  taking  two  to  three 
times  as  long  to  ignite.  The  amount  of  wood  destroyed  when 
exposed  to  the  action  of  a  flame  is  from  5  to  12  per  cent  greater 
in  the  case  of  an  untreated  wood  than  in  the  case  of  a  treated 
wood.  The  untreated  wood  furnished  more  flame  than  the 
treated  wood.  The  untreated  wood  will  sustain  flame  longer 
than  the  treated  wood  after  the  source  of  heat  has  been  re- 
moved. From  this  it  can  be  seen  that  the  fire-proofed  wood 
is  less  likely  to  ignite  and  less  likely  to  cause  the  spread  of 
fire  than  the  untreated  wood."  * 

Disadvantages. — Among  the  disadvantages  of  fire-proof 
wood  should  be  mentioned  an  increased  difficulty  in  working 
the  wood,  a  tendency  to  dull  woodworking  tools  more  rapidly 
than  untreated  wood.  Hence  an  increased  cost  in  the  use  of 
fire-proof  wood.  Professor  Woolson  estimates  this  increase  to 
be  from  $35  to  $65  per  thousand  feet,  the  hard  wood  costing 
the  most. 

The  salts  used  in  the  process  of  fire-proofing  being  hygroscopic 
tend  to  keep  the  woodwork  damp.  Hardware  or  other  metal 
work  in  contact  with  fire-proofed  wood  is  liable  to  corrode. 
The  strength  of  the  wood  is  often  affected,  and  in  some  cases 
the  wood  has  become  quite  brittle.  These  two  last-mentioned 
faults  can  be  largely  overcome  by  neutralizing  the  fire-proofing 
solution  by  a  proper  mixture  of  acid  and  alkaline  salts. 

Test. — The  test  known  as  the  timber  test  applied  to  fire-proof 
wood  in  New  York  City  consists  in  placing  a  stick  of  the  treated 
wood,  \  inch  by  1J  inches  in  cross-section  and  8  inches  long, 


*  See 
Professor 


Insurance  Engineering,   Vol.    IV,   p.    551;     also   Report    No.    1   of 
r  Norton  to  Boston  Manufacturers'  Mutual  Fire  Ins.  Co. 


738  FIRE-PROOFING    OF  BUILDINGS. 

for  two  minutes  over  a  crucible  gas  furnace  in  which  a  constant 
texxiperature  of  1700°  F.  is  maintained,  then  removing  the  test 
piece,  noting  the  time  it  continues  to  flame  and  glow,  then 
scraping  away  the  charred  wood  and  determining  the  percen- 
tage of  unburned  wood.  The  conditions  of  acceptance  are 
that,  "the  flame  and  glow  should  disappear  within  ten  to 
twenty  seconds  after  the  removal  of  the  test-piece  from  the 
furnace,  and  the  unburned  and  uncharred  section  at  the  center 
of  the  specimen  should  be  not  less  than  50  to  70  per  cent  of  the 
original  cross-section,  depending  on  the  variety  of  wood  under 
test." 

If  the  wood  has  been  thoroughly  treated,  a  splinter  of  it 
after  having  been  exposed  to  flame  and  withdrawn  will  show 
no  glow  or  flame.  Other  tests  have  been  suggested  and  used, 
but  need  not  be  described  here. 

At  the  present  time  fire-proof  treatment  of  wood  is  being 
done  by  The  American  Wood  Fire-proofing  Company,  The  Fire- 
proofine  Manufacturing  Company,  and  the  Electric  Fire-proof- 
ing Company,  all  of  New  York. 

Wire  Glass. — The  introduction  of  this  material  has  made 
it  possible  to  secure  fire  protection  in  many  cases,  without  the 
necessity  of  disfigurement  due  to  fire-shutters. 

Wire  glass  is  either  "  ribbed,"  "rough/'  "maze,"  or  polished 
plate  having  wire  imbedded  in  its  centre  during  the  process  of 
manufacture. 

"The  temperature  at  which  the  wire  is  imbedded  in  the  glass 
insures  adhesion  between  the  metallic  netting  and  the  glass, 
and  the  two  materials  become  one  and  inseparable,  so  that  if 
the  glass  is  broken  by  shock,  by  intense  heat,  or  from  other 
cause,  it  remains  intact."  It  is  this  property  of  remaining 
intact  that  gives  it  its  fire-retarding  qualities,  as  although  fire 
and  water  may  cause  cracks  to  spread  throughout  the  glass 
the  wire  holds  the  pieces  so  firmly  that  flames  cannot  pass 
through.  Many  severe  tests  during  actual  fires  have  posi- 
tively demonstrated  the  truth  of  the  above  claim.  For  ware- 
houses and  factories  the  "ribbed"  or  "maze"  glass  will  gen- 
erally be  preferable,  but  for  offices,  or  wherever  clear  trans- 
parent glass  is  desired,  the  "polished  plate"  is  nearly  if  not 
quite  as  acceptable  as  the  same  glass  without  the  wire,  the 
effect  being  the  same  as  looking  through  a  window  with  a 
screen  on  the  outside. 

*  See  also   p  1418. 


FORMS    OF   CONSTRUCTION.  739 

The  wire  netting  used  for  this  purpose  is  similar  to  the  ordi- 
nary " chicken  netting"  with  about  a  1-inch  mesh.  The  Missis- 
sippi Glass  Company  of  St.  Louis  is  the  chief  manufacturer  of 
wire  glass  in  this  country,  the  material  being  handled  by  the 
leading  glass  merchants  in  all  the  large  cities  of  the  country. 

Fire-proof  Paint. — Numerous  so-called  fire-proof  paints 
have  been  introduced  in  recent  years.  When  applied  to  wood- 
work they  provide  a  more  or  less  effective  protection  against 
fire  and  may,  for  this  reason,  prevent  the  spread  of  fire.  The 
Bureau  of  Buildings  of  New  York  makes  the  following  regu- 
lations regarding  fire-proof  paint: 

"First.  The  term  'fire-proof  paint'  shall  be  understood  to 
mean  any  preparation  used  to  cover  the  surfaces  of  wood  or 
other  materials  for  the  purpose  of  protecting  the  same  against 
ignition. 

"Second.  No  fire-proof  paint  will  be  considered  satisfactory 
unless  it  so  protects  the  wood  or  other  material  to  which  it  is 
applied  that  the  same  will  not  flame  or  glow  after  having  been 
subjected  to  the  flame  of  a  gasoline  torch  for  two  minutes. 

"Third.  Before  applying  fire-proof  paint  to  any  material  the 
surfaces  must  be  cleaned. 

"Fourth.  Application  of  fire-proof  paint  must  be  repeated 
whenever  it  is  found  that  the  material  to  which  it  is  applied 
is  no  longer  protected  to  fulfill  Specification  No.  2."  * 

Forms  of  Construction. 

Girder  and  Column  Protection. — As  the  columns  and 
girders  of  a  building  form  the  "back-bone"  of  the  structure, 
it  is  of  vital  importance  that  they  be  very  thoroughly  pro- 
tected from  heat.  As  a  rule,  the  manner  of  protecting  these 
structural  elements  depends  quite  largely  upon  the  floor  system 
adopted.  The  concrete  companies  naturally  prefer  to  use 
concrete  wherever  possible,  and  hence  where  concrete  is  used 
for  the  floor-construction  it  is  generally  employed  for  encasing 
the  columns  and  girders.  Where  hollow  tile  is  used  in  the 
floors,  the  same  material  is  almost  invariably  employed  for  pro- 
tecting the  steel  frame. 

The  methods  used  for  protecting  girders  are  described  under 
the  discussion  on  floor-construction,  pp.  795  to  799. 

*  Annual  Report  Bureau  of  Buildings,  Borough  of  Manhattan,  N.  Y., 
for  1904. 


740 


FIRE-PROOFING   OF    BUILDINGS. 


Necessity  for  Column  Protection. — It  is  now  generally 
recognized  that  iron  and  steel  columns  should  be  incased  with 
some  material  that  will  thoroughly  protect  the  metal  against 
fire. 

In  1896  a  committee  of  the  American  Society  of  Mechanical 
Engineers,  in  conjunction  with  representatives  from  other 
organizations,  made  a  series  of  fire  tests  on  full-sized  unpro- 
tected cast  iron,  and  steel  columns,  loaded  to  their  figured  safe 
capacities.  These  tests  showed  that  the  steel  columns  failed 
at  an  average  temperature  of  1150°  F.,  and  the  cast  iron  at  an 
average  temperature  of  1300°  F.,  the  failure  setting  in  after 
exposure  to  the  fire  of  from  23  minutes  to  1  hour  and  20  minutes, 
or  an  average  duration  of  about  50  minutes. 

For  the  purposes  of  determining  the  value  of  several  mate- 
rials as  satisfactory  protective  coverings,  the  Bureau  of  Build- 
ings of  New  York  made  a  series  of  tests  on  the  heat  conductivity 
of  these  materials.  A  cast-iron  plate  covered  with  the  material 
under  test  was  subjected  to  a  temperature  of  1700°  F.  for  two 
hours  over  a  crucible  furnace,  and  the  heat  of  the  plate  noted 
at  regular  intervals  of  time.  The  results  of  the  tests  is  shown 
in  the  following  table: 


Material  Under  Test. 

Temp, 
on  Face 
of  Pro- 
tective 
Mate- 
rial. 
0  Fahr. 

Temperature  of  Plate  at 
Back  of  Protective  Mate- 
rial (Degrees  Fahr.) 

Before 
Heat- 
ing. 

After 
Heat- 
ing, 
2  Hrs. 

Heat 

Trans- 
mission. 

Terra-cotta:   Dense,  hollow,  2"  thick  
Terra-cotta:   Semi-porous,  solid,  2"  thick. 
Plaster  of  Paris  and  shavings,  2"  thick.  .  . 
Plaster  of  Paris  and  asbestos,  2"  thick...  . 
Plaster  of  Paris,  wood  fibres,  and  infuso- 
rial earth    2"  thick  . 

1700 
1700 
1700 
1700 

1700 
1700 
1700 

1700 

75 
73 
69 

70 

72 
73 
66 

76 

223 
244 
159 
163 

167 
363 
248 

296 

148 
171 
90 
93 

95 

290 
182 

218 

Concrete  of  Ground  Cinders,  ITS"  thick  .  .  . 
Cinder  Concrete,  on  metal  lath,  2"  thick.' 
Metal  Lath  and  patent  plaster,    about  %"- 
thick  over  1"  air-space  

Terra-cotta  Column  Protection.— Fig.  1  shows  the 
manner  in  which  Z-bar  columns  are  protected  in  the  best  class 
of  fire-proof  buildings  (when  tile  fire-proofing  is  used).  Figs.  2, 
3,  and  4  show  common  methods  of  protecting  round  columns, 
and  Figs.  5  and  6  square  columns. 

The  steel  guard,  shown  in  Fig.  1,  is  often  employed  in  mer- 


FORMS  OF  CONSTRUCTION. 


741 


cantile  or  manufacturing  buildings  to  a  height  of  four  or  five 
feet  above  the  floor. 

f  Sheet  Steel  Gnard\ 

*  /Mortar  \          ,  2"  Hollow  Tile 


FlQ.    1. 


FIG.  2. 


FIG.  3. 


FIG.  5. 


FIG.  4. 


FIG.  6. 


Although  it  is  not  customary  to  do  so,  the  efficiency  of  this 
construction  is  greatly  increased  by  wrapping  the  column 
with  wire  lath  before  plastering. 

To  insure  the  protection  of  the  metal,  under  the  most  trying 
conditions,  it  is  imperative  that  the  protective  covering  shall 
not  be  detached  by  the  streams  from  the  firemen's  hose,  so  as 


742 


FIRE-PROOFING    OF    BUILDINGS. 


to  expose  the  steel.  This  can  be  positively  guarded  against 
only  by  using  two  layers  of  tiling  or  concrete  and  wrapping 
the  inner  layer  with  metal  lathing. 

Fig.  7  shows  a  column  protected  in  this  way,  the  construc- 
tion being  essentially  that  adopted  in  the  Fair  Building  in 
Chicago.  The  inner  layer  of  tiles  is  wrapped  with  wire  lath 
imbedded  in  the  mortar,  and  all  spaces  between  the  tiles  and 


FIG.  7. 

metal  filled  solid  with  cement  mortar.  The  protection  afforded 
by  this  construction  should  be  perfect. 

Concrete  Column  Protection. — Where  concrete  is  to  be 
used  for  column  protection,  the  most  efficient  construction  is 
undoubtedly  to  surround  the  metal  with  cinder  concrete, 
poured  inside  of  a  plank  form  set  around  the  column,  a  coat 
of  liquid  cement  being  first  applied  to  the  metal  with  a  brush. 
The  plank  form  should  be  set  at  least  2  ins.  outside  of  the 
metal.  Concrete  poured  in  this  way,  cannot  be  dislodged  by 
streams  of  water,  and  it  also  greatly  strengthens  the  column. 

Fig.  8  shows  the  method  of  protecting  steel  columns  employed 
by  the  Roebling  Construction  Company.  The  column  js  first 
furred  by  vertical  rods  held  in  place  by  clamps,  and  then  by 
band  iron  laced  to  the  rods,  stiffened  wire  lath  is  then  bent 
around  and  laced  to  the  furring.  The  space  between  the 
lathing  and  the  column  is  then  filled  with  a  moderately  dry 
mixture  of  cinder  concrete.  The  lathing  in  this  construction 
is  used  principally  as  a  form  to  confine  the  concrete,  in  place 
of  a  temporary  wooden  form,  but  it  also  serves  to  prevent  the 


FORMS   OF    CONSTRUCTION. 


743 


concrete  from  being  washed  away  during  a  fire.  Where  wooden 
forms  are  used  the  concrete  can  be  given  much  greater  strength, 
so  that  lathing  is  unnecessary, 
although  it  forms  an  additional 
safeguard. 

In  many  buildings  having 
reinforced  concrete  floors,  the 
columns  are  protected  simply 
by  metal  lath  and  plaster. 
When  but  a  single  covering  is 
provided,  as  in  Fig.  17,  Chap- 
ter XXII,  the  protection  can- 
not be  considered  as  fire-proof, 
but  when  two  coverings  are 
provided,  as  in  Fig  9,  it  is 
probably  all  that  is  necessary 
for  cast-iron  columns.  The  FIG.  8. 

greatest    defect    in    lath    and 

plaster  for  fire-proofing  is  that  the  plaster  is  liable  to  be  dis- 
lodged by  the  force  of  the  water  from  the  fireman's  hose. 


Clamp 


FIG.  9. 

When  there  are  two  coverings,  however,  this  danger  is  re- 
duced to  a  minimum. 

Plaster  Column  Covering — Plaster  blocks  have  been 
used  in  buildings  as  a  column  covering,  but  their  use  is  -not 
to  be  recommended.  While  it  is  true  that  their  non-con- 
ductivity is  in  their  favor,  they  are  difficult  to  secure  firmly, 
the  plaster  tends  to  promote  corrosion  in  the  metal;  they  are 
easily  washed  away  by  hose  streams,  and  they  are  subject  to 
greater  damage  than  other  materials.  In  unimportant  work 
their  cheapness  may,  at  times,  justify  their  use. 

Probably  the  most  defective  part  of  the  coverings  of  columns, 


744 


FIRE-PROOFING    OF   BUILDINGS. 


whatever  the  material  used,  is  about  the  connections  with  the 
beams  and  girders.  Concrete  undoubtedly  is  better  adapted 
for  covering  this  portion  of  the  column  than  any  other  material, 
as,  being  plastic,  it  can  be  made  to  fit  into  any  space  and  around 
any  form  of  connection. 

Recesses  for  Pipes. — "As  a  matter  of  economy,  both 
in  original  cost  and  in  the  matter  of  space,  it  has  been  the 
common  practice  to  run  water-,  waste-,  and  vent-pipes  imme-' 
diately  alongside  the  steel  columns,  and  inside  the  fireproofiing 
inclosure."  *  This  is  undoubtedly  bad  construction,  and  in 
the  better  types  of  fire-proof  buildings,  the  pipe  space  is  sepa- 
rated from  the  columns  by  the  fire-proofing. 

Figs.   10  and  11  show  the  method  of  running  the  pipes  in 


Girder 


.Mortar 


FIG.   10. 

some  of  the  latest  fire-proof  buildings,  and  is  probably  as  satis- 
factory as  any  method  where  the  pipes  are  to  be  run  beside  the 
columns. 

Space  for  Pipes:and  WiresN 
Concrete  \ 


FIG.  12. 


Fig.   12  shows  a  somewhat  similar  method  where  concrete 
and  metal  lath  and  plaster  are  employed  for  the  fire-proofing. 
*  Freitag. 


FIRE-PROOF   FLOORS.  745 

Fire-proof  Floors.* 

Fire-proof  Floors. — In  the  study  of  fire-proofing  materials 
by  far  the  largest  attention  has  been  given  to  floor-construction, 
and  a  very  large  number  of  types  have  been  developed,  of 
which  the  characteristic  and  leading  types  will  here  be  con- 
sidered. 

Requirements  for  a  Fire-proof  Floor.— It  goes  without 
saying  that  a  fire-proof  floor  shall  be  made  of  incombustible 
materials,  nor  does  it  seem  necessary  to  mention  that  it  shall 
resist  as  much  as  possible  the  transmission  of  heat,  so  as  to 
afford  thorough  protection  to  the  metal  encased  by  it  or  form- 
ing an  essential  part  of  it.  The  materials  used  should  not 
disintegrate  or  otherwise  fail  when  exposed  to  heat  or  flame. 
They  should  also  resist  the  action  of  water  that  may  be  used 
in  the  extinguishment  of  fire.  The  floor-construction  should 
be  essentially  water-tight,  so  as  to  prevent  damage  by  water 
in  a  floor  below.  It  should  be  capable  of  safely  carfying  its 
load  at  all  times. 

The  New  York  Building  Law,  after  describing  certain  accep- 
table forms  of  fire-proof  floors,  provides  for  a  fire  test  on  other 
types  as  a  precedent  condition  for  their  approval.  More  than 
fifty  tests  have  been  made  under  the  auspices  of  the  New  York 
authorities  and  these  with  a  few  made  by  other  city  authorities 
comprise  practically  all  made  in  this  country.  The  British 
Fire-prevention  Committee  of  London  have  also  made  a  number 
of  such  tests. f 

The  following  standard  test,  recommended  by  the  "  Com- 
mittee on  Fireproofing"  of  the  American  Society  for  Testing 
Materials,  is  essentially  the  same  as  required  by  the  New  York 
Building  Code  and  as  used  by  the  British  Fire-prevention  Com- 
mittee. 

Proposed  Standard  Test  for  Fire-proof  Floor   Con- 
struction. 

The  test  structure  may  be  located  at  any  place  convenient 
to  the  applicant,  where  all  the  necessary  facilities  for  properly 
conducting  the  test  are  provided. 

*  For  a  more  complete  discussion  of  the  subject  of  fire-proof  floors, 
the  reader  is  referred  to  Chap.  IX,  of  Part  I  of  Kidder's  "Building  Con- 
struction and  Superintendence"  and  J.  K.  Freitag's  "The  Fireproofing 
of  Steel  Buildings." 

t  For  a  list  of  these  tests  made  in  the  United  States  and  in  London, 
see  Proceedings  of  Am.  Soc.  T.  M.t  Vol.  VI,  p.  128. 


746  FIRE-PROOFING    OF   BUILDINGS. 

The  test  structure  may  be  constructed  of  walls  of  any  mate- 
rial not  less  than  12  inches  thick,  properly  buttressed  on  all 
sides. 

The  floor  construction  to  be  tested  shall  form  the  roof  of 
the  test  structure. 

At  a  height  of  not  less  than  2  feet  6  inches,  nor  more  than 
3  feet  above  the  ground  level,  a  metal  grate,  properly  supported, 
shall  be  provided,  covering  the  whole  inside  area  of  the  build- 
ing. 

In  the  walls  below  this  grate  level,  draught  openings  shall 
be  provided,  as  many  as  possible,  furnishing  openings  with  an 
aggregate  area  of  not  less  than  1  square  foot  for  every  10  square 
feet  of  grate  surface.  Means  for  temporarily  closing  these 
openings  should  be  provided. 

In  the  wall,  immediately  above  the  grate  level,  a  firing  door, 
3  feet  6  inches  by  5  feet  high,  must  be  provided  in  the  side  of 
the  building  at  right  angles  to  the  floor  beams.  A  second  door 
must  be*added  when  the  span  of  the  floor  slab  under  test  exceeds 
10  feet. 

Flues  should  be  supplied  at  each  of  the  corners,  and  oftener 
in  case  of  a  test  structure  exceeding  250  square  feet  of  grate 
surface,  with  sufficient  opening  to  insure  a  proper  draught, 
securely  supported  and  disposed  at  the  sides  of  the  structure 
in  such  manner  as  not  to  rest  on  the  floor  under  test.  In  no 
case  should  a  flue  area  be  less  than  180  square  inches. 

The  horizontal  dimensions  of  the  test  structure  will  depend 
upon  the  number  and  the  span  of  the  systems  under  considera- 
tion. The  clear  span  of  the  floor  beams  is  to  be  14  feet.  The 
distance  between  floor  beams,  or  span  of  slab,  may  be  varied 
according  to  the  design  of  the  system  to  be  tested,  and  should 
be  as  near  as  possible  to  usual  practice.  The  underside  of  the 
construction  under  test  must  not  be  less  than  9  feet  6  inches 
nor  more  than  10  feet  above  the  grate  level. 

The  construction  to  be  tested  should  be  designed  for  a  work- 
ing load  of  one  hundred  and  fifty  pounds  per  square  foot,  and 
no  more.  This  load  to  be  uniformly  distributed  without  arching 
effect,  and  to  be  carried  on  the  floor  during  the  fire  test. 

The  floor  may  be  tested  as  soon  after  construction  as  desired, 
but  within  forty  days.  Artificial  drying  will  be  allowed  if 
desired. 

The  floor  is  to  be  subjected  to  the  continuous  heat  of  a  wood 
fire,  averaging  not  less  than  1700°  F.  for  four  hours. 


TYPES    OF    FLOOR    CONSTRUCTION.  747 

The  heat  obtained  shall  be  measured  by  means  of  standard 
pyrometers,  under  the  direction  of  an  experienced  person. 
The  type  of  pyrometer  is  immaterial  so  long  as  its  accuracy  is 
secured  by  proper  standardization.  The  heat  should  be  meas- 
ured at  not  less  than  two  points  when  the  main  floor  span  is 
not  more  than  10  feet,  and  one  additional  point  when  it  exceeds 
10  feet.  Temperature  readings  at  each  point  are  to  be  taken 
every  three  minutes.  The  heat  determination  shall  be  made 
at  points  directly  beneath  the  floor  so  as  to  secure  a  fair  average. 

At  the  end  of  the  heat  test  a  stream  of  water  shall  be  directed 
against  the  underside  of  the  floor,  discharged  through  a  one 
and  one-eighth  inch  nozzle,  under  sixty  pounds  nozzle  pressure, 
for  ten  minutes. 

After  the  floor  has  sufficiently  cooled,  the  load  on  the  same 
shall  be  increased  to  six  hundred  pounds  per  square  foot, 
uniformly  distributed. 

The  test  shall  not  be  regarded  as  successful  unless  the  follow- 
ing conditions  are  met:  No  fire  or  smoke  shall  pass  through 
the  floor  during  the  fire  test;  the  floor  must  safely  sustain 
the  loads  prescribed;  the  permanent  deflection  must  not  exceed 
one-eighth  inch  for  each  foot  of  span  in  either  slab  or  beam. 

Types  of  Floor  Constructions. — In  considering  the  several 
systems  of  floor-construction,  they  are  for  convenience  divided 
into  the  following  types  or  groups: 

1.  Brick  Arches. 

2.  Terra-cotta  Floors. 

a.  Segment  al. 

6.  Flat  Side-construction. 

c.  Flat  End-construction. 

d.  Serrated. 

e.  Reinforced  Tile  Arches. 
/.  Guastavino. 

3.  Concrete  Floors. 

a.  Segmental. 
6.  Flat  Reinforced  Floors, 
c.  Sectional  Systems. 
.    4.  Composition  Systems. 

Brick  Arches.— The  first  attempt  at  fire-proof  floor  construc- 
tion between  wrought-iron  beams  was  by  using  brick  arches 
sprung  between  the  beams  and  resting  on  the  bottom  flange, 
as  illustrated  by  Fig.  13. 

The    bricks    should    be    hard,    well-burned    brick    or   hollow 


748 


FIRE-PROOFING  OF   BUILDINGS. 


brick  of  good  shape  laid  to  a  line  on  centers  without  mortar 
with  their  lower  edges  touching,  and  all  the  joints  filled  in 
with  cement  grout.  The  bricks  of  one  line  should  break  joints 
with  those  of  the  next  adjoining,  and  in  case  of  more  than  one 


FIG.  13. 

row,  the  joints  of  one  row  should  also  break  joint  with  that 
of  the  one  above  or  below. 

The  arches  need  not  be  over  4  inches  thick  for  spans  between 
6  and  8  feet,  provided  the  haunches  are  filled  with  a  good  cement 
and  gravel  concrete  put  in  rather  wet.  The  rise  of  the  arch 
should  be  about  J  of  the  span,  or  1J  inch  to  the  foot,  and  the 
most  desirable  span  is  between  4  and  6  feet. 

The  building  laws  of  many  cities  provide  that  when  the 
spans  exceed  5  feet  the  arches  shall  be  increased  in  thickness, 
generally  to  8  inches. 

The  haunches  should  be  filled  with  concrete  level  with  the 
top  of  the  arch. 

In  first-class  fire-proof  construction  the  bottom  flanges  of 
the  beams  should  be  protected  by  terra-cotta  skew-backs, 


Finished  Floor.. 


FIG.  14. 


as  in  Fig.  14,  which  shows  the  construction  used  in  the  main 
floors  of  the  Government  Printing  Office  at  Washington.* 


*  A  description  of  the  structural  features  of  this  building  may  be  found 
n  the  Engineering  Record  for  Dec.  6,  1902. 


ARCHES.  749 

A  4-inch  brick  arch  of  6-foot  span,  well  grouted  and  leveled 
off  with  Portland  cement  concrete,  should  safely  carry  300  or 
400  Ibs.  to  the  square  foot.  Experiments  have  shown  that 
brick  arches  will  stand  very  severe  pounding  and  a  great  amount 
of  deflection  without  failure. 

The  weight  of  a  floor,  such  as  shown  in  Fig.  1,  will  usually 
vary  from  70  to  75  Ibs.  per  square  foot,  depending  upon  the 
amount  of  concrete  required  for  levelling. 

Tie-rods,  as  described  on  p.  802,  should  always  be  provided. 

The  brick  arch  is  the  strongest  type  of  arch  for  the  span 
it  occupies,  with  the  exception  perhaps  of  the  stone  concrete 
arch.  It  is  perhaps  also  the  most  expensive.  Its  weight 
makes  a  heavier  framework  necessary  than  for  other  types. 
It  is  not  well  adapted  for  other  than  warehouse  buildings  on 
account  of  appearance. 

Terra-cotta  Arches. — Terra-cotta  as  a  fire-proof  material 
and  the  relative  merit  of  dense,  porous,  and  semi-porous  tile 
have  been  discussed  on  p.  732.  For  floor-construction  the 
semi-porous  tile  is  probably  best  as  compromising  on  the 
advantages  and  disadvantages  of  the  dense  and  porous  tile, 
particularly  as  to  strength  and  fire  resistance. 

As  indicated  on  p.  747  six  different  types  of  terra-cotta 
floor  construction,  including  a  larger  number  of  systems,  will 
be  discussed.  For  these  a  great  variety  of  shapes  and  sizes 
of  blocks,  of  the  dense,  porous  or  semi-porous  material,  are 
manufactured  in  this  country. 

The  largest  company  devoted  to  the  manufacture  and  erec- 
tion of  hollow-tile  fire-proofing  material  is  the  National  Fire- 
proofing  Co.,  of  New  York  and  Chicago.  Other  large  com- 
panies are  Henry  Maurer  &  Sons,  New  York;  the  Haydenville 
Co.,  Haydenville,  Ohio;  Delaware  Fire-proofing  Co.,  Delaware, 
Ohio;  and  the  Illinois  Terra-Cotta  Lumber  Co.,  of  Chicago. 
Any  one  of  these  companies  can  make  any  form  of  block  desired, 
except  such  as  are  covered  by  letters  patent,  and  as  a  rule  in 
either  dense,  porous  or  semi-porous  material. 

Advantages  of  Terra-cotta  Arches. — Many  architects 
prefer  the  use  of  terra-cotta  arches  in  buildings  because  there 
is  less  disturbance  to  the  mechanics  of  other  branches.  During 
the  placing  of  concrete  arches  there  is  such  a  continual  dripping 
as  to  interfere  seriously  with  other  work.  The  work  of  in- 
stalling tile  arches  is  generally  more  rapid  than  for  other  types 
and  it  is  not  nt  ssary  to  wait  for  them  to  dry  out.  The  quality 


750  FIRE-PROOFING    OF    BUILDINGS. 

of  terra-cotta  can  be  readily  judged  from  its  appearance,  not 
only  before  being  placed  but  also  after  it  is  set,  thus  not  re- 
quiring the  constant  supervision  necessary  for  materials  that 
are  mixed  as  they  are  put  in  place.  This  type  of  construction, 
generally  speaking,  assists  to  a  greater  extent  than  other 
types  in  the  stiffening  of  the  building  against  lateral  forces, 
such  as  wind. 

Disadvantages  of  Tile  Arches. — The  principal  disadvan- 
tage of  tile  arches  for  floor  construction  is  the  difficulty  of 
adapting  any  system  to  the  filling  of  irregular-shaped  spaces. 
The  arches  must  be  set  between  I-beams  or  channels,  and  to 
get  the  best  effect  the  supporting  beams  must  be  parallel  or 
nearly  so.  It  is  also  more  expensive  to  adapt  the  tile  systems 
to  a  panel  of  varying  width  than  with  the  concrete  systems. 
Tile  arches,  especially  of  the  end-constructions,  are  weakened 
more  by  holes  for  pipes  than  a  monolithic  floor.  As  there  is  no 
bond  betwreen  the  rows  of  tiles  in  the  end-construction  arch,  if 
a  single  tile  in  a  row  is  cut  out  or  omitted  there  is  nothing  to 
hold  up  the  remaining  tile  in  the  row  except  the  adhesion  of  the 
mortar  in  the  side  joints.  In  this  respect  side-method  arches 
have  an  advantage  over  the  end-construction.  Where  it  is 
necessary  to  use  considerable  concrete  filling  over  the  arch  the 
weight  of  the  floor  construction  will  usually  greatly  exceed  that 
of  the  concrete  systems,  and  this  additional  weight  also  means 
additional  expense. 

The  floor  blocks  are  liable  to  breakage  and  chipped  blocks 
in  the  floor  are  not  unusual.  This  is  perhaps  more  liable  to 
occur  when,  as  in  some  localities,  the  arches  are  set  by  brick- 
layers. When  the  manufacturers  can  use  their  own  men,  better 
work  can  be  expected. 

Inspection.— Flat  arches  of  hollow  tile  require  close  inspec- 
tion during  erection  to  see  that  broken  or  imperfect  tile  are  not 
used;  that  the  ribs  in  end-construction  tile  abut  opposite  each 
other;  that  all  joints  are  properly  mortared,  and  that  all  of  the 
steel  work  is  properly  protected.  Very  much  poor  workman- 
ship has  been  allowed  to  pass  rather  than  to  avoid  delay,  and 
also  because  it  cannot  be  discovered  until  the  centering  is 
removed.  A  tile  arch  will  generally  look  better  on  top  than  on 
the  bottom.  The  great  carelessness  which  may  obtain  in  the 
setting  of  tile  arches  was  well  shown  by  an  article  in  the  Engi- 
neering News  of  April  14,  1898. 

Setting  of  Tile  Arches. — Tile  arches   are  always  set  on 


ARCHES.  751 

Wooden  centres  suspended  by  bolts  hooked  over  the  tops  of  the 
I-beams.  For  all  spans  of  5  feet  and  over  the  centres  should 
be  slightly  cambered.  Before  any  floor  arches  are  set  all  girders 
projecting  below  floor  beams  should  be  completely  covered  on 
bottom  and  sides,  independent  of  the  floor  construction.  To 
protect  the  steel  from  rust  it  should  have  a  good  coat  of  Port- 
land-cement mortar  before  applying  the  tile.  After  the  centres 
are  in  place  the  beam  tile  should  first  be  placed  under  bottom 
of  beams  and  mortar  slushed  on  the  sides.  Then  cover  the 
entire  side  of  the  skew-backs  which  rest  against  the  floor  beams 
with  just  enough  mortar  to  give  a  perfect  bearing,  and  shove  it 
up  against  the  beam.  Then  follow  up  with  intermediate  blocks, 
covering  the  ribs  on  one  end  and  one  side  with  a  full  bed  of 
mortar,  and  shove  in  place. 

The  key  should  have  mortar  on  both  sides  and  one  end  (if 
side-method  key  is  used);  it  should  fit  snug,  but  not  tight. 
"  Under  no  conditions  should  a  key  be  rammed  in  place.  It  is 
better  to  use  a  smaller  key  and  fill  out  the  space  -left  with  either 
a  solid  slab  of  tile,  or  if  the  opening  is  too  small  by  a  piece  of 
slate." — (E.  A.  Hoeppner.) 

"  In  setting  tile  arches  it  is  very  common  to  build  the  arches 
in  string  courses,  first  fitting  all  the  skews,  then  all  the  interme- 
diates, and  finally  all  the  keys.  This  is  bad  practice,  as  it  loads 
the  centre,  both  planks  and  stringers,  to  excess,  causing  too 
great  a  deflection.  In  the  end-construction  the  arches  should 
be  built  one  by  one,  each  being  complete  before  the  next  is 
started.  In  side-construction,  where  joints  are  broken  longi- 
tudinally, the  arches  should  be  keyed  up  or  completed  at  the 
first  point  where  the  intermediates  meet  the  lines  of  the  key, 
thus  completing  the  successive  arches  as  rapidly  as  possible." 
— (Freitag.) 

All  joints  in  the  arches  should  be  filled  with  mortar,  especially 
at  the  top. 

Wetting  the  Tile.  — In  warm  weather  all  hollow  tile, 
whether  dense  or  porous,  should  be  well  wet  or  water-soaked 
before  laying.  In  freezing  weather  they  must  be  kept  dry. 

Mortar  for  Setting. — "  Mortar  for  setting  porous  hollow 
tile  should  never  be  made  of  cement  and  sand  alone,  as  such 
mortar  is  too  '  short'  and  rolls  off  the  tile  and  does  not  insure 
a  full  joint." — (E.  A.  Hoeppner.) 

One  part  Portland  cement  added  to  three  parts  rich  cold  lime 
mortar  makes  a  good  mixture  for  either  dense  or  porous  tile. 


752  FIRE-PROOFING    OF    BUILDINGS. 

A  better  mortar  is  made  by  mixing  the  cement  and  sand  and 
adding  enough  cold  lime  putty  to  make  it  work  smooth.  The 
mortar  should  be  thoroughly  worked.  Hot  lime  mortar  should 
never  be  used. 

In  dry  weather  the  centres  can  be  removed  in  3G  hours  after 
the  tile  are  in  place,  but  it  is  much  better  to  allow  48  hours  and 
even  longer  in  cold  or  wet  weather. 

Filling  above  Tile  Arches. — The  strength  of  all  tile  arches 
is  greatly  increased  by  wetting  the  tops  of  the  arches  and 
covering  with  a  rich  cinder  concrete  (mixed  with  Portland 
cement),  well  tamped  and  brought  level  with  the  tops  of  the 
steel  beams. 

If  the  floors  are  to  be  finished  in  wood,  nailing-strips  are 
required  for  securing  the  flooring. 

These  nailing-strips  are  usually  of  a  dovetail  shape  about 
2£  inches  wide  at  the  top,  3^  inches  at  the  bottom  and  If  to  2 
inches  thick.  It  is  preferable  to  lay  them  at  right  angles  to  the 
steel  beams,  so  'that  they  may  be  secured  to  the  top  flange  by  a 
metal  clip,  as  in  Fig.  15.  Before  the  nailing-strips  are  laid  all 
piping  and  wiring  which  must  go  above  or  through  the  tile 
arches  should  be  put  in  place.  After  the  nailing-strips  are  in 
place  the  tops  of  the  steel  beams  should  be  covered  with  a  thin 
coat  of  Portland  cement  and  sand  grout,  applied  with  a  brush. 
The  spaces  between  the  nailing-strips  should  be  filled  with  a 
l-to-8  or  10-cinder  concrete,  finished  about  |  inch  below  the 
top  of  the  strips. 

Terra-cotta  Filling-blocks. — In  cases  where  the  tops  of 
the  tile  arches  are  2  inches  or  more  below  the  tops  of  the  steel 
beams,  hollow  terra-cotta  blocks  are  sometimes  used  for  filling 
to  the  top  of  the  beams,  as  in  Fig.  28.  These  blocks  are  lighter 
than  good  concrete,  but  they  do  not  strengthen  the  arch  unless 
they  are  set  in  cement  mortar  and  all  the  tiles  and  the  tops  of 
the  arches  well  wet  just  before  laying  the  filling-blocks. 

Cement  Floors. — If  the  floors  are  to  be  finished  with 
cement,  the  cement  and  concrete  should  be  at  least  2^  inches 
and  preferably  3  inches  thick  above  the  steel  beams,  and  should 
be  blocked  out  in  sections  of  not  over  6  feet  square,  with  joints 
extending  through  the  concrete.  When  practicable  the  joints 
in  one  direction  should  be  over  the  beams. 

Weather  Protection. — Terra-cotta  arches  should  always 
be  protected  against  rain  or  snow,  especially  in  freezing  weather, 
as  both  the  blocks  and  the  mortar  in  the  joints  are  injured  by 


ARCHES. 


753 


freezing.  Porous  terra-cotta  especially  may  be  utterly  ruined 
by  freezing  when  soaked  with  water. 

Protection  from  Stains  in  Ceiling.—"  If  plastered  ceil- 
ings are  to  be  used,  the  terra-cotta  work  should  be  protected 
against  the  smoke  or  soot  from  the  hoisting-engines.  Stains 
are  also  quite  liable  to  occur  from  the  effects  of  iron  in  the 
clay,  or  from  the  cinders  in  the  concrete  over  the  arches,  if  the 
floor  is  allowed  to  become  wet." — (Freitag.) 

To  prevent  these  stains  several  hydraulic  paints  have  been 
used,  some  of  which  have  proved  very  effective.* 

Segmental  Terra-cotta  Arches. — "  This  form  of  arch  is 
the  strongest  and  cheapest.  It  is  particularly  adapted  to  ware- 
houses, lofts,  factories,  sidewalks,  or  wherever  great  strength  is 
required  and  a  flat  ceiling  is  not  necessary. 

"When  a  light,  strong  arch  is  required  in  deep  beams  and 
a  flat  ceiling  is  also  demanded,  this  result  can  be  obtained  by 
using  a  metal  lath  ceiling  suspended  below  the  beams."  f 

These  arches  are  usually  formed  by  either  6"  or  8"  hollow  tile, 
set  on  the  side-construction  principle  and  bonded  endways  like 
a  brick  vault.  They  can  be  used  for  spans  up  to  20  feet,  but 
it  is  better  to  limit  the  span  to  about  16  feet. 

"End-construction  blocks  may  be  used,  but  they  are  un- 
satisfactory, unless  the  arches  are  of  uniform  span  and  rise 
throughout.  The  rise  of  the  side-construction  arch  can  be 
varied  by  increasing  the  thickness  of  the  upper  or  lower  part 
of  the  mortar  joint,  but  this  cannot  be  done  with  the  end- 
construction  method."  t 


FIG.  15. 

Figs.  15,  16,  and  17  show  typical  forms  of  segment  arches. 
The  weight  of  the  arch  tile  will  run  about  26  Ibs.  per  square 
foot  for  6-inch  tile  and  32  Ibs.  for  8-inch  tile.     To  these  weights 

*  See  Antihydrine,  page  403,  Building  Construction,  Part  I. 
t  Bevier,  National  F.  P.  Co.,  N.  Y. 


754  FIRE-PROOFING    OF    BUILDINGS. 

should  be  added  the  weight  of  concrete  filling,  flooring,  plaster, 
etc. 


r  Marble  or  Tile  Floor 

*?/%%&**' 


FIG.  16. 


Span,  c.  to  c,  of  beams, 


FIG.   17. 


Thickness  of  Webs. — "For  general  use  the  webs  of  seg- 
ment tile  should  be  ^  inch  thick  for  semi-porous  tile  and  f  inch 
for  porous  tile.  The  skew-back  should  be  at  least  f  inch  thick 
for  the  first-named  material  and  1  inch  for  the  second.  For 
printing  establishments  or  any  other  building  where  a  large 
amount  of  vibration  occurs  the  webs  of  all  tile  must  be  designed 
in  proportionate  thickness  to  the  load  they  are  required  to 
carry." — (E.  A.  Hoeppner.)* 

Rise  of  Arch. — The  rise  of  the  soffit  of  the  arch  above 
the  springing  line  should  be  from  -^  to  J  of  the  span.  The 
greater  the  rise  the  less  will  be  the  thrust  of  the  arch. 

No  single  cell  tile  should  ever  be  used  in  any  form  of  terra- 
cotta arch  construction. 

Filling  the  Haunches. — The  haunches  of  segmental  arches 
should  be  filled  with  good  cement  concrete  levelled  up  to  a 
point  not  less  than  1  inch  above  the  crown  of  the  arch.  For 
short  spans  cinder  concrete  filling  may  be  used,  but  for  wide 
spans  it  is  better  to  use  gravel  concrete,  as  the  strength  of  the 

*  These  thicknesses  apply  to  Chicago  practice  more  particularly,  where 
a  stronger  tile  is  produced  than  in  the  East.  In  New  York  webs  are 
generally  |"  for  semi-porous  and  1"  for  porous  tile. 


ARCHES. 


arch  at.  the  haunches  depends  largely  upon  the  strength  of  the 
concrete  filling.  Voids  are  sometimes  formed  in  the  haunches, 
stiff  pasteboard  being  used  to  form  the  core. 

Tie-rods. — The  thrust  of  segrnental  arches  is  very  consid- 
erable, so  that  it  is  important  to  provide  plenty  of  tie-rods 
between  the  beams.  A  formula  for  determining  the  stress  in 
the  tie-rods  and  the  diameter  of  the  same  is  given  on  page  804. 

To  be  most  effective  the  tie-rods  should  be  spaced  within  the 
lower  third  of  the  beam,  or  preferably  at  the  centre  of  the  skew. 

Placing  the  tie-rods  within  the  lower  third  of  the  beam,  how- 
ever, will  cause  them  to  project  below  the  soffit  of  the  arch, 
giving  an  unsightly  appearance  to  the  ceiling  and  rendering 


.-Girder  Tile 


FIG.   18. — Longitudinal   sections. 

them  difficult  to  protect.     Occasionally  the  tie-rods  are  encased 
with  special  tile,  as  in  Fig.  18. 

Strength  of  Segmental  Arches. — The  safe  loads  per  square 
foot  on  6-  and  8-inch  segmental  arches,  side  construction,  of 
semi-porous  tile,  having  a  rise  of  one-eighth  of  the  span,  with 
webs  and  shells  of  |"  thickness,  with  a  factor  of  safety  of  7, 
as  obtained  from  table  of  the  National  Fire-proofing  Co.,  are 
as  follows: 


6-inch 

8-inch 

6-inch 

8-inch 

Feet. 

Arch, 
Pounds. 

Arch, 
Pounds. 

Feet. 

Arch, 
Pounds. 

Arch, 
Pounds. 

4 

1103 

1318 

11 

402 

480 

5 

878 

1049 

12 

370 

442 

6 

735 

883 

13 

340 

407 

7 

630 

735 

14 

317 

379 

8 

554 

662 

15 

296 

353 

9 

490 

585 

16 

278 

331 

10 

443 

529 

756  FIRE-PROOFING   OF  BUILDINGS. 

These  loads  include  the  weight  of  the  construction,  .so  that 
to  get  the  safe  live  load  all  the  dead  load  of  arch  block,  concrete 
fill,  plastering,  flooring,  etc.,  must  be  deducted. 

Side  Construction  Terra-cotta  Arches. — By  this  term  is 
understood  the  fl.it  tile  arches  in  which  the  voids  in  the  blocks 
run  parallel  with  the  beams,  as  shown  in  Fig.  19. 

On  account  of  its  greater  strength  at  nearly  the  same  cost 
the  end-construction  arch  has  largely  replaced  this  form  of 
floor  arch,  the  former  now  being  used  to  about  three  times  the 
extent  of  the  latter. 

One  advantage  of  this  arch  over  the  end-construction,  how- 
ever, is  the  breaking  of  joints  that  is  effected  in  the  setting 
of  the  blocks,  by  means  of  which  the  failure  of  a  single  block 
does  not  impair  the  strength  of  the  arch  beyond  that  block. 


FIG.   19. 

The  webs  should  not  be  less  than  J"  thick.  "Radial  joints 
are  sometimes  specified  but  should  be  avoided,  as  they  incur 
needless  expense  in  manufacture  and  endless  confusion  and 
delay  in  setting  without  any  compensating  advantage."  * 

In  the  skew-backs  a  web  should  always  be  provided  across 
the  block  at  the  lower  flange  of  the  beam,  as  at  this  point  comes 
the  greatest  pressure  in  this  block.  Arches  have  collapsed 
for  failure  to  provide  this  web. 

The  depth  of  the  arch  must  be  proportioned  to  the  span 
between  beams  and  to  the  load  to  be  carried.  For  ordinary 
loads  a  safe  rule  is  to  make  the  depth  of  the  block  1}  inches 
for  each  foot  of  span,  plus  the  amount  necessary  for  protection 
below  the  beams. 

Safe  loads  for  semi-porous  tile  arches,  side  construction, 
with  webs  £"  thick  and  a  factor  of  safety  of  7,  as  given  by 
the  National  Fire-proofing  Co.,  are  shown  in  table  on  page  757. 

These  loads  represent  the  gross  loads,  so  that  for  the  safe 
1'ive  loads  the  weight  of  the  construction,  including  arch  blocks, 
fill,  flooring,  plastering,  etc.,  must  be  deducted.  For  blocks 

*  Bevier,  National  F.  P.  Co.,  N.  Y. 


ARCHES. 


757 


Depth  of  Arch.  . 

6  Ins. 

7  Ins. 

8  Ins. 

9  Ins. 

10  Ins. 

12  Ins. 

Weight  of  Arch 
per  Sq.  Ft  ... 

24  Ibs. 

26  Ibs. 

27  Ibs. 

29  Ibs. 

34  Ibs. 

37  Ibs. 

Span  of  Arch 
in  Feet. 

Stre 

ngth  of  A 

rch  in  Po 

unds  per 

Square  F 

oot. 

4'  0" 
4'  6" 
5'  0" 
5'  6" 
6'  0" 
6'  6" 
7'  0" 

197 
156 

230 
182 
148 

263 

208 
168 
139 

296 
233 
189 
156 
131 

438 
346 
281 
232 
195 
166 

525 
415 
336 
278 
234 
199 
172 

with  thicker  webs  the  loads  may  be  increased  proportionately. 
Where  no  loads  are  given  in  the  table,  the  spans  are  considered 
excessive  for  the  depth  of  block  specified. 

The  weights  of  arch  given  in  the  table  are  for  the  lightest 
blocks.  If  thicker  webs  are  used  weight  of  block  must  be 
taken  proportionately  greater. 

End-construction  Flat  Arches. — In  this  construction  the 
sides  and  voids  of  the  individual  blocks  run  at  right  angles  to 
the  beams,  so  that  the  pressure  on  the  blocks  is  endways  of 
the  tile.  It  has  been  conclusively  demonstrated  that  hollow 
tile  are  much  stronger  in  end  compression  than  transversely, 
consequently  the  end-construction  arch  has  to  a  large  extent 
superseded  the  side  construction. 

"The  objection  urged  against  this  construction  is  that  it  is 
wasteful  of  mortar  and  difficult  to  get  the  edges  of  the  blocks 
properly  bedded.  They  do  require  slightly  more  mortar,  but 
the  second  objection  is  not  serious,  for,  if  the  blocks  are  cut  to 
a  proper  bevel,  the  tighter  they  are  set  the  stronger  the  arch."  * 

The  individual  blocks  in  the  end-construction  are  commonly 
made  rectangular  in  shape  and  advancing  by  1  inch  from  6 
to  15  inches  in  depth.  The  length  and  width  of  the  blocks 
may  also  be  varied,  but  the  standard  size  is  12  inches  for  both 
dimensions.  The  number  of  partitions  or  webs  in  the  blocks 
varies  with  the  size  of  the  block  and  also  with  the  strength 
desired.  The  6-,  7-,  and  8-inch  blocks  usually  have  two  vertical 
and  one  horizontal  partitions,  or  one  vertical  and  one  hori- 
zontal for  blocks  8  inches  wide.  The  10-  and  12-inch  arches 
may  have  either  one  or  two  horizontal  partitions.  Arch  blocks 
over  12  inches  deep  should  always  have  at  least  two  horizontal 


*  Bevier. 


758 


FIRE-PROOFING   OF   BUILDINGS. 


partitions.  In  the  strongest  blocks  the  voids  are  about  3 
inches  square. 

"The  arch  blocks  must  be  set  end  to  end  in  straight  courses 
from  beam  to  beam,  and  cannot  be  set  breaking  joints,  as  in 
the  side-construction  method."  *  So  that  if  one  block  fails, 
the  rest  of  the  arch,  for  the  width  of  that  block,  is  dependent 
for  its  strength  on  the  adhesion  of  the  individual  blocks  to 
those  adjoining. 

Thickness  of  Web. — This  should  be  at  least  f  inch  for 
porous  tiling  and  J  inch  for  semi-porous.  The  thicker  the 
webs  the  greater  will  be  the  strength  of  the  arch,  and  also  its 
fire  resistance. 

The  end  joints  are  always  bevelled,  as  in  Figs.  20  and  21, 


FIG.  20. 


FIG.  21. 

the  ends  being  parallel,  thus  all  the  intermediate  blocks  are 
made  with  the  same  die. 

Form  of  Skew- backs. — An  end-construction  arch  may 
have  skew-backs  formed  of  the  same  blocks,  with  a  notch  in  the 
end  of  the  block  to  fit  over  the  bottom  flange  of  the  beam,  as  in 
Fig.  22.  It  is  generally  considered  that  the  end-construction 
skew  is  much  strongar  than  the  side-construction  skew,  but  on 
account  of  the  large  amount  of  mortar  lost  in  the  voids  and  the 
difficulty  of  obtaining  an  even  bearing  with  end-construction 
skews,  and  also  because  of  the  greater  facility  with  which  the 
side-construction  skew-backs  can  be  used,  contractors  generally 
prefer  to  use  the  latter  and  this  has  given  rise  to  the  combina- 
tion arch}  shown  by  Fig.  23. 

But    a   more   important    reason   for   using   side-construction 

*  Bevier. 


ARCHES. 


skew-backs  with   end-construction   arches,    is  the   better  pro- 
tection against  fire  they  afford  to  the  beam  or  girder. 


Fig.  22. — End -construction  Skew-backs. 


.    .:/        ?>.    •*..  .  .;'  •_  ._*      •  ......    '••       .        ,-'    .  j" 

(  2"  x  4" Beveled  Floor  Strips  16"Center3 


FIG.  23. — Combination  Arch.  ^ 

To  develop  the  necessary  strength  side-construction  skews 
should  have  a  large  sectional  area  and  a  sufficient  number  of 
partitions,  following,  approximately,  the  lines  of  thrust. 


finished  Floor  Lii 


OF    -        . 


FIG.  24. — Longitudinal  Section. 

With  any  form  of  skew  the  recess  for  the  beam  flange  should 
be  wide  enough  so  that  when  the  tiles  are  set  the  protection 


760  FIRE-PROOFING   OF  BUILDINGS. 

flange  on  the  skew  will  not  touch  the  bottom  of  the  be.am,  but 
will  be  at  least  J  inch  below  it. 

A  great  variety  of  side-construction  skew-backs  are  made  to 
meet  all  possible  conditions. 

Keys. — Both  end-construction  and  side-construction  keys 
are  used  with  end- const  ruction  arches,  the  choice  of  the  key 
depending  principally  upon  its  length.  If  the  span  of  the  arch 
is  such  that  the  standard  intermediate  blocks  will  require  a  key 
6  inches  wide  or  more,  then  the  end-method  key  is  used,  as  in 
Fig.  20,  but  if  the  space  for  the  key  is  small,  a  side-method  key, 
such  as  shown  in  Figs.  21  and  23,  is  used.  As  the  key  is  almost 
entirely  in  compression,  a  side-construction  key  6  inches  wide 
or  less  will  usually  give  all  the  strength  required,  provided  that 
the  horizontal  webs  are  in  the  same  line  with  those  in  the  inter- 
mediate blocks.  Mr.  E.  V.  Johnson,  Western  manager  of  the 
National  Fire-proofing  Co.,  says:  "We  prefer  the  use  of  an  end- 
construction  key  in  all  cases  where  possible.  Our  custom  is  to 
use  side-construction  keys  for  spaces  of  6  inches  and  under  and 
end-construction  keys  for  larger  spaces.  When  using  the  latter 
keys  we  insert  a  J-inch  fire-clay  slab  between  the  ends  of  the 
tile." 

Raised  Skew-backs. — Where  flat  arches  are  sprung  be- 
tween 18-,  20-  or  24-inch  beams  it  is  necessary  either  to  use  a 


Fio.  25.— Raised  Skew-back. 

raised  skew-back  or  else  have  a  large  space  above  the  top  of 
the  tile  arches  which  must  be  filled  in  some  way.  Raised  skew- 
backs  are  preferable  to  a  hollow  space  above  the  tiles  and 
cheaper  than  concrete  filling.  They  are  often  used  for  roof 
arches,  because  it  is  seldom  necessary  to  make  the  arches  as 
deep  as  the  beams,  while  the  top  must  be  about  on  a  level  with 
the  beams. 


ARCHES. 


761 


Raised  skew-backs  are  almost  always  made  on  the  side- 
construction  method,  Figs.  25,  26,  and  27  showing  typical  forma 
for  end-construction  arches. 


18  Steel  Beam 


FIG.  26. 


d 


O 


O 


FIG.  27. 

Flat  vs.  Panelled  Ceilings.. — In  connection  with  the  rais- 
ing of  the  arches  above  the  bottom  of  the  beams  or  girders, 
Mr.  Freitag  calls  attention  to  the  advantages  of  flat  ceilings,  as 
follows: 

"Flat,  unbroken  ceilings  are  always  to  be  preferred  to  any 
type  of  terra-cotta  arch  which  may  require  a  panelled  effect  due 
to  the  projection  of  the  girders  or  beams  below  the  main  ceiling 


762 


FIRE-PROOFING    OF    BUILDINGS. 


line."  A  perfectly  flat  ceiling  reflects  more  light  and  gives  a 
better-lighted  room  and  also  deflects  heat.  Panelling  forms 
pockets  for  the  retention  of  heat  and  flame  and  greatly  increases 
the  exposed  area. 

Arches  should  be  of  Same  Depth  as  the  Beams. — 
A  deep  block  makes  a  much  stronger  floor  than  a  shallower 
one,  and  for  the  same  depth  of  beams  a  lighter  and  cheaper 
floor.  A  12-inch  arch  will  weigh  less  per  square  foot  than  a 
10-inch  arch  with  2  inches  concrete  filling  and  also  costs  less. 

Depth,  Span,  and  Weight. — The  maximum  spans  for 
different  depths  'and  the  average  weights  per  square  foot  of 
this  type  of  arch,  set  in  place,  are  as  follows: 


Depth  of  Arch. 

Maximum  Span. 

Weight  per  sq. 

ft. 

6  ins. 

4  ft.  6  ins. 

29  Ibs. 

8  ins. 

5  ft.  6  ins. 

31  Ibs. 

9  ins. 

6  ft. 

32  Ibs. 

10  ins. 

6  ft,  6  ins. 

33  Ibs. 

12  ins. 

8  ft. 

39  Ibs. 

15  ins. 

9  ft. 

46  Ibs. 

16  ins. 

10  ft. 

50  Ibs. 

The  depth  of  arch  most  frequently  used  is  10  inches,  the 
girders  being  spaced  to  use  10-inch  I-beams  for  joists  spaced 
from  5  to  6  feet  apart.  As  a  rule  the  depth  of  the  arch  should 
be  about  equal  to  the  depth  of  the  beam,  as  it  is  just  about  as 
cheap  and  much  better  construction  to  use  deeper  tiling  and 
less  concrete  filling. 

The  weights  per  square  foot,  as  given  by  different  manufac- 
turers, vary  greatly,  no  doubt  due  to  the  character  of  the  material 
used  and  to  the  thickness  of  the  webs. 

Safe  Loads  for  End-construction  Arches.  —  The 
strength  of  flat  arches  of  hollow  tile  depends  upon  the  crush- 
ing resistance  of  the  material,  the  sectional  area,  per  lineal 
foot  of  arch,  and  upon  the  depth  and  span.  For  these  reasons 
it  is  impossible  to  give  a  table  for  strength  which  will  apply  to 
all  arches.  The  table  on  the  following  page  is  condensed  from 
two  tables  prepared  by  Mr.  H.  L.  Hinton,  who  has  gone  very 
elaborately  into  the  strength  of  tile  arches,  in  the  handbook 
prepared  by  him  for  the  National  Fire-proofing  Co. 

The  values  given  for  end-construction  arches  are  based  on 
arch-blocks  of  the  cross-sectional  areas  (per  foot)  given  at  the 
head  of  the  table,  and  are  intended  to  have  a  factor  of  safety  of 
7  with  the  weight  of  the  tile  only  deducted. 


ARCHES 


763 


Mr.  Hinton  says:  "The  safe  loads  as  they  stand  in  the  table 
afford  a  safe  general  statement  of  safe  loads  for  all  sections, 
since  they  represent  specifically  a  light  section  in  the  case  of 
each  arch." 


SAFE  LOADS  PER  SQUARE  FOOT  OF  FLOOR. 

END-CONSTRUCTION    FLAT   ARCHES. 

(H.  L.  HINTON.) 
Semi-porous  material  of  sectional  area  per  lineal  foot  as  given  in  second  line. 


Depth  of  Arch. 

6" 

1" 

8" 

A 

9" 

10" 

12" 

15" 

Areas,  Sq.  Ins. 

310 

340 

370 

400 

430 

490 

580 

Spans. 
4'  6"  .      

Ibs. 
196 

Ibs. 
254 

Ibs. 
319 

Ibs. 
391 

Ibs. 
470 

Ibs. 
648 

Ibs. 
968 

5' 

155 

202 

254 

312 

376 

519 

777 

5'  6"  
6' 

163 

206 
170 

254 

209 

306 
253 

424 
352 

636 
529 

6'  6" 

141 

175 

212 

295 

446 

7'      

147 

179 

251 

380 

7'  6" 

153 

215 

326 

8'     

185 

232 

Patented  End-method  Arches. — Figs.  28  and  29  show 
two  variations  of  a  type  of  arch  invented  and  patented  by 
Mr.  E.  V.  Johnson  when  manager  of  the  Pioneer  Company,, 
of  Chicago.  The  right  to  manufacture  and  use  this  arch,  in 
certain  territory,  was  granted  to  the  Pioneer  Company;  also 


FIG.   28. 

to  Henry  Maurer  &  Son,  of  New  York,  and  to  the  Hayden- 
ville  (Ohio)  Company.  The  original  shape  of  the  arch  tile  is 
illustrated  by  Fig.  29,  and  this  shape  is  still  used  by  the  Pioneer 
Company.  Henry  Maurer  &  Son  have  modified  the  shape  to 
that  shown  by  Fig.  28,  considering  that  this  shape  gives  a  stronger 


764 


FIRE-PROOFING    OF  BUILDINGS. 


(and  also  a  slightly  heavier)  arch  than  the  original  shape.  The 
advantages  of  this  arch  are  reduced  weight,  with  equal  strength 
and  a  clear  space  of  5  inches  between  the  tile,  wilich  avoids 
cutting  of  the  blocks  for  the  tie-rods. 

This  arch  can  be  adapted  to  any  span  up  to  10  feet  by  using 
a  suitable  depth  of  block. 


FIG.  29. 


The  limit  of  span,  weight  per  square  foot  and  safe  load  of  the 
"Excelsior"  arch  is  given  by  Maurer  &  Son  as  follows: 


Depth  of  Arch. 

Limits  of  Span. 

Weight  per  sq.  ft. 

Safe  Load  per 

sq.  ft. 

8  ins. 
9  ins. 
10  ins. 
12  ins. 

5  ft.  to  6  ft, 
6  ft.  to  7  ft. 
7  ft.  to  8  ft. 
8  ft.  to  9  ft. 

27  Ibs. 
29  Ibs. 
33  Ibs. 
38  Ibs. 

300  Ibs. 
350  Ibs. 
300  Ibs. 
350  Ibs. 

The  Pioneer  Company  have  made  arches  as  deep  as  20  inches 
and  weighing  56  Ibs.  per  square  foot.  Both  companies  use 
semi-porous  material  for  the  arch-blocks.  It  should  be  noticed 
that  the  arch  made  by  the  Pioneer  Company  has  an  end-con- 
struction skew,  while  Maurer  &  Son  use  a  side-construction 
skew.  The  Pioneer  Company  formerly  used  the  side-construc- 
tion skew,  but  found  that  when  arches  of  this  type  were  tested 
to  destruction  the  skew-backs  were  almost  invariably  the  parts 
which  failed,  hence  their  adoption  of  the  end-construction  skew. 
Messrs.  Maurer  &  Son,  however,  have  tested  the  Excelsior 
arch,  with  spans  of  8  and  10  feet,  with  loads  of  over  1000  Ibs. 
per  square  foot,  without  failure,  with  skew-backs  as  shown  by 
them. 

This  arch  has  been  very  extensively  used  in  both  Eastern 
and  Western  cities  and  is  undoubtedly  a  very  good  type. 


ARCHES. 


765 


Reinforced  Tile  Arches. — In  order  to  obtain  a  wide  span  flat 
arch  or  to  obtain  a  reduced  depth  of  arch  block  for  the  shorter 
spans,  the  manufacturer  of  terra-cotta  have  applied  to  their 
floor  construction  the  principle  of  reinforcement  with  metal 
that  is  the  basis  of  reinforced  concrete  construction. 

Compared  with  reinforced  concrete,  even  when  cinders  are 
used  for  the  aggregate,  their  greater  depth  and  hollow  con- 
struction secure  for  them  greater  strength  for  the  same  weight 
of  construction  per  square  foot.  On  the  other  hand,  however, 
they  are  undoubtedly  more  expensive  than  cinder  concrete 
construction,  because  of  the  material  used  and  the  increased 
height  of  the  building  due  to  thicker  floors. 

The  "  Herculean  "  Arch.  * — This  floor  is  built  of  semi- 
porous  terra-cotta  blocks  12  inches  by  12  inches  on  top  and 


FIG.  30.— The  "Herculean"  Arch. 

varying  from  6  to  12  inches  in  depth,  according  to  the  span 
and  load.  In  the  sides  of  the  blocks  are  grooves  to  receive 
liXHX  3/16-inch  T-bars.  The  blocks  are  laid  end  to  end  the 
entire  length  of  the  span,  with  a  bearing  of  4  to  6  inches  on  the 
walls  or  girders,  presenting  two  continuous  grooves,  which  are 
filled  with  cement,  and  into  which  the  T-bars  are  then  inserted. 
The  T's  must,  of  course,  extend  the  full  length  of  the  span. 
The  grooves  in  the  next  course  are  then  filled  with  cement 
and  the  blocks  pushed  into  place,  thus  thoroughly  covering 
the  steel  with  cement. 

*  Patented  and  manufactured  by  Henry  Maurer  &  Sons,  1898  and  1900. 


766  FIRE-PROOFING    OF    BUILDINGS. 

All  joints  between  the  blocks  are  filled  with  cement  and  the 
blocks  are  laid  to  break  joint  endways,  as  in  Fig.  30. 

Span. — This  floor  is  adapted  to  spans  up  to  25  feet  and  has 
been  extensively  used  for  spans  varying  from  19  to  23  feet. 

Weight. — The  weight  of  the  terra-cotta  blocks  and  steel  tees 
per  square  foot  is  given  at  26  Ibs.  for  blocks  6  inches  deep, 
33  Ibs.  for  8-inch  blocks,  42  Ibs.  for  10-inch  blocks,  and  51  Ibs. 
for  12-inch  blocks. 

Strength. — The  manufacturers  estimate  the  safe  load  for  this 
construction  as  follows: 

For  12-inch  arch,  20-foot  span,  400  Ibs.  per  square  foot. 

For  10-inch  arch,   16-foot  span,  400  Ibs.  per  square  foot. 

For    8-inch  arch,   12-foot  span,  150  Ibs.  per  square  foot. 

Fire-proofing  Qualities. — The  steel  tension  members,  being 
buried  in  the  terra-cotta  blocks  over  2  inches  everywhere,  are 
well  protected  against  fire,  and  being  imbedded  in  cement  are 
protected  also  against  corrosion. 

Advantages. — The  chief  advantage  of  this  construction  is 
said  to  be  its  low  cost  as  compared  with  systems  equally  fire- 
proof and  requiring  steel  beams  every  6  or  8  feet. 

It  is  particularly  well  adapted  to  buildings  having  masonry 
walls  and  partitions,  as  in  such  buildings  little  or  no  structural 
steel  is  required. 

The  floor  also  affords  an  unusually  smooth  under  surface, 
thereby  reducing  the  cost  of  plastering. 

No  tie-rods  are  required  for  this  floor. 

The  Johnson  Long-span  Flat  Construction. — Another 
leading  reinforced  tile  floor  was  invented  by  Mr.  E.  V.  Johnson, 
and  is  now  controlled  and  erected  by  the  National  Fire-proofing 
Company. 

The  general  construction  of  this  floor  is  as  follows: 

A  temporary  flat  centring  is  first  erected  and  over  this  is 
spread  a  layer  of  rich  Portland  cement  mortar  about  f  inch 
thick.  On  top  of  this  mortar  is  laid  a  woven  fabric  containing 
steel  rods  varying  from  J  inch  to  ^  inch  in  diameter,  according 
to  the  span,  and  spaced  from  2  inches  to  8  inches  centre  to  centre. 
Another  layer  of  the  same  mortar  is  then  spread  on  top  and 
hollow  tiles  from  3  to  12  inches*  in  depth,  according  to  the 
span,  are  then  set  in  the  mortar  and  laid  with  u  break  joint, " 
so  as  to  form  continuous  rows  from  one  support  to  the  other, 
the  same  as  in  end-construction  flat  arches,  except  that  in  the 
Johnson  construction  the  ends  of  the  tile  are  square  to  the  beds. 


ARCHES. 


767 


A  layer  of  concrete  about  2  inches  thick  is  also  usually  spread 
on  top  of  the  tile. 

Fig.  31  shows  the  general  method  of  construction  of  this 
system,  but  without  the  rods,  which  are  inserted  in  place  as 
the  fabric  is  used.  For  short  spans  the  fabric  can  be  used 
without  the  rods. 

As  already  stated,  this  system  differs  from  the  flat  concrete 
systems  only  in  the  substitution  of  hollow  tile  for  the  concrete 
in  the  upper  portion  of  the  slab,  its  strength  depending  upon 
the  reinforcement  and  the  adhesion  of  the  cement  mortar  to  the 
eteel  and  tile.  As  the  tile  are  covered  both  on  the  bottom  and 


FIG.  31. — Johnson  Arch.1 

top  with  concrete  the  fire-proofing  quality  is  also  measured  by 
the  resistance  of  the  concrete  and  not  of  the  tile. 

Many  tests,  however,  have  shown  that  the  adhesion  of  the 
mortar  is  perfect  and  that  it  will  stand  a  high  temperature 
without  injury. 

Span. — This  construction  can  be  used  for  any  span  up  to 
25  feet,  the  most  advantageous  span  being  about  16  feet. 

Weight. — The  weight  per  square  foot  of  this  floor,  includ- 
ing the  fabric  and  the  cement  on  the  bottom  and  in  the  joints, 
but  not  on  top  of  the  tile,  is  as  follows: 

For  depth  of  tile  of  12  inches,  10  inches,  9  inches,  8  inches, 
7  inches,  6  inches,  5  inches,  4  inches. 

Weight  per  square  foot,  Ibs.,  60,  55,  45,  42,  37,  34,  26,  24 

The  concrete  above  the  tile  should  be  figured  at  12  Ibs.  per 
square  foot  for  each  inch  in  thickness. 


768 


FIRE-PROOFING   OF   BUILDINGS. 


Strength. — The  proprietors  of  this  system  give  the  following 
for  the  ultimate  strength  of  the  floors  with  1  inch  of  1  to  3 
Portland-cement  mortar  on  top  of  the  tile. 


JOHNSON  SYSTEM. 

With  1"  Portland-cement  Floor  Surface. 


Spans 

Ultimate  Strength  in  Pounds  per  Square  Foo';. 

from 

10  to  24 

Thick- 

Thick- 

Thick- 

Thick- 

Thick- 

Thick- 

Thick- 

Thick- 

Thick- 

Feet. 

ness 

ness 

ness 

ness 

ness 

ness 

ness 

ness 

ness 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

of  tile. 

12" 

10" 

9" 

8" 

7" 

6" 

5" 

4" 

3" 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

10  feet 

3375 

2580 

2140 

1850 

1525 

1265 

1000 

775 

560 

11  feet 

2800 

2340 

1780 

1536 

1264 

1052 

832 

640 

464 

12  feet 

2350 

1800 

1480 

1280 

1064 

880 

700 

540 

390 

13  feet 

2000 

1540 

1265 

1100 

910 

752 

595 

460 

334 

14  feet 

1730 

1325 

1100 

950 

780 

650 

510 

400 

290 

15  feet 

1500 

1160 

950 

830 

680 

590 

450 

348 

250 

16  feet 

1320 

1010 

840 

720 

600 

500 

395 

305 

220 

17  feet 

1180 

900 

740 

640 

578 

440 

350 

270 

194 

18  feet 

1020 

795 

664 

570 

473 

392 

310 

242 

174 

20  feet 

844 

645 

535 

462 

381 

314 

250 

194 

22  feet 

700 

536 

445 

384 

316 

263 

208 

24  feet 

587 

450 

370 

320 

266 

220 

With  this  table  the  following  factors  of  safety  should  be  used: 

Factor  4. — Floors  of  offices,  school  rooms,  hospital  and  asylum  wards, 
dwellings,  and  roofs. 

Factor  5. — Floors  of  stores,  warehouses,  theatres,  public  halls,  and 
assembly  rooms. 

Factor  6. — Floors  of  buildings  where  vibration  of  machinery  or  loads 
causing  a  sudden  impact,  occurs. 

A  section  of  this  floor,  16  feet  square,  supported  on  walls 
around  the  four  edges,  was  loaded  over  its  entire  area  with  a 
total  uniformly  distributed  load  of  187,680  Ibs.  or  733  Ibs.  to 
each  square  foot.  The  deflection  of  the  floor  was  as  follows: 
Under  a  load  of  350  Ibs.  per  square  foot,  ^  inch  scant;  733  Ibs. 
per  square  foot,  £  inch  full. 

Advantages. — The  advantages  of  this  system  are  the  same  as 
noted  for  all  long-span  flat  systems;  the  system  can  be  used  to 
special  advantage  for  roofs  and  for  buildings  divided  by  masonry 
partitions,  so  that  the  spans  do  not  exceed  25  feet.  For  such 
buildings  very  little,  if  any,  structural  steel  will  be  required. 

"New  York"  Reinforced  Terra-cotta  Arch. —  This 
arch  (Fig.  32)  was  designed  by  Mr.  P.  H.  Bevier,  of  the  New 
York  branch  pf  the  National  Fire-proofing  Co.,  for  use  "when 


ARCHES. 


769 


a  light  and  cheap  but  strong  floor  construction  with  a  flat 
ceiling  is  required,  and  is  particularly  adapted  to  wide  spans 
in  shallow  beams.  When  light  floor  construction  with  deep 
beams  is  necessary  it  can  be  secured  by  setting  the  blocks  level 


Soffit  Skew  Plain  Skew 

FIG.  32. — "New  York"  Reinforced  Arch  (Bevier  Patent). 

with  the  tops  of  the  beams  and  using  a  flat  metal  lath  ceiling, 
or  by  omitting  the  ceiling  a  panel  effect  is  obtained. " 

"When  shallow  beams  are  used  the  blocks  are  set  level  and 
1  inch  below  the  bottom  of  the  beams.  Light  cinder  concrete 
or  dry  cinders  is  used  to  level  up  to  the  top  of  the  beams." 

"The  wire  truss  reinforcement,  Fig.  33,  used  in  this  system 
is  shipped  to  the  building  in  reels,  and  is  cut  to  proper  lengths 


FIG.  33. — Wire  Truss  Reinforcement. 

on  the  job  as  required.  It  is  embedded  in  Portland  cement 
mortar  between  the  blocks,  so  that  it  is  protected  both  against 
rust  and  fire.  The  open-work  construction  of  the  wire  truss 
enables  the  mortar  to  flow  freely  all  about  it  and  the  joint  can 
be  thoroughly  filled  between  the  blocks  and  the  wire  perfectly 
embedded." 

"The  6-inch  arch  for  6-foot  span,  and  8  inch  arch  for  7-foot 
6-inch  span,  have  been  tested  by  the  Bureau  of  Buildings,  of 
New  York,  and  accepted  for  live  load  of  150  Ibs.  per  square 
foot." 

"The  'New  York'  arch  has  been  used  in  a  number  of  large 
buildings  in  New  York.  Load  tests  were  made  to  determine 


770  FIRE  PROOFING    OF  BUILDINGS. 

the  ultimate  strength  of  the  6-inch  arch  on  a  6-foot  span,  and 
it  was  found  to  be  1600  Ibs.  per  sauare  foot." 

The  Guastavino  Tile  Arch  System.— This  is  a  peculiar 
method  of  constructing  floors,  partitions,  staircases,  etc.,  by 
means  of  thin  tile  1  in.  in  thickness  and  about  6  ins.  wide  and 
of  lengths  varying  from  12  to  24  ins.,  all  bonded  together  in 
Portland  cement  so  as  to  make  one  solid  mass.  It  was  devised 
by  R.  Guastavino  of  New  York  and  Boston,  and  is  executed 
solely  by  the  R.  Guastavino  Company. 

The  floors  in  this  system  are  built  by  spanning  the  space 
between  the  girders  with  a  single  arch,  vault,  or  dome,  con- 
structed of  two  or  three  or  more  thicknesses  of  these  1-inch 
tile,  depending  upon  the  dimensions  of  the  arch  or  vault.  In 
its  best  application,  steel  is  used  in  tension  only  as  tie-members, 
and  in  place  of  steel  girders  tile  girders  are  constructed  of  the 
same  material;  wherever  steel  is  used  it  is  imbedded  in  the 
masonry  construction. 

One  of  the  earliest  notable  buildings  in  this  system  is  that 
of  the  Boston  Public  Library,  built  about  fourteen  years  ago, 
and  some  of  the  later  important  constructions  are  the  Hall 
of  Fame  and  Library  Building  of  the  University  of  New  York, 
and  the  Metropolitan  Museum  of  Art,  in  New  York,  Massa- 
chusetts Horticultural  Building,  American  Type  Foundry 
Building,  and  Massachusetts  General  Hospital,  in  Boston, 
Minnesota  State  Capitol  Building,  St.  Paul,  Minn. 

As  indicating  the  spans  which  can  be  safely  applied,  the 
floor  above  the  crypt  of  the  Cathedral  of  St.  John  the  Divine, 
in  New  York,  measuring  56X60  ft.  with  no  interior  supports 
and  designed  to  carry  a  safe  load  of  400  Ibs.  per  square  foot, 
was  constructed  on  this  principle. 

Wherever  a  vaulted  ceiling  is  desired  this  seems  to  be  the 
best  system  of  construction  yet  devised. 

Floors  built  on  this  principle  have  been  tested  under  the 
supervision  of  the  New  York  Building  Department  up  to  3700 
pounds  per  square  foot,  with  spans  of  10  ft. 

When  used  between  I-beams  the  only  steel  beams  required 
are  those  spanning  from  column  to  column. 

Architects  contemplating  the  use  of  this  system  of  construc- 
tion are  advised  to  consult  the  R.  Guastavino  Company  before 
letting  any  contracts. 

Wherever  vaulted  ceilings  are  desired  this  construction  should 
be  as  cheap,  and  generally  is  cheaper  than  any  other  form  of 


ARCHES.  771 

equally  fire-proof  construction — a  particular  advantage  of  the 
system  being  that  frequently  the  soffit  course  of  tile  is  of  pressed 
or  glazed  material,  making  a  most  effective  arid  permanent 
finish,  as  in  the  case  of  the  City  Hall  Station  of  the  New  York 
Subway,  which  was  constructed  for  very  heavy  loads  without 
the  use  of  steel. 

Concrete  Floors. — Concrete  used  in  fire-proof  floors  may 
be  either  plain  or  reinforced.  Without  reinforcement  its  use 
is  not  generally  practicable  in  any  thing  but  very  short  spans, 
on  account  of  its  expense  or  great  weight.  In  this  chapter 
it  will  be  considered  only  as  a  floor  filling  between  steel  beams. 
The  following  chapter  will  be  devoted  to  a  discussion  of  the 
principles  governing  its  design  and  use. 

Advantages  of  Reinforced  Concrete  for  Floor  Con- 
struction.— Although  many  advantages  are  claimed  for  rein- 
forced concrete  over  the  tile  systems,  the  principal  advantage 
is  that  of  economy,  taking  into  account  the  cost  of  both  the 
steel  framework  and  the  filling  between.  The  other  important 
advantages  are  less  weight  per  square  foot  of  floor  (usually  but 
not  always),  adaptability  to  irregular  framing  and  rapidity 
of  construction. 

Except  in  the  immediate  locality  of  the  tile  factories,  fire- 
proof floors  of  concrete  can  usually  be  placed  at  less  expense 
than  those  of  hollow  tile,  and  when  the  spans  will  permit  of 
the  use  of  cinder  concrete,  the  concrete  floors  will  be  lighter 
than  those  of  the  tile,  when  both  floors  have  the  same  strength. 
Some  of  the  long-span  tile  systems,  on  the  other  hand,  are  much 
lighter  than  many  of  the  concrete  floors  that  are  now  being 
built. 

The  materials  entering  into  the  construction  of  reinforced 
concrete  floors  are  readily  obtained  in  almost  any  locality, 
no  special  prepared  material  is  required,  except  perhaps  in  a 
few  special  forms  of  reinforcement,  and  the  work  can  be  done 
almost  entirely  by  unskilled  labor.  Less  capital  is  required 
for  concrete  work  than  for  the  tile  constructions,  and  no  material 
need  be  carried  in  stock  during  an  idle  period,  except  tools, 
mixing  machines,  old  centering,  etc. 

That  the  above  advantages  are  real  is  sufficiently  proven 
by  the  immense  amount  of  reinforced  concrete  now  under 
construction  throughout  the  world. 

Wherever  a  floor  is  to  have  a  finished  cement  surface,  rein- 
forced concrete  constructions  will  be  considerably  cheaper 


772  FIRE-PROOFING    OF    BUILDINGS. 

than  any  tile  system,  because  in  the  former  construction,  the 
entire  concrete  is  used  to  give  strength,  while  with  the  flat- 
tile  arches  it  merely  increases  the  dead  weight. 

Disadvantages. — One  decided  disadvantage  connected  with 
concrete  floor  construction  is  the  interference  in  a  large  measure 
with  the  progress  of  other  parts  of  the  work.  During  its  in- 
stallation, there  is  a  constant  dripping  from  the  floor,  making 
it  sometimes  impossible  to  continue  other  lines  of  work.  After 
completion  of  the  floors  a  long  time  is  required,  depending  on 
the  weather,  for  the  drying  out,  before  interior  finishing  can 
proceed. 

Composition  of  the  Concrete. — The  materials  used  for 
concrete  are  discussed  on  p.  733.  Only  Portland  cement  should 
be  used  in  any  floor  construction. 

For  most  reinforced  concrete  floors,  having  a  span  between 
the  steel  beams  of  8  feet  or  less,  cinder  concrete  is  generally 
used  for  the  reason  that  concrete  mixed  with  cinders  is  much 
lighter  than  that  mixed  with  broken  stone  or  gravel.  The 
usual  proportions  of  cinder  concrete  are  one  of  cement  to  two 
of  sand  and  five  or  six  of  cinders. 

To  make  a  first-class  concrete  the  cinders  must  be  screened 
through  at  least  a  f-inch  mesh,  and  only  hard  coal  cinders 
should  be  used.  Good  cinders  may  sometimes  be  obtained 
from  power-plants  using  soft  coal,  but  it  must  be  well  screened 
to  free  from  the  ash.  Concrete  mixed  with  common  ashes, 
as  is  sometimes  done,  has  little  strength  and  is  totally  unre- 
liable. 

For  all  spans  exceeding  8  ft.,  either  gravel  or  broken  rock 
should  be  used,  and  these  should  be  mixed  with  one  part  cement 
to  two  of  clean,  sharp  sand  and  four  of  stone  or  gravel. 

The  weight  of  cinder  concrete  will  vary  from.  80  to  110  Ibs. 
per  square  foot,  depending  upon  the  coarseness  of  the  mate- 
rial, quantity  of  sand,  and  the  amount  of  tamping.  For  ordi- 
nary purposes  a  1:2:5  cinder  concrete  should  be  taken  at 
96  Ibs.  per  cubic  foot,  or  8  Ibs.  per  square  foot  per  inch  in  thick- 
ness. 

Forms  of  Reinforcement. — While  steel  in  small  sections 
is  used  almost  entirely  for  the  reinforcement,  there  is  a  great 
variety  in  the  shape  and  character  of  the  metal  employed. 

Different  forms  of  reinforcement  are  described  and  discussed 
in  the  next  chapter.  All  of  them  may  be  and  most  of  them 
are  being  used  in  floor  construction.  In  addition  to  those 


ARCHES.  773 

discussed  there,  others  that  are  not  readily  adapted  to  beam 
construction  are  used  in  floor  construction.  Such  are  the 
metal  fabrics  described  farther  on  under  the  different  types 
of  construction. 

The  proper  position  for  reinforcement  in  a  floor  construction 
is  that  in  which  it  will  take  the  tensional  stresses,  that  is,  in 
floor  slabs,  near  the  lower  surface.  The  most  logical  form  would 
be  a  rod  or  bar.  A  greater  number  of  small  rods  or  bars  is 
preferable  to  a  smaller  number  of  larger  ones,  because  the 
proportion  of  the  area  of  adhesion  between  steel  and  concrete 
to  the  sectional  area  of  steel  is  greater  in  the  former  case.  This 
would  apparently  be  attained  in  such  systems  as  use  wire 
fabrics.  But  the  disadvantage  of  the  smaller  reinforcement  is 
the  greater  possibility  of  corrosion  and  consequent  failure. 
The  wire  fabrics  have  the  further  disadvantage  that  they  are 
easily  displaced  in  the  process  of  placing  of  concrete — either 
getting  too  low  and  becoming  exposed  to  fire  or  corrosion,  or 
getting  too  high  with  a  corresponding  weakening  of  the  floor. 
Another  point  that  must  be  remembered  in  the  use  of  metal 
fabric,  is  that  the  mesh  shall  be  large  enough  to  permit  a  good 
bond  between  the  concrete  above  and  below  it. 

Reinforcement  in  the  form  of  bars  set  vertically  in  the  concrete 
has  a  tendency  to  shear  through  the  slab  under  heavy  loads. 

The  best  and  most  logical  reinforcement  for  fire-proof  floors 
consists  of  ^  inch  to  f  inch  round  or  square  rods,  either  plain 
or  deformed,  spaced  at  varying  distances  to  suit  the  spans 
and  loads. 

Necessity  for  Longitudinal  Bars. — Where  wire  strands 
or  bars  are  used  for  reinforcement  it  is  essential  that  there 
be  longitudinal  as  well  as  transverse  bars,  for  the  reason  that 
under  heavy  concentrated  loads,  or  when  a  heavy  body  falls 
upon  the  slab  the  concrete  will  crack  between  the  carrying 
bars.  This  can  be  readily  demonstrated  in  testing  a  floor 
slab  without  longitudinal  wires  under  a  drop  test.  When  the 
load  is  uniformly  distributed  the  longitudinal  wires  are  not 
brought  into  play,  but  floor  loads  are  more  often  concentrated 
than  uniformly  distributed. 

Segmental  Concrete  Arches.— For  heavy  warehouse  floors 
the  arched  systems  are  preferable  to  the  flat  systems,  as  the 
concrete  is  thus  used  in  its  strongest  form,  and  less  reinforce- 
ment is  required.  In  warehouses,  also  a  ceiling  formed  of  a 
series  of  arches  is  not  objectionable. 


77 i  FIRE-PROOFING   OF  BUILDINGS. 

For  spans  between  floor  beams  of  5  ft.  or  less,  a  1  to  6  gravel- 
concrete  arch,  3  ins.  thick  at  crown  and  without  any  reinforce- 
ment should  sustain  a  distributed  load  of  1500  Ibs.  per  square 
foot  without  cracking. 

For  spans  exceeding  5  ft.,  the  celebrated  Austrian  experi- 
ments (1891-92)  seem  to  show  that  reinforcing  concrete  with 
small  I-beams  adds  greatly  to  the  strength  of  the  arch,  but 
that  small  rods  or  netting  are  not  of  sufficient  advantage  to 
warrant  the  additional  expense.*  Tests  made  on  arches  of 
8-ft.  span  gave  the  following  results:  Concrete  arch,  3f  ins. 
thick,  9^  ins.  rise,  broke  at  1130  Ibs.  per  square  foot.  A  Monier 
arch  (wire  netting),  1[|  ins.  thick,  10J  ins.  rise,  or  about  half 
the  thickness  of  the  concrete  arch,  failed  at  1217  Ibs.  per  square 
foot.  Brick  arch,  5^  ins.  thick,  9.85  ins.  rise,  failed  at  885  Ibs. 
per  square  foot.  A  hollow  brick  arch,  3{%  ins.  thick,  5ri  ins. 
rise,  failed  at  401  Ibs.  per  square  foot.  A  13-ft.  span,  con- 
crete arch,  3H  ins.  thick,  15J  ins.  rise,  failed  at  812  Ibs.  per 
square  foot.  Melan  arch,  3J  ins.  thick,  11.4  ins.  rise,  broke 
at  3360  Ibs.  per  square  foot.  The  Melan  arch  had  I-beams 
3^  ins.  deep,  spaced  40  ins.  apart.  The  structure  was  one 
year  old  when  tested. 

While  there  are  several  patented  arched-floor  systems,  a 
plain  concrete  arch  can  be  built  by  any  one,  and  if  reinforcing 
is  desired  for  wide  spans,  plain  rods  or  bars,  small  tees  or  chan- 
nels, and  various  forms  of  netting  may  be  used  without  in- 
fringing on  any  patents.  The  principal  advantages  of  the 
patented  arch  systems  lie  in  the  matter  of  economy  in  putting 
the  arches  in  place. 

The  concrete  arch,  considered  as  a  monolithic  construction, 
if  built  of  stone  concrete,  is  superior  to  the  brick  arch. 

The  cinder-concrete  arch  is  inferior  only  in  point  of  strength. 
Such  an  arch  should  be  at  least  4  inches  deep  at  the  crown, 
and  the  rise  should  be  not  less  than  one-eighth  of  the  span. 
The  strength  of  such  an  arch  for  ordinary  cinder  concrete 
would  be  about  the  same  as  that  of  a  6-inch  segmental  tile 
arch  of  same  span,  as  given  in  table  on  p.  755. 

All  arched  systems  require  tie-rods  between  the  beams  to 
take  up  the  thrust  of  the  arches,  the  same  as  for  tile  arches, 
see  p.  804. 

The  Roebling  Arch-floor  System. — This  system  is  now  so 
widely  known  as  to  require  but  brief  description.  It  has  been 

*  See  Architecture  and  Building,  Jan.  4,  1896. 


ARCHES  775 

used  in  many  of  the  best  buildings  in  the  Eastern  States,  and 
has  proven  one  of  the  strongest  floor  systems  in  use,  and  when 
the  bottoms  of  the  steel  beams  are  protected  as  in  Types  2 


(  %  Steel  Rod  woven  into 
V  No.  20  Wire  Lathing 

FIG.  34. — Type  1.     For  buildings  requiring  level  ceilings. 

and  4  is  unquestionably  first-class  fire-proof  construction.  The 
three  principle  types  of  floor  construction  are  shown  by  Figs. 
34,  35,  and  36.  Type  3  is  similar  to  Type  2,  but  has  a  sus- 


FIG.  35. — Type  2.     Warehouse  construction. 

pended  flat  ceiling  in  addition,  which  may  be  adjusted  at  any 
level  below  the  floor  beams  to  admit  piping,  etc.,  as  may  be 
desired.  The  distinctive  feature  of  this  system  is  the  per- 
manent wire  centering  which  is  always  erected  in  advance  of 
the  concreting,  thus  enabling  the  work  to  progress  continu- 


776 


FIRE-PROOFING   OF   BUILDINGS. 


ously.     The   centering   is   made   of   the   proper   size   and   form 
at  the  factory,  so  that  it  is  readily  placed  in  position. 

The    advantages   of   this   centering,    aside   from   the    saving 
over  wood  centres,  and  the  rapidity  with  which  it  can  be  put 


18    Steel  Rod,  "woven 
into  Wire  Lathing 


FIG.  36. — Type  2.      Warehouse  construction  with  sleeperd  depressed. 

* 

in  place,  are,  that  it  allows  the  superfluous  water  to  drip  out  of 
the  concrete  as  soon  as  it  is  in  position  arid  it  also  forms  a 
valuable  safeguard  against  the  falling  of  workmen,  as  it  is 
sufficiently  strong  to  sustain  a  considerable  load  of  itself. 


x  %  Steel  Spaces 
!     ^  2'  x  2"x%'T.  24 'C.  to  0. 


FIG.  37. — Type  4.     For  spans  exceeding  10  feet. 

Sections  of  the  Roebling  arch  floor  have  been  tested  to  from 
1400  to  4100  Ibs.  per  square  foot  without  failure. 

With  spans  of  from  5  to  6  ft, ,  the  author  considers  that  they 
will  support  1000  Ibs  to  the  square  foot  with  an  ample  factor 
of  safety. 

The  maximum  spans  that  are  desirable  for  the  different 
types  are  given  hi  the  illustrations.  Type  4,  Fig.  37,  however, 


ARCHES. 


has  been  installed  with  success  up  to  18  ft.  between  18-inch 
beams. 

Wide  spans  require  a  corresponding  depth  at  the  haunches, 
as  the  clear  j-ise  of  the  arch  for  Types  1,  2,  and  3  should  be 
1£  ins.  per  foot  of  span.  In  the  18-foot  span,  above  mentioned, 
the  clear  rise  above  beam-flange  was  16  ins.  For  14-foot 
spans  between  18-inch  beams,  the  rise  would  be  14  ins. 

The  following  table,  prepared  by  the  Roebling  Construction 
Company,  gives  the  weight  per  square  foot  for  different  spans: 


When  concrete  is 
to  be  leveled 
above  underside 
of  floor  beams 
to  a  height  of 

Maximum  spacing 
of  iron  floor 
beams  (independ- 
ent of  size  of 
beams)  should 
not  exceed 

Thickness  of 
crown  at  centre 
of  arch. 

Weight  per  sq. 
ft.  including 
only  concrete 
and  wire. 

8" 

4'   0" 

3" 

33  Ibs. 

9" 

4'   6" 

3" 

34  Ibs. 

10" 

5'   0" 

3" 

36  Ibs. 

VI" 

6'   0" 

3" 

41  Ibs. 

15" 

V   6" 

3" 

47  Ibs. 

The  weights  given  are  for  concrete  to  the  level  indicated  in 
the  first  column,  with  a  3-inch  crown  and  for  all  wire  con- 
struction, including  arch  wire  for  floors  and  lathing  for  ceiling. 

Flat  Reinforced  Floors. — The  floors  consist  of  a  slab  of 
concrete,  varying  in  thickness  according  to  span  and  load  set, 
between  the  steel  floor  beams  and  reinforced  near  the  lower 
surface  with  steel  in  one  of  the  shapes  referred  to  on  p.  772, 
and  further  described  under  each  system.  For  ordinary  loads 
the  thickness  of  the  slab  should  be  at  least  -g-  inch  for  each 
foot  of  span,  with  a  minimum  thickness  of  3J  inches.  Thinner 
slabs  have  been  used  but  they  should  be  carefully  studied  for 
each  condition. 

The  floor  slabs  are  not  usually  of  the  same  depth  as  the 
beams  supporting  them.  The  position  of  the  slab  will  there- 
fore determine  the  character  of  the  ceiling.  When  the  bottom 
of  the  slab  is  placed  at  or  below  the  lower  flanges  a  flat  ceiling 
is  obtained,  and  the  space  over  the  slab  must  be  filled  with 
some  incombustible  material  to  the  underside  of  the  flooring, 
thus  often  increasing  the  weight.  When  the  slab  is  set  at  the 


778 


FIRE-PROOFING    OF    BUILDINGS. 


^op  flange,  a  paneled  ceiling  is  obtained,  unless  a  hung  ceiling 
is  provided. 

The  type  of  reinforcement  used  is  generally  the  distinguish- 
ing feature  of  the  different  so-called  systems,  but  the  principles 
involved  is  the  same  in  all. 

Expanded  Metal. — This  material  is  now  so  well  known 
as  to  require  but  little  description.  The  diamond  mesh  shown 


FIG.  38. — Expanded  Metal,  Diamond  Mesh. 

by  Fig.  38  is  used  in  floor  construction.  For  this  purpose 
the  3-inch  mesh  is  used,  the  mesh  being  designated  by  the 
width  of  the  diamonds.  It  comes  in  sheets  8  or  12  feet  long, 
and  varying  from  3  to  6  feet  in  width,  according  to  the  width 
of  the  mesh.  It  is  made  from  a  soft,  tough  steel  of  fine  tex- 
ture, varying  in  thickness  from  No.  16  to  No.  4  Stubbs  gauge. 

When   used   between   I-beams  without   other  reinforcement, 
the  spans  usually  vary  from  5  to  6  feet,  although  panels  11  feet 


FIG.  39. — Expanded  Metal  Floor  Construction. 

wide  between  beams  have  been  constructed.  Of  the  numerous 
styles  of  floor  construction  possible  with  expanded  metal 
reinforcement,  that  shown  in  Fig.  39  is  most  generally  used 
and  L  recommended.  At  the  right  hand  of  the  figure  is  shown 
the  construction  when  steel  beams  are  used,  and  at  the  left 
hand  when  reinforced  concrete  beams  are  employed. 

The  advantages  of  expanded  metal  as  reinforcement  are 
claimed  to  be  a  better  arrangement  in  the  concrete  than  an 
equal  amount  of  material  in  any  other  form;  great  efficiency 


REINFORCED    FLOORS. 


779 


in  the  carrying  of  concentrated  loads,  due  to  the  obliquity 
of  the  strands;  a  uniform  distribution  of  small  sections  at  fre- 
quent intervals  as  preferable  to  larger  sections  at  greater  in- 
tervals; an  increased  ultimate  strength  and  high  elastic  limit 
due  to  the  method  of  manufacture,  thus  combining  the  advan- 
tages of  a  low-carbon  steel  with  high  ultimate  strength;  and 
a  mechanical  bond  with  the  surrounding  concrete. 

Welded  Metal  Fabric.— The  Clinton  Wire  Cloth  Company 
manufacture  a  welded  fabric  or  mesh  which  has  been  extensively 
used  in  the  United  States  as  a  reinforcement  for  concrete  con- 
struction of  all  kinds. 

Fig.  40  shows  the  general  style  of  the  fabric,  although  the 
meshes  and  wires  can  be  varied  to  an  almost  endless  extent, 

_  if    . .  i   .    n 


I 


FIG.  40. 


the  only  limit  being  as  to  mesh,  1  in.  being  about  the*  closest 
that  can  be  made. 

The  advantage  claimed  for  this  fabric  as  reinforcement  for 
slab  construction  is  that  the  carrying  wires  may  be  varied, 
both  in  size  and  spacing,  to  give  the  necessary  area  for  any 
given  weight  and  span,  and  the  distributing  or  cross  wires  may 
also  be  varied  in  the  same  way.  The  direction  of  the  wires 
coincides  with  the  line  of  stress,  so  that  there  is  no  tendency 
to  distort  the  rectangle  of  the  mesh. 

The  cross  wires,  being  welded  to  the  carrying  wires,  are  rigidly 
held  in  place  and  prevent  the  latter  from  slipping  in  the  con- 
crete. 

In  the  meshes  most  commonly  used  the  carrying  wires  vary 
from  No.  10  to  No.  3,*  and  from  1  to  4  ins.  on  centres,  while 
*  Washbum  &  Moen  gauge. 


780 


FIRE-PROOFING  OF  BUILDINGS. 


the  distributing  wires  vary  from  No.  11  to  No.  6,  and  from 
3  to  12  ins.  on  centres. 

Welded  metal  is  manufactured  in  long  rolls,  and  by  its  use, 
all  joints  and  laps  are  avoided,  and  a  floor  can  be  made  with 
a  continuous  metallic  bond  from  wall  to  wall  (i.e.,  when  the 
mesh  is  laid  over  the  top  of  the  steel  beams). 

The  width  of  rolls  varies  from  48  to  86  inches. 

This  material  can  be  used  in  all  the  ways  in  which  other 
meshes  are  used,  and  the  author  understands  can  be  purchased 
by  any  responsible  party.  Mr.  E.  Lee  Heidenreich  states  that 
he  has  obtained  remarkable  results  with  this  material  as  to 
strength  and  lightness. 

Lock-woven  Fabric.* — -This  fabric  is  woven  from  high 
carbon  steel  wires,  crossing  each  other  at  right  angles,  and 


*  9  Cross 


-Width  - 


Wires 


LOCK-WOVEN  STEEL  FABRIC 

FIG.  41. 

locked  at  the  intersection  by  means  of  No.  9  wire  twisted  around 
the  strands,  as  shown  in  Fig.  41. 

The  standard  fabric  is  56  ins.  wide,  and  is  put  up  in  rolls  of 
330  to  500  lineal  feet,  or  of  any  shorter  lengths  desired. 

The  longitudinal  strands  are  No.  10  wire,  B.  &  S.  gauge, 
4  ins.  on  centres,  and  the  cross  strands  No.  9  wire,  6  ins.  on 
centres.  The  standard  fabric  weighs  two-tenths  pounds  per 
square  foot. 

This  fabric  can  be  woven  of  any  gauge  wire  and  with  any 


*  Manufactured  and  for  sale  by  W.  N.  Wight  &  Co.,  New  York. 


REINFORCED  FLOORS. 


781 


larger  mesh,  either  square  or  oblong,  that  may  be  required. 
It  can  also  be  made  up  to  88  ins.  wide. 

It  is  sold  either  bright  or  galvanized — the  galvanized  costs 
but  1J  cents  per  square  yard  more  than  the  bright. 

This  fabric  has  the  same  advantage  as  the  welded  and  tie- 
lock  fabrics  in  that  it  can  extend  from  wall  to  wall,  thus  mak- 
ing a  continuous  tie. 

It  is  used  to  best  advantage  in  a  construction  like  Fig.  42, 
but  may  be  used  in  any  way  suitable  to  an  open  mesh  fabric. 


TYPZA. 

FIG.  42. 

For  spans  exceeding  8  ft.,  the  fabric  may  be  used  in  two 
thicknesses,  one  directly  over  the  other,  and  with  the  strands 
staggered,  this  arrangement,  however,  being  covered  by  a 
patent  controlled  by  tJie  manufacturers. 

Fig.  43  shows  a  system  recommended  by  the  manufacturers 
for  apartment  houses,  hotels,  etc.,  or  for  any  building  v/here 


Ml  iiiil 

:li!t 


fltyt/ 

FIG.  43. 

the  loads  are  not  excessive.  The  special  advantage  of  this 
system  is  that  it  gives  a  level  ceiling  combined  with  strength 
and  comparatively  light  weight. 

The  manufacturers  issue  a  folder  showing  various  forms  of 
floor  arches  that  may  be  constructed  with  their  fabric.  Most 
of  these  devices  have  been  patented,  but  all  are  free  to  those 
who  buy  the  fabric. 

Strength. — Systems  1,  2,  and  3  have  been  approved  by  the 
Bureau  of  Buildings  of  the  City  of  New  York  for  the  spans 
and  live  loads  indicated. 


782 


FIRE-PROOFING    OF   BUILDINGS. 


In  Sept.,  1902,  six  floor  arches,  reinforced  with  lock- woven 
fabric,  were  tested  for  strength  by  the  Bureau  of  Buildings, 
Borough  of  Manhattan.*  An  arch  like  Fig.  42,  44  ins.  thick 
and  6-foot  span,  was  loaded  to  1452  pounds  per  square  foot, 
and  one  of  8  ft.  span,  5  ins.  thick,  to  1412  pounds  per  square 
foot.  The  latter  arch  had  two  layers  of  fabric. 

An  arch  like  Fig.  43,  with  concrete  4^  ins.  thick  and  6-foot 
span,  slowly  failed  under  1165  pounds  per  square  foot. 


FIG.  44. 

An  arch  like  Fig.  44,  6-foot  span,  was  loaded  to  3018  pounds 
per  square  foot  without  breaking. 

Steel  Wire  Reinforcement. — The  American  Steel  and 
Wire  Co.,  of  Chicago,  has  placed  on  the  market  a  wire  fabric 
for  reinforcement  of  fire-proof  floors.  Two  types  are  being 
manufactured  for  this  purpose,  known  as  "  Triangular  Mesh/' 
Fig.  45,  and  "Square  Mesh,"  Fig.  46. 

The  triangular  mesh  is  built  up  of  either  stranded  or  solid 
longitudinal  or  tension  members,  with  the  cross  or  bond  wires 
running  diagonally  across  the  width  of  the  fabric.  The  square 
mesh  is  similar  to  that  made  by  other  manufacturers  of  this 
style,  but  the  longitudinal  or  tension  members  may  be  either 
single  or  stranded  wires.  The  cross  or  bonded  wires  in  this 
case  run  at  right  angles  writh  the  tension  members. 

The  manufacturers  recommend  the  use  of  the  triangular 
mesh,  as  it  is  claimed  that  it  not  only  affords  the  most  even 
distribution  of  the  steel,  reinforcing  in  every  possible  direction, 
but  also  provides  a  better  mechanical  bond  between  the  steel 
and  concrete.  Tests,  made  by  the  manufacturers,  would  seem 
to  show  that  the  triangular  mesh  have  a  decidedly  higher  ten- 


*  Complete  details  of  these  tests  are  published  in  Insurance  Engineering 
for  Oct.,  1902. 


REINFORCED  FLOORS. 


783 


sional  value  than  the  square  mesh  of  the  same  weight  per  square 
foot.     The  cost  of  the  two  types,  of  equal  weight,  is  said  to  be 


ATwWwwv/wV 


FIG.  45. 

the  same.     The   use  of  the  stranded  wire  fabric  is  also  recom- 
mended over  the  single  wire  fabric,  because  of  the  mechanical 


1 


FIG.  46. 


bond  afforded  by  the  stranding  in  addition  to  the  adhesion  of 
the  concrete  to  the  steel. 


784  FIRE-PROOFING   OF    BUILDINGS. 

For  floor  reinforcement  this  fabric  is  used  in  the  same  manner 
as  any  of  the  other  fabrics  previously  described,  and  as  indi- 
cated in  Figs.  31,  34,  39,  42,  and  43. 

Of  the  triangular  mesh  the  manufacturers  offer  88  stock 
styles,  giving  variations  in  the  cross-sectional  area  of  the  longi- 
tudinal wires  from  about  0.023  square  inch  to  about  0.36  square 
inch  per  foot  in  width  of  fabric,  or  a  variation  in  weight  per 
square  foot  of  fabric  from  about  0.2  Ib.  to  1.5  Ibs.  These  styles 
vary  in  three  ways:  (1)  The  longitudinal  wires  are  spaced  either 
4  or  2  inches  apart;  (2)  the  longitudinal  wires  consist  either 
of  a  single  wire  or  of  two  or  three  wires  stranded;  and  (3) 
the  cross  or  bond  wires  are  either  No.  14  or  No.  12J  gauge. 
This  great  variety  affords  an  opportunity  for  selecting  very 
closely  the  cross-sectional  area  of  reinforcement  required. 
Special  sizes,  of  larger  areas,  can  be  provided  on  application. 

Of  the  square  mesh  only  the  single  wire  strand  fabric  is  kept 
in  stock,  there  being  28  styles,  representing  2-  and  4-inch 
spacing  of  longitudinal  wires,  of  cross-sectional  areas  varying 
from  0.026  square  inch  to  0.295  square  inch,  and  a  6-  and 
12-inch  spacing  of  No.  12  cross  wires.  The  weight  of  this  fabric 
varies  from  0.13  Ib.  to  1.15  Ibs.  per  square  foot. 

Patented  Systems  of  Flat  Floor  Construction.  —  The 
following  systems  of  floor  construction,  while  based  upon  the 
same  general  principles  as  those  already  described,  are  patented 
and  can  be  used  only  by  the  patentees: 

Roebling  Flat  Construction.  — This  system  was  intro- 
duced by  the  Roebling  Construction  Company  to  meet  the 
demand  for  a  light  economical  floor,  with  greater  spans  between 
the  I-beams  than  is  practicable  for  their  arched  system. 

This  flat  construction  is  a  reinforced  concrete  system,  differ- 
ing from  other  flat  systems  only  in  the  reinforcing  frame.  The 
details  of  construction  are  quite  clearly  shown  in  Fig.  47.  The 
main  tension  members  consist  of  flat  bars,  usually  2  ins.  in 
width  and  varying  from  J  to  J  in.  in  thickness,  according  to 
the  spacing  of  the  beams  and  the  load  to  be  supported.  These 
bars  stand  on  edge  in  the  concrete,  and  are  twisted  at  the  end  to 
lie  flat  on  the  I-beams,  and  are  also  bent  around  the  flange.  The 
bars  are  held  in  position  laterally  by  means  of  spacers,  formed 
from  half-oval  iron,  with  a  hook  at  each  end  to  fit  over  the  bars. 

It  was  the  original  intention  of  the  patentees  to  apply  the 
Roebling  stiffened  wire  lath  to  the  underside  of  the  tension 
bars  by  means  of  lacing  wire,  to  serve  as  a  centering  for  the 


FLAT   CONSTRUCTION. 


785 


concrete,  and  under  certain  conditions  the  wire  centering  ia 
still  used.  When  the  building  is  to  be  erected  in  a  large  city, 
it  has  been  found  more  advantageous  to  use  wood  centering, 
for  the  reason  that  the  concrete  is  not  as  easily  damaged  by 
workmen  walking  over  it  before  it  has  thoroughly  set  as  when 
wire  centering  is  used. 

The  latter,  however,  has  important  advantages  when  the 
work  is  to  be  erected  in  cold  weather,  as  it  permits  the  moisture 
to  drip  away  rapidly  and  prevents  the  concrete  from  being 


X  2\  /\*  Flat  Bar,  Imbedded 

in  Concrete 
%\3/is  Steel  Rod  Spacer 

.—-No.  18  Gal.  Lacing  Wire 


24- 


'  x/6"  Steel  Rod  Spacer 


2*x  */il  Flat  Ba 


FIG.  47. — Roebling  Flat  Construction. 

injured  by  freezing.  In  isolated  places,  where  the  lumber  for 
centering  would  have  to  bo  purchased  new  and  then  disposed 
of  at  a  sacrifice,  the  wire  centering  is  also  the  more  economical. 

Besides  the  type  of  construction  shown  by  Fig.  47  three 
other  types,  differing  principally  in  the  manner  of  supporting 
the  steel  bars,  are  employed. 

In  Type  4  the  tension  bars  are  supported  on  the  bottom 
flange  of  the  I-beams,  so  as  to  give  a  level  ceiling  between  the 
beams.  This  type,  however,  is  not  desirable  when  the  I-beams 
are  more  than  7  ins.  deep. 


786 


FIRE-PROOFING  OF  BUILDINGS. 


When  the  distance  between  the  steel  beams  is  greater  than 
9  or  10  ft.,  the  tension  bars  are  bent  downward  so  as  to  give  a 
sag  of  about  2  ins.  or  more  at  the  center  of  the  span,  as  in  Fig.  48, 
the  spacers  being  used  as  in  Fig.  47.  Type  5  has  been  success- 
fully used  in  spans  up  to  22  ft.  Under  ordinary  conditions, 
however,  considering  both  the  steel  work  and  the  fire-proofing, 
the  most  economical  results  will  be  obtained  when  the  girders 
are  spaced  from  14  to  16  ft.  apart.  With  this  system  a  sus- 
pended ceiling  is  not  necessary  or  desirable. 

The  concrete  used  with  this  system  is  composed  of  high-grade 
Portland  cement,  sharp  sand,  and  clean  cinders,  mixed  ordi- 
narily in  the  proportion  of  1,  2J,  and  6. 


FIG.  48. — Long-span  System.     (Type  5.) 

Adaptation. — This  floor  system  is  particularly  adapted  to 
public  buildings,  offices,  theatres,  schools,  hospitals,  hotels, 
residences,  etc.,  or  where  there  is  no  great  weight  to  be  sup- 
ported, and  the  fire  hazard  is  not  as  great  as  in  stores,  factories, 
etc. 

The  system  can  be  successfully  adapted,  however,  to  stores 
and  warehouses,  but  will  require  shorter  spans  and  heavier 
construction. 

Strength. — The  Roebling  Construction  Company  claims  that 
Type  1  has  a  safe  carrying  capacity,  with  factor  of  safety  of  4, 
of  200  Ibs.  per  square  foot  with  a  span  of  8  ft.,  and  that  Type  5, 
with  a  span  of  16  ft.,  will  safely  support  a  load  of  100  Ibs.  per 
square  foot. 

A  section  of  floor  4  ft.  5  ins.  wide  and  16  ft.  span,  carried 
a  total  load  of  17,250  Ibs.  with  a  deflection  of  only  ^  inch. 

The  Columbian  System.*— This  is  a  flat  concrete  system, 
with  ribbed  steel  bar  tension  members  differing  from  the  system 
previously  described,  principally  in  the  shape  of  the  reinforcing 

*  Controlled  by  the  Columbian  Fireproofing  Co.,  Pittsburgh,  Pa. 


FLAT    CONSTRUCTION. 


787 


bars,  which  are  entirely  different  in  shape  from  those  used  in  any 
other  system,  and  very  much  deeper.  The  general  shape  of  the 
1,  2,  2J,  and  3J  inch  bars  is  shown  by  the  hole  in 
the  stirrup,  Fig.  49;  the  larger  sizes  have  more 
ribs,  as  shown  by  the  reduced  section  at  A. 

The  Columbian  floors  are  made  in  two  styles, 
"long  span"  and  "short  span." 

The  short  span  consists  of  the 
use  of  ribbed  steel  bars  sus- 
pended from  the  steel  beams, 
and  supported  on  edge  by 
means  of  steel  stirrups  which 
have  the  profile  of  the  bar  cut 
in  them,  as  shown  by  Fig.  49,  Fl^49._Stirrups  for 
these  bars  being  surrounded  Bars.  (reduced!, 

by  and  completely  imbedded  in  concrete.     This  type  of  paneled 
construction  is  plainly  shown  by  the  sectional  drawing,  Fig.  50. 

If  a  level  ceiling  beneath  the  beam  is  required,   it  is  con- 
structed independently   of  the  floor   by   means  of   solid   con- 

Cinder  filling  x 


:;p^l 


FIG.  50. 

Crete  ceiling  on  lower  flange  of  beams,  wire  lath  expanded 
metal,  or  any  other  form  of  metallic  lath  upon  which  the  plas- 
tering is  applied. 

In  this  way  all  portions  of  the  steel  are  completely  imbedded 
in  solid  concrete.  The  bottom  flange  of  the  beam,  which  is 
the  most  vulnerable  point,  being  protected  by  a  concrete  slab, 
Fig.  51,  with  insulating  air  space.  Three  sizes  of  bars  are 
used  for  this  floor  construction,  viz.,  2^,  2,  and  1  ins.,  the 
maximum  spacing  of  the  bars  being  24  ins.  The  carrying 
capacity  of  this  floor  is  given  by  the  table  on  page  790. 


788 


FIRE-PROOFING  OF  BUILDINGS. 


The  most  economical  spacing  of  floor  beams  for  this  type  will 
usually  be  6  ft.  for  hotels,  apartment-houses,  and  office-buildings, 
using  1-inch  bars,  and  from  6  to  9  ft.  for  greater  floor  loads, 


Fio.  51. — Showing  Protection  of  Bottom  Flange. 

using  2-  and  2J-inch  bars,  depending  upon  the  load  required  to 
be  carried. 

This  floor  may  be  finished  on  top  in  the  usual  way  by  im- 
bedding nailing  strips  in  cinder  filling,  or  the  floor  strips  may 


FIG.  52. — Long-span  System. 


be  nailed  directly  to  the  concrete  floor,  and  the  filling  omitted. 
The  economy  of  this  type  of  construction  is  that  wall  channels 
are  not  required,  and  beams  may  be  spaced  up  to  9  ft.  centre 
to  centre. 

Long-span   Construction. — In   the   second   type   of  this   con- 
struction,  or  what   is   commonly  known  as  "long   span,"   the 


FLAT  CONSTRUCTION.  789 

rolled  and  ribbed  steel  bars  are  imbedded  in  the  concrete,  as 
in  the  short  span,  and  either  hung  in  specially  formed  stirrups 
or  framed  directly  to  the  beam,  as  shown  by  Fig.  52,  these 
bars  being  anchored  at  intervals  into  the  wall,  and  forming 
a  continuous  tie  across  the  entire  floor  of  the  building,  thus 
making  of  the  entire  floor  a  monolith  of  reinforced  concrete. 
This  permits  of  the  elimination  of  the  floor  beams  between 
girders,  the  monolithic  slab  of  concrete  and  steel  taking  their 
place.  In  this  way  a  level  ceiling  is  obtained  between  girders, 
so  that  increased  head  room  can  be  obtained  with  the  same 
amount  of  masonry,  or  the  same  head  room  with  decreased 
height  of  masonry.  This  is  possible  because  of  the  fact  that 
the  extreme  thickness  of  this  floor  construction  on  a  span  of 
20  ft.  between  beams,  is  but  6J  ins.,  whereas  for  a  span  of 
15  ft.,  with  lighter  load,  the  thickness  of  concrete  may  be 
reduced  to  5  ins.  The  sizes  of  bars  used  in  this  type  of  con- 
struction are  3^,  4J,  5,  and  6  ins.,  giving  respectively  5,  5^v 
6^,  and  7^  ins.  of  concrete. 

Carrying  Capacity. — The  table  on  page  790  gives  the  loads 
that  the  Columbian  Company  guarantees  their  various  forms  of 
floors  will  carry  safely.  They  call  attention  to  the  line  of 
deflection  of  their  1,  2,  and  2J  ins.  bars,  below  which  the  loads 
given  for  the  respective  spans  should  only  be  used  for  ceilings 
or  pitched  roofs. 

This  table  is  compiled  from  actual  tests  on  sections  of  floor, 
vising  a  safety  factor  of  4.  Bars  can  be  spaced  down  to  18 
ins.,  thereby  increasing  the  strength  of  floor,  but  2  ft.  is  the 
maximum  spacing. 

This  construction  is  especially  strong  in  resisting  drop  or 
jarring  loads.  A  ram  weighing  238  Ibs.  was  dropped  from  a 
height  of  8  ft.  on  the  centre  of  a  span  several  times  and  without 
perceptible  effect  on  the  floor.  In  case  of  overloading  the 
floor  will  not  fail  suddenly,  but  the  construction  will  gradually 
bend,  thus  giving  warning  of  danger.  .It  als©  offers  a  great 
resistance  to  concentrated  loads,  which  occur  a't  times  in  build- 
ings, to  an  extent  beyond  what  the  floor  is  designed  to 
carry. 

After  a  fire-  and  water-test  of  three  hours'  duration  made  on 
this  system  in  Boston,  published  in  the  Engineering  News  of 
Nov.  21,  1901,  this  floor  on  a  span  of  11  ft.  3  ins.  carried 
1650  Ibs.  with  deflection  of  only  If  inch.  Before  the  floor  slab 
began  to  show  any  sign  of  failure,  loading  had  to  be  stopped 


790 


FIRE-PROOFING  OF  BUILDINGS. 


SAFE  LOADS  FOR  COLUMBIAN  FLOORS. 
(In  addition  to  the  weight  of  floor  construction.) 


Distance 
between 
Supports. 

Floor  Loads  in  Pounds, 
Uniformly  Distributed. 
Bars  24"  on  Centres. 

Distance 
between 
Supports, 

Floor  Loads  in 
Pounds,  Uniformly 
Distributed. 
Bars  24"  on  Centres. 

6" 
Bar. 

5" 

Bar. 

4i" 
Bar. 

3V 
Bar. 

2V* 

Bar. 

1" 
B*ar. 

1" 

Bar. 

Feet. 

Feet. 

12 

412 

362 

312 

275 

5 

400 

340 

290 

13 

346 

306 

265 

235 

6 

275 

242 

200 

14 

296 

260 

230 

200 

7 

200 

178 

140 

15 
16 

256 
225 

226 
200 

200 
175 

175 

8 
9 

150 
125 

135 

112 
70 

100 

17 

18 

200 
177 

175 
150 

125 

10 
11 

100 

70 

80 

19 

140 

100 

20 

100 

80 

Concrete 
thickness 

7i" 

6i" 

51" 

5" 

4" 

3i" 

3" 

on  account  of  the  fact  that  the  walls  of  the  test  hut  which  car- 
ried the  floor  began  to  crack. 

Dovetail   Corrugated    Sheets    (Fcrroinclave) ,  —  Sheets 
of  thin  steel  corrugated  so  as  to  form  dovetail  grooves  have 


FIG.  53. — Ferroinclave. 

been  used  by  several  parties,  as  a  reinforcement  and  center- 
ing for  concrete  steel,  the  dovetailing  serving  to  unite  the  sheets 
to  the  concrete. 

The  Brown  Hoisting  Machinery  Company  of  Cleveland  have 
patented,  under  the  name  of  ferroinclave,  a  tapered  corruga- 


FLOOR  CONSTRUCTION.  791 

tion  which  is  small  enough  to  hold  hard  mortar,  and  hence 
can  be  plastered  on  the  under  side,  which  is  a  great  advantage. 
Fig.  53  shows  a  partial  section  of  the  ferroinclave  corrugated 
sheets,  reduced  a  little  more  than  one  half,  the  actual  size  of 
the  corrugations  being  ^  in.  in  depth,  and  2  ins.  centre  to  centre 
of  corrugation,  with  an  opening  between  the  edges  of  f  inch. 

The  tapering  of  the  corrugations  is  also  an  advantage,  espe- 
cially for  roofs,  as  it  enables  the  sheets  to  be  lapped  at  the  end 
joints,  so  as  to  make  a  roof  that  will  be  absolutely  tight,  even 
if  water  should  penetrate  the  cement  coating. 

The  principal  advantages  of  corrugated  sheets  for  floor  con- 
struction lies  in  their  ability  to  sustain  the  concrete  (with 
moderate  spans)  before  it  has  set,  thus  saving  the  cost  of 
centering  and  the  time  required  in  putting  it  in  place.  This 
advantage,  however,  appears  to  be  offset  by  the  high  cost  of 
the  sheets  when  they  have  to  be  shipped,  which  brings  the 
cost  of  the  completed  floor  fully  as  high  as  the  average  of  the 
reinforced  concrete  systems,  and  higher  than  some. 

For  roofs,  however,  it  makes  a  light  and  cheap  construction, 
as  the  total  thickness  need  not  exceed  1^  ins.  for  spans  of  4  ft. 
10  ins.,  and  it  only  requires  a  coat  of  asphaltic  paint  over  the 
cement  to  make  the  roof  watertight. 

With  a  good  coat  of  hard  plaster  or  gauged  mortar  on  the 
under  side,  the  iron  will  not  be  affected  by  heat  until  a  con- 
siderable time  has  elapsed,  and  even  if  the  mortar  on  the  under 
side  should  be  more  or  less  dislodged  by  the  streams  of  water, 
it  can  be  replaced,  at  a  very  slight  expense.  Another  advan- 
tage of  ferroinclave  for  roofs  is  that  the  building  can  be  covered 
and  made  watertight  in  the  most  severe  winter  weather  and  the 
cement  can  be  applied  during  the  following  spring. 

Ferroinclave  is  made  in  sheets  20  ins.  wide  and  up  to  10  ft. 
in  length  and  usually  of  No.  24  gauge. 

For  roofs  the  ferroinclave  is  attached  to  purlins  in  the 
same  manner  as  iron  roofing,  the  most  economical  spacing 
of  the  purlins  being  4  ft.  10J  ins.  centre  to  centre,  which 
accommodates  sheets  10  feet  long  with  an  end  lap  of  3  inches. 

For  the  cement  top  coat,  a  mixture  of  one  part  Portland 
cement  to  two  parts  sand,  applied  to  a  thickness  of  f-inch 
above  the  top  of  the  sheets,  is  sufficient  for  roofs.  For  floors 
c.  rich  gravel  or  crushed  stone  concrete  should  be  used,  the 
thickness  being  governed  by  the  span  and  loads  to  be  supported. 

The  following  table  shows  the  ultimate  strength  of  No.  24 


792 


FIRE-PROOFING  OF  BUILDINGS. 


ferroinclave  with  different  thicknesses  of  concrete,  as  deter- 
mined by  actual  tests  with  sheets  20  ins.  wide  and  4  ft.  10*  ins. 
span: 

Thickness  of  1  to  2  mortar  above  the  metal. .   1%'    2"     2|"      3"      3^"      4" 
Ultimate  strength  in  Ibs.  per  square  foot 

(span  4  feet  10i  inches) 615  915  1220  1560  1860  2120 

A  factor  of  safety  of  6  should  be  ample  for  ordinary  loads. 

About  a  million  square  feet  of  ferroinclave  has  thus  far 
been  used  for  floors,  roofing,  and  side  walls.  It  is  especially 
adapted  for  the  walls,  roof,  and  floors  of  large  manufacturing 
plants,  and  may  be  used  to  advantage  for  partitions,  gutters, 
stair  treads,  vats,  water-closets  partition,  and  fire-proof  doors. 

Berger's  "Multiplex  Steel  Plate."  — Fig.  54  shows  a 
section  of  a  corrugated  steel  plate  manufactured  by  the  Berger 


FIG.  54. 

Manufacturing  Company  for  floor  and  roof  construction,  the 
plate  being  an  invention  of  G.  Fugman,  architect.  As  shown 
by  the  illustration,  it  consists  of  a  series  of  vertical  corruga- 
tions of  sheet  steel,  painted  or  galvanized,  ending  at  the  top 
and  bottom  in  three  half  circle  arches,  separating  the  vertical 
sides  of  the  corrugations  from  each  other,  and  giving  stiffness 
to  the  top  and  bottom  of  the  plate. 

This  plate  is  made  with  depths,  D,  of  2,  2J,  3,  and  4  ins., 
and  a  uniform  width  of  2  ins.  between  manifolds.  The  sheets 
are  made  at  present  in  lengths  up  to  8  ft.,  but  the  company 
expects  to  make  greater  lengths  in  the  near  future. 

It  can  be  made  of  any  gauge  of  steel  from  No.  16  to  No.  24, 
but  No.  18  is  as  heavy  as  would  generally  be  required. 

For  floors  and  roofs,  the  corrugated  plate  is  laid  on  top  of 
the  beams  and  the  top  portion  filled  with  concrete  and  leveled 


FLOOR   CONSTRUCTION.  793 

off  about  1  inch  above  the  plate.  For  wood  floors  the  nailing 
strips  may  be  imbedded  in  the  concrete,  the  bottom  of  the 
strips  being  raised  only  about  -J  inch  above  the  top  of  the  plate. 

This  construction  is  very  light  and  strong  and  requires  no 
centering.  It  cannot  be  plastered  underneath,  however,  and 
where  a  plaster  ceiling  is  required  it  must  be  constructed  inde- 
pendently of  the  plate  by  means  of  furring  strips  and  metal 
lath. 

The  weight  of  the  4-inch  plates,  No.  18  gauge,  with  rock 
concrete  leveled  1  in.  above  top  of  plate,  is  about  39  Ibs.  per 
square  foot,  and  the  safe  load  for  an  8-foot  span  is  given  at 
430  Ibs.  per  square  foot. 

While  this  floor  has  several  practical  advantages,  i,t  cannot 
be  considered  as  thoroughly  fire-proof,  on  account  of  the  metal 
being  exposed  on  the  bottom.  However,  with  a  plastered 
ceiling  underneath,  the  iron  would  probably  not  be  affected 
by  any  ordinary  fire  before  the  latter  could  be  controlled. 

Sectional  Systems. — Several  types  of  fire-proof  floor  con- 
struction have  been  devised  that  contemplate  the  use  of  factory- 
made  units  to  be  taken  to  the  building  and  set  in  place  between 
the  steel  beams  without  centering,  or  at  least  very  little  center- 
ing. The  advantages  of  such  system,  if  practicable,  are  obvious. 
Few  of  these  constructions  have,  however,  had  commercial 
success.  The  systems  of  Hyatt,  Pelton,  and  De  Mann  have  dis- 
appeared from  the  market. 

Thacher  Floor  Unit.— The  so-called  Thacher  Floor  Unit, 
shown  in  Fig.  55,  is  the  product  of  the  Concrete-Steel  Engi- 

Granitoid  Floor 


Metaflath  and  plaster 

FIG.  55. 

neering  Co.,  of  New  York.  These  units  are  manufactured  in 
suitable  moulds  of  any  convenient  width  for  handling  (usually 
about  2  feet)  and  allowed  to  set,  preferably  about  a  month  or 
more,  until  they  gain  nearly  full  strength.  Then  they  are  set 
in  place  and  dovetailed  together  with  cement  mortar.  This 
design  gives  a  very  light,  strong  and  economical  noor  and  may 
be  made  for  any  desired  load  or  span. 


794  FIRE-PROOFING  OF  BUILDINGS. 

Waite's  Concrete  Beam.— In  Fig.  56  is  shown  a  type  of 
sectional  floor  construction  that  has  been  used  in  a  number 
of  buildings  by  the  Standard  Concrete-Steel  Co.  of  New  York. 
The  floor  construction  consists  of  a  series  of  concrete  I-beams 
10  or  12  inches  in  depth,  supported  on  the  lower  flanges  of  the 
steel  beams,  which  are  spaced  5  to  7  feet  apart.  The  concrete 
beams  are  set  about  12  inches  apart  and  the  space  between  the 
lower  flanges  is  filled  in  with  a  cinder  concrete  of  same  compo- 
sition as  the  I-beams.  This  produces  a  level  ceiling.  On  the 
tops  of  the  concrete  beams  is  placed  a  metal  fabric  of  small 
mesh  on  which  a  lean  concrete  slab  is  laid.  This  makes  a 
comparatively  light  floor  construction,  because  of  the  large 
spaces  betAveen  concrete  beams. 

The  concrete  I-beams  are  cast  at  the  shop  and  allowed  to 
harden  before  being  sent  to  the  job.  In  the  lower  flange  is 


Beam.Co.veri] 

'Cope  on.Conci 


Rod  Reinforcement 
innel.Reinforcement 


FIG.  56. — Concrete  I  Beams. 

inserted,  as  shown,  a  steel  rod  or  other  small  shape  to  furnish 
the  necessary  tensile  strength.  The  beams  are  cast  to  their 
proper  lengths,  in  accordance  with  the  plans;  and  any  slight 
variations  at  the  job  is  made  up  by  filling  the  space  between 
the  end  of  the  concrete  beams  and  the  web  of  the  steel  beam 
with  the  concrete  used  for  the  steel  beam  covering  between 
concrete  beams. 

A  similar  construction,  consisting  of  a  series  of  T-beams, 
with  lower  flanges  1J"  thick  and  12V  wide,  and  stems  2"  thick 
and  12"  deep,  of  1:4  cinder  concrete,  reinforced  with  T/' 
rods  near  the  flanges,  without  floor  finish  of  any  kind,  success- 
fully withstood  the  fire,  water,  and  load  test  of  the  New  York 
Bureau  of  Buildings  (see  p.  745)  after  having  been  constructed 
28  days. 

Disadvantages  of  Sectional  System. — The  reason  that 
the  sectional  systems  have  not  found  favor  is  the  necessity 


FLOOR  CONSTRUCTION.  795 

for  a  fairly  uniform  spacing  of  beams  throughout  a  structure, 
which  is  generally  impracticable.  Furthermore,  the  casting 
of  the  parts  is  generally  not  commercially  successful,  as  the 
forms,  although  they  may  be  used  repeatedly,  are  more  ex- 
pensive than  the  centering  on  the  job,  and  the  concrete  must 
generally  be  a  richer  and  more  carefully  prepared  mixture, 
to  stand  handling.  Even  with  all  possible  care,  the  breakages 
in  transportation  will  be  considerable. 

Merrick  System. — A  floor  construction  deserving  of  further 
notice  as  fire-proof  is  the  Merrick  System,  described  in  Chap. 
XXIV,  and  shown  in  Fig.  24,  on  p.  SSlv.  The  construction 
there  described  consists  of  stone  concrete  with  a  cinder  concrete 
ceiling  plate.  The  same  construction,  entirely  of  1:  2:  5  cinder 
concrete  between  steel  beams  7'  6"  apart,  has  been  approved 
by  the  New  York  Bureau  of  Buildings  for  loads  of  150  Ibs. 
per  square  foot  after  the  required  fire,  water,  and  load  test. 
(See  p.  745.)  The  concrete  beams  were  3  ins.  thick,  reinforced 
at  the  bottom  with  a  J  in.  rod;  the  ceiling  plate  was  2  ins. 
thick,  and  the  floor  plate  1^  ins.  thick;  the  total  depth  from 
ceiling  surface  to  top  of  floor  plate  was  13^  ins. ;  and  the  con- 
crete beams  were  spaced  24  ins.  on  centres. 

Protection  of  Girders  and  Beams. — No  form  of  floor  con- 
struction can  be  considered  thoroughly  fire-proof  unless  it 
includes  a  protection  of  the  lower  flanges  of  all  steel  beams 
and  girders,  or  provides  for  the  protection  of  all  steel  used  in 
its  construction  or  support.  The  material  used  for  the  pro- 
tective covering  is  generally  the  same  as  that  used  in  the  floor 
construction  itself.  The  principal  materials  are  terra-cotta, 
either  dense,  porous,  or  semi-porous,  and  concrete,  either  of 
cinders,  stone,  or  slag.  Plaster  compositions  have  also  been 
used,  but  are  not  recommended.  (See  p.  743.) 

Beam  protection,  where  the  floor  construction  incases  the 
sides  of  the  beam,  as  in  Figs.  16,  19,  or  43,  should  never  be 
less  than  1  inch  thick.  Where  paneled  ceilings  are  used,  that 
is,  where  the  lower  portion  of  the  beams  is  below  the  lower 
side  of  the  floor  construction,  as  in  Figs.  17,  42,  or  51,  the 
protection  should  be  increased  to  at  least  1^  inches  at  all  points. 

Terra-cotta  Protection.  —  In  the  case  of  terra-cotta,  two 
types  of  protection  are  in  use.  In  one  case  the  blocks  incasing 
the  lower  flanges  of  the  steel  beam  meet  at  the  center  of  the 
flange ;  in  the  other,  they  simply  turn  under  the  edges  of  the  flanges 
and  hold  a  flat  tile  with  beveled  edges  against  the  lower  side 


796 


FIRE-PROOFING  OF  BUILDINGS. 


of  that  flange.  The  former  is  the  better  method,  as  in  the 
latter  the  danger  of  breakage  of  the  part  extending  under  the 
flange,  is  supplemented  by  the  possibility  of  omitting  the  flat 
protection  tile.  The  blocks  incasing  the  lower  flange  may  be 
the  skew-backs  of  the  arch,  or  they  may  be  separate  blocks. 


FIG.  57. 

Different  forms  and  conditions  are  illustrated  in  Figs.  14,  25 
27,  19,  26,  17,  20,  21,  22,  23,  and  16.  Fig.  31  shows  the  entire 
depth  of  beams  protected  by  blocks  on  either  side. 

Girders,  where  they  project  below  the  ceiling  line,  as  is  com- 
monly the  case,  are  much  more  exposed  to  the  effects  of  fire 


FIG.  58 

and  water  than  the  floor  beams,  and  should,  therefore,  have  the 
most  efficient  protection.  As  a  rule,  such  girders  should  be 
provided  with  not  less  than  4  inches  of  terra-cotta  protection 
at  the  sides  and  1-J-  inches  of  solid  tile  under  the  bottom  with  a 
space  of  i  inch  between  the  tile  and  the  beam. 


FLOOR  CONSTRUCTION. 


797 


Figs.  57  and  58  are  typical  of  the  latest  methods  of  protect- 
ing girders  by  means  of  hollow  tile.  The  bottoms  of  the  skews 
(Fig.  57)  are  prevented  from  spreading  by  wire  ties  placed  in 
the  end  joints  between  the  soffit  tile  and  hooked  into  the  round 
holes  in  the  skew-backs.  Single-beam  girders  are  usually  pro- 
tected, as  shown  by  Figs.  26  and  59,  the  latter  figure  showing 


FIG.  59. 

more  particularly  the  protection  of  a  beam  at  the  side  of  an 
opening  in  the  floor. 

Concrete  Protection, — A  more  thorough  incasing  of  the 
webs  and  lower  flanges  of  beams  and  girders  can  be  accom- 
plished by  the  use  of  concrete.  The  superior  fire-proof  character 
of  cinder  concrete  makes  it  the  best  material  for  that  purpose. 
If  of  sufficient  thickness  and  properly  applied,  it  will  hold 
securely  around  the  flanges  of  beams  and  girders  without  rein- 
forcement. But  where  it  is  less  than  2  inches  thick  wire  or 
metal  lath  wrapped  around  the  flange  should  be  imbedded 
in  it.  Different  forms  of  concrete  protection  are  shown  in 
Figs.  35,  36,  and  37. 

In  Fig.  51  the  soffit  of  the  beam  is  protected  by  a  concrete 
slab  with  an  insulating  air  space.  This  method  is  one  that 
may  be  advantageously  used  for  the  protection  of  girders. 
A  fire  test  made  in  the  Butterick  Building,  New  York,  on  this 
form  of  girder  protection  thoroughly  established  its  efficiency. 


798 


FIRE-PROOFING  OF  BUILDINGS. 


A  typical  girder  protection  in  cinder  concrete  is  shown  in 
the  Roebling  method  in  Fig.  60. 

Hung  ceilings  are  sometimes  used  as  the  protection  for  the 
steel  beams.  This  is  very  bad  practice,  as  these  ceilings  are 


FIG.  60. 


more  than  likely  to  collapse  in  a  severe  fire.  The  experience 
in  the  Baltimore  fire  confirms  this  belief. 

Trusses.  —  Where  steel  trusses  are  used  to  support  the  roof 
or  several  stories  of  a  building  it  is  very  important  that  they 
be  protected,  not  only  from  heat  sufficient  to  warp  them,  but 
so  that  they  will  not  expand  sufficient  to  affect  the  vertical 
position  of  the  columns  by  which  they  are  supported. 

The  following  description  of  the  covering  of  the  trusses  in 
the  new  Tremont  Temple,  Boston,  furnishes  a  good  illustration 
of  the  way  in  which  this  should  be  accomplished: 

"The  steel  girders  were  first  placed  in  terra-cotta  blocks  on 
all  sides  and  below,  these  blocks  being  then  strapped  with  iron 
all  around  the  girders,  and  upon  this  was  stretched  expanded 
metal  lathing,  covered  with  a  heavy  coating  of  Windsor  cement  ; 
over  this  comes  iron  furring,  which  receives  a  second  layer  of 
expanded  metal  lath,  the  latter,  in  turn,  receiving  the  finished 
plaster.  There  is,  consequently,  in  this  arrangement  for  fire 
protection,  first,  a  dead  air-space,  then  a  layer  of  terra-cotta, 
a  Windsor  cement  covering,  another  dead-air  space,  and  finally, 
the  external  Windsor  cement." 

Numerous  shapes  of  terra-cotta  tiles  are  made  for  casing  the 


FLOOR   CONSTRUCTION. 


799 


structural  shapes  commonly  used  in  steel  trusses.  Some  of 
these  are  shown  by  Fig.  61.  The  tiles  should  always  be  secured 
in  place  by  metal  clamp's  passing  entirely  around  the  envelope, 
or  better  still,  by  wrapping  with  wire  lath.  The  tiling  should 
then  be  plastered  with  hard  wall  plaster. 

Trusses  may  also  be  fire-proofed  by  completely  incasing  the 
several  members  in  cinder  concrete,  either  with  or  without 
metal  reinforcement. 


SECTION  OF  BRACING 
SEQJJON  OF  STRUT 

FIG.  61. — Tiles  for  Protecting  Steel  Trusses. 

Where  trusses  are  to  be  fire-proofed,  the  additional  weight 
must  be  provided  for  in  the  strength  of  the  truss. 

Steel  Framing  for  Fire-proof  Floors.  — Before  the 
framing  plans  of  a  building  can  be  made,  it  is  necessary  to 
decide,  in  a  general  way,  upon  the  system  of  floor  construction 
or  fire-proofing  that  will  be  employed;  thus  if  any  of  the  long- 
span  systems,  such  as  the  Herculean,  Johnson,  and  many  of 
the  concrete  systems,  is  to  be  adopted,  the  girders  should  be 
spaced  so  that  the  floor  construction  will  span  between  them, 
-without  floor  beams,  as  shown  in  Fig.  62,  while  if  an  ordinary 
flat  tile  arch  is  to  be  used,  floor  beams  will  be  required,  spaced 
from  5i  to  9  ft.  apart,  and  these  beams  must  be  supported  by 
girders,  as  indicated  in  Fig.  63. 

When  there  are  no  floor  beams,  a  strut  beam  should  be 
riveted  between  the  columns,  as  in  Fig.  62,  to  hold  the  latter 
in  place  during  erection  and  to  stiffen  the  building. 

It  should  be  remembered  that  with  floor  beams  spaced  not 
over  7  ft.  from  centres,  almost  any  system  of  floor  construction 
may  be  employed,  while  if  the  floor  beams  are  omitted,  one  must 
select  from  but  a  few  systems. 

With  any  form  of  filling  between  beams  or  girders,  less  steel 


800 


FIRE-PROOFING  OF  BUILDINGS. 


I'f 

(^.Column 

Girder 

1 

\       t 

1,, 

\     ' 

'I 

i 

!         ,      r 

t 

If 

ii 

1 

i 

2 

w 

•d' 

1 

e 

1 

1 

CO 

"S      I 

^ff» 

0 

II 

16  to  20'—  - 
Girder 

—  ,  

P 

ii 

d 

! 

[I 

il    ~^ 

,P 

[j 
FIG.  62. — Typical  Framing  for  Long-span  Constructions. 


J 

"IxColumn 

]                Girder            f 

i                Pr 

I 

(     ^ 

1           —  T  

I  N 

if 

il 

Tie  Rod 

.,  ^ 

- 

Tie  Rod 

-, 

/  . 

f/  .. 
.66  ^ 

— 

11  . 

_ 

Girder 

IL. 

u 

~ 

L 

-J 

FIG.  63,—Typical  Steel  Framing  for  Short-span  Arches. 


FLOOR   CONSTRUCTION.  801 

will  be  required  for  moderate  spans  of  beams  or  girders  than 
when  they  are  excessive. 

Computations  for  the  Steel  Framing. — The  computa- 
tions for  the  steel  beams  and  girders  of  a  fire-proof  floor  are 
very  much  the  same  as  for  a  wooden  floor,  viz..  first  estimating 
the  load  or  loads  which  any  given  beam  will  be  required  to 
support  and  then  finding  the  necessary  size  of  beam  to  support 
the  load.  The  dead  load  for  any  fire-proof  floor  may  be  esti- 
mated with  sufficient  accuracy  by  means  of  the  data  given 
in  tliis  chapter  in  connection  with  the  different  systems  of 
floor  construction.  The  dead  load  should  include  weight  of 
beams,  weight  of  fire-proofing,  including  all  concrete  filling, 
weight  of  plastering,  furring,  and  lathing,  nailing  strips  and 
flooring. 

The  live  loads  may  be  estimated  by  means  of  the  data  given 
in  Chapter  XXI. 

Example. — The  best  arrangement  for  the  posts  in  a  retail 
store  is  18  ft.  on  centres  in  one  direction,  and  19  ft.  6  ins.  in 
the  other.  It  is  decided  to  run  the  girders  as  shown  by  Fig.  63, 
and  to  put  a  beam  opposite  each  column  and  two  between; 
what  size  of  beams  and  girders  will  be  required,  using  an  ordi- 
nary end- arch  construction  between  the  beams? 

Ans. — From  the  table  on  page  762,  we  find  that  the  least  depth 
of  arch  which  it  is  desirable  to  use,  is  10  in.,  but  as  we  will 
probably  have  to  use  12-inch  beams  it  will  be  better  to  figure 
on  a  12-inch  arch,  as  this  will  give  less  filling  on  top.  The 
wreight  of  the  12-inch  arch  will  be  about  39  Ibs.  per  square  foot. 
We  shall  probably  require  2  ins.  of  concrete  filling  on  top,  which 
will  weigh  16  Ibs.,  and  1£  ins.  of  light  filling  between  nailing 
strips,  weighing,  say  9  Ibs.  The  flooring  and  nailing  strips  will 
weigh  about  4  Ibs.,  the  plastering  on  ceiling  5  Ibs.,  and  we  must 
allow  at  least  6  Ibs.  per  square  foot  for  the  weight  of  the  beams 
themselves.  These  make  a  total  dead  weight  of  79  Ibs.  per 
square  foot.  The  live  load  for  a  retail  store  should  be  taken 
at  150  Ibs.  per  square  foot — making  a  total  load  per  square  foot 
on  the  beams  of  229  Ibs.  The  total  load  that  each  beam  must 
be  capable  of  supporting  will  be  6V  X  18' X 229  Ibs.  =  13.4  tons, 
which  is  assumed  to  be  uniformly  distributed.  From  the 
table,  p.  516,  we  find  that  this  load,  with  a  span  of  18  ft.,  will 
require  either  a  12-inch,  50-lb.  beam,  or  a  15-inch,  42-lb.  beam. 
The  latter  will  be  both  stronger  and  cheaper,  but  will  increase 
the  thickness  of  the  floor  by  3  ins.  and  require  additional  filling. 


802  FIRE-PROOFING  OF  BUILDINGS. 

The  girder  must  support  two  concentrated  loads  of  13.4  tons 
each.  On  p.  514  it  is  stated  that  when  a  beam  supports  two 
equal  loads  applied  one-third  of  the  span  from  each  end,  the 
equivalent  uniformly  distributed  load  may  be  found  by  multi- 
plying one  load  by  2f.  Multiplying  13.4  by  2f  we  have*  35.73 
tons  as  the  equivalent  distributed  load  on  the  girder,  to  which 
should  be  added  the  weight  of  the  girder.  This  requires  a 
24-inch  80-lb.  beam. 

If  instead  of  using  tile  arches  between  beams,  6^  ft.  apart, 
we  conclude  to  use  the  Herculean  or  Johnson  construction 
spanning  from  girder  to  girder,  we  should  frame  our  floor  as  in 
Fig.  62.  For  this  span  we  would  require  10-in.  tile,  weighing 
55  Ibs.  per  foot.  Allowing  8  Ibs.  for  1  in.  of  concrete,  9  Ibs.  for 
filling,  4  Ibs.  for  flooring  and  strips,  and  5  Ibs.  for  plastering, 
we  have  81  Ibs.  as  the  dead  load  per  square  foot  (we  have 
added  nothing  for  weight  of  girder,  as  this  will  be  fully  offset 
by  portions  of  floor  not  loaded).  The  live  load  per  square  foot 
will  be  150  Ibs.  as  before,  and  the  total  load  to  be  supported 
by  the  girder  18'Xl9'  6"X231  Ibs.  =  40.5  tons,  which  will  re- 
quire a  24-inch  80-lb.  beam;  hence  by  this  arrangement  we 
save  the  weight  of  the  floor  beams,  but  a  6-inch  strut  beam 
should  be  placed  between  the  columns,  as  in  Fig.  62.  The 
calculations  for  any  other  floor  construction  are  made  exactly 
as  above,  the  variations  being  only  in  figuring  the  dead  weight 
of  the  construction. 

Tables  for  Floor  Beams. — It  is  a  difficult  matter  to  prepare 
tables  showing  the  size  of  steel  beams  required  for  fire-proof 
floors  that  may  be  generally  used,  for  the  reason  that  such 
beams  are  often  irregularly  spaced,  a-nd  because  of  the  wide 
va  iation  in  the  dead  loads.  The  following  tables,  however, 
may  be  used  in  making  approximate  estimates  and  in  checking 
the  computations  for  any  particular  floor.  The  sizes  of  I-beams 
given  may  be  safely  used  where  the  total  live  and  dead  load 
does  not  exceed  the  value  given  in  the  headings.  The  total 
load  should  include  sufficient  allowance  for  the  weight  of  any 
partitions  that  the  floor  beams  may  be  called  upon  to  support. 

Tie-rods. — In  all  segmental  arches  and  such  other  types  in 
which  a  thrust  is  exerted  against  the  beams,  tie-rods  must  be 
provided  to  prevent  the  beams  from  being  pushed  apart,  and 
especially  to  prevent  the  outer  bays  from  spreading.  They 
should  run  from  beam  to  beam  from  one  end  of  the  building 
to  the  other.  If  the  outer  a-rches  spring  from  an  angle,  as  in 


FLOOR    CONSTRUCTION. 


SOS 


TABLE  L— SIZE  AND  WEIGHT  OF  I-BEAMS  FOR  FLOORS 
IN  OFFICES,  HOTELS,  AND  APARTMENT-HOUSES. 

Total  load,  120  pounds  per  square  foot. 


Span  of 
Beams 
in  Feet. 

Distance  between  Centres  of  Beams. 

4.V  Feet, 

5  Feet. 

5*  Feet. 

6  Feet. 

7  Feet. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

10 

6  12.i 

6  12* 

6  12* 

6  12* 

7  15 

11 

6  12* 

6  12^ 

7  15 

7  15 

7  15 

12 

6  12* 

7  15 

7  15 

7  15 

8  18 

13 

7  15 

7  15 

7  15 

8  18 

8  18 

14 

7  15 

8  18 

8  18 

8  18 

9  21 

15 

8  18 

8  18 

8  18 

9  21 

9  21 

16 

8  18 

9  21 

9  21 

9  21 

10  25 

17 

9  21 

9  21 

9  21 

10  25 

10  25 

18 

9  21 

9  21 

10  25 

10  25 

12  31* 

19 

9  21 

10  25 

10  25 

10  25 

12  31* 

20 

10  25 

10  25 

12  31* 

12  31* 

12  31* 

21 

10  25 

12  31* 

12  31* 

12  31* 

12  31* 

22 

10  25 

12  31* 

12  31* 

12  31* 

15  42 

23 

12  31* 

12  3H 

12  31* 

12  31* 

15  42 

24 

12  31* 

12  3U 

12  31* 

15  42 

15  42 

25 

12  31* 

12  3U 

15  42 

15  42 

15  42 

TABLE  II.— SIZE  AND  WEIGHT  OF  I-BEAMS  FOR 
FLOORS  IN  RETAIL  STORES  AND  ASSEMBLY 
ROOMS. 

Total  load,'  200  pounds  per  square  foot. 


Span  of 


Distance  between  Centres  of  Beams. 


in  Feet. 

4*  Feet, 

5  Feet. 

5*  Feet. 

6  Feet, 

7  Feet. 

ins.   Ibs. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

iris.  Ibs. 

10 

7  15 

7  15 

7  15 

8   18 

8  18 

11 

7  15 

8  18 

8  18 

8   18 

9  21 

12 

8  18 

8  18 

9  21 

9  21 

9  21 

13 

8  18 

9  21 

9  21 

10  25 

10  25 

14 

9  21 

9  21 

10  25 

10  25 

12  31* 

15 

9  21 

10  25 

10  25 

12  31* 

12  31* 

16 

10  25 

10  25 

12  3H 

12  3H 

12  31* 

17 

10  25 

12  31* 

12  31* 

12  31* 

12  40 

18 

12  31* 

12  31* 

12  31* 

12  40 

12  40 

19 

12  31-i- 

12  31* 

12  40 

12  40 

15  42 

20 

12  31* 

12  40 

12  40 

15  42 

15  42 

804 


FIRE-PROOFING  OF  BUILDINGS. 


TABLE    III.— SIZE    AND    WEIGHT    OF    I-BEAMS    FOR 
FLOORS  IN  WAREHOUSES. 

Total  load,  270  pounds  per  square  foot. 


Span  of 
Beams 

Distance  between  Centres  of  Beams. 

in  Feet. 

44  Feet. 

5  Feet, 

54  Feet, 

6  Feet. 

64  Feet. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

ins.  Ibs. 

10 

8  18 

8  18 

8   18 

9  21 

9  21 

11 

8  18 

9  21 

9  21 

9  21 

10  25 

12 

9  21 

9  21 

10  25 

10  25 

10  25 

13 

10  25 

10  25 

10  25 

12  314 

12  314 

14 

10  25 

12  314 

12  314 

12  3H 

12  314 

15 

12  314 

12  314 

12  314 

12  314 

12  40 

16 

12  3H 

12  3l| 

12  314 

12  40 

12  40 

17 

12  314 

12  40 

12  40 

12  40 

15  42 

18 

12  40 

12  40 

15  42 

15  42 

15  42 

19 

12  40 

15  42 

15  42 

15  42 

15  42 

20 

15  42 

15  42 

15  42 

15  45 

15  55 

Fig.  13,  the  tie-rods  in  this  bay  should  be  anchored  into  the 
wall  with  large  plate  washers. 

The  tie-rids  should  be  located  in  the  line  of  thrust  of  the 
arch,  which  is  ordinarily  below  the  centre  of  the  beam,  and  in 
some  cases  near  the  bottom  flange. 

If  their  appearance  is  objectionable,  they  should  be  hidden 
by  a  hung  ceiling. 

For  constructional  purposes  tie-rods  are  desirable  in  all 
types  of  floor  construction,  even  though  the  floors  do  not  exert 
a  thrust  on  the  beams. 

As  a  rule  tie-rods  are  proportioned  and  spaced  by  some 
"thumb  rule"  rather  than  by  actual  calculations  of  the  thrust. 
For  the  interior  arches  this  practice  is  probably  safe  enough, 
but  for  outside  spans,  and  particularly  for  segmental  arches, 
the  thrust  of  the  arch  should  be  computed  and  the  rods  pro- 
portioned accordingly.  The  spacing  of  the  rods  is  generally 
taken  at  eight  times  the  depth  of  the  supporting  beam,  but 
never  more  than  8  feet.  For  interior  flat  tile  arches,  the  follow- 
ing rule  can  usually  be  safely  followed:  For  spans  of  6  ft. 
and  under,  use  f-inch  rods  spaced  about  5  ft.  apart;  for  7-ft. 
spans,  use  |-inch  rods,  5  ft.  centre  to  centre,  and  for  a  9-ft. 
span,  J-inch  rods,  4  ft.  centre  to  centre. 

The  horizontal  thrust  of  an  arch  may  be  found  by  the  follow- 
ing formula: 


2R~ 


FLOOR  CONSTRUCTION.  805 

in  which  T  =  pressure  or  thrust  in  pounds  per  lineal  foot  of  arch  ; 
itf  =  load  on  arch  in  pounds  per  square  foot,  uniformly 

distributed  ; 

L  =  span  of  arch  in  feet; 
R  =  rise  of  segmental  arch,  or  effective  rise  of  flat  arch 

in  inches. 

The  rise  of  a  segmental  arch  is  measured  from  the  spring- 
ing line  to  the  soffit  of  the  arch  at  the  centre.  For  flat  hollow- 
tile  arches,  the  effective  rise  may  be  figured  from  the  top  of 
the  beam  flange  to  the  top  of  the  tile.  As  the  tiles  usually 
project  from  1£  to  2  ins.  below  the  bottom  of  the  beam,  the 
effective  rise  will  be  from  2  to  2^  ins.  less  than  the  thickness  of 
the  arch. 

For  the  interior  arches  of  a  floor,  w  may  be  taken  for  the  live 
load  only,  but  for  the  exterior  arches,  w  should  include  both 
the  full  dead  and  live  load. 

Having  found  the  thrust  of  the  arch,  the  spacing  of  the  rods  " 
(of  any  particular  size)  may  readily  be  determined  by  dividing 
the  safe  load  given  for  that  size  of  rod  in  the  table  on  p.  340 
(allowing   15,000  Ibs.   unit   stress)   by  the  thrust.     The  result 
will  be  the  spacing  in  feet. 

Example.  —  What  size  of  tie-rods  and  what  spacing  should 
be  used  for  the  floor  construction  described  on  p.  801? 

Ans.—  The  depth  of  the  tile  arch  is  12  ins.,  the  dead  load 
79  Ibs.,  and  the  live  load  assumed  at  150  Ibs.  The  span 
between  beams  is  6J  ft.  Then  for  the  interior  arches,  w  = 

^  V  1  ^O  V  4-9  9^ 

150  Ibs.,  #=12-2i  =  9i  ins.  and  L  =  6i  and  T  = 


=  1000  Ibs.  The  strength  of  a  f-inch  rod,  not  upset,  at  15,000  Ibs. 
is  (from  p.  340)  4500  Ibs.  Dividing  by  1000  we  have  4J  ft. 
as  the  spacing. 

The  strength  of  a  J-inch  rod  is  given  as  6300  Ibs.,  which  would 
admit  of  a  spacing  of  6.3  feet. 

For  the  outer  spans,  w  should  be  taken  at  150  +  79  =  229  Ibs., 

when  T  will  equal  3-^29^42'25  =  1526  Ibs. 


For  this  thrust  we  should  use  f-inch  rods  spaced  about  4  ft. 
2  ins.  centre  to  centre. 

Load  Tests.  —  It  may  be  desirable  at  times  to  test  fire-proof 
floors  after  the  same  have  been  installed.  The  same  pre- 
cautions should  be  observed  as  for  tests  on  reinforced  concrete 
construction,  described  on  p.  882p.  If  it  is  desired  to  determine 


806  FIRE-PROOFING  OF  BUILDINGS. 

from  such  tests  the  ultimate  strength,  a  section  of  the  floor 
of  a  width  equal  to  the  span  should  be  cut  loose  from  the  rest 
and  loaded  to  destruction,  the  supporting  steel  beams  being 
shored  up  during  the  test.  The  safe  working  load  is  found 
by  dividing  the  breaking  load  by  the  proper  factor  of  safety. 

Roof. — Flat  roofs  are  constructed  in  the  same  way  as  the 
floors,  except  that  the  beams  and  girders  are  set  so  as  to  give 
a  slight  pitch  to  the  roof,  for  draining  the  water.  As  the  roof- 
loads  are  usually  less  than  the  floor-loads  and  there  are  no 
partitions  to  be  supported,  the  arches  or  roof-panels  are  usuallv 
considerably  lighter  than  the  floor-panels,  but  the  general 
construction  is  practically  the  same  for  both. 

When  the  roof  is  formed  of  reinforced  concrete,  the  beams 
should  be  set  so  that  the  concrete  will  give  the  desired  incli- 
nation to  the  roof,  with  a  nearly  uniform  thickness,  as  this 
reduces  the  amount  of  concrete  required,  and  also  the  weight. 

If  the  roof  is  to  be  covered  with  tin  or  copper,  nailing-strips 
should  be  imbedded  in  the  concrete,  the  same  as  for  wooden 
floors,  and  the  entire  roof  sheathed,  as  it  is  claimed  that  tin 
or  copper  laid  over  terra-cotta  or  concrete  will  rust  out  in  a 
few  years.* 

Gravel  or  tile  roofs  require  no  woodwork  of  any  kind. 

Whether  terra-cotta  or  concrete  is  used  for  the  roof  panels, 
the  sides  and  bottoms  of  the  steel  beams  and  girders  should 
be  efficiently  protected,  and  all  columns  or  other  structural 
metal  in  the  roof  space  should  also  be  well  protected.  In  the 
ordinary  building,  having  stair  or  elevator  wells,  the  roof  and 
upper  ceiling  are  likely  to  be  more  severely  tested  by  heat, 
in  case  of  fire,  than  any  of  the  floors  below,  and  experience  has 
shown  that  this  is  often  the  poorest  protected  portion  of  the 
building. 

Pitched  Roofs. — Pitched  roofs  may  be  constructed  in  various 
ways,  according  to  the  material  that  is  to  be  used  and  the  kind 
of  roofing  that  is  to  be  employed. 

When  terra-cotta  is  to  be  used  for  the  fire-proofing,  the  most 
common  method  of  construction  is  to  frame  the  roof  with 
I-beam  rafters  and  T-iron  purlins,  set  horizontally,  and  spaced 
1  inch  more  than  the  length  of  the  tile.  Between  the  tees, 
book  or  roofing  tiles  are  placed  as  in  Fig.  64,  and  the  roofing  is 
applied  directly  to  the  surface  of  the  tile.  If  the  roofing  is  to  be 

*  Freitag,  page  288. 


FLOOR  CONSTRUCTION. 


807 


of  slate  or  clay  tiles,  solid  porous  terra-cotta  blocks  should  be 
used,  between  the  tees,  as  the  solid  blocks  hold  the  nails  better 
than  the  hollow  tile.  The  same  construction  may  be  used  for  a 
flat  roof,  but  on  account  of  the  expense  of  the  tees  it  will  usually 
be  more  expensive  than  the  construction  above  described, 
and  not  as  strong  or  desirable.  With  the  construction  shown 
in  Fig.  64,  it  is  impossible  to  efficiently  protect  the  bottom 
of  the  tees  from  the  effects  of  heat  by  any  economical  method. 


Fio.  64. 

The  author  believes  that  reinforced  cinder  concrete,  or 
reinforced  porous  terra-cotta  tile  (Johnson  System)  afford 
the  best  and  also  the  most  economical  construction  for  fire- 
proof pitched  roofs.  Either  of  these  constructions  may  be 
filled  between  or  on  top  of  the  rafters  without  the  use  of  purlins, 
except  about  once  in  6  to  10  feet,  to  prevent  sliding  and  to 
stiffen  the  roof. 

"Three-inch  plates  of  concrete  with  expanded  metal  im- 
bedded have  been  successfully  used  up  to  spans  of  6  to  7  feet 
and  in  some  cases  even  to  8  feet. 

"The  concrete  is  deposited  on  wooden  centrings,  as  in  the 
floor  construction,  and  the  upper  side  is  smoothed  off  during 
the  setting  and  is  then  floated  smooth  and  straight  to  receive 
the  roof-covering."  *  The  roof-covering,  usually  slate,  or 

*  Freitag. 


808 


FIRE-PROOFING  OF  BUILDINGS. 


clay  tiles,  may  be  nailed  directly  to  the  concrete,  as  cinder 
concrete  holds  the  nails  nearly  as  well  as  does  wood.  (Note. — • 
The  above  applies  only  to  cinder  concrete,  as  it  is  quite  im- 
possible to  nail  into  rock  or  gravel  concrete.) 

With  concrete  roofs  the  rafters  should  also  be  surrounded 
with  concrete  held  in  place  by  metal  lath.  With  terra-cotta 
roofs,  the  beams  should  be  incased  with  terra-cotta  blocks. 

Fig.  65  shows  the  standard  shapes  of  book  tile  and  solid 
roofing  tile.  These  are  made  2,  2j-,  and  3  ins.  thick,  and  15£, 


BOO.K  TILE 


GOVE.RNM.ENT  ROOFING*TILE 
FIG.  65. 


17J,   and   23J   ins.   long.     Three-inch   book  tile  weighs   about 

13  pounds  per  sq.  ft.  and  the  2J-inch  solid  tile  about  16  pcfunds. 
Both  of  these  shapes  are  also  used  for  ceilings  and  where  a 

light  fire-proof  filling  is  required. 

Mansard  Roofs  are  usually  framed  with  4-,  5-,  or  6-inch 

rafters,  riveted  or  bolted  to  a  wall-plate.     The  space  between 

the  rafters  may  be  filled  with 
cinder  concrete,  hollow  parti- 
tion tile,  or  blocks  extending 
from  rafter  to  rafter,  as  in  Fig. 
66.  Slate  or  tiles  may  be  nailed 
directly  to  cinder  concrete  or  to 
porous  terra-cotta. 

Probably  the  best  provision 
for  attaching  slate  or  tiles, 
however,  is  to  nail  1J''X2" 
wood  strips  to  the  outer  face  of 
the  concrete  or  terra-cotta,  the 
strips  being  set  at  the  proper 
distances  apart  to  receive  the 
slate  or  tile,  and  then  plaster- 
ing between  the  strips  with 

cement    mortar.     This  gives  a  better  nailing   for  the  roofing, 


FIG.  66. — Mansard  Roof. 


ROOFS. 


809 


and  the  wood  strips  would  not  be  affected  by  fire  until  the 
slate  was  practically  destroyed. 

With  concrete  or  partition  tile  filling,  the  rafters  may  be  spaced 
5  to  6  feet  apart,  while  with  single  blocks,  as  in  Fig.  66,  they 
cannot  be  spaced  more  than  2  feet  on  centres. 

Suspended  Ceilings.  —  Office  buildings,  apartment-houses, 
etc.,  having  a  flat  roof,  require  a  ceiling  below  the  roof  for 
appearance  in  the  rooms,  and  also  for  heat  insulation. 

In  office  buildings  the  upper  ceiling  is  often  framed  and  con- 
structed similarly  to  the  floors,  but  with  lighter  construction. 
More  often  the  ceiling  is  suspended  from  the  roof,  as  this  re- 
quires much  less  steel  and  is  consequently  much  cheaper,  while 
it  answers  the  purpose  fully  as  well — i.e.,  if  the  roof-beams  are 
efficiently  protected. 

Fig.  67  shows  a  common  construction  for  such  ceilings; 
wrought-iron  hangers  about  l"Xi",  split  at  one  end  to  hook 


1-*~gz=gp?«i***-ifi*-igf5r_ Y~'  ]-L£. 
Reinforcement 

Roof  Construction 


.1%  Channel  Bars     vMetal  Lath :  Laced  to  Channel  Bars 
FlG.    67. 

over  the  lower  flanges  of  the  roof-beams,  are  used  to  support 
flat  steel  bars,  spaced  about  4  feet  on  centres,  and  to  the  under- 
side of  these  are  laced  f-inch  or  J-inch  channels,  12  or  16  ins. 
on  centres  which  receive  the  metal  lathing.  The  bottom  of 
the  hangers  are  bent  at  right  angles  to  form  a  seat  for  the  bar, 
and  the  bar  is  laced  to  the  hangers.  No  bolting  or  riveting  is 
required,  all  connections  being  made  by  lacing  wire,  or  by 
bending  the  iron.  Where  stiffened  wire  lath,  such  as  the 
Roebling  or  Clinton,  is  used,  the  channels  may  be  spaced  16  ins. 
on  centres,  but  if  the  ordinary  expanded  laths  are  used,  it  is 
better  to  place  the  channels  12  ins.  on  centres,  and  if  ordi- 
nary lime  mortar  is  used  for  plastering,  a  12-inch  spacing  is 
really  necessary. 


810 


FIRE-PROOFING  OF  BUILDINGS 


Another  system  is  to  use  only  one  set  of  horizontal  bars, 
which  are  spaced  close  enough  to  receive  the  lathing,  and 
every  bar  is  supported  by  hangers.  With  stiffened  wire  lath- 
ing, and  roof-beams  spaced  not  over  5  feet  apart,  and  short 
hangers,  this  may  be  the  cheaper  system,  but  without  the 
stiffened  lathing,  there  is  no  stiffness  to  the  ceiling  at  right 
angles  to  the  bars.  Where  the  hangers  are  3,  4,  or  5  feet  long, 
and  the  spans  between  beams  are  more  than  5  feet,  the  two-bar 
system,  shown  by  Fig.  67,  will  require  less  steel,  for  the  reason 


FIG.  68. 

that  the  channels,  having  a  span  of  only  4  feet,  may  be  made 
very  light,  and  only  J  or  J  as  many  hangers  are  required. 


In  place  of  the  small  channels,  small  tees  or  flat  bars  may 
be  used,  but  where  the  bars  are  held  by  lacing,  the  channels 
are  to  be  preferred. 

Figs.  68  and  69  (from  Freitag's  "Fireproofing,"  p.  286) 
show  very  satisfactory  details  for  the  construction  of  the  two- 
bar  system. 


ROOFS. 


811 


Instead  of  the  hook  shown  in  Fig.  68,  the  hanger  may  be 
split  at  the  top,  and  one  half  bent  around  one  side  of  the  beam 
flange  and  the  other  half  bent  around  the  other  side. 

Where  the  ceiling  is  suspended  below  terra-cotta  arches, 
toggle- bolts  are  used  for  the  support  of  the  hangers. 

The  ends  of  the  small  bars  supporting  the  lathing  are  usually 
spliced  by  means  of  sheet-iron  clamps,  about  6  ins.  long, 
wrapped  closely  around  the  bars  and  hammered  tight. 

For  suspended  ceilings  under  segmental  or  paneled  floor 
construction,  the  same  methods  are  employed,  except  that  the 
hangers  are  replaced  by  clips  holding  the  ceiling  bars  close  to 
the  soffits  of  the  beams, 

Steel  Clips  for  Fastening  Angle-  or  Tee-bars  to  I- 
beams  and  Channels. — Several  years  ago  Mr.  H.  A.  Streeter, 


As  Furnished 


ie  Outstanding  Flanges 
of  Clip  to  be  bent  around 
v  Beam  when  applied 


Clip  as  Furnished 
FIG.  70. — Clips  for  Fastening  Tees  and  Angles  to  Beams  and  Channels. 

of  Chicago,  patented  a  steel  clip  for  connecting  angles  and  tees 
to   I-beams  without   drilling   or   bolting,   arid   they   have    been 


812 


FIRE-PROOFING  OF  BUILDINGS. 


extensively  used,  particularly  in  roof  construction  and  for 
suspended  ceilings.  Besides  the  saving  effected  in  doing  away 
with  the  drilling  and  bolting  required  by  the  old  method,  they 
also  enable  the  connections  to  be  more  quickly  made  and 
afford  an  easy  method  of  adjusting  T-bars  to  any  width  of 
tile.  Several  forms  of  clips  with  their  application  are  illustrated 


As  Purnished 


FIG.  71. — Clips  for  Suspending  Tees,  Angles,  or  Channels  below  I-beams 
and  Channels.  Clip  N  may  be  used  for  Suspending  any  Kind  of  a 
Section  from  a  Beam. 

by  Figs.  70  and  71.     Other  forms  are  also  made  on  the  same 
principle. 

The  safe  load  which  may  be  supported  by  clips  like  N,  or  NN, 
1J  ins.  wide,  is  as  follows: 

No.  12  gauge  =  0.0808  in.,  600  Ibs. 
No.  14  gauge  =  0.0641  in.,  414  Ibs. 
No.  16  gauge  =  0.0508  in.,  215  Ibs. 

No.  14  gauge  is  generally  used,  the  material  being  specially 
made  for  this  purpose.  The  strength  of  the  clip  may  be  in- 
creased by  increasing  the  width. 

Partitions. 

Requirement  of  Fire-proof  Partitions.— As  a  rule  the 
partitions  in  fire-proof  buildings  are  not  required  to  support 
any  weight,  but  merely  to  serve  the  purpose  of  dividing  the 


PARTITIONS.  813 

space  into  rooms,  and  to  confine  a  fire  to  the  compartment  in 
which  it  originates.  No  greater  strength  is  therefore  required 
in  a  partition  than  is  necessary  to  carry  its  own  weight.  How- 
ever, rigidity  is  required,  and  that  in  proportion  to  its  height 
and  unsupported  length.  Where  partitions  separate  apart- 
ments or  sections  of  a  story,  that  is,  when  they  practically  are 
without  window  or  door  openings,  they  should  be  rigid  enough 
to  prevent  the  passage  of  water  from  a  hose  stream  as  well  as 
flame.  In  other  cases  this  may  be  unnecessary;  in  fact,  at 
times  it  may  seem  desirable  that  the  partitions  are  easily  re- 
moved for  the  purpose  of  getting  at  a  fire  spreading  through 
doors  or  windows. 

The  materials  of  partitions  should  be  incombustible.  They 
should  also  be  poor  conductors  of  heat.  It  is  also  desirable 
that  they  shall  not  be  affected  by  water.  Lightness  is  also  a 
desirable  quality,  as  any  increase  in  the  dead  weight  of  the 
construction  adds  to  the  cost  of  the  structure.  Partitions 
should  also  be  as  sound-proof  as  possible. 

So  far  as  may  be,  fire-proof  partitions  should  have  no  window 
openings  in  them,  and  even  as  few  door  openings  as  possible. 
In  many  buildings,  however,  where  halls  have  no  openings 
into  streets  or  courts  such  windows  are  necessary  for  lighting 
the  halls.  When  this  is  the  case  the  frames  should  be  made  fire- 
proof and  wire  glass  should  be  used,  the  sash  being  stationary 
if  possible. 

Fire  Tests  on  Partitions. — The  Bureau  of  Buildings  of 
New  York  does  not  permit  the  use  of  any  materials  or  type  of 
construction  for  partitions  in  fire-proof  buildings  that  have 
not  met  the  required  fire  test. 

This  test  is  made  as  follows:  A  test  structure,  15  feet  3  inches 
long  by  10  feet  3  inches  wide,  on  a  12-inch  masonry  foundation 
2^  feet  high,  is  erected  with  the  material  or  construction  to 
be  tested  forming  the  long  sides  of  the  structure.  A  fire  door 
is  provided  in  one  end  of  the  structure  for  the  purpose  of  charg- 
ing the  fuel.  Draft  openings  are  provided  in  the  foundation 
walls,  and  four  flues  are  provided,  one  at  each  corner.  The 
ends  and  roof  of  the  structure  are  made  of  any  material  that 
will  stand  the  fire.  Upon  a  grate,  resting  on  the  foundation 
walls,  a  wood  fire  is  built  and  maintained  continuously  for  one 
hour.  The  temperatures  are  read  and  recorded  by  means  of 
a  standard  pyrometer  under  the  supervision  of  a  competent 
person.  A  temperature  of  1700°  Fahr.  must  be  attained  at 


814  FIRE-PROOFING  OF  BUILDINGS 

the  end  of  the  first  half  hour,  and  maintained  during  the  second 
half  hour.  At  the  end  of  the  hour  a  stream  of  water,  at  30 
pounds  pressure  through  a  IJ-inch  nozzle,  is  directed  against 
the  construction  under  test,  for  2J  minutes.  The  conditions 
for  acceptance  are  that  at  no  time  during  the  test  shall  any 
fire  or  water  pass  through  the  construction  under  test,  nor 
shall  the  construction  warp  or  bulge  to  any  great  extent. 

Types  of  Partitions. — Fire-proof  partitions  that  are  in 
common  use  may  be  grouped,  according  to  the  materials  used 
or  the  method  of  construction,  as  follows: 

(a)  Brick; 

(b)  Terra-cotta; 

(c)  Concrete — stone  or  cinder; 
O/)  Plaster  block; 

(e~)  Plaster  and  Metal. 

The  choice  of  construction  should  be  influenced  in  some 
degree  by  the  character  of  the  building,  and  the  purposes  for 
which  it  is  used. 

Partition  Walls.— For  bearing  partitions  (those  which 
support  floor  beams)  there  are  probably  no  materials  more 
satisfactory  than  brick  and  concrete.  The  latter  may  be  used 
either  in  the  form  of  blocks,  or  may  be  poured  between  forms. 
Partitions  of  brick  should  be  at  least  12  ins.  thick,  as  thick 
walls  are  less  affected  by  heat  than  thin  walls. 

Dense  tile  is  also  being  used  for  bearing  walls  with  satis- 
factory results.  Some  recent  tests  made  at  Columbia  Uni- 
versity show  a  crushing  strength  equal  to  brick.  (See  p.  732.) 

Terra-cotta  Partitions. — These  are  usually  built  of  blocks 
either  square  or  brick-shaped,  according  to  the  particular 
product  used.  The  square  blocks  are  usually  12"Xl2"  on 
the  face,  and  the  brick-shaped  blocks  are  usually  12  ins.  long 
but  of  varying  heights.  Both  shapes  are  made  in  thicknesses 
varying  from  3  to  12  ins.,  the  3-,  4-,  and  6-inch  blocks  being 
most  commonly  used ;  the  4-inch  blocks  being  the  most  popular 
for  ordinary  work.  Fig.  72  shows  typical  shapes  of  both  the 
square  and  brick-shaped  blocks. 

The  blocks  are  commonly  set  with  the  voids  horizontal,  as 
in  Fig.  72,  the  blocks  breaking  joint  like  bricks,  but  at  the 
ends,  and  in  filling  small  spaces  they  are  sometimes  set  verti- 
cally. 

Fig.  73  shows  round-  and  angle-cornered  partition-blocks, 
which  must  be  set  vertically. 


PARTITIONS. 


815 


"Terra-cotta  partitions  of  a  2-inch  thickness  have  been 
placed  on  the  market,  but  have  not  been  extensively  used.  A 
2-inch  terra-cotta  partition  of  any  strength  or  efficiency  is 
quite  impracticable,  and  where  floor  area  is  so  valuable  that 


FIG.  72. — Terra-cotta  Partition-blocks. 

more  space  cannot  be  occupied,  terra-cotta  is  not  the  material 
to  be  employed."  *  Through  the  addition,  however,  of  band- 
iron  laid  between  the  courses  and  patented  under  the  style 

*  Freitag. 


816 


FIRE-PROOFING  OF  BUILDINGS. 


" Phoenix,"  the  strength  of  a  2-inch  tile  partition  is  greatly  in- 
creased. 

The  "New  York"  partition  (Bevier  Patent)  consists  of 
2-inch  tile  reinforced  with  truss  metal,  such  as  is  used  in  the 
"New  York"  floor  arch.  (See  Fig.  33.) 


FIQ.  73. — Partitioh-blocks  with  Angular  and  Circular  Corners. 

Porous  vs.  Dense  Material. — For  inside  partitions  the 
porous  material  is  preferable  to  the  dense,  while  for  outside 
walls  the  dense  material  should  be  used.  With  dense  tiling 
it  is  necessary  to  insert  either  wooden  nailing  strips,  which  is 
bad  practice,  or  blocks  of  porous  tile  for  the  same  purpose. 

Mortar. — Tile  partition-blocks  should  be  set  in  mortar  made 
of  one  part  lime-putty,  two  parts  cement,  and  two  to  three 
parts  sand-  The  blocks  should  be  well  wet  before  setting  and 
the  partition  wet  down  before  the  plastering  is  applied. 

Height  and  Length. — "The  safe  height  of  terra-cotta  par- 
titions in  inches,  may  be  approximated  by  multiplying  the 
thickness  in  inches  by  40.  Common  practice  allows  a  safe 
height  of  12  ft.  for  3-inch,  16  ft.  for  4-inch,  and  20  ft.  for  6-inch 
partitions.  For  partitions  without  side  supports  the  length 
should  not  materially  exceed  the  safe  height.  Doors  and  high 
windows  may  be  considered  as  side  supports,  provided  the 
studs  run  from  floor  to  ceiling.57  * 


*  Freitag. 


PARTITIONS.  817 

Weight.  -The  weights  of  either  porous  or  dense  terra-cotta 
partitions  will  vary  as  follows: 

2-inch  partition,  10  to  14  Ibs.  per  sq.  ft.; 
3-inch  partition,  12  to  16  Ibs.  per  sq.  ft.; 
4-inch  partition,  13  to  19  Ibs.  per  sq.  ft.; 
5- inch  partition,  20  to  22  Ibs.  per  sq.  ft.; 
6-inch  partition,  22  to  23  Ibs.  per  sq.  ft.; 
8-inch  partition,  28  to  33  Ibs.  per  sq.  ft.; 

not  including  plastering,  which  will  add  about  10  Ibs.  per  sq.  ft. 
for  both  sides. 

Concrete  Partitions. — Partitions  of  stone  concrete  are 
seldom  used  because  of  the  necessity  of  forms  in  their  erection, 
making  a  comparatively  expensive  partition.  Unless  rein- 
forced they  take  up  too  much  room.  Furthermore  they  are 
the  heaviest  of  all  partitions.  Even  in  buildings  that  are 
entirely  of  reinforced  concrete  they  are  not  always  used. 

Cinder  concrete  partitions  are  somewhat  lighter  and  con- 
siderably cheaper  than  those  of  stone  concrete.  Yet  even 
these  are  too  heavy  and  troublesome  of  construction  to  be 
satisfactory.  Among  the  partitions  tested  and  approved  by 
the  New  York  Building  Bureau  is  one  that  consists  of  cinder 
concrete  blocks,  2J  and  3  inches  in  thickness  (the  thicker 
ones  being  hollow),  12  inches  high  and  18  inches  long. 
They  have  their  edges  cast  with  tongues  and  grooves  that 
furnish  more  or  less  of  a  bond  between  the  blocks  when  they 
are  set. 

Hollow  concrete  building-blocks  make  fairly  good  partitions, 
but  are  objectionable  on  account  of  their  thickness. 

Plaster  Block  Partitions.— Blocks  made  of  plaster  cf 
Paris  combined  with  various  substances,  such  as  cinders,  wood 
chips,  cocoanut  fibre,  asbestos,  etc.,  have  been  used  to  quite 
an  extent  for  forming  partitions  in  fire-proof  buildings,  but 
while  they  are  to  be  preferred  to  partitions  built  with  wooden 
studding,  and  will  resist  fire  for  a  considerable  period  of  time, 
they  cannot  be  considered  as  absolutely  fire-proof,  or  suitable 
for  first-class  fire-proof  buildings.  The  principal  advantage 
claimed  for  these  partitions  is  their  great  lightness  and  re- 
duced cost  as  compared  with  terra-cotta  tile.  Plaster  blocks 
can  be  readily  cut  with  a  saw,  and  will  receive  and  hold  nails 
tolerably  well. 


818 


FIRE-PROOFING  OF  BUILDINGS. 


In  the  fire  tests  they  have  generally  shown  considerable 
resistance  to  the  flame  and  have  transmitted  less  heat  than 
any  other  form  of  partition.  They  did  not,  however,  always 


FIG.  74.— Scaglioline  Block. 

stand  the  hose  stream,  some  of  them  being  easily  pierced,  and 
all  of  them  being  more  or  less  washed  away  by  the  water. 


FIG.  75. — Doweled  Construction. 

They  are  made  of  thicknesses  varying  from  2  to  4  inches, 
those  less  than  3  inches  thick  generally  being  solid. 

The  edges  of  the  blocks  are  generally  grooved  or  otherwise 
arranged  so  that  the  mortar  joint  forms  a  key  between  the 


PARTITIONS.  819 

• 

blocks.  In  the  "  Scaglioline ' ;  *  block  this  keying  of  the  mortar 
is  carried  to  greater  extent  than  in  other  blocks,  as  shown  in 
Fig.  74.  The  joints  are  sometimes  further  reinforced  hori- 
zontally by  rods  as  indicated  in  the  cut. 

In  some  forms  of  partitions  the  blocks  are  bonded  together 
by  means  of  metal  dowels, f  running  across  the  horizontal  and 
vertical  joints  from  one  block  into  the  adjoining,  as  shown  in 
Fig.  75.  The  cut  illustrates  the  use  of  the  block  in  the  con- 
struction of  dumb-waiter  shafts  and  shows  how  the  blocks  are 
anchored  at  the  corners  by  iron  dowel  angles. 

The  mortar  used  in  laying  up  plaster  blocks  is  made  of  the 
same  materials  and  mixed  in  the  same  proportions  as  that  for 
terra-cotta  partitions.  (See  p.  816.) 

All  of  the  partitions  in  the  newer  portions  of  the  Monadnock 
Block,  Chicago,  and  in  many  other  prominent  buildings  of  Chicago 
and  New  York  are  of  plaster  blocks. 

Weight. — Plaster  blocks  make  the  lightest  practical  parti- 
tion known.  The  weight  of  the  blocks  per  square  foot  may 
be  taken  as  follows: 

Thickness  of  block,  inches  .  .  2  2£  3  34-  4568 
Weight  in  Ibs.  per  sq.  ft..  ...  7  8J  94  10i  12  15  18  22 

The  plaster  boards,  1  in.  thick,  weigh  4  Ibs.  per  sq.  ft.  About 
8  Ibs.  per  sq.  ft.  should  be  added  to  the  weight  of  the  partition 
tile  to  obtain  the  weight  of  the  partition  when  plastered  both 
sides. 

Mackollte. — The  best  known  and  most  extensively  used  of 
the  plaster  blocks  are  the  Mackolite  Hollow  Blocks,  made 
by  Mackolite  Fireproofing  Company  of  Chicago.  Mackolite 
partition  tile  are  made  of  the  general  shape  shown  by  Fig.  76, 
and  of  3,  34,  4,  6,  8,  and  12  ins.  in  thickness.  The  3-,  3J-, 
and  4-inch  tile  are  made  48  inches  long,  and  the  others  30  inches 
long,  all  of  the  tile  being  12  inches  high.  The  blocks  are  laid 
in  regular  courses,  breaking  joint  as  in  cut-stone  work.  Lime 
mortar  is  used  for  setting.  In  fitting  around  openings  or  at 
angles  the  blocks  are  cut  with  a  saw  which  effects  a  material 
saving  in  time  and  material.  It  is  claimed  that  the  blocks  make 
a  very  strong  partition.  The  composition  of  the  blocks  is 

*  Made  and  controlled  by  the  Fireproof  Partition  Co.,  1  Madison  Ave., 
N.  Y. 

f  Patented  by  the  Sanitary  Fireproofing  and  Contracting  Co.,  N.  Y. 


820 


FIRE-PROOFING  OF  BUILDINGS. 


plaster  of  Paris  mixed  with  certain  chemicals,  reeds,  and  fibre. 
Reeds  of  the  same  length  as  the  blocks  are  placed  in  the  moulds, 
and  the  plaster  of  Paris  and  fibre  is  then  mixed  with  water  to 
which  the  chemical  has  been  added  and  poured  around  the 
reeds  so  that  they  shall  be  nowhere  exposed.  The  reeds  give 
longitudinal  strength  to  the  blocks  while  the  fibre  makes  them 
tough  and  elastic.  The  material  sets  in  about  one  half  hour, 
after  which  the  blocks  are  kiln-dried  for  four  days. 


FIG.  76. — Maukolite  Partition  Tile. 

Gypsinite  Partitions. — A  partition  that   bids  fair   to  make 
an  economical  fire-proof  partition  has  recently  been  put  on  the 
market  by  the  Gypsinite  Co.,  of  New  York.     The  main  feature 
of  this  partition  is  the  stud  which  is  handled  and  erected  in  the 
same  manner  as  a  wooden  stud  in  the  ordinary  non-fire-proof 
partition.     The  stud  is  composed  of  wood  nailing  strips  com- 
pletely protected  and  imbedded  in  a  material  known  as  gyp- 
smite    concrete,    a   plaster    composition,    not    a   true   concrete. 
The  studs  are  carefully  made  and  are  plumb  and  true.     Metal 
lath  or  plaster  boards  are  secured  to  the  studs  and  plastered, 
completing  the  partition,  about  4J  inches  thick.     (See  Fig.  77.) 
This  partition  is  but  slightly  heavier  than  the  ordinary  par- 
tition of  wooden  construction.     It  is  quite  as  stiff  and  strong 
as  a  good  tile  or  other  partition,  and  the  nailing  feature  of  the 
studding  facilitates  the   application  of  wood-trim.     It   is  said 
to  be.  particularly  sound-proof,   and  the  spaces  between  studs 
afford  an  opportunity  for  the  concealment  of  pipes,  wires,  etc. 
Gypsinite  studding  in  stock  size  are  3"X3"X12',   and  weigh 
3  pounds  to  the  foot.     They  can  be  made  any  size  that  may 
be  required. 


PARTITIONS, 


821 


In  the  partitions  the  studs  are  usually  placed  16  inches  on 
centres  and  bridged  as  may  be  required.  They  are  fastened 
to  the  floor  or  ceiling  by  the  use  of  sills  and  plates  of  the  same 
material,  or  light  channel  irons,  which  are  spiked  to  the  fire- 
proofing.  The  manufacturers  believe  that  in  large  quantities 
they  can  be  furnished  as  cheaply  as  wooden  studs  and  that  the 
partitions  can  be  erected  as  cheaply  as  ordinary  lath  or  plaster 
partitions. 


FIG.  77. 

Plaster  and  Metal  Partitions. — Thin  partitions  of  plaster 
applied  to  metal  lath  and  studding  so  as  to  make  a  solid  partition 
finishing  about  2  inches  thick,  have  been  very  extensively  used 
i:i  fire-proof  buildings. 

They  are  remarkably  stiff,  owing  to  the  adhesion  of  the 
plaster  to  the  steel,  and  they  are  lighter  and  occupy  less  space 
than  any  other  practical  fire-proof  partition  of  equal  strength. 

In  the  fire  tests  these  partitions  act  very  much  as  the  plaster- 
block  partitions,  resisting  thoroughly  the  passage  of  the  flames. 
But  the  plaster  always  washes  off  when  the  hose  is  applied 
and  the  lath  becomes  exposed.  The  rigidity  of  the  metal 


822  FIRE-PROOFING  OF  BUILDINGS. 

fabric  on  the  metal  studding  has  been  considered  by  firemen 
a  disadvantage,  as  it  is  very  difficult  to  cut  through  when  it 
becomes  necessary  to  get  at  a  fire. 

The  construction  of  the  partition  is  practically  the  same  for 
the  different  fabrics  used  and  described  on  pp.  778  to  784. 
This  lath  or  fabric  appears  to  be  subject  to  corrosive  influences 
of  the  plaster.  In  the  demolition  of  the  Pabst  Building,  New 
York,  the  metal  lath  used  throughout  in  the  partitions  was 
found  to  be  corroded,  in  about  four  years,  to  a  great  extent, 
even  though  the  lath  had  all  been  painted. 

Weight. — The  weight  of  a  2-inch  solid  partition  will  be 
about  20  Ibs.  per  sq.  ft.  when  dry.  The  weight  of  partitions 
of  greater  thicknes-s  may  be  estimated  on  a  basis  of  120  Ibs. 
per  cu.  ft.  for  plaster  and  96  Ibs.  for  cinder  concrete,  slightly 
tamped. 

Construction. — Figs.  78  and  79  show  the  usual  -aethod  of 
constructing  2-inch  partitions.  The  studs,  usuall^  &-  or  1-inch 
channels,  are  bent  and  punched  at  the  ends,  and  at  the  bottom 
are  nailed  to  wood  strips,  which  are  first  secured  to  the  floor- 
panels,  or  to  the  top  of  the  steel  beams  where  the  partitions 
come  over  them.  These  wood  strips  have  been  found  necessary 
as  a  sort  of  cushion  to  permit  of  the  expansion  of  the  studding 
in  case  of  fire. 

At  the  top  the  studs  are  nailed  to  the  underside  of  the 
floor-panels,  or,  in  the  case  of  a  suspended  ceiling,  are  wired 
to  the  bars  supporting  the  ceiling.  At  the  openings  1 X  1  X  &- 
inch  angles  are  used,  and  these  are  bored  every  16  inches  for 
No.  12  screws  used  in  attaching  the  rough  wood  frame  to  the 
angles. 

After  the  studding  is  in  position,  the  metal  lathing  is  laced 
to  one  side  of  the  studding  with  No.  18  galvanized  wire. 

After  the  lathing  is  in  place  the  carpenter  should  attach 
wooden  grounds  for  securing  the  base,  chair-rail,  picture- 
moulding,  etc.  These  are  secured  by  staples  and  when  the 
partition  is  plastered  become  very  rigid. 

In  plastering  these  partitions,  five  coats  of  plaster  are  re- 
quired to  make  a  good  job:  a  scratch  coat  on  one  side,  a  brown 
coat  on  each  side,  and  the  usual  white  coat  on  each  side  for 
finishing. 

It  is  essential  for  all  thin  partitions  that  a  hard-setting 
mortar  be  used,  such  as  Acme  cement,  King's  Windsor,  Ada- 
mant, Rock  Wall,  and  many  others. 


PARTITIONS. 


823 


The  partitions  acquire  thier  stiffness  largely  from  the  solidity 
of  the  plastering,  hence  the  firmer  and  harder  the  plastering 
the  more  substantial  the  walls. 


"     ."'  '  t 


* 


1 


Staple 


%"  Naili 


'No. 


I 

•e  Lathing 

/Staple^ 
SS^S^a 
*  Strip// 

8  Gal.  Wire 
Lacing 


I    -  %  Channel 


i' 'Nailing 
'  Strip 


FIG.  78. 


^"ChanneK 
3?urring  for  Base  K    \          1"  x.  l"  x  j^s"  Lx         ^I'jfi 

/Rough  Fram« 
*+ 

•  3Slil|l^  '.'       ^P 

Staple/ 
No.  18  Gal.  Wire  Lacing^^ 
FIG    79. 

Double  Partitions. — Electric  wires  and  J-inch  gas-pipe 
can  be  run  in  the  2-inch  solid  partition,  but  if  it  is  desired  to 
run  larger  pipes,  double  partitions,  i.e.,  partitions  with  lathing 
on  each  side  of  the  studding  must  be  used.  For  these  parti- 
tions, 2-,  3-,  or  4-inch  channels  or  flat  bars  set  edgeways  may 


824 


FIRE-PROOFING  OF  BUILDINGS. 


be  used,  sheet  steel  channels  being  probably  the  most  economi- 
cal. When  the  space  between  the  studding  is  not  filled  with 
mortar  or  concrete,  the  double  partition  will  not  stand  fire 
and  water  as  well  as  the  solid  partition,  while  it  is  much  more 
expensive, 


*"Steel 


No.  18  Gal.  Wire  Lacing 


FIG.   80. 


Fig.  80  shows  a  partial  section  through  a  solid  partition 
finishing  4  inches  thick  when  plastered,  which  possesses  great 
strength  and  absolute  resistance  to  fire 
and  water,  besides  affording  convenient 
space  for  pipes  and  a  thicker  jamb  for 
door  frames.  This  partition  has  a  core 
of  cinder  concrete,  with  metal  lath  on 
both  sides,  and  is  plastered  in  the  usual 
way.  As  the  concrete  will  receive  nails, 
no  wood  furring  is  necessary  in  order 
to  attach  the  base-board,  chair-rail,  or 
picture-moulding. 

Berger's  Economy  Studding  and 
Furring.— Fig. 81  illustrates  a  patent  stud 
manufactured  by  the  Berger  Manu- 
facturing Company.  It  is  made  of  No. 
18  or  No.  20  sheet  steel,  and  in  five 
sizes,  varying  from  f  to  11  inches.  The 
peculiar  advantage  of  this  stud  is  the 
provision  for  attaching  the  lath.  For 
this  purpose  prongs  are  punched  from 
both  sides  of  the  flange,  which  are  left 
standing  at  right  angles  to  the  face  of  the 
flange.  The  '..lath is  placed  against  the 
stud,  the  prongs  pressed  through  the 
meshes  and  then  turned  up  over  the 
lath  with  a  hammer,  fastening  the  lath 
more  firmly  and  securely  than  by  any 
other  method. 
The  ends  of  the  studs  are  secured  by  sockets  which  are 


FIG.  81. 


PARTITIONS.  825 

fastened  to  the  floor  and  ceiling,  a  clear  space  being  left 
above  the  top  of  the  stud  to  permit  of  expansion. 

•Where  partitions  interesct  or  angles  occur,  angle-irons 
with  prongs  are  used  in  place  of  the  T. 

By  using  this  stud  and  expanded  metal  lathing,  a  saving  in 
cost  can  be  effected  over  the  construction  shown  by  Fig.  13. 
These  T's  are  also  used  for  supporting  suspended  ceilings  under 
I-beams,  the  T's  being  secured  to  the  flange  of  the  beams  by 
specially  designed  clips.  Furring  strips  and  channels  are  also 
made  on  the  same  principle. 

Spacing  of  Studding. — For  2-inch  solid  partitions  with 
f-inch  rolled  channels  or  1-inch  economy  studs,  the  studs 
should  be  placed  12  inches  on  c  ;ntres  when  the  height  of  the 
story  exceeds  10  feet.  When  the  height  of  the  story  is  less 
than  10  feet,  a  spacing  of  16  inches  will  answer.  For  hollow 
partitions  with  2-inch  studs,  the  studs  can  be  spaced  16  inches 
on  centres  for  story  heights  of  16  feet  and  less.  For  greater 
heights  they  should  be  placed  12  inches  on  centres. 

Truss  Metal  Lath.*  —  A  remarkably  rigid  and  strong 
partition,  without  the  use  of  studding,  is  being  constructed 


FIG.  82.— Truss  Metal  Lath  (Kuhne  Patent). 

from  truss  metal  lath.  This  is  an  expanded-metal  lath  of 
the  form  shown  in  Fig.  82.  The  thickness  of  the  sheets  or 
depth  of  the  truss  is  about  1  inch. 

It  is  at  present  manufactured  in  the  form  of  sheets  up  to 
30  ins.  wide  and  to  9  ft.  4  ins.  long.  It  is  at  present  made 
from  soft  steel,  black  and  galvanized,  of  No.  24,  26,  and  28 
gauges. 

It  is  much  heavier  and  stiffer  than  any  other  expanded-melat 
form,  the  No.  28  gauge  weighing  0.67  Ibs.  per  square  foot,  with 
a  cross-section  of  0.18  square  inch  per  foot  in  width,  the  No.  26 
gauge  0.8  Ibs.  per  square  foot,  with  a  cross-section  of  0.216 

*  Manufactured  by  the  Truss  Metal  Lath  Co.,  New  York. 


826  FIRE-PROOFING    OF    BUILDINGS. 

square  inch  per  foot  in  width,  and  the  No.  24  gauge,  1.06  Ibs. 
per  square  foot,  with  a  cross-section  of  0.3  square  inch  per  foot 
in  width. 

This  lath  is  said  to  take  mortar  better  than  any  other  form. 

A  partition  of  this  construction  in  one  of  the  test  structures 
at  Columbia  University  has  passed  through  and  withstood, 
without  any  sign  of  distress,  the  fire  and  hose  streams  of  five 
successive  tests. 

Triangular  Mesh  Fabric.—  In  Figs.  83  and  84  are  shown 
two  methods  in  which  tlie  fabric  of  the  American  Steel  and 

^-  —  ^Triangular  SieBh  Reinforcement  placed'  vertloallj 


FIG.  83. 

Wire  Co.  (Fig.  45)  can  be  employed  in  the  construction  of  good, 
stiff  solid  partitions.  The  cross  or  bond  wires  of  the  fabric 
are  so  woven  to  the  longitudinal  wires  that  the  fabric  can  be 
placed  in  the  position  indicated.  Fig.  83  shows  how  a  6  -inch 
partition  would  be  made,  while  Fig.  84  indicates  the  use  of  the 

Note  hinge  joint  on  each  longitudinal  member 


FIG.  84. 

fabric  for  a  thinner  partition.  For  the  filling-in  material, 
either  stone  or  cinder  concrete  or  even  a  plaster  composition 
can  be  used. 

Styles  of  Wire  Lathing. — Wire  lathing  is  now  made  in 
great  variety  to  meet  the  requirements  of  the  different  plaster- 
ing compositions  and  the  varying  conditions  of  construction. 

Plain  lathing  is  plain  wire  cloth,  usually  2^X2|  meshes  to 
the  inch,  made  from  No.  17  to  No.  20  wire.  No.  20  is  more 
generally  used  than  any  other  gauge. 

The  lathing  is  also  sold  plain,  painted,  and  galvanized. 
Painted  or  galvanized  lathing  should  be  used  in  connection 
with  special  hard-plaster  compounds.  Painted  lathing  costs 
about  one  cent  per  square  yard  more  than  " bright''  lathing. 

Galvanizing  the  wire  cloth  after  it  is  woven  adds  very  much 
to  its  stiffness,  as  the  zinc  solders  the  wires  together  wHere  they 


PARTITIONS.  827 

cross.  Galvanized  lathing  is  also  less  liable  to  corrosion  before 
the  plastering  is  applied  than  the  plain  lathing. 

The  usual  widths  of  plain  lathing  are  32  and  36  ins.,  although 
the  Roebling  lath  may  be  obtained  of  any  width  up  to  8  feet. 

All  wire  lathing  should  be  stretched  tight  when  applied,  so 
as  to  insure  a  firm  surface  for  plastering.  For  this  purpose 
stretchers  are  supplied  by  the  manufacturers. 

Stiffened  Wire  Lath. — Owing  to  the  difficulty  of  stretch- 
ing plain  wire  cloth  tight  enough  to  make  a  firm  foundation 
for  plaster  and  the  necessity  for  short  spacings  for  the  bear- 
ings, three  varieties  of  stiffened  wire  lath  have  been  intro- 
duced and  extensively  used  with  very  satisfactory  results. 
All  three  varieties  are  applied  so  that  the  stiffening  rib  will 
run  at  right  angles  to  the  bearings. 

The  Clinton  stiffened  lath  has  corrugated  steel  furring  strips 
attached  every  8  ins.  crosswise  of  the  fabric  by  means  of  metal 
clips.  These  strips  constitute  the  furring,  and  the  lath  is 
applied  directly  to  the  underside  of  the  floor-joist,  or  to  plank- 
ing, furring,  brick  walls,  etc.  This  lath  is  made  in  32-in.  and 
36-in.  widths,  and  comes  in  100-yard  rolls.  The  manufacturers 
of  this  lath  also  make  a  lath  stiffened  with  round  rods  J  in.  to 
|  in.  in  diameter,  spaced  from  8  ins.  to  12  ins.  apart.  It  can 
be  had  either  galvanized  or  japanned,  18  to  22  gauge. 

The  Roebling  standard  wire  lath  is  made  of  plain  wire  cloth, 
in  which  at  intervals  of  7%  ins.  stiffening  ribs  are  woven.  These 
ribs  have  a  V-shaped  section  and  are  made  of  No.  24  sheet- 
steel  J  and  1  in.  in  depth.  The  ^-in.  rib  is  the  standard  size 
for  lathing  on  woodwork.  This  lathing  requires  no  furring, 
and  is  applied  directly  to  woodwork  or  walls  with  steel  nails 
driven  through  the  bottom  of  the  V,  as  shown  in  Fig.  85. 

The  No.  20  V-rib  stiffened  lathing  affords  a  satisfactory 
surface  for  plastering,  when  attached  to  studs  or  beams  spaced 
16  ins.  apart. 

The  1-inch  V-rib  lathing  is  used  for  furring  exterior  walls. 
It  provides  an  air  space  between  the  wall  and  plaster. 

Where  this  lath  is  to  be  applied  to  light  iron  furring  a 
iV  or  ^-inch  solid  steel  rod  is  substituted  for  the  V-rib,  and 
the  lathing  is  attached  to  light  iron  furring  with  lacing  wire. 
This  lath  is  distinguished  by  the  term  "  solid  rib  stiffened 
wire  lath." 

The  Roebling  lath,  whether  plain  or  stiffened,  is  made 
with2J-X2J,  3X3,  and  2^X4  "mesh,  the  latter  being  known 


828 


FIRE-PROOFING   OF    BUILDINGS. 


FIG.  85. 


as    "clos3  warp."       The  2JX2J  mesh    should     be     used    for 
ordinary  lime  and  hair   mortar,    and   the   3X3   or  2^X4  mesh 

for  hard  plasters  and  thin  par- 
titions. This  lathing  is  also 
sold  bright,  painted,  and  gal- 
vanized. 

The  No.  20  painted  wire  has 
been      extensively     used      and 
much  of  it  has  been  in  service 
for    from  six  to  eight  years  and 
is  now  apparently  as  good  and 
strong  as    ever,  so    that    there 
appears   to    be  no  necessity  in 
ordinary  work   of  using  heavier 
wire  or  galvanized  netting. 
The  galvanized  wire  is  stiffer  than  the  painted,  and  would 
possible  wear  longer,  but  it  is  doubtful  if  the  advantages  are 
at  all  proportionate  \\'th  the  cost. 

Width. — Wire  lath  can  be  furnished  to  order  in  any  re- 
quired width  up  to  10  feet.  In  widths  less  than  18  ins.  there 
is  a  small  charge  for  "stripping."  Before  ordering,  it  is  very 
important  to  ascertain  the  proper  width,  especially  in  stiffened 
lath,  as  it  is  desirable  to  have  the  edges  of  the  lath  joined  at 
supports  when  applied  to  woodwork ;  and  lap  at  supports  when 
laced  to  iron  furring.  When  the  lath  is  not  of  the  proper 
width  the  results  will  not  be  so  good  and  there  is  liable  to  be 
a  waste  of  material. 

The  standard  width  of  plain  and  of  V-rib  stiffened  lath  is 
36  ins.  When  beams  or  studs  are  spaced  16  ins.  centre  to 
centre,  the  kith  should  be  32  or  48  ins.  wide. 

Expanded  Metal  Lath. — The  first  expanded  lath  was  in- 
vented by  Mr.  John  F.  Golding,  and  the  patents  on  the  lath 
and  the  method  of  manufacturing  are  controlled  by  the  Expanded 
Metal  Company.*  Very  large  quantities  of  this  lath  have 
been  used  for  both  fire-proof  work  and  for  lathing  on  wooden 
construction.  It  is  made  from  strips  of  thin,  soft,  and  tough 
steel  by  a  mechanical  process  which  pushes  out  or  expands 
the  metal  into  oblon  meshes,  and  at  the  same  time  reverses 
the  direction  of  the  eu  \  so  that  the  flat  surface  of  the  cut 
strand  is  nearly  at  right  ,.  ^les  with  the  general  surface  of  the 
sheet. 


*  Main  office,  New  York. 


LATHS. 


829 


For  plastering,  two  styles,  "A"  and  "B"  lath,  Fig.  86  (0.6  X  1.5 
ins.  rnesh),  and  the  " Diamond/'  Fig.  87  (0.41X1.2  ins.  mesh, 
24  and  26  Stubbs  gauge).  Both  kinds  are  made  in  sheets 
8  ft.  long  and  from  18  to  24  ins.  in  width. 

This  lath  being  flat  and  of  considerable  stiffness,  does  not 
require  to  be  stretched,  and  can  be  fastened  directly  to  the 
underside  of  floor-joist  or  to  wood  studding.  If  used  on  plank 
it  should  be  fastened  over  metal  furring  strips.  When  applied 
to  studding  the  lath  should  be  placed  so  that  the  long  way  of 
the  mesh  will  be  at  right  angles  to  the  studding,  as  this  insures 


FIG.  86.— "A"  and  "B"  Lath. 


FIG.  87.— Diamond  Lath. 

the  greatest  rigidity.  The  studding  or  furring  strips  should 
be  spaced  12  or  16  ins.  on  centres,  and  the  lathing  secured 
with  staples  1  in.  long,  driven  about  5  ins.  apart  on  the  stud 
or  joist.  The  lath,  when  applied,  is  a  scant  J  in.  thick,  and 
to  obtain  a  good  wall  ^-inch  grounds  should  be  used. 

Herringbone  Lath. — This  is  another  form  of  expanded 
metal  lath  that  has  been  extensively  used  during  the  past  three 
or  four  years.  It  is  made  in  four  grades,  A  and  A. A,  B  and  BB. 
The  B  grades  are  made  in  wider  sheets,  and  are  more  open  and 


830 


FIRE-PROOFING   OF  BUILDINGS. 


consequently  not  as  heavy  or  stiff  as  the  A  grades.  The  general 
appearance  of  the  A  and  B  grades  is  shown  by  Fig.  88. 

The  A  and  A  A  grades  and  the  B  and  BB  grades  differ  only 
in  that  the  A  A  and  BB  grades  have  a  smaller  mesh  and  are 
consequently  stiffer  than  the  A  and  B  grades.  The  A  A  grade 
is  the  stiffest  of  all  and  the  most  expensive,  the  A  grade  comes 
next,  the  BB  third,  and  the  B  grade  is  the  lightest  of  all. 

The  A  grade  is  probably  most  used.  For  ceilings  "A  flat" 
or  "  A  A  flat"  should  be  specified.  The  short  cross  ribs  of  the 
"flat"  lath  are  turned  after  being  expanded,  diminishing  the 
size  of  the  key  and  presenting  a  larger  surface  to  support  the 
plaster.  The  heavy  longitudinal  ribs  are  at  an  angle  of  about 


FIG.  88. — Herringbone  Lath. 


45  degrees  to  the  general  surface  of  the  lath  and  give  much 
stiffness  to  it. 

In  applying  the  lath  the  sheets  should  run  at  right  angles 
to  the  studding  or  joists,  and  the  longitudinal  ribs  should  slope 
down  against  the  studding  so  as  to  hold  the  mortar.  For 
fastening  to  wood,  the  No.  12  or  14  "poultry"  staple  is  used. 
Except  for  the  A  A  grade,  it  is  best  to  space  the  studding 
12  ins.  on  centres,  although  the  A  grade  can  be  used  with  a 
10-inch  spacing. 


FIG. 


-Imperial  Lath. 


Imperial  or  Spiral  Lath. — Fig.  89  shows  still  another  form 
of    expanded-metal  lath  on  the  market.     This  lath  is  lighter 


LATHS. 


831 


than  most  of  the  laths  made  from  sheet  metal,  and  is  also  a 
little  cheaper.  It  is  furnished  in  sheets  48^  ins.  long  and 
16  ins.  wide,  put  up  in  bundles  of  25  sheets.  Being  so  short 
the  sheets  nest  and  pack  very  closely  and  are  easily  handled 
by  one  man.  Large  quantities  of  this  lath  have  been  used, 
and  it  seems  to  be  much  liked  by  plasterers. 

Perforated  Sheet-metal  Laths. — There  are  some  six  or 
more  styles  of  metal  lath  made  from  sheet  iron  or  steel  by 
perforating  the  sheets  so  as  to  give  a  clinch  to  the  mortar. 
The  sheets  are  generally  corrugated  or  ribbed,  also,  in  order 
to  stiffen  them  and  keep  them  away  from  the  wood.  There  is 
not  a  great  difference  between  these  laths,  although  some  styles 
may  possess  certain  advantages  over  the  others. 

In  general,  those  styles  which  have  the  greatest  amount  of 
preforations,  or  which  approach  the  nearest  to  the  expanded 


FIG.  90. — Bostwick  Lath. 

lath,  are  to  be  preferred.  AlPof  these  laths  come  in  flat  sheets 
about  8  ft.  long  and  15  to  24  ins.  in  width,  and  are  readily 
applied  to  woodwork  by  means  of  barbed-wire  nails.  The  nails 
should  be  driven  every  3  ins.  in  each  bearing,  commencing  at 
the  centre  of  the  sheet  and  working  toward  the  ends.  These 
laths  work  very  nicely  in  forming  round  corners  and  coves. 
Metal  lath  should  never  be  cut  at  the  angles  of  a  room,  but  bent 
to  the  shape  of  the  angle  and  continued  to  the  next  stud  beyond. 
This  strengthens  the  wall  and  prevents  cracks  at  the  angles. 

Of  the  various  forms  of  sheet-metal  lath  in  common  use  the 
Bostwick  lath  (Fig.  90)  is  perhaps  the  best  known.  It  is  made 
of  sheet  steel,  with  ribs  every  |  of  an  inch  in  the  width  of  the 
sheet,  and  loops,  |Xl|  ins.,  punched  out  between  the  ribs. 
It  has  been  extensively  used,  and  is  favored  by  plasterers  be- 
cause it  is  stiff  and  easy  to  apply  and  requires  less  plaster  than 


832  FIRE-PROOFING    OF    BUILDINGS.  , 

the  more  open   laths.     The   lath   should   be   applied   with  the 
loop  side  out. 

Sackett's  Wall  Board. — This  is  a  composite  board  of  alter- 
nate layers  of  plaster  and  paper,  the  whole  being  about  J  inch 
thick  and  designed  to  take  the  place  of  either  wood  or  metal 
lath  with  some  advantages  over  both. 

It  is  claimed  that  this  board  will  not  warp,  buckle,  or  shrink, 
and  that  plastering  applied  to  it  will  not  fall  off.  As  a  fire 
retardent,  it  is  claimed  to  be  equal  to  metal  lath,  and  when 
wired  to  metal  studding  may  be  considered  as  a  fire-proof 
partition.  It  has  the  advantage  of  being  very  light,  and  re- 
quiring but  little  plastering  material,  with  a  consequent  reduc- 
tion in  the  amount  of  water  used  in  plastering. 

The  boards  are  32X36  ins.,  they  may  be  nailed  to  wooden 
studding  or  flat  against  solid  beams,  or  plank,  and  can  be  cut 
with  a  saw. 

For  plastering  the  best  results  are  obtained  by  applying 
first  a  brown  coat  of  hard  wall-plaster  J  to  |  inch  thick;  when 
this  is  thoroughly  set  it  should  be  finished  with  a  thin  coat  of 
regular  hard  finish  (lime-putty  and  plaster). 

This  board  has  been  extensively  used  in  the  Eastern  States, 
and  in  many  prominent  buildings. 

Considering  the  saving  effected  in  the  plastering,  the  board 
costs  less  than  metal  lath,  and  but  a  trifle  more  than  wood 
laths. 

Plaster  Boards. — Wall  boards,  varying  in  thickness  from 
•J  in.  to  2  ins.,  are  made  of  similar  composition  to  the  plaster 
blocks  described  on  p.  817.  These  are  intended  to  be  used  in 
the  same  manner  and  for  the  game  purposes  as  Sackett's  wall 
board. 

Shaft  Construction. — The  most  important  partitions  in  a 
building  are  those  inclosing  interior  shafts.  Vertical  openings 
through  buildings  form  flues  and  cause  up-drafts.  In  all 
buildings,  fire-proof  as  well  as  non-fire-proof,  therefore,  they 
should  be  inclosed  for  two  reasons:  first,  to  prevent  a  fire  that 
would  find  a  natural  outlet  in  such  openings  from  spreading 
to  other  floors;  and  secondly,  to  prevent  as  far  as  possible  fire 
getting  into  these  openings  where  the  draft  would  greatly 
increase  its  fury. 

To  be  thoroughly  effective  the  inclosed  walls  should  be  of 
the  same  construction  as  the  outside  walls  of  the  buildings, 
namely,  brick,  stone,  or  concrete.  They  need  not  necessarily 


SHAFT    CONSTRUCTION.  833 

be  of  the  same  thickness  as  the  outside  walls,  but  12  ins.  is 
recommended  as  a  minimum.  In  less  important  structures 
terra-cotta  partitions  are  sometimes  used  as  such  inclosure 
walls. 

In  the  walls  inclosing  elevator  shafts  no  openings  except 
those  necessary  for  entrance  doors  should  be  permitted.  The 
doors  should  be  of  fire-proof  construction  (see  p.  846)  and  solid. 
Glass  lights  are  sometimes  provided  in  such  doors,  though  not 
good  practice,  and  if  so  wire  glass  only  should  be  used  in 
accordance  with  limitations  given  on  p.  848. 

In  interior  light  and  vent  shafts  openings  must  necessarily 
be  provided,  but  here  again  the  construction  of  the  window 
frames  and  sash  and  the  glazing,  should  be  as  far  as  possible 
as  described  on  pp.  847  and  848. 

Whenever  the  occupancy  of  a  building  admits  of  it,  the 
staircases  should  also  be  inclosed  in  masonry  walls,  with  fire- 
proof doors  at  the  openings.  Unless  so  inclosed  the  staircase 
forms  a  flue  for  the  flames,  so  that  the  stairs  are  exposed  to 
intense  heat.  In  such  situations,  even  an  absolutely  fire-proof 
stairway  could  not  be  used  during  a  fire,  and  possibly  it  is  for 
this  reason  that  greater  pains  have  not  been  taken  to  make 
stairs  fire-proof. 

Shaft  walls  should  in  all  cases  be  carried  three  feet  or  more 
above  the  roof.  / 

Deadening  Quality. —  The  resistance  to  the  passage  of 
sound  through  fire-proof  partitions  is  an  important  considera- 
tion in  buildings  used  for  apartments,  and  where  the  rooms 
are  to  be  used  as  music  studios  or  for  conservatory  work,  it 
becomes  a  matter  of  great  importance. 

In  Jan.,  1895,  some  tests  were  made  to  determine  the  relative 
deadening  qualities  of  the  different  partitions  shown  by  Fig.  91, 
the  object  being  to  decide  upon  the  construction  that  should 
be  used  in  Steinway  Hall,  Chicago. 

The  rank  in  sound-proof  efficiency  of  the  different  partitions 
tested  is  shown  by  the  numbers  at  the  right  of  Fig.  91. 

The  4-inch  porous  partition  was  used,  but  was  not  a  success. 
In  the  Fine  Arts  Building,  in  the  same  city,  double  partitions, 
similar  to  No.  1,  were  used,  and  it  is  said  that  they  have  been 
a  great  success. 

It  is  surprising  to  note  that  in  the  tests  above  mentioned, 
the  2-inch  solid-plaster  partition  (common  mortar)  ranked 
higher  than  those  with  double  studding.  The  relative  cost 


834 


FIRE-PROOFING    OF   BUILDINGS. 


%"  Air  Space 


/Plaster 


x  ^P 

' 


solid. 


*\   .Angle  Ironx 1         \#"  Iron  Rod       Filled  in  soli 
J2 "Centers  V  with  Plastei 

^VVire  Cloth  Laced  to  Rod. 
SOLID  PLASTER  PARTITION 


is  ^2"  Stu 


ds  16"  Centers 


Wire  Cloth  Laced  to  Rods 

J^"  Rod  12"  Centers 

_  PI  aster  x  _ 

^  y—  -Iron  J6  ''  Centers  I 


Plaster/ 


Expanded-MetaK 


/%"  Rod  12 "Centers 


2"lron  Studs  16"  Centers 


e  Cloth  Laced  to  Rod 


/Iron  16"  Centers 


Expanded  MetaK 


Expanded  Metal\ 


NIron  16  "Centers 


Fid.  91. — Sound  carried  through  probably  because  of  Metal  Connections, 


SHAFT   CONSTRUCTION. 


835 


of  partitions  Nos.  1,  2,  and  3,  including  plastering,  is  given 
by  the  Illinois  Terra-cotta  Lumber  Company  as  $1.86,  $1.16, 
and  $1.14  respectively. 

In  1892,  Prof.  Charles  L.  Norton  tested  the  sound-deadening 
qualities  of  several  forms  of  partitions,  with  the  purpose  of 
selecting  the  best  incombustible  sound-proof  partition  for  the 
dormitories  of  the  New  England  Conservatory  of  Music,  in 
which  practically  every  room  is  a  music  studio.  The  results 
of  these  tests,  with  a  description  of  the  partitions,  was  pub- 
lished in  Insurance  Engineering  for  August,  1902. 

The  various  partitions  were  rated  by  Prof.  Norton  as  follows: 


No. 

Room. 

Side. 

Scale. 

Composition. 

1 

E 

Left 

100 

Cabot's  quilt,  3  thick  +  metal  lath. 

2 

E 

Right 

95 

"2       "    +       "       " 

3 

E 

Rear 

95 

"2       "    -f       "       " 

4 

C 

Rear 

85 

Sackett  board,  2  felt  on  Us. 

5 

C 

Left 

85 

"       2    "     "    C. 

6 

C 

Right 

80 

«  i           •  i       2   '  • 

7 

D 

Rear 

75 

Metal  lath  +  paper. 

8 

D 

Right 

75 

"       "    +       "    +felt. 

9 

B 

Right 

60 

Two  2-in.  Keystone  block  with  2-in  air  space. 

10 

A 

Rear 

50 

4-in.  National  terra-cotta  blocks. 

11 

B 

Rear 

50 

3-in.  Keystone  blocky. 

12 

A 

Right 

45 

3-in.  National  terra-cotta  blocks. 

13 

B 

Left 

40 

2-in.  Keystone  blocks. 

14 

A 

Left 

40 

2-in.  National  terra-cotta  blocks. 

15 

D 

Left 

30 

2-in.  metal  lath,  solid  plaster. 

"Nothing  more  is  to  be  inferred  from  the  numerical  effi- 
ciencies (under  ' scale')  than  that  the  first  partition  is  about 
three  times  as  good  as  the  last,  and  that  the  numerical  interval 
between  any  two  partitions  on  the  list  merely  indicates  the 
order  of  the  magnitude  of  the  difference  between  the  parti- 
tions." 

Professor  Norton  recommended  a  partition  of  Sackett  board 
and  plaster  with  two  thicknesses  of  Cabot's  quilt  between  *the 
plaster  board,  and  this  construction  was  adopted.  The  stud- 
ding was  put  up  the  same  as  for  the  2-inch  solid  partition,  the 
quilt  secured  to  each  side  of  the  studs,  and  the  plaster  board 
was  wired  on  to  the  studding  through  the  quilt.  This  also 
makes  about  as  light  a  partition  as  it  is  possible  to  obtain. 

Furring  of  Outside  Walls. — The  outside  walls  of  fire- 
proof buildings  are  generally  finished  on  the  inside  by  plastering 
applied  directly  to  the  masonry.  When  the  walls  are  of  brick, 
it  is  often  desirable  to  fur  them  so  that  there  will  be  an  air 
space  between  the  plaster  and  the  masonry  to  prevent  the 


836 


FIRE-PROOFING    OF  BUILDINGS. 


passage  of  moisture.  This  furring  should  be  either  of  terra- 
cotta or  metal,  and  never  of  wood. 

For  this  purpose  furring  brick  are  most  generally  used. 
They  are  made  of  brick  clay  and  of  the  same  size  as  common 
brick,  but  are  hollow.  They  are  built  up  with  the  rest  of  the 
wall,  on  the  inside  face,  and  bonded  into  the  rest  of  the  wall 
by  the  usual  header  courses. 

Partition  tile  are  also  often  used  for  the  inner  4  ins.  of  brick 
walls,  the  tile  taking  the  place  of  a  row  of  brick,  as  in  Fig.  92. 


FIG.  92. 


By  this  means  dampness  is  excluded  without  additional  thick- 
ness to  the  walls,  and  the  only  additional  expense  is  the  extra 
cost  of  the  hollow  tile  over  the  common  brick.  When  using  either 
furring  blocks  or  hollow  tile,  the  mason  should  be  careful  not 
to  drop  mortar  into  the  hollow  spaces. 

Where  walls  are  furred  or  lined  with  tile,  solid  porous  terra- 
cotta blocks  should  be  built  in  wherever  nailings  are  required 
for  base,  picture  moulding,  etc. 

In  some  cities,  as  in  New  York,  the  laws  require  that  when 


FLOORING  837 

furring  brick  or  tile  is  used  it  shall  not  be  counted  as  a  part  of 
the  thickness  of  the  wall.  Wire  lathing,  with  a  1-in.  V-rib 
woven  in  every  7J  ins.,  also  makes  a  good  furring  for  brick 
walls,  as  it  is  easily  applied  and  affords  an  air-space  between 
the  wall  and  plaster. 

All  of  these  devices  also  protect  the  walls  from  being  warped 
by  heat  during  a  fire,  and  prevent  the  passage  of  heat  through 
the  walls  in  summer  and  winter. 

Metal  Furring. — To  produce  architectural  forms  in  the 
interior  decoration  of  fire-proof  buildings,  metal  furring  and 
lathing  are  now  used  almost  universally. 

The  furring  is  always  of  a  sham  nature,  and  is  never  employed 
to  carry  loads  of  any  magnitude,  so  that  the  only  requirement 
is  that  it  shall  be  incombustible  and  furnish  a  satisfactory 
ground  for  attaching  the  metal  lath. 

For  coves,  cornices,  false  beams,  etc.,  the  furring  members 
are  made  of  light  bars,  angles,  tees,  or  channels  attached  to  the 
walls  by  means  of  nails,  staples,  or  toggle  bolts,  and  to  the 
steel  beams  by  means  of  bolts,  hangers,  clips,  etc.  The  furring 
pieces  are  bent  or  shaped  to  the  approximate  outline  of  the 
finished  plaster  work,  so  that  when  the  lathing  is  applied  it 
will  not  require  more  than  H  or  2  ins.  of  plaster  to  give  the 
desired  outline.  For  plane  surfaces  the  furring  should  be 
brought  to  within  f  in.  of  the  plaster  line.  Deep  beams,  etc., 
should  be  braced  by  diagonal  rods,  to  prevent  distortion. 

All  structural  steel  members  should  always  be  fireproof ed 
back  of  the  furring. 

The  lathing  is  secured  to  the  furring  by  means  of  No.  18 
galvanized  lacing  wire. 

The  spacing  of  the  furring  should  be  either  12  or  16  ins., 
according  to  the  kind  of  lath  that  is  to  be  used. 

When  chases  in  walls  are  covered  over,  it  should  be  done 
with  metal  furring  and  lath.  The  casings  for  vertical  pipe 
lines  should  also  be  of  this  construction  with  the  space  at  the 
floor  level  filled  solidly  about  the  pipe  with  fire-proof  material, 
to  cut  off  all  connection  between  stories. 

Fire-proof  Flooring.  — The  floor  surfaces  of  most  fire-proof 
buildings  consist  of  hard-wood  flooring  secured  in  the  usual 
manner  to  nailing  strips  imbedded  in  the  concrete  or  in  the 
filling  above  the  same.  It  is  sometimes  desired  to  have  a 
flooring  that  is  incombustible.  The  New  York  Building 
Code  requires  that  in  all  buildings  over  150  feet  in  height, 


83S  FIRE-PROOFING    OF   BUILDINGS. 

the  floor  surfaces  shall  be  of  stone,  cement,  tiling,  or  similar 
incombutsible  material,  or  they  may  be  of  wood  treated  by 
some  process  to  render  it  fire-proof.  For  warehouses  and 
factories,  floors  finished  with  Portland  cement  are  about  as 
satisfactory  as  any  flooring,  and  cement  floors  have  been  con- 
siderably used  for  the  guest  rooms  of  hotels.  In  the  latter 
rooms,  the  floor  is  covered  by  a  carpet,  which  is  secured  to 
wood  st«rips  imbedded  in  the  cement  around  the  borders  of  the 
room.  This  makes  a  very  sanitary  floor,  and  is  as  easy  to  the 
feet  as  a  carpeted  wood  floor. 

For  public  corridors,  banks,  lobbies,  toilet  rooms,  etc.,  either 
encaustic,  vitreous,  ceramic,  or  marble  tiling  is  generally  used. 
In  France  and  Germany  large  quantities  of  cement  tile  are 
used.  Cement  tiles  have  also  been  introduced  in  this  country, 
but  as  yet  they  have  not  been  able  to  compete  with  encaustic  tile. 

In  most  buildings,  however,  the  use  of  stone,  cement,  or  tile 
flooring  is  undesirable.  These  materials  are  cold  and  trying 
to  the  feet.  Cement  floor  surfaces  do  not  generally  wear  well. 
Asphaltic  flooring  is  sometimes  used,  but  it  is  not  pleasing  in 
appearance.  This  material  and  different  floor  tiles  are  dis- 
cussed on  pp.  1448  and  1444  respectively. 

The  characteristics  of  fire-proof  wood  and  its  availability 
for  this  purpose  are  quite  fully  covered  in  the  discussion  of 
that  material  on  p.  736. 

Composition  Flooring.  —  Several  attempts  have  been 
made  to  obtain  a  flooring  material  which  could  be  spread  over 
an  entire  floor  without  joints,  and  at  the  same  time  be  elastic, 
wear  well,  and  withstand  water,  acids,  etc.,  and  not  be  too 
expensive.  Various  mixtures  of  magnesite,  asbestos,  fine 
sand,  sawdust  mixed  with  linseed-oil  and  some  binder  like 
chloride  of  magnesium,  have  been  put  on  the  market  under 
different  names,  all  more  or  less  meeting  the  requirements 
above  stated  and  also  being  fire-proof. 

These  materials  are  shipped  in  the  form  of  a  dry  powder 
to  the  point  where  they  are  to  be  used,  there  to  be  mixed  with 
a  specially  prepared  liquid.  The  resultant  is  a  plastic  mate- 
rial which  is  laid  upon  the  surface,  to  be  covered  much  like 
ordinary  cement  or  plaster.  The  materials  harden  in  from 
twelve  to  twenty-four  hours  in  moderately  dry  weather,  when 
the  floor  is  ready  for  use.  When  properly  laid  the  floor  presents 
a  smooth,  fine-grained,  and  continuous  surface,  resembling 
linoleum. 


FLOORING.  839 

These  materials  are  made  in  various  colors,  such  as  red, 
white,  yellow,  brown,  gray,  black,  blue,  and  green,  and  can 
be  laid  on  wood,  stone,  concrete,  asphalt,  cement,  or  metals. 
Another  advantage  is  that  they  can  be  carried  up  on  the 
walls  so  as  to  form  a  coved  base,  without  cracks  or  joints. 

Among  such  floorings  that  are  on  the  market  and  have  been 
used  in  a  number  of  buildings  may  be  mentioned:  Asbestolith, 
made  by  the  Asbestolith  Manufacturing  Co.  of  New  York; 
Lignolith,  controlled  by  the  Hecla  Iron  Works,  Brooklyn,  N.  Y. ; 
Monolith;  Crown  Sanitary  Flooring,  made  by  the  Robt.  A. 
Keasbey  Co.,  New  York;  Alignum;  Taylorite,  made  by 
Ronald  Taylor;  New  York;  and  Magnesia  Building  Lumber, 
sold  by  Keasbey  &  Mattison  Co.,  New  York. 

Interior  Finish. — In  buildings  in  New  York  City  in  which 
the  flooring  must  be  of  incombustible  material,  the  interior 
finish,  including  the  doors,  door  jambs,  window  frames,  sash, 
base,  and  trim,  must  also  be  of  incombustible  materials.  The 
same  materials  that  are  acceptable  as  flooring  can  also  be 
used  for  this  interior  finish.  Several  of  the  largest  buildings 
in  New  York,  including  the  Fuller  Building,  have  all  the  trim 
of  fire-proof  wood.  In  the  Hotel  Gotham,  New  York,  all  the 
doors  and  interior  finish  are  made  of  alignum. 

Kalamein. — Besides  these  materials  metal  or  wood  covered 
with  metal  may  be  used.  In  the  Kalamein  process,  thin  sheets 
of  metal  are  drawn  through  dies  in  such  a  manner  that  they 
take  the  shape  of  any  board  or  moulding  and  have  the  edges 
pressed  into  the  wood  so  that  the  metal  covering  is  held 
tightly.  Copper  and  zinc  are  generally  used  for  this  pur- 
pose. 

Metal-cov7ered  Door  Jambs  and  Trim  are  manufactured 
by  the  Fire-proof  Door  Company 'in  a  great  variety  of  styles 
to  match  their  doors.  (See  p.  846). 

Electroplated  Trim. — A  process  recently  introduced  consists 
in  electrically  depositing  a  layer  of  copper  on  the  outer  surface 
of  wood  mouldings  or  doors.  The  metallic  deposit  preserves 
the  markings  of  the  wood  grain  and  makes  a  very  presentable 
door.  A  good  sample  of  this  work  has  been  installed  in  the 
United  Engineering  Building,  New  York,  by  the  New  York 
Central  Metal  Co.  of  New  York. 

Some  very  fine  work  of  this  kind  has  been  done  by  the  Hecla 
Iron  Works  of  New  York  by  electroplating  on  a  fire-proof 
material  known  as  lignolith. 


840 


FIRE-PROOFING    OF   BUILDINGS. 


Cement  Trim.  —  Keene's  cement  has  been  used  for  many 
years  for  running  base  mouldings,  door  arid  window  trim, 
etc.,  and  in  many  European  buildings  practically  all  of  the 
interior  finish  is  of  this  material.  Any  moulding  can  be  "run" 
in  it  with  good  sharp  angles,  and  it  is  sufficiently  hard  to  stand 
ordinary  usage. 

Fig.  93  shows  a  door  opening  with  trim  of  Keene's  cement. 
This  detail  can  be  further  improved  by  covering  the  wooden 


Cement 


FIG.  93. — Section  through  Door  Jamb. 

frame  arid  door  writh  thin  metal.     The  metal  and  cement  can 
be  painted  as  desired. 


FIG.  95. 


Moulded  Hollow  Tiles  are  also  being  substituted  for  th£ 
ordinary  wood  finish.     The  "Amelia  Apartments/'  erected  by 


STAIRS  841 

H.  B.  Camp  at  Akron,  Ohio,  in  1901,*  is  built  almost  entirely 
of  hollow  tile.  "The  base,  picture-mould,  and  architraves 
around  doors  were  made  of  special  formed  tile,  as  shown  by 
Figs.  94  and  95.  These  tile  were  afterward  painted  to  harmonize 
with  the  color-decoration  scheme.  All  of  the  floors  throughout 
the  building  are  covered  with  a  cement  composition  composed 
of  Sandusky  cement  and  ground  wood,  troweled  down  smooth 
and  level." 

Metallic  Furniture  and  Fittings.— In  offices,  banks,  libra- 
ries, and  public  buildings,  the  furniture  and  fixtures  are  about 
the  only  articles  on  which  a  fire  can  feed — if  the  building  itself 
is  fire-proof — and  if  these  a:  s  made  of  incombustible  mate- 
rials there  is  no  chance  for  a  fire  to  gain  headway,  or  to  do 
much  damage.  For  a  number  of  years  The  Art  Metal  Con- 
struction Company  has  been  making  metallic  fixtures  from  rolled 
steel  plates  finely  finished  in  baked  enamels  relieved  by  brass 
and  bronze  trimmings.  Almost  anything  in  the  way  of  furni- 
ture and  fittings,  even  to  roll-top  desks  and  highly  ornamental 
cabinets,  may  now  be  obtained  in  metal,  and  many  libraries, 
banks,  and  court  houses  have  been  fitted  up  and  furnished 
entirely  with  incombustible  cabinet  work. 

Stairs. — In  a  majority  of  fire-proof  buildings  the  architects 
have  contented  themselves  with  putting  in  incombustible  stairs 
of  iron,  with  perhaps  slate  or  marble  treads.  As  pointed  out  in 
the  first  pages  of  this  chapter,  unprotected  iron  cannot  be 
considered  as  fire-proof,  but  it  is  difficult  to  protect  the  iron 
work  of  a  stairway,  as  usually  built,  and  at  the  same  time  pre- 
serve an  ornamental  effect.  If  exposed  metal  construction  is 
to  be  used,  cast  iron  is  much  to  be  preferred  to  steel,  as  the 
cast  metal  will  retain  its  shape  under  severe  heat  far  better 
than  thin  facings  or  frameworks  of  steel. 

Slate  and  marble  treads  and  platforms  should  never  be  used 
in  stairs  without  a  support  beneath.  When  subjected  to  heat, 
marble  and  slate  will  crack  and  fall  away,  leaving  the  stairs 
impassable.  A  fire  department  captain  in  New  York  City 
recently  lost  his  life  through  the  collapse  of  a  marble  platform. 
If  these  materials  are  to  be  used,  therefore,  there  should  be 
a  sub-tread  of  iron  or  concrete  beneath  them. 

A  really  fire-proof  stair  should  be  constructed  with  as  little 
iron  work  as  possible,  and  that  incased  in  fire-resisting  mate- 
rials. 

*  Described  in  Fireproof,  for  July,  1903% 


S42 


FIRE-PROOFING   OF    BUILDINGS. 


It  is  possible  and  practicable  to  build  stairs  of  clay  tiles, 
brick  or  reinforced  concrete  that  are  absolutely  fire-proof.  The 
stairs  in  the  Pension  Building  at  Washington  are  built  01  brick 
with  slate  treads,  and  in  many  of  the  earlier  government 
buildings  the  stairs  are  of  stone.  Stones  suitable  for  stairs, 
however,  will  not  stand  heat  as  well  as  cast  iron.  Part  I.  of 
"Building  Construction'7*  contains  descriptions  with  illus- 
trations of  some  brick  stairs. 

The  Guastavino  Company  have  built  several  stairways  on 
their  system,  ushig  flat  clay  tile  imbedded  in  cement.  No 
iron  work  whatever  is  used  in  this  construction,  hence  it  is 
eminently  fire-proof. 

Fig.  96  shows  a  partial  section  of  a  tile  stairway  used  in  the 
Amelia  Apartment  Building,  Akron,  Ohio.  The  blocks  were 


FIG.  96. 

of  hard-burned  material,  glazed,  and  4  ft.  long.  They  were 
supported  upon  the  partition  walls  and  were  used  by  the  me- 
chanics for  carrying  up  material  during  the  erection  of  the 
building. 

Reinforced  concrete  with  slate  or  marble  treads  also  offers 
a  good  material  for  the  construction  of  stairs  and  permits  of 
very  elaborate  and  complicated  construction.! 

Fig.  97  J  shows  the  construction  of  the  stairs  in  the  new 
Government  Printing  Office  at  Washington. 

These  stairs  have  steel  girders  and  strings  which  are  inclosed 
in  the  solid  concrete,  which  is  moulded  to  form  the  steps  and 
risers,  as  shown  in  the  detail.  The  steel  strings,  however,  are 
hardly  necessary,  as  the  reinforcing  bars  will  give  sufficient 
strength 

*  By  Frank  E.  Kidder. 

t  See  also  page  881  p,  Chap.  XXIV. 

$  From  the  Engineering  Record,  of  Dec.  6,  1902. 


STAIRS. 


843 


Some  excellent  details  for  ornamental  iron  stairs  were  pub- 
lished in  the  March,  1903,  number  of  Fireproof,  in  an  article 
by  Mr.  J.  K.  Freitag. 

The  corrugated  sheet  metal,  known  as  Ferro-in-clave  (see 
p.  790)  offers  a  very  convenient  foundation  for  cement  stairs. 


&"".Bar,  12*  on  Centers 


FIG.  97. 


when  built  between  walls  or  partitions  or  with  an  open  string 
Fig.  98  shows  one  way  in  which  the  material  has  been  used 


Pis.  98. — Stairs  with  Treads  and  Risers  of  Ferro-in-clave. 

the  stairs  being  finished  with  about  2  ins.  of  cement  over  the 
metal  and  plastered  underneath.  The  Ferro-in-clave  is  bolted 
to  lugs  or  brackets  screwed  to  or  cast  on  the  strings.  Slate 


844  FIRE-PROOFING  OF  BUILDINGS. 

or  marble  treads  and  risers  may  be  bedded  in  the  mortar  if 
desired. 

Hoof  Coverings. — The  materials  ordinarily  used  for  the 
roof  covering  of  fire-proof  buildings  are:  1.  Tar  and  gravel; 
2.  Asphalt  and  gravel  or  sand;  3.  Vitrified  tiles,  brick  or  slate 
tiles  over  tarred  felt.  Tar  and  gravel,  or  asphalt  felting  and 
gravel,  or  sand,  offer  the  cheapest  roof  suitable  for  a  fire-proof 
building,  and  when  a  good  quality  of  felt  and  distilled  pitch 
or  the  best  grades  of  asphalt  are  used,  make  a  very  satisfactory 
covering.  Such  roofs,  however,  require  to  be  renewed  about 
every  ten  years. 

The  roofing  is  put  on  in  the  same  manner  as  over  wooden 
construction,  the  felt  being  laid  directly  on  the  concrete. 

Probably  the  best  flat  roof  that  can  be  put  on  a  building 
is  one  of  vitrified  or  slate  tiles,  laid  over  five  plys  of  tarred  felt. 
The  felt  is  laid  and  mopped  as  for  a  gravel  roof,  and  the  tiles 
are  bedded  on  the  felt  in  cement  mortar.  Vitrified  tiles,  about 
8  ins.  square  and  1J  ins.  thick,  are  made  for  this  purpose,  and 
slate  tiles  12  ins.  square  by  1  in.  thick  have  been  used.  Flat 
vitrified  brick  tiles  are  also  used. 

Gravel  roofing  should  not  be  used  on  roofs  having  an  incli- 
nation exceeding  |  inch  in  1  foot.  For  pitch  roofs,  either  slate, 
clay  tiles,  or  metal  tiles  may  be  used.  Clay  tiles  will  stand 
exposure  to  fire  better  than  slate,  and  are  to  be  preferred, 
especially  some  of  the  patent  interlocking  tiles.  (See  also 
pp.  1426  to  1437.) 

Window  Protection. — To  be  thoroughly  protected  against 
the  outside  hazard,  buildings  must  have  the  openings  in  the 
outside  walls  provided  with  some  means  of  effectively  closing 
that  opening  against  flame.  The  same  provision  should  be 
made  for  openings  in  the  partition  walls  of  large  buildings. 

Four  general  types  of  devices  are  in  use  for  this  purpose: 
(a)  tin-covered  wood  shutters;  (6)  steel  shutters  or  doors; 
(c)  metal  frames  and  sash,  glazed  with  wire  glass;  and  (d) 
water  curtains. 

Merits  of  Different  Types.— When  properly  constructed 
the  tin-covered  wood  shutter  is  still  the  most  effective  window 
protection.  "In  a  very  severe  fire  in  Lynn,  Mass.,  in  which 
the  heat  was  intense  enough  to  melt  most  of  the  tin  from  the 
outside  of  the  tinned  plates  covering  the  shutters,  it  was  found 
afterward  that  the  wood  was  charred  only  to  a  depth  of  about 
|  inch.  The  shutters  were  warped  slightly  but  afforded  suffi- 


WINDOW    PROTECTION.  845 

cient  protection  against  the  heat  to  allow  men  to  remain  behind 
them  to  put  out  such  fire  as  occasionally  crept  through.  This 
would  not  have  been  possible  behind  iron  shutters  under  similar 
conditions."  * 

Steel  shutters,  under  the  action  of  heat,  warp  very  readily 
and  transmit  considerable  heat.  They  are  the  cheapest  type 
of  window  protection. 

"  There  is  one  objection  to  the  use  of  shutters  on  window 
openings  and  that  is,  that  they  depend  on  fallible  human  agency 
to  be  effective.  They  must  necessarily  be  open  while  the  build- 
ing is  in  use.  When  the  need  for  them  comes  they  are  apt 
to  be  overlooked  and  are  not  closed.  Certain  it  is  that  on 
many  buildings  they  are  not  closed  at  night."  f 

The  metal  frame  and  wire-glass  windows  are  not  unsightly, 
as  most  any  kind  of  shutters  is  apt  to  be.  They  are  more  likely 
to  be  closed  at  night  and  more  readily  closed  when  necessary. 
They  do  not  hide  a  fire  and  are  more  easily  opened  when  neces- 
sary to  reach  a  fire.  The  one  serious  objection  to  them  is  the 
intense  radiation  of  heat  through  the  wire  glass. 

Tin  Covered  Wood  Shutters  and  Doors. — The  effective- 
ness of  this  device  depends  on  its  construction.  "Only  well- 
seasoned  non-resinous  wood,  dressed,  tongued  and  grooved 
in  narrow  boards,  should  be  used.  Wood  containing  moisture 
or  resin  may  generate,  under  heat,  sufficient  steam  or  gas  to 
force  off  the  tin  covering  and  expose  the  wood  to  the  flame. 
The  body  of  the  door  should  consist  of  two  or  three  layers  of 
such  boards  laid  at  right  angles  with  each  other  and  fastened 
together  by  clinch  nails.  The  best  grade  of  tin  should  be  used. 
No  solder  must  be  used,  and  the  tin  plates  should  be  lock- 
jointed,  with  the  nails  in  the  seams.  The  nails  must  be  long 
enough,  at  least  l-o-  inches,  to  secure  a  good  hold  beyond  the 
depth  to  which  the  wood  is  likely  to  char,  which  is  about  f 
inch.  Under  intense  heat  the  wood  is  certain  to  char,  but  if 
the  nails  are  long  enough  to  hold  the  tin  up  against  the  wood, 
and  the  tin  is  properly  put  on  so  as  to  keep  the  air  out  to 
prevent  burning,  the  shutter  will  stand  under  severe  strains."! 

The  hinges,  fastenings,  or  hangers  must  be  bolted  to  the 
door,  not  nailed  or  screwed,  as  the  latter  would  pull  out  during 
a  fire.  If  hung  on  hinges,  the  hinge-hook  should  be  built  into 
the  wall.  This  door  was  designed  for  use  in  mills,  but  it  has 

*  Insurance  Engineering,  Dec.  1902,  p.  557. 
t  Insurance  Engineering  t  Dec.  1902, 


846  FIRE-PROOFING    OF   BUILDINGS. 

worked  so  satisfactorily  that  it  is  generally  adopted  wherever 
a  fire-proof  door  is  wanted  and  the  appearance  is  not  objectior .- 
able. 

Fire-proof  shutters  are  also  made  in  the  same  way. 

The  National  Board  of  Fire  Underwriters  issues  complete 
specifications  *  for  this  type  of  door  and  shutter  which  should 
be  closely  followed  for  satisfactory  results. 

Doors  of  this  type,  provided  on  openings  in  interior  partition 
walls,  are  often,  and  should  be  wherever  possible,  hung  on 
inclined  tracks  so  that  they  will  close  automatically.  Where 
it  is  desirable  to  keep  them  open  ordinarily,  an  automatic  release 
operated  by  a  fusible  link  is  provided. 

Other  Metal  Covered  Wood  Doors. — Wood  doors  covered 
by  the  Kalamein  process  (see  p.  839)  are  sometimes  used  as 
fire  doors  where  appearance  is  a  consideration.  They  are  not 
considered  equal  to  the  standard  tin-covered  wood  doors. 

Paneled  fire-proof  doors  suitable  for  offices,  hotels,  and 
public  buildings  are  made  on  the  same  principle  as  the  standard 
tin-covered  door,  stamped  sheet  steel  being  used  in  place  of 
tin. 

The  Thorp  Fire-proof  Door  Co.  of  Minneapolis  manufacture  a 
,  very  ornamental  door  having  a  core  of  three  thicknesses  of  pine, 
asbestos  covered,  and  the  whole  covered  with  two  sheets  of 
steel  which  are  joined  on  the  edges  by  a  patented  joint.  Panels 
are  sunk  by  hydraulic  pressure.  The  doors  are  made  with 
solid  and  glass  panels,  and  special  panelling  and  moulding  may 
be  made  to  detail.  The  doors  are  finished  either  duplex  copper 
or  brass,  any  finish,  solid  copper  or  brass,  or  painted  one  coat 
at  factory  for  finishing  at  building  to  match  wood. 

All  hardware  is  fitted  to  the  doors  at  the  factory  without 
charge.  Aside  from  their  fire-proof  quality  these  doors  have 
the  advantage  that  they  do  not  swell  or  shrink. 

Steel  Fire  Doors  and  Shutters. — For  a  satisfactory  steel 
door  an  J-inch  sheet  of  steel  should  be  used,  reinforced  on  the 
back  with  a  frame  of  angle  irons  not  less  than  lJ-"Xli"Xj", 
and  increasing  in  size  with  the  door  or  shutter. 

These  doors  or  shutters  may  operate  in  one  of  three  ways: 
(1)  Swinging  on  hinges,  (2)  sliding  on  tracks,  or  (3)  rolling 
vertically. 

The  swinging  doors  or  shutters  are  the  most  reliable  as  there 

*  To  be  had  for  the  asking. 


DOORS.  847 

are  no  complicated  parts  to  get  out  of  order.  They  should 
be  hung  on  eyes  built  into  the  masonry  walls. 

Sliding  doors  or  shutters  must  have  the  rails  on  which  they 
operate  protected  by  metal  shields  to  prevent  obstruction. 

For  larger  openings  the  rolling  shutters  are  generally  pre- 
ferred. They  are  made  in  horizontal  jointed  sectional  strips, 
which  wind  up  on  a  roller  placed  in  a  pocket  above  the  open- 
ing, the  ends  moving  in  metal  grooves  to  hold  them  in  place. 

They  generally  operate  vertically,  though  some  are  made  to 
operate  horizontally,  the  rollers  being  set  vertically  in  pockets 
at  the  sides  of  the  openings.  These  latter  are  more  liable  to 
derangement. 

The  vertically  operated  doors  or  shutters  are  balanced  by 
springs  or  weights  so  as  to  make  them  move  up  or  down  easily. 
Where  they  are  intended  to  be  closed  only  when  needed,  they 
are  slightly  weighted  and  held  open  by  means  of  fusible  links, 
so  that  in  case  of  fire  they  will  close  automatically. 

Sheet-metal  Window  Frames  and  Sash  are  now  made 
f  which  are  weather-tight  and  perfectly  practicable  in  all  respects, 
'and  should  be  used  wherever  fire-proof  windows  are  desired. 
The  sash  are  made  especially  for  holding  wire  glass. 

These  sheet-metal  windows  are  made  in  a  great  variety  of 
forms  to  meet  all  purposes,  the  sashes  may  be  stationary, 
pivoted  either  horizontally  or  vertically,  hinged  or  double 
hung  with  weights,  like  an  ordinary  window.  For  factories, 
warehouses,  stairways,  and  elevator  shafts  a  stationary  lower 
and  pivoted  upper  sash  is  quite  commonly  used,  as  this  is  the 
cheapest  type  of  window. 

The  double-hung  windows  are  now  made  to  work  as  smoothly 
as  wooden  sash  in  ordinary  box  frames.  For  offices,  hotels, 
etc.,  a  window  having  two  sashes,  glazed  with  wire  glass,  that 
close  and  lock  automatically  in  case  of  fire,  and  a  third  inner 
sash  glazed  with  clear  glass,  gives  all  of  the  advantages  of  an 
ordinary  window  with  the  additional  advantage  of  fire-pro- 
tection and  a  better  diffusion  of  light.  Metal  fly-screens  can 
also  be  used  with  these  windows. 

All  movable  sash,  glazed  with  wire  glass,*  should  be  pro- 
vided with  a  device  by  which  the  sash  will  close  and  lock  auto- 
matically in  case  of  fire. 

When  the  contents  of  the  building  are  inflammable  and  the 

*  See  page  738. 


848  FIRE-PROOFING    OF    BUILDINGS. 

exposure  severe,  two  thicknesses  of  wire  glass  should  be  used 
with  a  ventilated  air-space  of  at  least  1  in.  between  the  lights. 

Material. — The  frames  and  sash  should  be  of  at  least 
No.  24  gauge  galvanized  iron,  or  18-oz.  copper.  No.  22  gal- 
vanized iron  and  20-oz.  copper  are  sometimes  used  for  large 
frames. 

The  National  Board  of  -Fire  Underwriters  have  adopted 
rules  governing  the  construction  of  metal  frames  and  sash  for 
fire-proof  windows,  which  may  be  obtained  from  the  Mississippi 
Wire  Glass  Company,  One  of  these  rules  provides  that  "The 
unsupported  surface  of  the  glass  shall  in  no  case  exceed  24X30 
ins."  Hence  metal  sash  with  a  glass  opening  more  than  24  ins. 
in  width  or  30  ins.  in  height  must  be  divided  by  muntins. 

The  principal  manufacturers  of  sheet-metal  window  frames 
and  sash  are  the  Smith-Warren  Company  of  Boston,  Mass.; 
Voigtmann  &  Co.  of  Chicago;  George  Hayes  Co.  of  New  York; 
David  Lupton's  Sons  Co.,  Philadelphia;  and  W.  H.  Mullins  Co. 
of  Salem,  Ohio,  from  whom  circulars  may  be  obtained  giving 
complete  information  as  to  styles  and  details  of  construction. 

Frames  and  sash  of  wood  covered  with  metal  are  sometimes 
used,  the  wood  furnishing  the  strength  and  the  metal  the 
protection.  "The  contention  that  wood  thus  inclosed  is  liable 
to  dry  rot  is  not  confirmed  by  experience,  so  far  as  we  are  aware, 
and  yet  the  process  of  drawing  the  metal  over  the  wood  excludes 
the  air  sufficiently  to  prevent  combustion  when  subjected  to 
heat."  The  use  of  such  wood  covered  with  metal  is  recom- 
mended, however,  only  when  the  better  and  more  expensive 
form  of  hollow  metal  construction  cannot  be  secured."* 

Water  Curtains. — "The  vulnerable  portion  of  buildings 
generally  is  the  front,  where  great  window  openings  are  desired 
for  purposes  of  light,  and  where  it  is  considered  objectionable 
on  account  of  appearance  to  have  shutters  or  even  wire-glass 
windows.  These  large  window  openings  afford  great  oppor- 
tunities for  the  spread  of  fire  across  streets.  The  danger  of 
damage  is  much  increased  where  the  fronts,  as  is  very  common, 
are  made  of  unprotected  metal  work.  A  notable  example, 
illustrating  such  danger,  was  the  building  of  the  Manhattan 
Savings  Institution,  New  York  City,  which  was  severely  damaged 
and  almost  destroyed  by  a  fire  in  a  six-story  non-fire-proof 
building  across  the  street.  Such  conditions  might  be  over- 
come to  some  extent  perhaps  by  the  introduction  of  some 

t  Insurance  Engineering,  Dec.  1902. 


WINDOW  FRAMES  AND   SASH.  849 

system  such  as  the  water  curtains  that  were  placed  on  the 
Chicago  Public  Library.  This  is  practically  a  sprinkler  system 
set  along  the  edge  of  the  cornice  of  the  building,  and  so  arranged 
as  to  furnish  a  thin  sheet  of  water  in  front  of  the  building. 
Such  a  sheet  would,  however,  not  extend  far  before  it  is  turned 
into  spray  and  thus  become  practically  useless.  A  similar 
arrangement  placed  at  each  window  opening  might  be  more 
useful,  though  it  is  doubtful  whether  it  would  be  of  much  value 
in  any  severe  conflagration."  * 

Precautionary  Measures. — No  matter  how  thoroughly  a 
building  may  be  fire-proofed,  if  it  is  filled  with  combustible 
goods,  as  in  warehouses,  stores,  and  factories,  there  is  always 
the  possibility  of  a  fire,  which  if  unchecked  when  first  started 
must  necessarily  entail  a  great  loss  and  more  or  less  damage  to 
the  building.  If  a  fire  is  discovered  and  checked  in  its  incipient 
stage  this  loss  is  avoided.  There  are  now  many  valuable 
devices  for  detecting  and  checking  fires,  which  should  be  in- 
stalled in  every  warehouse,  and  which  may  often  be  placed 
with  advantage  in  buildings  used  for  other  purposes. 

The  more  important  of  these  are: 
Automatic  alarms. 
Automatic  sprinklers. 
Standpipes,  hose-reels,  etc. 

Automatic  Alarms. — By  means  of  very  sensitive  thermo- 
stats, a  rise  in  temperature  of  35  degrees  above  the  normal 
maximum  temperature  to  be  expected  in  the  building  will 
cause  an  alarm  to  be  sounded. 

The  Montauk  Multiphase  Cable  Company  make  a  fire- 
detecting  wire  or  cable  which  can  be  used  in  dwellings  and  other 
buildings  in  place  of  the  ordinary  bell  wire,  and,  by  judicious 
distribution  and  arrangement  in  elevator-  and  dumb-waiter 
shafts,  coal  and  wood  cellars,  closets,  store-rooms,  and  other 
unoccupied  rooms,  may  be  used  to  give  timely  warning  of  fire 
originating  in  any  of  these  places. 

This  fire-detecting  wire  consists  of  two  conductors.  The 
central  wire  or  core  which  forms  one  side  of  the  circuit  has  a 
thick  coating  or  wall  of  fusible  metal ;  over  this  is  an  insulating 
coating.  A  number  of  fine  wires  are  wound  over  this  coating 
to  form  a  second  conductor.  The  whole  is  then  covered  with 
suitable  insulation.  When  flame  or  a  dangerous  degree  of  heat 

*  Insurance  Engineering,  Dec.  1902. 


850  FIRE-PROOFING   OF  BUILDINGS. 

comes  into  contact  with  this  wire  it  will  establish  electrical 
connection  between  the  two  conductors  and  give  a  signal  on 
the  premises  equipped. 

This  wire  was  approved  by  the  New  York  Board  of  Under- 
writers, Feb.  20,  1901,  and  has  been  quite  extensively  used 
in  the  Eastern  States. 

Automatic  Sprinklers. —  "An  automatic  sprinkler  is  a 
device  for  distributing  water  by  means  of  a  valve  which  is 
arranged  to  open  under  the  action  of  heat,  as  from  a  fire  which 
it  is  intended  to  extinguish. 

"The  distribution  of  water  which  results  from  properly 
located  sprinklers,  occurs  in  the  form  of  a  rain  of  jets  or  drops, 
and  is  sufficient  to  drench  almost  any  inflammable  stock  be- 
yond the  point  of  ignition.  The  distribution  is  also  economi- 
cal, as  the  water  is  more  evenly  applied  than  from  a  nozzle 
attached  to  a  fire-hose,  and  the  source  is  directly  above  the  fire. 

"Whenever  combustible  merchandise  constitutes  the  con- 
tents of  a  building,  automatic  sprinklers  are  of  great  value,  and 
in  buildings  of  a  height  so  great  as  to  make  the  upper  stories 
difficult  of  access,  especially  if  containing  large  areas  and  very 
combustible  contents,  sprinklers  constitute  the  best  protection 
obtainable."  * 

Information  pertaining  to  the  installation  of  automatic 
sprinklers,  their  cost,  where  they  may  be  obtained,  etc.,  may 
be  obtained  from  the  Insurance  Engineering  Station,  Boston, 
Mass. 

Stand-pipes  and  Hose  Reels. —In  office-buildings,  hotels, 
and  apartment-houses,  where  sprinkler  systems  are  hardly 
suitable,  stand-pipes  with  hose  reels  on  each  floor  and  the 
roof  ready  for  instant  use,  constitute  the  best  means  of  quickly 
controlling  a  fire.  The  stand-pipe  should  be  from  2J  to  6  ins. 
in  diameter,  according  to  the  size  and  height  of  the  building, 
and  should  be  connected  with  the  water  supply  of  the  building 
and  provided  with  Siamese  connections  at  the  street  level  for 
the  fire-department.  Check  valves  should  be  provided,  so  that 
when  the  fire-department  engines  are  attached  their  force  will 
be  added  to  that  of  the  buildings,  pumps,  or  to  that  of  the 

water  system. 

dfci^  — - 

*  J.  K.  Freitag. 


HISTORY.  851 


CHAPTER  XXIV. 
REINFORCED    CONCRETE. 

By  RUDOLPH  P.  MILLER,  C.E. 

Definition. — The  term  reinforced  concrete  is  well  defined 
in  the  regulations  of  the  New  York  Bureau  of  Buildings  as  "an 
approved  concrete  mixture  reinforced  by  steel  of  any  shape,  so 
combined  that  the  steel  will  take  up  the  tensional  stresses  and 
assist  in  the  resistence  to  shear."  * 

The  regulations  use  the  term  "concrete-steel"  which,  like  the 
similar  term,  "steel-concrete "  has  now  gone  out  of  general  use. 

History. — The  great  value  of  concrete  as  a  structural 
material  when  subjected  to  compression  only,  has  been  recognized 
for  centuries.  The  use  of  reinforced  concrete,  however,  as  a 
practicable  and  commercial  form  of  construction  is  comparatively 
recent.  It  is  true  that  as  far  back  as  1869,  Francois  Coignet  of 
Paris  took  out  letters  patent  on  a  combination  of  iron  and  con- 
crete and  that  even  before  this,  in  1867,  the  principle  of  reinforc- 
ing concrete  with  iron  had  been  applied  by  P.  A.  J.  Monier,  a 
gardener  of  Paris,  to  the  making  of  large  flowerpots,  still  the 
general  application  to  building  construction  did  net  occur  till 
about  the  middle  of  the  last  decade  of  the  nineteenth  century. 
In  its  development  from  its  first  use  to  its  application  to  buildings, 
it  was  first  applied  to  bridge  construction. 

The  discussion  of  the  subject  in  this  chapter  will  be  confined 
to  its  use  in  the  construction  of  buildings. 

The  earliest  example  of  a  building  of  reinforced  concrete  in 
this  country,  and  probably  in  the  worid,  is  th<*c  erected  in  1875 
by  W.  E.  Ward,  near  Porchester,  New  York,  in  which  "not  only 
all  the  external  and  internal  walls,  cornices  and  towers  were 
constructed  of  concrete,  but  all  of  the  beams  and  roofs  were 

*  This  is  also  the  definition  of  reinforced  concrete  in  the  building  laws 
of  Chicago.  San  Francisco,  Buffalo,  and  St.  Louis. 


852  REINFORCED  CONCRETE. 

exclusively  made  of  concrete  reinforced  by  light  iron  beams  and 
rods.57* 

Erection. — In  general  outline,  a  building  operation  in 
reinforced  concrete  consists  in  the  usual  preparation  of  the  site 
by  excavation  or  otherwise,  the  provision  of  suitable  foundations 
for  walls,  columns  or  other  supports,  the  erection  of  a  series  of 
wooden  molds  or  forms,  the  placing  of  the  necessary  steel  rein- 
forcement, the  pouring  of  the  concrete  and  the  removal  of  the 
forms  after  the  concrete  has  set  sufficiently  to  sustain  itself  and 
the  load  that  may  come  on  it  during  construction.  From  the 
beginning  of  the  erection  of  the  forms  the  successive  steps  are 
progressive,  that  is,  the  placing  of  the  steel  and  pouring  of  the 
concrete  are  going  on  in  the  lower  sections  or  stories  while  the 
forms  are  being  erected  for  the  upper  sections  or  stories.  So  that 
in  a  large  operation  the  carpenters,  the  steel-setters  and  the 
concreters  may  all  be  working  at  the  same  time,  one  set  slightly 
in  advance  of  the  others  without  interference  one  with  the  others. 
These  several  steps  -in  the  operation  will  be  considered  in  more 
detail  in  the  paragraphs  on  "Erection." 

Materials. 

The  materials  used  in  reinforced  concrete  are  concrete  and 
steel.  The  concrete  forms  the  mass  of  the  construction.  Its 
proper  use  is  to  resist  compression.  While  it  has  some  tensile 
strength  the  amount  is  so  small  and  so  variable  that  it  should 
always  be  neglected. 

Steel  is  used  for  the  reinforcing  material  as  it  furnishes  the 
greatest  amount  of  strength  at  the  least  expense.  Wrought  iron 
could  be  used,  but  it  is  practically  unobtainable  under  present 
conditions,  and,  as  already  intimated,  its  use  is  not  economical. 

Concrete. — The  concrete  consists  of  a  mixture  of  cement 
and  some  aggregate,  in  definite  proportions  with  the  necessary 
water  to  cause  the  setting  of  the  cement. 

Cement. — Portland  cement  should  always  be  used  in 
reinforced  concrete,  and  it  should  always  be  tested  before  being 
used.  Even  in  small  jobs  it  is  important  to  know  that  the 
cement  is  strong  and  sound.  In  purchasing  the  cement,  the 
certificate  of  some  reliable  testing  laboratory  should  be  made 

*  For  a  further  and  more  extended  history  the  reader  is  referred  to  the 
larger  treatises  on  this  subject  and  to  Mr.  Edwin  Thacher's  article  in  the 
Engineering  News  of  March  26,  1903. 


MATERIALS.  853 

one  of  the  conditions  of  acceptance.  Under  any  circumstances, 
it  is  always  best  to  have  the  testing  done  at  some  well  established 
and  properly  equipped  cement  testing  laboratory.  The  results 
of  tests  in  temporary  laboratories  are  often  abnormal  and  may 
lead  to  unnecessary  controversies  with  the  manufacturers. 

To  be  acceptable,  a  cement  should  meet  the  following  require- 
ments as  called  for  in  the  standard  specifications  of  the  American 
Society  for  Testing  Materials.* 

Specific  Gravity. — The  specific  gravity  of  the  cement,  thor- 
""bughly  dried  at  100°  C.,  shall  be  not  less  than  3.10. 

Fineness. — It  shall  leave  by  weight  a  residue  of  not  more  than 
8  per  cent,  on  a  No.  100,  and  not  more  than  25  per  cent,  on  a 
No.  200  sieve. 

Time  of  Setting. — It  shall  develop  initial  set  in  not  less  than 
thirty  minutes,  but  must  develop  hard  set  in  not  less  than  one 
hour,  nor  more  than  ten  hours. 

Tensile  Strength. — The  minimum  requirements  for  tensile 
strength  for  briquettes  one  inch  square  in  section  shall  be  within 
the  following  limits,  and  shall  show  no  retrogression  in  strength 
within  the  periods  specified : 

Neat  Cement. 

24  hours  in  moist  air 150-200  Ibs. 

7  days  (1  day  in  moist  air  6  days  in  water) 450-550  " 

28  days  (1  day  in  moist  air,  27  days  in  water) 550-650  " 

One  Part  Cement,  Three  Parts  Sand. 

7  days  (1  day  in  moisi  air,  6  days  in  water) 150-200  " 

28  days  (1  day  in  moist  air,  27  days  in  water) 200-300   " 

Constancy  of  Volume. — Pats  of  neat  cement  about  three  inches 
in  diameter,  one-half  inch  thick  a"t  the  centre,  and  tapering  to  a 
thin  edge,  shall  be  kept  in  moist  air  for  a  period  of  twenty-four 
hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature  and 
observed  at  intervals  for  at  least  28  days. 

(6)  Another  pat  is  kept  in  water  maintained  as  near  70°  F. 
as  practicable,  and  observed  at  intervals  for  at  least  28  days. 

(c)  A  third  pat.  is  exposed  in  any  convenient  way  in  an  atmos- 

*  For  the  complete  standard  specification  see  Trans.  Am.  Soc.  for  Testing 
Materials,  Vol.  IV,  p.  109.  Copies  may  be  had  on  request  from  the  Assocn. 
*>f  Am.  Portland  Cement  Manfrs.,  Phila. 


854  REINFORCED  CONCRETE. 

phere  of  steam,  above  boiling  water,  in  a  loosely  closed  vessel 
for  five  hours. 

These  pats,  to  satisfactorily  pass  the  requirements,  shall 
remain  firm  and  hard  and  show  no  signs  of  distortion,  checking, 
cracking  or  disintegrating. 

Sulphuric  Acid  and  Magnesia. — The  cement  shall  not  contain 
more  than  1.75  per  cent,  of  anhydrous  sulphuric  acid  (SOa),  nor 
more  than  4  per  cent,  of  magnesia  (MgO). 

The  test  for  constancy  of  volume  or  soundness  is  of^particular 
importance  for  reinforced  concrete  work.  When  used  in  large 
masses  an  occasional  batch  of  concrete  made  with  unsound 
cement  may  not  seriously  affect  the  final  result,  but  in  reinforced 
concrete  building  operations,  where  the  different  members  of 
the  structures  are  comparatively  small,  the  safety  of  the  entire 
building  may  be  jeopardized  by  the  use  of  a  small  amount  of 
unsound  cement  in  some  important  part,  such  as  a  column. 

Aggregate. — BV  the  term  aggregate  is  understood  the 
materials  mixed  with  the  cement  to  make  the  concrete,  including 
the  sand.  In  practically  all  cases,  the  sand  is  a  necessary  element. 

Sand. — "The  sand  should  be  clean.  One  may  obtain  some 
idea  of  its  cleanliness  by  placing  it  in  the  palm  of  one  hand  and 
rubbing  it  with  the  fingers  of  the  other.  If  the  sand  is  dirty, 
it  will  discolor  the  palm.  If  the  use  of  dirty  sand  is  unavoidable, 
its  effect  upon  the  strength  of  the  mortar  should  be  investigated. 
Preference  should  be  given  to  sand  containing  a  mixture  of 
coarse  and  fine  grains.  Extremely  fine  sand  can  be  used  alone, 
but  it  makes  a  weaker  mortar  than  either  coarse  sand  alone  or  a 
mixture  of  coarse  and  fine  sand."* 

Coarser  Aggregate. — For  the  coarser  material  of  the 
aggregate  many  materials  are  used  and  many  others  have  been 
suggested.  Its  selection  is  generally  dependent  upon  local 
conditions,  If  possible  gravel  or  crushed  stone  should  be  used. 
Whatever  is  used  should  be  a  clean  hard  substance  that  will 
secure  to  the  concrete  the  necessary  strength;  that  is,  the  crush- 
ing strength  of  this  material  should  be  equal  to  or  greater  than 
that  of  the  mortar  used,  at  least  at  the  age  of  28  days. 

In  any  case,  where  no  reliable  information  is  to  be  had  on  the 
strength  of  a  concrete  made  from  a  given  aggregate,  careful 
investigation  should  be  made  before  such  material  is  used. 


*  Taylor  &  Thompson,   "Treatise  on  Concrete,   Plain   and  Reinforced." 
John  Wiley  &  Sons,  New  York. 


MATERIALS.  855 

Gravel.— Gravel,  like  sand,  should  be  clean.  If  dirty  it 
should  be  washed  before  being  used.  To  get  the  most  satisfactory 
or  uniform  results,  gravel  should  be  screened  arid  graded  and 
then  mixed  in  definite  proportions,  as  the  run  of  the  bank  will 
generally  not  give  uniform  results. 

Stone. — The  most  satisfactory  stone  that  can  be  used  is 
trap  rock  (under  which  term  are  included  most  of  the  rocks  of 
igneous  origin),  because  of  its  toughness  and  great  compressive 
strength. 

The  granites  as  they  are  commercially  known,  are  considered 
by  some  equal  in  quality  to  trap  rock  for  the  making  of  concrete. 
The  presence  of  mica  in  considerable  proportion  in  some  of  tha 
so-called  granites  would  seem  to  make  them  unsuitable. 

Lime  stones,  if  the  soft  varieties  are  excepted,  make  excellent 
concrete  so  far  as  strength  is  concerned.  They  would,  however, 
seem  to  affect  the  fireproof  character  of  the  concrete.  (See 
p.  881y.) 

The  harder  and  more  compact  sandstones,  too,  may  be  used 
successfully,  but  great  care  must  be  exercised  in  their  selection. 
Conglomerate,  which  is  in  reality  a  hard  coarse  sandstone,  should 
give  very  satisfactory  results. 

On  account  of  low  crushing  strength,  slate  or  shale  should 
not  be  used  in  concrete. 

Besides  the  stones  thus  far  mentioned,  broken  brick,  terra 
cotta,  furnace  clinker  and  furnace  slag  have  been  suggested.* 

In  the  selection  of  broken  brick  or  terra  cotta  care  must  be 
taken  to  get  hard  burned  material.  The  crushing  strength  of 
such  material,  when  well  selected,  is  a  little  more  than  that  of 
acceptable  concrete,  twenty-eight  days  old.  But  ordinarily 
commercial  brick  or  terra  cotta  will  not  meet  the  requirement  for 
a  good  aggregate,  and  this  material  should  be  used  only  as  a  last 
resort  and  then  only  after  careful  investigation. 

Cinders. — Furnace  clinkers  should  be  clean  and  entirely 
free  from  combustible  matter.  The  writer  knows  of  no  data  on 
the  strength  of  clinker  concrete.  Cinders  are  used  often  where 
fireproofing  is  the  primary  consideration,  and  no  doubt  good 
constructions  may  be  obtained,  with  extreme  care,  by  the  use  of 
clinker  or  cinder  concrete,  especially  if  the  material  is  ground, 
screened  and  graded  as  suggested  for  gravel.  But  in  general 


*  See  Sec.  110.     Building  Code  Recommended  by  National  Board  of  Fire 
Underwriters. 


856  REINFORCED  CONCRETE. 

practice  the  concrete  is  not  uniform  in  quality  and  is  unreliable 
in  strength.  It  will  therefore  not  be  considered  in  this  chapter, 
but  is  treated  of,  more  at  length,  in  the  previous  chapter  on  fire- 
proofing.  (Seep.  734). 

Size  of  Aggregate. — The  size  of  the  aggregate  may  vary 
from  one-fourth  inch  to  two  and  one-half  inches  in  largest  dia- 
metrical dimension,  depending  on  the  particular  purpose  for 
which  it  is  to  be  used.  Where  the  mass  of  concrete  is  compara- 
tively large  the  aggregate  may  run  as  high  as  two  and  one-half 
inches  in  size.  This  may  sometimes  be  the  case  in  foundations 
and  in  large  piers  and  thick  walls.  In  columns,  girders,  beams 
and  slabs,  very  unsatisfactory  results  would  be  obtained  if  so 
large  a  stone  were  used.  For  such  work  no  stone  or  other  aggre- 
gate should  be  used  larger  than  would  pass  a  one-inch  screen. 
In  important  girders  and  columns,  especially  when  the  rein- 
forcing bars  are  closely  spaced,  the  size  should  be  made  even 
smaller. 

The  maximum  sizes  allowed  for  the  aggregate  in  reinforced 
concrete  in  the  different  cities  are  given  below. 

New  York,  Chicago,  St.  Louis,  Buffalo:  stone  that  will  pass  a 
¥  ring,  i.e.,  " Three-quarter  inch  stone." 

Cleveland:  for  floors  and  fireproofing,  J"  stone;  for  other 
concrete,  2"  stone. 

San  Francisco:  for  floors  and  fireproofing,  V  stone;  for  foun- 
dations, 2"  stone. 

Proportion. — The  proper  proportion  of  the  materials 
entering  into  the  concrete  is  dependent  on  the  size  and  character 
of  the  material.  In  cities  where  there  are  regulations  governing 
reinforced  concrete  construction  the  mixture  to  be  used  is 
generally  specified.  In  the  absence  of  other  considerations  the 
most  satisfactory  and  reliable  mixture  is  one  part  of  Portland 
cement,  two  parts  sand  and  four  parts  stone  or  gravel.  It  is  the 
mixture  that  has  been  used  in  most  of  the  experimental  work  on 
reinforced  concrete,  and  there  is  therefore  much  trustworthy 
information  to  be  had. 

In  the  case  of  large  or  important  operations,  however,  great 
economy  can  often  be  effected  by  a  preliminary  study  of  the 
materials  to  be  used  and  their  proper  proportions.  In  general, 
the  most  economical  mixture  is  also  the  strongest,  for  given 
materials. 

The  old  method  of  determining  the  proportions  of  concrete  by 
measuring  the  voids  in  the  coarser  particles  by  means  of  water 


MATERIALS.  857 

poured  into  a  box  containing  one  cubic  foot  of  the  material  and 
then  providing  that  quantity  of  finer  material,  assuming  the 
cement  the  same  as  sand,  is  not  to  be  recommended.  It  does  not 
give  accurate  or  satisfactory  results. 

A  better  method  is  to  take  the  materials  to  be  used  and  make 
trial  mixtures  by  varying  the  proportions,  but  always  using  the 
same  amount  of  cement  and  water.  Place  these  trial  mixtures 
successively  in  a  measuring  vessel  of  fixed  size,  tamping  the  same 
and  noting  the  height  to  which  the  vessel  is  filled  for  each  mixture. 
The  proportions  that  give  the  lowest  height,  or  result  in  the 
smallest  volume,  will  give  the  most  satisfactory  concrete. 

The  best  and  most  scientific  method,  however,  is  that  known  as 
the  Mechanical  Analysis,  devised  by  Mr.  Wm.  B.  Fuller.  In  this 
method  the  available  materials,  including  the  cement,  are 
separated  into  the  various  sizes  by  means  of  a  series  of  sieves; 
curves  are  plotted  which  indicate  the  percentages  of  the  whole 
mass,  which  pass  the  several  sieves;  from  a  study  of  these  curves 
the  proportions  of  the  different  aggregates  are  determined.  For 
a  detailed  description  of  this  method  the  reader  is  referred  to  the 
chapter  on  " Proportioning  Concrete"  in  Taylor  &  Thompson's 
" Treatise  on  Concrete,  Plain  and  Reinforced." 

As  an  example  of  the  saving  possible,  the  following  case,  given 
in  the  work  just  referred  to,  will  be  of  interest: 

"The  ordinary  mixture  for  water-tight  concrete  is  about 
1:2J:4J,  which  requires  1.37  barrels  of  cement  per  cubic  yard 
of  concrete.  By  carefully  grading  the  materials  by  methods  of 
mechanical  analysis  the  writer  has  obtained  water-tight  work 
with  a  mixture  of  about  1:3:7,  thus  using  only  1.01  barrels  of 
cement  per  cubic  yard  of  concrete.  This  saving  of  0.36  barrels  is 
equivalent,  with  Portland  cement  at  $1.60  per  barrel,  to  $0.58 
per  cubic  yard  of  concrete.  The  added  cost  of  labor  for  propor- 
tioning and  mixing  the  concrete  because  of  the  use  of  five  grades 
of  aggregate  instead  of  two  was  about  $0.15  per  cubic  yard,  thus 
effecting  a  net  saving  of  $0.43  per  cubic  yard.  On  a  piece  of  work 
involving,  say,  20,000  cubic  yards  of  concrete  such  a  saving 
would  amount  to  $8600.00,  an  amount  well  worth  considerable 
study  and  effort  on  the  part  of  those  in  responsible  charge." 

In  the  ordinances  or  regulations  governing  reinforced  concrete 
of  various  cities  the  proportions  to  be  used  are  generally  pre- 
scribed. 

In  New  York  and  St.  Louis  "the  concrete  must  be  mixed  in 
the  proportions  of  one  of  cement,  two  of  sand  and  four  of  stone 


858 


REINFORCED  CONCRETE. 


or  gravel;  or  the  proportions  may  be  such  that  the  resistance 
of  the  concrete  to  crushing  shall  not  be  less  than  2,000  Ibs.  per 
square  inch  after  hardening  for  twenty-eight  days.  The  tests 
to  determine  this  value  must  be  made  under  the  direction  of 
the  Superintendent  of  Buildings." 

In  Cleveland  no  mixture  is  specified,  but  the  strength  to  be 
developed  is  provided  for  as  for  New  York. 

In  Boston  and  San  Francisco  the  proportion  is  given  as  one 
of  cement  to  six  of  aggregate. 

In  Buffalo  a   1 :2 :5  mixture  is  required. 

In  Chicago  a  1:3:5  mixture  is  called  for. 

All  these  cities  require,  however,  that  the  strength  developed 
in  28  days  shall  be  at  least  2,000  Ibs.  per  square  inch. 

Strength. — For  reinforced  concrete  work  no  mixture  should 
be  used  that  does  not  develop  a  strength*  of  at  least  2,000  Ibs. 
per  square  inch  at  the  age  of  twenty-eight  days. 

The  crushing  strength  of  various  concretes  is  shown  in  the 
following  table; 

TABLE  I. 

COMPRESSIVE  STRENGTH  OF  PORTLAND  CEMENT 
CONCRETE  OF  DIFFERENT  PROPORTIONS. 


Proportion 

tc 
..    rj 

Com: 

c 

tJ 

0 

81 

Strength 

AUTHORITY. 

Ja> 

c 

o 

| 

per  sq0 

2 

QQ 

in. 

1 

i 

0 

4 

4370 

James  E.  Howard-Tests  at  Watertown  Arseii-J 

1 

2 

0 

4 

2506 

" 

1 

3 

0 

4 

1812 

" 

1 

4 

0 

4 

830 

1 

5 

0 

4 

532 

1 

6 

0 

4 

169 

1 

7 

0 

4 

118 

1 

2 

4 

4 

2178 

1 

3 

6 

4 

1815 

1 

4 

8 

4 

1135 

1 

5 

10 

4 

707 

1 

6 

12 

4 

738 

1 

2 

2 

4 

1768 

1 

2 

3 

4 

1911 

1 

2 

4 

4 

2147 

1 

2 

5 

4 

2452 

1 

2 

6 

4 

2124 

1 

2 

7 

4 

1650 

1 

2 

8 

4 

1295 

" 

1 

2 

4 

1 

2399 

G.  A.  Kimball-Tests  of  Metals  U.  S.  A, 

1 
1 

3" 

5 
5 

1 
1 

3255 
2042 

Taylor  &  Thompson-Tests  at  Watertown  Arsenal. 
Watertown  Arsenal-Tests  of  Metals  U.  S,  A. 

MATERIALS.  859 

Working  Stresses. — Some  formulae  for  the  strength  of 
reinforced  concrete  construction  provide  for  the  use  of  the 
ultimate  strength  of  the  concrete  and  the  application  of  a  factor 
of  safety.  This  practice  is  not  to  be  recommended  as  it  necessi- 
tates either  the  test  of  the  concrete  or  the  assumption  of  an 
ultimate  stress.  While  it  is  undoubtedly  desirable  that  the 
concrete  should  be  tested,  this  is  generally  impracticable  when 
the  building  is  being  designed.  It  should  be  done  during  con- 
struction and  is  done  on  the  best  work,  to  make  sure  that  the 
concrete  is  up  to  the  requirements. 

Various  factors  of  safety  from  two  and  one-half  to  ten  have 
been  proposed.  Different  factors  of  safety  are  used  for  different 
members  of  a  structure  or  for  different  conditions.  This  furnishes 
another  reason  why  it  would  be  better  to  use  working  stresses  as 
against  ultimate  stresses. 

The  following  working  stresses  are  recommended  for  concrete 
£that  will  develop  a  crushing  strength  of  2,000  Ibs.  per  square 
.inch  at  twenty-eight  days: 

Extreme  fibre  stress  in  compression 500  Ibs.  per  sq.  m. 

Shearing    stress 75  "     "     "     " 

Direct  Compression    350  "     "     "     " 

The  table  on  the  next  page  gives  the  stresses  allowed  by 
various  building  ordinances  and  other  authorities. 

Steel  Reinforcement. — The  function  of  the  steel  rein- 
forcement is  to  take  up  the  tensional  stresses,  to  assist  in  the 
resistance  to  shear  and  in  some  cases,  as  in  columns  and  in  beams 
reinforced  at  the  top,  to  give  additional  compressive  strength. 

Mild  or  High  Steel. — Two  grades  of  steel  are  used  for 
the  reinforcement,  mild  steel  and  high  carbon  steel. 

Mild  or  medium  steel  is  used  for  all  structural  shapes  and  is 
the  ordinary  merchant  steel.  It  has  an  ultimate  tensile  strength 
of  60,000  to  70,000  Ibs.,  and  its  elastic  limit  is  about  one- half  of 
the  ultimate  strength. 

High  carbon  steel  has  a  greater  percentage  of  carbon,  and  is 
therefore  more  brittle.  Its  ultimate  strength  is  about  105,000 
Ibs.  per  square  inch,  and  its  elastic  limit  about  55,000  Ibs. 

The  use  of  high  carbon  steel  would  permit  greater  stresses  in 
the  reinforcement,  and  consequently  a  less  amount  of  steel  and  a 
greater  economy  in  construction.  On  account  of  its  greater 
brittleness,  however,  it  is  liable  to  sudden  failures  under  stress. 
It  is  also  often  found  to  be  cracked  or  broken  when  sent  to  the 


860 


REINFORCED  CONCRETE. 

TABLE  II. 
WORKING  STRESSES. 


P. 

| 

.2  c' 

in  Concrete 
n. 

'oncrete 
n. 

to  Concrete 
n. 

"a; 

1 

fl  _C 

o 

Authority. 

Extreme  Fibre  Sti 
in  concrete  per 

II 

M 

1 

Direct  Comp.  in  C 
per  sq. 

Adhesion  of  Steel 
per  sq.  i 

G    • 

1  o 
£  ft 
W 
0 

1 
& 

1  « 
£  <3 
02  ft 

i1 

o 

S3*8 

New  York  
Chicago  

500 
500 

50 
75 

350 
350 

50 
75J 

16000 
Elastic 

10000 
10000 

12 
12 

St.  Louis  

500 

50 

350 

50 

Limit 

18 

Boston            . 

500 

60 

416  MX 

15    in 

Cleveland  
Buffalo  

500 
500 

50 
50 

347  Mn 

350 
350 

50 
50 

16000 
16000 

10000 
10000 

Beams 
and 
slabs 
10  in 
Col's 
15 
12 

San  Francisco  . 

National  Board 
of  Fire 
Underwriters 

500 
500 

75 
50 

450 
350 

75 

50 

£  Elastic 
Limit 

10000 

15 

18 

work,  and,  unless  very  carefully  inspected  there  is  great  liability 
of  defective  material  getting  into  the  structure.  Furthermore, 
much  of  the  so-called  high  carbon  steel  in  practice  has  been 
found  upon  test  to  fall  far  short  of  the  specifications.  Its  use  is 
therefore  to  be  avoided,  unless  special  care  is  taken  to  secure  an 
absolutely  reliable  article  and  to  have  it  inspected  and  tested. 
For  large  important  work  this  would  be  desirable.  Ordinarily, 
however,  mild  steel  should  be  used,  as  commercially  it  is  manu- 
factured and  sold  under  such  standard  conditions  that  it  is 
reliable.  As  the  modulus  of  elasticity  of  high  carbon  steel  is 
practically  the  same  as  that  of  medium  steel,  the  deformation 
under  any  given  loading  is  the  same  and  there  is  no  special 
advantage  in  the  use  of  one  over  the  other. 

Working  Stresses. — The  generally  accepted  working 
stresses  for  medium  steel  are  16,000  pounds  per  square  inch  in 
tension  and  10,000  pounds  per  square  inch  in  shear.  Tests  have 
shown  that  in  cases  where  the  failure  of  reinforced  concrete 


MATERIALS.  861 

beams  is  due  to  the  failure  of  the  reinforcement,  the  stress  in 
the  metal  had  not  more  than  reached  the  yield  point.  This 
point  is  somewhat  lower  than  the  elastic  limit.  The  working 
stress  in  the  steel,  therefore,  should  be  a  fixed  proportion  of  the 
yield  point  or  the  elastic  limit.  It  is  held  by  some  that  this  ratio 
should  not  be  as  high  as  one  to  two,  but  more  nearly  one  to  three, 
reducing  the  working  stress  in  mild  steel  as  given  above  to 
10,000  or  12,000  pounds  per  square  inch.  In  using  high  carbon 
steel  they  would  advocate  a  similar  ratio  of  the  elastic  limit, 
whatever  that  may  be  according  to  test.  Ordinarily  20,000 
pounds  per  square  inch  is  taken  as  the  working  stress  for  high 
carbon  steel. 

Allowable  working  stresses  in  steel  reinforcement  in  va- 
rious cities  are  given  in  Table  II  on  p.  860. 

Tension  Members.  —  Reinforcement  is  used  in  a  variety 
of  shapes  and  combinations,  nearly  all  of  them  patented  and  some 
of  them  forming  the  basis  for  so-called  systems. 

Where  the  reinforcement  is  employed  to  take  up  tension,  as  in 
a  beam  or  girder,  the  bond  between  the  concrete  and  the  steel  is 
relied  upon  to  develop  the  tensional  stresses  in  the  steel. 

The  plain  bars  depend  entirely  upon  the  adhesion  of  the  steel 
and  the  concrete  for  the  action  of  the  two  materials  in  combi- 
nation, or  the  full  tensile  strength  of  the  rod  is  developed  by 
anchoring  the  rods  into  the  concrete  at  the  ends,  in  which  case 
the  beam  becomes  more  analogous  to  a  trussed  beam  with  the 
»rod  as  the  tension  member.  In  cross-section,  plain  bars  are 
usually  round  or  square,  though  sometimes  flat  bars,  angles,  tees, 
or  other  shapes  are  used.  In  the  use  of  square  bars  and  some 
other  shapes,  it  is  contended  that  the  edges  start  initial  cracks  in 
the  concrete  while  shrinking  during  setting. 

Deformed  Bars. — In  the  deformed  bars  the  adhesion  of 
the  concrete  to  the  steel  is  supplemented  by  a  mechanical  bond 
due  to  the  shape  of  the  bar.  Among  them  the  following  are 
8uch  as  have  been  and  are  being  widely  used. 

Bansome  Bar. — The  Ransome  Twisted  Bars  (Fig.  1),  are 
iinade  of  square  bars  twisted  cold.  The  work  on  the  bars  in  the 
twisting  process  increases  the  tensile  strength  of  the  steel.  On 
this  account  the  users  of  this  bar  generally  assume  a  working 
stress  of  20,000  pounds  per  square  inch.  The  patent  on  this  bar 
ihas  expired  and  its  use  is  now  open  to  anyone,  although  because 
of  special  machinery  and  facilities  the  Ransome  Machinery  Com- 
pany can  probably  furnish  the  bars  at  less  cost  than  they  could 


862 


REINFORCED  CONCRETE. 


otherwise  be  obtained.    Strictly  speaking,  this  is  not  a  deformed 
bar. 

These  bars  can  be  obtained  in  all  sizes,  varying  by  one  eighth 


FIG.  1. 


of  an  inch,  from  J  to  1J  inch.    Larger  sizes  can  also  be  obtained 
on  special  order. 

Thacher     Bar.— The     Thacher    Bulb    Bar    (Fig.    2),    also 
patented,  has  had  extensive  use,  but  more  particularly  in  bridges 


Fio.  2. 

and  arches.  Its  particular  features  need  not  be  discussed  further 
as  the  patentees  have  practically  replaced  it  by  their  new 
Diamond  Bar. 

Johnson  Bar. — The  Johnson  Corrugated  Bar  (patented) 
(Fig.  3),  made  by  the  St.  Louis  Expanded  Metal  Company  is  also 
said  to  be  made  of  high  carbon  steel  with  an  elastic  limit  of  about 
58,000  pounds  per  square  inch.  In  this  bar  the  mechanical  bond 


FIG.  3. — Johnson  Bar. 


is  effected  by  a  series  of  corrugations  on  the  sides  of  a  square  rod, 
alternating  in  position  and  lapping  so  that  the  effective  area 
remains  the  same  for  the  full  length  of  the  bar.  The  shoulders 
formed  by  the  corrugations  have  an  inclination  with  the  axis  of 
the  bar,  such  that  there  cannot  be  any  sliding  of  the  concrete  on 
the  same  under  the  force  tending  to  pull  the  steel  through  the 
concrete. 


MATERIALS. 


863 


DATA  ON   JOHNSON   BAR. 


Nominal 
Size  of  Bar. 

i 


Net  Section. 
0.06 
0.11 
0.14 
0.25 
0.39 
0.56 
0.77 
1.00 
1.56 


Weight  per  Foot. 
0.24  Ibs 
0.38  Ibs 
0.48  Ibs 
0.85  Ibs 
1.33  Ibs 
1.91  Ibs 
2 . 60  Ibs 
3 . 40  Ibs 
5.31  Ibs 


Diamond  Bar.— The  Diamond  Bar  (Fig.  4),  recently  put 
on  the  market  by  the  Concrete  Steel  Engineering  Company,  is 
claimed  as  the  only  deformed  bar  of  absolutely  uniform  section. 
There  is  consequently  no  waste  of  metal  due  to  the  deformations 


FIG.  4. — Diamond  Bar. 

as  in  other  bars.  The  bar  is  practically  a  round  bar  and  sudden 
transitions  from  one  section  to  another  are  avoided  so  that  all 
tendency  to  produce  initial  cracks  in  the  concrete  is  overcome. 

The  weights  and  areas  of  Diamond  bars  are  equal  to  those  of 
plain  square  bars  of  like  denominations.  Bars  may  be  obtained 
from  the  Concrete  Steel  Engineering  Company,  of  New  York, 
from  J  inch  up  to  1|  inches. 

Cold  Twisted  Lug  Bar. — This  bar  is  manufactured  by 
the  General  Fireproofing  Company,  Youngstown,  Ohio,  and,  as; 
its  name  implies,  is  a  twisted  bar  having  small  projections  or  lugs 
at  intervals.  It  is  claimed  for  this  bar  that  the  lugs  effectually 


FIG.   5. — Lug  Bar. 

resist  any  tendency  on  the  part  of  the  bar  to  untwist  under 
tension,  and  that  the  twisting  increases  the  ultimate  strength 
and  raises  the  elastic  limit,  at  the  same  time  reducing  the  elon- 
gation. (Fig.  5.) 


864 


REINFORCED  CONCRETE. 


Cold  twisted  lug  bars  are  rolled  in  sections  corresponding  in 
sectional  area  to  J",  i",  -f",  \" ,  I",  I",  1J"  and  1J"  square  bars. 


DATA  ON  COLD  TWISTED  LUG  BAR. 


Size. 


1 

li 
H 


Approx. 
Wt.  per  Foot. 

.222 

.492 

.870 
1.350 
1.940 
2.640 
3.450 
4 . 350 
5 . 370 
7.700 


Net  Sec.  Area. 

Working  Load 
at  20000  Pounds. 

.0625 

1250 

.1406 

2810 

.2500 

5000 

.3906 

7810 

.5625 

11250 

.7656 

15300 

1.0000 

20000 

1.2656 

25200 

1  .  5625 

31250 

2.2500 

45000 

Cup  Bar. — The  cup  bar  (Fig.  6),  as  implied  by  the  name,  is 
provided  with  a  series  of  cups,  which,  being  filled  with  concrete, 
resist  the  tendency  to  pull  out.  It  is  claimed  for  this  bar  that  the 


FIG.  6. — Cup  Bar. 

cups  are  scientifically  designed  so  that  the  bar  will  not  slip 
through  the  concrete  nor  shear  the  concrete  along  the  line  of  the 
bar.  This  bar  is  manufactured  by  the  Trussed  Concrete  Steel 
Company,  Detroit,  Michigan. 

Other  types  of  patented  reinforcing  bars  which  may  be  men- 
tioned are  the  following: 

De  Man  Undulated  Bar. — A  bar  having  an  approxi- 
mately uniform  cross  section,  with  undulating  faces  which  are 
intended  to  increase  the  bond. 

Universal  Type  Corrugated  Bar.— A  flat  corrugated 
bar  having  rounded  undulating  edges  and  depressions  rolled 
in  the  flat  faces.  This  bar  is  manufactured  by  the  Expanded 
Metal  and  Corrugated  Bar  Company,  St.  Louis,  Mo. 

The  Kahn  and  Golding  bars  are  plain  bars,  which  because  of 
other  features  will  be  considered  in  more  detail  further  on. 

Different  methods  of  anchoring  the  tension  bars  in  reinforced 
concrete  have  been  used.  In  the  Hennebique  System  of  con- 
struction, where  plain  bars  are  used,  the  ends  of  the  rods  are  split 
and  flared  out.  (See  Fig.  7.)  In  other  constructions  the  ends  of 


MATERIALS.  865 

the  bars  are  simply  turned  at  right  angles  in  such  direction  as  is 
most  suitable.  In  some  instances  nuts  and  washers  have  been 
placed  at  the  ends  of  reinforcing  rods.  Where  reinforced  concrete 


Fig.   7. — Hermebiquo  System. 

floors  are  used  in  connection  with  steel  columns  the  rods  are  run 
through  the  web  plates  or  through  angle  brackets  and  secured 
with  nuts.  • 

Adhesion. — The  bond  between  concrete  and  steel  for 
various  forms  of  bars  and  differing  conditions  is  shown  in  the 
table  on  the  next  page. 

Shear  Members.  —  In  many  of  the  tests  on  full  sized 
concrete  beams  failure  occurred  by  the  development  of  diagonal 
breaks  near  the  supports.  These  are  considered  by  some  as  the 
result  of  the  horizontal  and  vertical  shear  which  is  greater 
toward  the  supports.  More  recently  they  are  supposed  to  be 
due,  in  part  at  least,  "to  internal  tension  caused  by  a  stretching 
and  slipping  of  the  rods  employed  in  the  reinforcement."  * 

Stirrups. — On  the  assumption  that  they  are  due  to  shear, 
it  has  been  attempted  to  overcome  the  defect  by  placing  stirrups 
in  the  concrete  either  vertically  or  diagonally.  In  the  older 
constructions  they  are  placed  loosely,  making  only  an  attempt 
to  keep  them  in  their  relative  positions  in  the  beams. 

In  view  of  the  second  cause  mentioned,  however,  the  tendency 
of  the  reinforcement  to  slip  in  the  concrete  should  be  minimized 
by  one  or  more  of  the  following  methods:  (1)  By  securing  the 
greatest  possible  adhesion  of  the  steel  to  the  concrete:  (2)  by 
attaching  the  stirrups  firmly  to  the  tension  rods;  (3)  by  provid- 
ing some  form  of  anchoring  at  ends;  (4)  by  mechanical  bond. 

Kahn  Bar. — In  the  Kahn  Trussed  Bar  the  attachment  of 
the  stirrups  to  the  tension  member  is  positively  secured.  The 
*  Lewis  J.  Johnson  in  Journal  of  Am.  Eng.  Soc.,  June,  1904,  p.  308 


866 


REINFORCED  CONCRETE. 


O 

HH 

in 
W 


E    w  Q 

^      H  55 

g  gj 

^      O  H 

>  ° 
feP 


QQ 

H 

3 

o 
fc 

i 


d 

o3 

H 


^5-     :  3     g5     3     3     S     2     3 


.COCO 


::1J::| 


T3  <u  a)  y>  y>  o  a;®  o>  a 


'C'C'C' 
cr  cr,.^  r^  r> 
iccrHHH 


MATERIALS. 


867 


bar  is  a  square  bar  with  webs  rolled  on  tho  same  at  two  diagonally 
opposite  edges.  The  stirrups  are  formed  by  shearing  these  webs 
for  part  of  their  length  along  the  bar  and  turning  them  up,  as 
shown  in  the  cut.  (Fig.  8.)  These  stirrups  may  be  placed  so  as 


FIG.  8. — Kahn  Bar, 

to  turn  up  in  pairs  or  so  as  to  alternate  on  opposite  sides  of  the 
bar,  making  the  spacing  of  the  stirrups  closer  than  when  turned 
up  in  pairs.  Another  advantage  incidental  to  the  use  of  this  bar 
is  that  the  greater  effective  cross  section  in  the  steel  is  at  the 
centre,  the  point  of  greatest  bending  moment.  Two  disadvan- 
tages, however,  are  the  separation  of  the  concrete  by  the  wings 
above  and  below  the  bar,  and  the  limitation  as  to  the  effective 
stirrup  length  in  deep  beams.  This  bar  is  controlled  by  the 
Trussed  Concrete  Steel  Company  of  Detroit. 

The  Kahn  Trussed  Bar  can  be  obtained  in  the  following  sizes : 


Size. 


3"xl 


2A 

3 

3| 


B 

i 

1 
H 


i 
A 

i 


Weight 
pei- 
foot. 

1.4 
2.7 
4.8 
6.9 


Area 
sq.  in. 

0.38 
0.78 
1.42 
2.00 


Golding  Bar.— The  Golding  Bar  (Fig.  9),  the  product  of 
the  Monolith  Steel  Company  of  Washington,  D.  C.,  i§  a  plain 
bar  of  the  cross  section  shown  in  the  cut.  The  grooves  in  the 
sides  serve  not  only  to  increase  the  area  of  contact  between  steel 
and  concrete  for  a  given  area  of  cross  section,  but  form  a  means 


868 


REINFORCED  CONCRETE. 


of  attachment  for  the  stirrups  as  indicated.  The  grasp  of  the 
metal  on  the  stirrups,  which  is  accomplished  by  machinery,  is 
so  great  that  the  stirrup  will  rupture  before  a  separation  will  take 


FIG.  9. — Golding  Bar. 

place,  as  shown  by  actual  test.     Stirrups  may  be  placed  at  any 
point  and  as  close  together  as  desired. 

This  bar  may  be  obtained  in  the  following  sizes; 


Size 

Area 

Web  Member. . 


w 

2* 


1" 
1 


8/10" 
64/100 


3/16 


Steel  in  Compression. — The  steel  reinforcement  in  rein- 
forced concrete  is  used  in  certain  cases  to  assist,  in  developing 
compressive  strength  when  the  concrete  is  not  sufficient  for  the 
purpose,  as  in  the  case  of  beams  and  girders  with  rods  placed 
above  the  neutral  axis,  and  columns  with  rods  placed  vertically. 
The  use  of  the  steel  reinforcement  in  resisting  compression  will 
be  treated  more  at  length  in  the  paragraph  on  the  design  of 
beams,  girders  and  columns. 

On-  account  of  the  uncertainty,  however,  of  the  steel  and 
concrete  each  receiving  its  proportionate  share  of  the  load,  the 
use  of  steel  in  compression  should  be  avoided  as  much  as  possible. 

Position  of  the  Reinforcement. — The  importance  of  the 
exact  position  of  the  reinforcement  in  the  concrete  will  be- 
come more  apparent  in  the  discussion  of  the  design  of  beams 
(p.  872).  It  will  appear  that  a  slight  displacement  of  the  steel 
will  materially  affect  the  construction.  If  the  steel  shifts  upward 
the  beam  is  weakened,  if  it  shift  downward  the  protection  of  the 
steel  against  rust  or  fire  is  reduced.  In  the  so-called  "Unit" 
systems  the  reinforcement,  including  the  tension  rods  and 
stirrups,  are  so  tied  and  framed  together  that  after  being  placed 


MATERIALS. 


869 


n  the  forms  the  possibility  of  shifting  their  positions  with  respect 
to  the  other  surfaces  of  the  beam  or  to  one  another  is  practically 
entirely  removed. 


Unit  System. — The  particular  advantages  in  the  use  of  a 
unit  system  of  reinforcement  is,  as  already  indicated,  the  assur- 


870  REINFORCED  CONCRETE. 

ance  that  each  and  every  part  of  the  reinforcement  is  in  its  exact 
relative  position,  and  maintains  that  position  during  the  placing 
of  the  concrete.  The  reinforcement  for  each  beam  or  girder  is  as 
carefully  laid  out  as  the  location  of  cover  plate,  stiffeners,  con- 
nection angles  and  rivets  in  a  built  up  steel  girder.  It  can  con- 
sequently bo  thoroughly  inspected  and  checked  before  being 
placed  in  position.  Being  marked,  its  exact  location  is  easily 
determined  by  the  foreman  on  the  job,  from  the  erection  plan. 
After  being  placed  a  quick  inspection  will  show  at  once  whether 
correctly  placed  or  not,  as  it  must  fit  and  extend  the  full  length 
of  the  mold.  Being  fabricated  "off  the  job"  there  is  less  inter- 
ference between  workmen.  The  fabrication  can  be  done  while 
the  molds  are  getting  ready  so  that  there  can  be  more  speed  in 
erection.  The  frames  are  readily  transported  and  less  liable 
to  get  mixed  than  loose  rods  sent  to  the  job. 

The  following  are  types  of  unit  systems: 

The  Unit  System,  shown  in  Fig.  10,.  is  the  pioneer  of  this 
type  of  construction  and  at  present  is  manufactured  by  the  Unit 
Concrete  Steel  Frame  Company  of  Philadelphia.  Its  particular 
features  are  the  bending  up  of  some  of  the  longitudinal  reinforce- 
ment near  the  supports  and  the  use  of  flat  strap  U  shaped  stirrups, 
punched  near  the  upper  ends  through  which  the  slab  rods  are 
threaded. 

The  Pin  Connected  Girder  Frame  shown  in  Fig.  11, 
is  manufactured  by  the  General  Fire  Proofing  Company  of 
Youngstown,  Ohio.  In  this  frame  some  of  the  reinforcement  is 
bent  up  near  the  supports,  and  this  reinforcement  in  adjoining 


LOOP  TRUSS 


DN  AS  USED 


AS  FURNISHED  AND  SHIPPED    / 
FIG.   12. — Cummings  System. 

girders  is  fastened  together  by  means  of  links  and  pins  forming  a 
tie  over  the  supports  making  the  reinforcement  practically 
continuous. 

The  Cummings  System,  shown  in  Fig.  12,  is  manufac- 
tured by  the  Electric  Welding  Company,  Pittsburg,  Pa.  The 
particular  feature  of  this  system  is  the  inverted  U  shaped  stirrups 
which  are  shipped  flat  with  the  longitudinal  reinforcement,  but 


DESIGN. 


871 


are  bent  up  to  an  inclined  position  on  the  work.    The  rods  are 
held  together  by  means  of  a  patented  chair. 

Design. 

Girders,  Beams,  and  Slabs.  —  Different  formula}  have 
been  devised  by  different  investigators  based  on  various  theo- 
retical considerations.  The  formula  here  given  have  been 
widely  accepted  and  are  offered  as  simple  in  form  and  giving 
satisfactory  results.  If  anything  they  err  on  the  side  of  safety, 
and  furthermore  have  been  found  to  give  results  closely  in  accord 
with  actual  tests.  They  have  been  adopted  by  the  Prussian 
Minister  of  Public  Works  (see  Regulations  of  1904),  are  used  b;y 
the  New  York  Building  Bureau  and  are  accepted  by  other 
authorities. 

Assumptions. — The  formula  are  based  on  the  following 
assumptions : 

(a)  The  bond  between  the  concrete  and  steel  is  sufficient  to 
make  the  two  materials  act  together. 

(6)  A  plane  section  before  bending  remains  a  plane  section 
after  bending,  and  the  stress  and  strain  in  any  fiber  are  directly 
proportionate  to  the  distance  of  that  fiber  from  the  neutral  axis. 

(c)  The  modulus  of  elasticity  of  the  concrete  remains  constant 
within  the  assumed  working  stresses. 

(d)  The  tensional  stress  is  taken  entirely  by  the  steel;   that  is 
the  tensile  strength  of  the  concrete  is  not  considered. 

Fig.  13  represents  a  longitudinal  section  of  a  reinforced  con- 
crete beam  under  load. 


kg. 

*Neutral  Axis          \ 

4             * 

j       d 

1 

J 

FIG.  13. 


The  fibers  above  the  neutral  axis  are  in  compression  and 
according  to  our  assumptions  the  strains  vary  in  direct  proportion 
to  the  distance  from  the  neutral  axis,  so  that  the  area  of  compres- 
sion, representing  the  total  compressive  force,  is  indicated  by  the 
shaded  triangle. 


872  REINFORCED  CONCRETE. 

The  total  tensional  force  is  concentrated  at  the  center  of 
gravity  of  the  steel  reinforcement,  and  in  order  that  there  shall 
be  equilibrium  the  resultant  compressive  force  and  the  total 
tensional  force  must  be  equal. 

Formulae  for  Beams.— From  these  conditions  the  follow- 
ing formulae  are  derived,  in  which 

/S  =  the  allowable  tension  or  working  stress  in  the  steel. 
C=the  allowable  unit   compression  or  working  stress  in  the 

extreme  fibre  of  the  concrete. 
r  =  the  ratio  of  the  modulus  of  elasticity  of  steel  to  the  modulus 

of  elasticity  of  the  concrete. 
d  =  the  effective  depth  of  the  beam,  that  is  the  distance  from  the 

center  of  gravity  of  the  steel  reinforcement  to  the  extrema 

fibre  in  compression. 
#  =  the  ratio  of  depth  of  the  neutral  axis  from  the  extreme  fibre  in 

compression,  to  the  effective  depth  of  the  beam,  so  that 
xd  —  the  distance  of  the  neutral  axis  from  the  extreme  fibre  in 

compression. 

6  =  the  width  of  the  beam. 
p  =  the  ratio  of  cross  section  of  the  steel  to  the  cross  section  of  the 

beam,  considering  the  beam  all  of  that  part  of  the  concrete 

above  the  center  of  gravity  of  the  steel. 

M  —  the  moment  of  resistance  of  the  beam,  which  must  of  course 
be  equal  to  or  greater  than  the  moment  of  the  external 
forces  acting  on  the  beam. 

K  —  a  factor  used  for  simplification  of  the  formula.  This  factor 
is  constant  for  any  given  steel  and  concrete. 

For  beams  of  rectangular  cross  section 

M  =  Kbd*\]  (a) 

the  value  of  K  being  determined  by  the  following: 


which  formula  can  be  deduced  from  the  laws  of  flexure  and  the 
assumptions  noted  above. 

In  the  use  of  this  formula  for  the  value  of  K  it  must  be  remem- 
bered that  the  ratio  of  S  to  C,  for  any  given  ratio  of  steel  to  con- 
crete, v.  is  a  constant  so  that  corresponding  values  of  S  and  C 


DESIGN. 


873 


must  be  used.     This  ratio  p,  often  spoken  of  as  the  percentage 
of  reinforcement,  is  the  expression  in  the  first  bracket 


The  value  of  x  is  derived  from  the  expression 


(d) 


Values  for  K  and  x  for  corresponding  values  of  p,  for  different 
conditions  fixed  by  the  building  authorities  of  different  cities  are 
given  in  Tables  IV  and  V. 

TABLE  IV. 

X  =  Coefficient,  which  multiplied  by  d  gives  position  of  Neutral 

Axis. 

K  =  Coefficient  f  or£determining  Resisting  Moment.    M  =  Kbd2 
C  =  Extreme  fibre  stress  in  concrete. 
S  =  Extreme  fibre  stress  in  steel. 

r-f?-12 

EC 


p 

x 

K 

C 

S 

K 

C 

S 

K 

C 

S 

.0005 

.104 

5.8 

115 

12000 

6.8 

135 

14000 

7.7 

154 

16000 

.0010 

.143 

11.4 

168 

" 

13.3 

196 

" 

15.2 

224 

" 

0015 

.172 

17.0 

209 

" 

19.8 

244 

" 

22.6 

279 

" 

.0020 

.196 

22.4 

245 

" 

26.2 

286 

" 

29.9 

327 

" 

.0025 

.217 

27.8 

276 

" 

32.5 

323 

37.1 

369 

" 

.0030 

.235 

33.2 

306 

" 

38.7 

357 

44.2 

409 

" 

.00,35 

.251 

38.5 

335 

" 

44.9 

390 

51.3 

446 

" 

.0040 

.266 

43.8 

361 

" 

51.1 

421 

58.4 

481 

" 

.0045 

.279 

49.0 

387 

" 

57.1 

452 

63.3 

500 

15500 

.0050 

.291 

54.2 

412 

" 

63.2 

481 

65.7 

14550 

.0055 

.303 

59.3 

436 

" 

68.1 

500 

13773 

68.1 

" 

13773 

.  0060 

.314 

64.4 

459 

" 

70.3 

" 

13083 

70.3 

" 

13083 

.0065 

.325 

69.6 

480 

" 

72.5 

" 

12500 

72.5 

" 

12500 

.0070 

.334 

74.2 

500 

11929 

74.2 

" 

11929 

74.2 

" 

11929 

.0075 

.344 

76.2 

11467 

76.2 

" 

11467 

76.2 

" 

11467 

.0080 

.353 

77.9 

11030 

77.9 

" 

11030 

77.9 

" 

11030 

,0085 

.361 

79.4 

10618 

79.4 

" 

10618 

79.4 

" 

10618 

.0090 

.369 

80.9 

10250 

80.9 

" 

10250 

80.9 

" 

10250 

0095 

.377 

82.4 

9921 

82.4 

" 

9921 

82.4 

" 

9921 

.0100 

.384 

83.7 

" 

9600 

83.7 

" 

9600 

83.7 

" 

9600 

.0105 

.392 

85.2 

" 

9333 

85.2 

" 

9333 

85.2 

" 

9333 

.0110 

.399 

86  .-5 

9068 

86.5 

9068 

86.5 

9068 

874 


REINFORCED  CONCRETE. 


TABLE  IV. — Continued. 


p 

X 

K 

C 

S 

K 

,  C 

a 

K 

C 

S 

.0115 

.405 

87.6 

500 

8804 

87.6 

500 

8804 

87.6 

500 

8840 

.0120 

.412 

88.9 

8583 

88.9 

" 

8583 

88.9 

" 

8583 

.0125 

.418 

90.0 

" 

8360 

90.0 

" 

8360 

90.0 

" 

8360 

.0130 

.424 

91.0 

« 

8154 

91.0 

" 

8154 

91.0 

" 

8154 

.0135 

.430 

92.1 

" 

7963 

92.1 

" 

7963 

92.1 

" 

7963 

0140 

.436 

93.2 

" 

7786 

93.2 

" 

7786 

93.2 

" 

7786 

.0145 

.441 

94.0 

" 

7603 

94.0 

" 

7603 

94.0 

" 

7603 

0150 

.446 

94.9 

" 

7433 

94.9 

" 

7433 

94.9 

" 

7433 

.0155 

.452 

96.0 

" 

7290 

96.0 

" 

7290 

96.0 

" 

7290 

0160 

.457 

96.8 

" 

7141 

96.8 

" 

7141 

96.8 

" 

7141 

.0165 

.462 

97.7 

" 

7000 

97.7 

" 

7000 

97.7 

" 

7000 

.0170 

.467 

98.6 

" 

6868 

98.6 

" 

6868 

98.6 

" 

6868 

.0175 

.471 

99.3 

" 

6729 

99.3 

" 

6729 

99.3 

" 

6729 

.0180 

.475 

99.9 

" 

6597 

99.9 

" 

6597 

99.9 

" 

6597 

.0185 

480 

100.8 

" 

6486 

100.8 

" 

6486 

100.8 

" 

6486 

.0190 

.485 

101.7 

" 

6382 

101.7 

" 

6382 

101.7 

" 

6382 

.0195 

489 

102.3 

« 

6269 

102.3 

" 

6269 

102.3 

" 

6269 

0200 

.493 

103.0 

" 

6163 

103.0 

" 

6163 

103.0 

" 

6163 

.0005 

.104 

8.7 

173 

18000 

9.7 

192 

20000 

10.6 

212 

22000 

.0010 

.143 

17.1 

252 

" 

19.0 

280 

20.9 

308 

" 

.0015 

.172 

25.4 

314 

28.3 

349 

" 

31.1 

384 

" 

.0020 

.196 

33.6 

367 

" 

37.4 

408 

" 

41.1 

449 

" 

0025 

217 

41.8 

415 

" 

46.4 

461 

" 

50.3 

500 

21700 

.'0030 

.235 

49.8 

460 

" 

54.2 

500 

19583 

54.2 

" 

19583 

.0035 

251 

57.5 

500 

17929 

57.5 

" 

17929 

57.5 

" 

17929 

.0040 

.266 

60.6 

16625 

60.6 

" 

16625 

60.6 

" 

16625 

.0045 

.279 

63.3 

" 

15500 

63.3 

" 

15500 

63.3 

" 

15500 

!ooso 

291 

65.7 

« 

14550 

65.7 

" 

14550 

65.7 

" 

14550 

!0055 

.303 

68.1 

« 

13773 

68.1 

" 

13773 

68.1 

" 

13773 

.0060 

314 

70.3 

« 

13083 

70.3 

" 

13083 

70.3 

" 

13083 

!0065 

.325 

72.5 

« 

12500 

72.5 

" 

12500 

72.5 

" 

12500 

!oo7o 

334 

74.2 

" 

11929 

74.2 

" 

11929 

74.2 

" 

11929 

!0075 

'.344 

76.2 

« 

11467 

76.2 

" 

11467 

76.2 

" 

11467 

!ooso 

.353 

77.9 

" 

11030 

77.9 

" 

11030 

77.9 

" 

11030 

.361 

79.4 

« 

10618 

79.4 

" 

10618 

79.4 

" 

10618 

OflQO 

369 

80.9 

« 

10250 

8.0.9 

" 

10250 

80.9 

" 

10250 

0095 

377 

82.4 

« 

9921 

82.4 

" 

9921 

82.4 

" 

9921 

.0100 

384 

83.7 

" 

9600 

83.7 

" 

9600 

83.7 

" 

9600 

ioios 

.392 

85.2 

« 

9333 

85.2 

" 

9333 

85.2 

" 

9333 

!ono 

399 

86.5 

" 

9068 

86.5 

" 

9068 

86.5 

" 

9068 

!oii5 

.405 

87.6 

« 

8804 

87.6 

" 

8804 

87.6 

" 

8804 

.0120 

412 

88.9 

" 

8583 

88.9 

" 

8583 

88.9 

" 

8583 

*0125 

.418 

90.0 

• 

8360 

90.0 

" 

8360 

90.0 

" 

8360 

!oiso 

424 

91.0 

* 

8154 

91.0 

" 

8154 

91.0 

" 

8154 

!oi35 

.430 

92.1 

« 

7963 

92.1 

" 

7963 

92.1 

" 

7963 

!oi40 

.436 

93.2 

« 

7786 

93.2 

" 

7786 

93.2 

" 

7786 

0145 

.441 

94  0 

« 

7603 

94.0 

" 

7603 

94.0 

" 

7603 

0150 

446 

94  9 

« 

7433 

94.9 

" 

7433 

94.9 

" 

7433 

!0155 
.0160 

!452 
.457 

96.0 
96.8 

„ 

7290 
7141 

96.0 
96.8 

« 

7290 
7141 

96.0 
96.8 

N 

7290 
7141 

!oi65 

97.7 

« 

7000 

97.7- 

" 

7000 

97.7 

" 

7000 

0170 

467 

98.6 

" 

6868 

98.6 

'' 

6868 

98.6 

" 

6868 

!0175 
.0180 
.0185 
.0190 
.0195 
.0200 

!471 
.475 
.480 
.485 
.489, 
.493 

99.3 
99.9 
100.8 
101.7 
102.3 
103.0 

« 

6729 
6597 
6486 
6382 
6269 
6163 

99.3 
99.9 
100.8 
101.7 
102.3 
103.0 

« 

6729 
6597 
6486 
6382 
6269 
6163 

99.3 
99.9 
100.8 
101.7 
102.3 
103.0 

« 

6729 
6597 
6486 
6382 
6269 
6163 

DESIGN. 


875 


TABLE  V. 
Es 


p 

X 

K 

C 

S 

K 

C 

8 

K 

C 

S 

.0005 

.115 

5.8 

104 

12000 

6.7 

122 

14000 

7.7 

139 

16000 

.0010 

.159 

11.4 

151 

* 

13.3 

176 

" 

15.2 

201 

.0015 

.191 

16.9 

188 

" 

19.7 

220 

" 

22.5 

251 

.0020 

.217 

22.3 

221 

" 

26.0 

258 

29.7 

295 

.0025 

.239 

27.6 

251 

" 

32.2 

293 

36.8 

335 

.0030 

.258 

32.9 

279 

" 

38.4 

326 

43.9 

372 

.0035 

.276 

38.1 

304 

" 

44.5 

355 

50.9 

406 

.0040 

.292 

43.3 

329 

" 

50.6 

384 

57.8 

438 

.0045 

.306 

48.5 

353 

" 

56.6 

412 

64.7 

471 

" 

.0050 

.320 

53.6 

375 

" 

62.6 

438 

71.5 

500 

" 

.0055 

.332 

58.7 

398 

M 

68.5 

464 

73.8 

" 

15091 

.0060 

.344 

63.8 

419 

" 

74.4 

488 

" 

76.2 

* 

14333 

.0065 

.355 

68.8 

439 

" 

78.3 

500 

13654 

78.3 

" 

13654 

.0070 

.365 

73.8 

460 

" 

80.1 

" 

13036 

80.1 

" 

13036 

.0075 

.375 

78.8 

480 

" 

82.0 

" 

12500 

82.0 

" 

12500 

.0080 

.384 

83.7 

500 

• 

83.7 

" 

12000 

83.7 

* 

12000 

.0085 

.393 

85.4 

" 

11559 

85.4 

" 

11559 

85.4 

" 

11559 

.0090 

.402 

87.0 

11167 

87.0 

u 

11167 

87.0 

« 

11167 

.0095 

.410 

88.5 

10789 

88.5 

" 

10789 

88.5 

" 

10789 

.0100 

.418 

89.9 

10450 

89.9 

" 

10450 

89.9 

M 

10450 

.0105 

.425 

91.2 

10119 

91.2 

" 

10119 

91.2 

" 

10119 

.0110 

.433 

92.6 

9841 

92.6 

" 

9841 

92.6 

" 

9841 

.0115 

.440 

93.9 

9565 

93.9 

" 

9565 

93.9 

« 

9565 

.0120 

.446 

94.9 

9292 

94.9 

" 

9292 

94.9 

" 

9292 

.0125 

.453 

96.2 

9060 

96.2 

" 

9060 

96.2 

" 

9060 

.0130 

.459 

97.2 

8827 

97.2 

" 

8827 

97.2 

" 

8827 

.0135 

.465 

98.2 

8611 

98.2 

" 

8611 

98.2 

" 

8611 

.0140 

.471 

99.3 

8411 

99.3 

" 

8411 

99.3 

« 

8411 

.0145 

.477 

100.3 

8224 

100.3 

" 

8224 

100.3 

" 

8224 

.0150 

.483 

101.3 

8050 

101.3 

« 

8050 

101.3 

« 

8050 

.0155 

.488 

102.2 

7871 

102.2 

" 

7871 

102.2 

" 

7871 

.0160 

.493 

103.0 

7703 

103.0 

" 

7703 

103.0 

" 

7703 

.0165 

.498 

103.8 

" 

7545 

103.8 

" 

7545 

103.8 

« 

7545 

.0170 

.503 

104.6 

" 

7397 

104.6 

" 

7397 

104.6 

" 

7397 

.0175 

.508 

105.5 

" 

7257 

105.5 

" 

7257 

105.5 

" 

7257 

.0180 

.513 

106.3 

" 

7125 

106.3 

" 

7125 

106.3 

" 

7125 

.0185 

.518 

107.2 

" 

7000 

107.2 

" 

7000 

107.2 

" 

7000 

.0190 

.522 

107.8 

" 

6868 

107.8 

" 

6868 

107.8 

« 

6868 

.0195 

.527 

108.6 

" 

6756 

108.6 

" 

6756 

108.6 

" 

6756 

.0200 

.531 

109.3 

6638 

.109.3 

6638 

109.3 

6638 

876 


REINFORCED  CONCRETE. 


TABLE  V. — Continued. 


p 

X 

K 

C 

S 

K 

C 

S 

K 

C 

S 

.0005 

.115 

8.7 

157 

18000 

9.6 

174 

20000 

10.6 

191 

22000 

.0010 

.159 

17.1 

226 

" 

18.9 

252 

20.8 

277 

.0015 

.191 

25.3 

283 

" 

28.1 

314 

30.9 

346 

.0020 

.217 

33.4 

332 

" 

37.1 

369 

40.8 

406 

.0025 

.239 

41.4 

377 

<« 

46.0 

418 

50.6 

460 

.0030 

.258 

49.3 

419 

" 

54.8 

465 

58.9 

500 

21500 

.0035 

.276 

57.2 

457 

" 

62.7 

500 

19714 

62.7 

" 

19714 

.0040 

.292 

64.0 

493 

" 

65.9 

" 

18250 

65.9 

" 

18250 

.0045 

.306 

68.7 

500 

17000 

68.7 

" 

17000 

68.7 

" 

17000 

.0050 

.320 

71.5 

" 

16000 

71.5 

" 

16000 

71.5 

" 

16000 

.0055 

.332 

73.8 

" 

15091 

73.8 

" 

15091 

73.8 

" 

15091 

.0060 

.344 

76.2 

" 

14333 

76.2 

" 

14333 

76.2 

" 

14333 

.0065 

.355 

78.3 

" 

13654 

78.3 

11 

13654 

78.3 

13654 

.0070 

.365 

80.1 

" 

13036 

80.1 

" 

13036 

80.1 

" 

13036 

.0075 

.375 

82.0 

" 

12500 

82.0 

" 

12500 

82.0 

12500 

.0080 

.384 

83.7 

" 

12000 

83.7 

" 

12000 

83.7 

" 

12000 

.0085 

.393 

85.4 

" 

11559 

85.4 

" 

11559 

85.4 

" 

11559 

.0090 

.402 

87.0 

" 

11167 

87.0 

" 

11167 

87.0 

11167 

.0095 

.410 

88.5 

" 

10789 

88.5 

" 

10789 

88.5 

" 

10789 

.0100 

.418 

89.9 

" 

10450 

89.9 

M 

10450 

89.9 

" 

10450 

.0105 

.425 

91.2 

" 

10119 

91.2 

" 

10119 

91.2 

" 

10119 

.0110 

.433 

92.6 

" 

9841 

92.6 

a 

9841 

92.6 

" 

9841 

.0115 

.440 

93.9 

" 

9565 

93.9 

" 

9565 

93.9 

" 

9565 

.0120 

.446 

94.9 

" 

9292 

94.9 

" 

9292 

94.9 

" 

9292 

.0125 

.453 

96.2 

" 

9060 

96.2 

" 

9060 

96.2 

" 

9060 

.0130 

.459 

97.2 

" 

8827 

97.2 

" 

8827 

97.2 

" 

8827 

.0135 

.465 

98.2 

" 

sen 

98.2 

" 

8611 

98.2 

" 

8611 

.0140 

.471 

99.3 

" 

8411 

99.3 

" 

8411 

99.3 

" 

8411 

.0145 

.477 

100.3 

fc 

8224 

100.3 

" 

8224 

100  .  3 

" 

8224 

.0150 

.483 

101.3 

" 

8050 

101.3 

" 

8050 

101.3 

" 

8050 

.0155 

.488 

102.2 

" 

7871 

102.2 

" 

7871 

102.2 

" 

7871 

.0160 

.493 

103  .  0 

" 

7703 

103.0 

" 

7703 

103.0 

" 

7703 

.0165 

.498 

103.8 

" 

7545 

103.8 

" 

7545 

103.8 

" 

7545 

.1070 

.503 

104.6 

" 

7397 

104.6 

" 

7397 

104.6 

" 

7397 

.0175 

.508 

105.5 

" 

7257 

105.5 

" 

7257 

105.5 

" 

7257 

.0180 

.513 

106.3 

" 

7125 

106.3 

" 

7125 

106.3 

" 

7125 

.0185 

.518 

107.2 

" 

7000 

107.2 

" 

7000 

107.2 

" 

7000 

.0190 

.522 

107.8 

" 

6868 

107.8 

" 

6868 

107.8 

" 

6868 

.0195 

.527 

108.6 

" 

6756 

108.6 

" 

6756 

108.6 

" 

6756 

.0200 

.531 

109.3 

6638 

109.3 

6638 

109.3 

6638 

A  table  of  value  of  K  for  cinder  concrete  is  also  given,  Table 
VI,  which  is,  however,  recommended  to  be  used  only  for  slabs. 
Cinder  concrete,  though  an  excellent  fireproofing  material,  lacks 
strength  and  should  not  be  used  as  a  structural  material  for  other 
parts  than  slabs  between  beams. 


DESIGN. 
TABLE  VI. 


877 


ip 

X 

K 

C 

S 

K 

C 

S 

.0005 

.170 

7.5 

94 

16000 

7.5 

94 

16000 

.0010 

.232 

14.8 

138 

" 

14.8 

138 

16000 

.0015 

.276 

21.8 

174 

" 

18.8 

150 

13800 

.0020 

.311 

28.7 

206 

" 

20.9 

" 

11633 

.0025 

.340 

33.9 

225 

15300 

22.6 

" 

10200 

.0030 

.365 

36.1 

" 

13688 

24.0 

" 

9125 

.0035 

.387 

37.9 

" 

12439 

25.3 

" 

8293 

.0040 

.407 

39.6 

" 

11447 

26.4 

" 

7631 

.0045 

.425 

41.0 

" 

10625 

27.4 

" 

7083 

.0050 

.442 

42.4 

" 

9945 

28.3 

" 

6630 

.0055 

.457 

43.6 

" 

9348 

29.1 

" 

6232 

.0060 

.471 

44.7 

" 

8831 

29.8 

" 

5888 

.0065 

.484 

45.7 

" 

8377 

30.4 

" 

5585 

.0070 

.497 

46.7 

" 

7988 

31.1 

" 

5325 

.0075 

.508 

47.5 

" 

7620 

31.6 

" 

5080 

.0080 

.519 

48.3 

" 

7298 

32.2 

" 

4866 

.0085 

.529 

49.0 

" 

7001 

32.7 

" 

4668 

.0090 

.539 

49.7 

" 

6738 

33.2 

" 

4492 

.0095 

.548 

50.4 

" 

6489 

33.6 

" 

4326 

.0100 

.557 

51.0 

" 

6266 

34.0 

" 

4178 

.0105 

.565 

51.6 

" 

6054 

34.4 

" 

4036 

.0110 

.573 

52.1 

" 

5860 

34.8 

" 

3907 

.0115 

.581 

52.7 

B 

5684 

35.1 

" 

3789 

.0120 

.588 

53.2 

" 

5513 

35.5 

" 

3675 

.0125 

.595 

53.7 

" 

5355 

35.8 

" 

3570 

.0130 

.602 

54  .  1 

" 

5210 

36.1 

" 

3473 

.0135 

.608 

54.5 

" 

5067 

36.4 

" 

3378 

.0140 

.615 

55  0 

" 

4942 

36.7 

" 

3295 

.0145 

.621 

55.4 

" 

4818 

36.9 

" 

3212 

.0150 

.626 

55.7 

" 

4695 

37.1 

" 

3130 

.0155 

.632 

56.1 

" 

4587 

37.4 

" 

3058 

.0160 

.637 

56.4 

• 

4479 

37.6 

• 

2986 

.0165 

.643 

56.8 

" 

4384 

37.9 

" 

2923 

.0170 

.648 

57.2 

" 

4288 

38.1 

* 

2859 

.0175 

.652 

57.4 

" 

4191 

38.3 

" 

2794 

.0180 

.657 

57.7 

" 

4106 

38.5 

" 

2738 

.0185 

.662 

58.1 

* 

4026 

38.7 

« 

2684 

.0190 

.666 

58.3 

" 

3943 

38.9 

" 

2629 

.0195 

.671 

58.6 

" 

3871 

39.1 

« 

2581 

.0200 

.675 

58.9 

3797 

39.2 

2531 

Rectangular  Beams.  —  In  determining  the  size  of  beam 
required  for  any  given  case,  r  and  the  limiting  values  of  C  and  S 
are  generally  given,  and  K  can  be  determined  for  any  ratio,  p, 
of  concrete  to  steel.  The  value  of  M  is  determined  from  the 
conditions  of  loading,  span  and  spacing,  and  the  width  and  depth 
of  beams  are  to  be  found.  Formula  (a)  may  then  be  put  in  the 
more  convenient  form. 


Kb 

A  value  for  b  is  assumed  and  the  equation  solved  for  d. 


878  REINFORCED  CONCRETE.  . 

Architectural  or  structural  reasons  will  often  limit  the  width  or 
depth  and  several  trials  may  have  to  be  made. 

Slabs. — For  the  strength  of  slabs  the  same  formulae  apply. 
The  slab  may  be  treated  as  a  rectangular  beam  of  unusual  width, 
or  it  may  be  considered  as  a  series  of  beams  set  one  alongside  the 
other,  of  a  width  equal  to  the  spacing  of  the  reinforcing  rods, 
using  one  rod  for  each  beam;  or  it  may  be  considered  a  series  of 
beams  of  a  unit  width,  using  for  the  area  of  steel  the  area  of 
reinforcement  per  unit  of  width. 

Check  Formulae. — It  may  sometimes  happen  that  it  is 
desired  to  check  a  given  or  existing  beam  construction  either  as 
to  strength  or  to  compliance  with  specifications  for  working 
stresses.  In  that  case  the  following  formulae  will  be  convenient : 


If  the  strength  of  the  beam  for  assumed  working  stresses  is 
wanted,  these  values  of  S  and  C  are  inserted  in  formulae  (/)  and 
(#),  and  the  least  value  of  M  is  taken.  If  the  values  of  M  resulting 
from  these  equations  are  not  equal,  it  indicates  that  the  full 
benefit  of  either  one  of  the  materials  is  not  being  obtained. 

If  the  stresses  in  the  steel  or  concrete  due  to  a  given  loading  are 
wanted  the  formulae  would  be  placed  in  the  following  form; 


pb<r-   i- 


These  formulae  apply  to  rectangular  beams  only.  M  in  (6) 
and  (c)  is  taken  as  the  moment  of  the  external  forces,  viz;  the 
bending  moment.  The  value  of  x  can  be  determined  from 
Tables  IV,  V  and  VI. 

In  formula  (6)  it  will  be  noted  that  the  denominator  of  the 
fraction  is  an  expression  for  the  area  of  the  steel  multiplied  by 
the  lever  arm  (distance  from  the  center  of  gravity  of  the  steel 
to  the  center  of  compression  in  the  concrete).  Similarly  in 
formula  (c)  the  denominator  of  the  fraction  is  an  expression  for 


DESIGN.  879 

the  area  of  the  concrete  in  compression  times  the  lever  arm, 
x  again  being  determined  by  (d)  and  M  being  the  bending 
moment  due  to  external  forces. 

Tee  Beams. — In  most  instances  in  building  construction 
floor  slabs  occur  where  beams  or  girders  are  used.  These  slabs  if 
cast  with  the  beams  or  girders  add  very  much  to  the  strength  of 
beam  or  girder.  Some  authors  prefer  not  to  consider  this  addition- 
al strength,  but  to  regard  it  as  increasing  the  factor  of  safety. 
This  position  is  tenable  only  when  the  slabs  are  cast  or  built 
independently.  If  made  at  same  time,  economical  design  re- 
quires that  the  slab  shall  be  considered. 

The  width  of  slab  that  may  be  taken  as  part  of  the  beam 
is  given  by  the  New  York  regulations  as  "ten  times  the  width 
of  beam  or  girder,"  that  is  the  stem.  In  the  Prussian  regulations 


Neutral  Axis 


FIG.  14. 

the  width  of  flange  is  fixed  at  one-third  of  the  span  of  the  beam 
as  a  maximum.  In  any  case  the  width  of  flange  must  not  be 
taken  as  more  than  the  distance  between  beams. 

In  an  ordinary  floor  construction  the  spacing  of  beams,  girders 
and  columns  is  generally  an  architectural  or  commercial  con- 
sideration. It  is,  therefore,  generally  the  simplest  procedure  to 
determine  at  first  the  thickness  of  slab  required  for  the  given 
spacing  of  beams.  This  will  fix  the  thickness  of  the  flange  of 
the  T  beam. 

In  the  calculation  of  the  girder,  it  is  not  objectionable  to  use 
the  same  slab,  or  as  much  of  it  as  may  be  permissible,  that  has 
been  used  in  the  consideration  of  the  beam  framing  into  that 
girder;  inasmuch  as  the  compression  stresses,  in  the  two  cases, 
act  at  right  angles  to  and  practically  assist  one  another. 

Formulae  for  Tee  Beams.— Fig.  14  gives  a  cross  section 
of  a  tee  beam  resulting  from  the  use  of  the  slab  as  part  of  the 


880  REINFORCED   CONCRETE. 

beam,  and  also  shows  clearly  the  notation  used  in  the  formulae. 

There  may  be  three  cases  in  such  a  construction. 

Case  1.  —  The  neutral  axis  may  fall  below  the  flange  in  which 
case 


or 

(I) 

In  these  formulae  the  small  area  of  concrete  in  compression 
below  the  flange  has  been  neglected  and  the  center  of  com- 
pression has  been  assumed  at  the  center  of  the  flange.  This  has 
been  done  to  simplify  the  formulse.  The  result  is  not  materially 
affected  and  errs  on  the  side  of  safety. 

The  position  of  the  neutral  axis  is  given  by  formula  (m) 

and  the  most  economical  percentage  of  steel  by  formula   (n) 

CW  . 
P  =  2Sbd  (See          ^  ^ 

Case  2.  —  The  neutral  axis  may  coincide  with  the  under  side  of 
the  flange,  in  which  case 


(o) 
\       *J/ 

and 

.,      C6W/,  -hl\ 

M=^r(d-3)-  <« 

which  are  the  same  as  formulae  (k)  and  (/) 

The  economical  value  of  p  in  this  case  is  the  same  as  in  Case  1, 
formula  (n) 

Case  3. — The  neutral  axis  may  fall  above  the  lower  edge  of  the 
flange.  This  case  is  the  same  as  Case  2,  as  for  purposes  of  calcula- 
tion all  the  concrete  in  the  flange  below  the  neutral  axis  is 
neglected  and  h  becomes  xd  in  this  case  as  in  the  last. 

Note.— In  determining  the  ratio  of  steel  to  concrete  in  these 
tee  beams  only  that  part  of  the  area  of  the  concrete  is  taken 
that  lies  above  the  center  of  gravity  of  the  steel  and  between 
the  sides  of  the  stem,  that  is,  the  area  bd. 


DESIGN. 


881 


Moduli  of  Elasticity.  —  In  the  derivation  of  all  these 
formulae  and  in  the  determination  of  the  values  of  K,  the  ratio 
of  the  modulus  of  elasticity  of  steel  to  that  of  concrete  plays  an 
important  part.  It  is  necessary  then  to  know  what  value  to 
use.  The  modulus  of  elasticity  of  steel  is  generally  accepted  as 
30,000,000.  The  modulus  of  elasticity  of  concrete  varies  with 
many  conditions.  Even  in  the  same  mixture,  the  character  of 
the  materials  affect  it  as  well  as  the  manner  of  mixing  and 
placing.  The  modulus  increases  with  the  age  of  the  concrete. 
It  also  increases  with  the  richness  of  the  mixture.  It  seems  to 
decrease  with  an  increase  in  load  on  the  concrete. 

The  different  values  for  the  ratio  of  the  modulus  of  elasticity 
of  steel  to  the  modulus  of  elasticity  of  concrete,  to  be  used  in  the 
design  of  reinforced  concrete  construction,  as  fixed  by  the  build- 
ing regulations  of  various  cities  and  other  authorities,  is  given 
in  Table  II,  page  860. 

Values  for  the  modulus  of  elasticity  of  concrete  under  different 
loads  and  for  different  mixtures  as  determined  by  actual  tests 
at  the  Watertown  Arsenal  are  given  in  Table  VII. 

TABLE  VII. 

ELASTIC  PROPERTIES  OF  BROKEN  STONE  CONCRETE 
12  IN.  CUBES. 


Composition. 

Modulus  of  Elasticity 
between  loads  per  sq.  in. 

a 

o 

-d 

M 

£0; 

•S  S 

Age. 

of 
100  Ibs. 

of 
100  Ibs. 

of 
1000  Ibs. 

Tests 
Made  by 

s 

3 

2° 

and 

and 

and 

4! 

TJl 

&m 

600  Ibs. 

1000  Ibs^ 

2000  Ibs. 

1 

2 

4 

7  days 

2593000 

2054000 

1351000 

*Geo.  A.  Kimball. 

1 

2 

4 

1  mo. 

2662000 

2445000 

1462000 

1 

2 

4 

3  mos. 

3671000 

3170000 

2158000 

"     " 

1 

2 

4 

6mos. 

3646000 

3567000 

2582000 

" 

1 

3 

6 

7  days 

1869000 

1530000 

" 

1 

3 

6 

1  mo. 

2438000 

2135000 

1219000 

" 

1 

3 

6 

3  mos. 

2976000 

2656000 

1805000 

" 

1 

3 

6 

6  mos. 

3608000 

3503000 

1868000 

" 

1 

6 

12 

1  mo. 

1376000 

" 

1 

6 

12 

3  mos. 

1642000 

1364000 

" 

1 

6 

12 

6  mos. 

1820000 

1522000 

" 

Working  Stresses.  —  The  working  stresses  for  concrete 
and  steel  allowed  by  various  cities  and  as  recommended  by  other 
authorises,  are  given  in  Table  II  on  p.  860.  In  the  determination 

*  Tests  of  metals,  U.  S.  A.,  1899,  p.  741. 


88  la 


REINFORCED    CONCRETE. 


of  K  the  value  of  C,  S  and  r  as  taken  from  Table  II  are  substituted 
in  formula  (b),  or,  the  value  of  K  may  be  taken  directly  from 
Tables  IV  and  V,  pp.  873  to  877  and  substituted  in  formula  (e). 
For  M  in  that  formula  the  bending  moment  due  to  the  external 
forces  is  used. 

Bending  Moments  in  Beams.  —  Beams  and  girders  are 
usually  considered  as  supported  at  both  ends,  though  in  many 
instances  they  are  actually  carried  as  continuous  beams  over  the 
supports.  If  continued  over  the  supports  there  is  a  negative 
bending  moment  produced  at  the  support  which  should  be  taken 
care  of  by  reinforcement  in  the  upper  part  of  the  beam.  This 
bending  moment  is  one-half  that  at  the  middle  of  a  supported 
beam,  loaded  at  the  center  and  two-thrids  that  at  the  middle  of 
a  uniformly  loaded  supported  beam.  In  the  case  of  supported 
beams  loaded  either  at  the  center  or  uniformly,  the  bending  . 
moment  decreases  toward  the  support. 

cb 


FIG.  15. 


FIG.  16. 

For  these  reasons  it  is  well  in  fixing  the  steel  to  be  used  for  the 
tensional  reinforcement  to  select  the  bars  or  rods  in  pairs,  so  that 
as  the  supports  are  approached  a  part  of  the  reinforcement  may 
be  turned  up  toward  the  top  and  carried  across  the  supports  near 
the  top  as  indicated  in  Figs.  15  and  16. 

Bending  Moments  in  Slabs.— As  floor  slabs  are  usually 
carried  continuously  across  the  supports,  the  bending  moment 
due  to  uniform  load  is  assumed  to  be  less  than  in  beams  simply 
supported  at  ends.  The  New  York  Regulations  provide  that 
"when constructed  continuous  and  when  provided  with  reinforce- 


DESIGN.  8816 

ment  at  top  of  plates  over  the  supports  the  bending  moment 

Wl 

for  uniformly  distributed  loads  may  be  taken  as  ^77*"   The  same 

regulations  provide  that  for  floor  plates  reinforced  in  both  direc- 
tions and  supported  on  all  sides,  the  bending  moment  may  be 

A  Wl 

assumed  as  —  —  . 

The  following  formula  by  Prof.  C.  Bach  *  is  applicable  to  slabs 
or  plates  supported  on  four  sides  and  reinforced  in  both  directions  : 

1     a2x62 

~~' 


in  which  M  =  maximum  bending  moment  for  a  uniformly  distri- 

buted  load, 
a  =  length  of  slab, 
6  =  width  of  slab, 
p*=unit  load. 

Shrinkage  and  Temperature  Stresses.  —  In  slabs 
resting  on  or  carried  over  two  supports  some  reinforcement  should 
be  provided,  in  any  case,  at  right  angles  to  the  tension  rods  to 
provide  against  shrinkage  and  temperature  stresses.  Inci- 
dentally, this  reinforcement  may  also  serve  to  keep  the  tension 
rods  properly  spaced. 

Disposition  of  Steel.  —  In  designing  the  reinforcement 
for  any  form  of  loading,  the  full  sectional  area  required  must  be 
provided  at  the  point  of  maximum  bending  moment.  As  the 
supports  are  approached,  part  of  the  reinforcement,  as  already 
indicated,  is  turned  up,  but  care  must  be  taken  to  keep  it  so 
distributed  that  at  any  point  there  is  still  sufficient  reinforcement 
below  the  neutral  axis  to  furnish  the  necessary  tensional  resist- 
ance. The  arrangement  of  reinforcement  for  a  uniformly  dis- 
tributed or  symmetrically  disposed  load  is  shown  in  Fig.  15,  and 
for  a  concentrated  or  unsymmetrical  load,  in  Fig.  16. 

In  the  first  instance  the^  maximum  bending  moment  is  at  the 
center  of  the  beam  and  the  reinforcement  is  symmetrical  about 
that  point,  and  as  much  as  one-half  the  amount  of  reinforcement 
may  be  turned  up.  In  the  second  instance  the  maximum  bending 
moment  is  at  some  other  point  than  the  center  and  the  reinforce- 
ment must  be  so  disposed  as  to  get  the  full  amount  required  under 

*  "Elasticitat  u.  Festigkeit"  page  598.  See  also  Concrete  Engineering 
July  1,  1907. 


88  Ic  REINFORCED   CONCRETE. 

the  load  or  at  the  point  of  maximum  bending  moment,  and  the 
turning  up  must  be  done  between  that  point  and  the  support. 
Other  conditions  might  require  that  less  than  half  the  reinforce- 
ment shall  turn  up.  As  the  calculations  involved  in  continuous 
beams  are  usually  complicated,  and  as  in  most  cases  beams  are 
figured  as  supported  at  ends,*  the  turning  up  of  part  of  the 
reinforcement  becomes  largely  a  matter  of  judgment. 

There  is  another  consideration  for  turning  up  the  reinforcement 
toward  the  ends,  besides  its  value  to  take  up  negative  bending 
moment,  and  that  is  the  resistance  to  shear  afforded  by  the 
metal  running  through  the  concrete  at  the  points  where  the 
diagonal  cracks  usually  occur  in  tests  on  full-sized  beams. 

Percentage  of  Reinforcement.  —  The  amount  of  the 
reinforcement  in  any  case  is  determined  by  formula  (c)  and  (n) 
for  rectangular  and  tee  beams  respectively.  The  values  there 
obtained  give  the  most  economical  amount.  This  may  vary  from 
one-fourth  of  one  per  cent,  to  one  and  one-half  per  cent,  of  the 
area  of  concrete,  but  will  usually  run  about  seven-tenths  of  one 
per  cent.  The  nearest  stock  size  of  rods  giving  this  amount  or  a 
slightly  greater  amount  can  be  selected  from  the  table  given  on 
page  1350,  or  from  the  catalogues  of  the  manufacturers  of  the 
various  deformed  bars.  The  number  of  rods  used  to  make  up 
the  necessary  sectional  area  must  be  determined  by  consider- 
ations stated  in  the  following  paragraphs. 

Number  of  Rods. — As  already  suggested  an  even  number 
adapts  itself  better  to  a  symmetrical  or  balanced  arrangement 
both  in  cross  section  and  horizontal  section.  One  rod  does  not 
permit  of  the  turning  up  toward  the  support. 

Two  rods  may  be  made  either  to  continue  along  the  lower  edge 
of  the  beam,  or  one  may  start  at  one  support  running  along  the 
lower  part  and  turn  up  beyond  the  center  as  it  approaches  the 
second  support  and  the  second  rod  run  similarly  along  the  bottom 
from  the  second  support  and  turn  up  after  passing  the  center  as 
it  approaches  the  first  support.  Three  rods  may  be  arranged  so 
that  two  continue  along  the  bottom  and  the  third  (center  one) 
turns  up  as  it  approaches  the  supports. 

The  arrangement  for  4,  5  or  6  will  naturally  suggest  itself  from 
what  is  already  said. 

Too  large  a  number  of  rods  is  not  desirable  as  in  such  a  case  the 

*  The  regulations  of  New  York,  Chicago,  Cleveland,  San  Francisco, 
Buffalo  and  St.  Louis,  require  that  beams  and  girders  shall  be  considered 
as  simply  supported  at  the  ends. 


DESIGN.  881d 

rods  act  more  or  less  as  a  screen  for  the  coarser  particles  of  the 
concrete  and  prevent  a  close  contact  of  the  concrete  with  the  steel. 
This  matter  of  complicated  reinforcement  is  one  of  considerable 
practical  importance. 

On  the  other  hand,  if  satisfactory  encasing  of  the  steel  with 
concrete  can  be  obtained,  a  larger  number  of  smaller  rods  is  pre- 
ferable to  a  smaller  number  of  larger  rods.  The  area  of  contact 
in  a  rod  of  smaller  size  is  proportionately  greater  than  in  a  rod  of 
larger  size,  as  the  perimeter  varies  directly  as  the  diameter  or 
size,  and  the  sectional  area  as  the  square  of  diameter  or  size.  In 
order  that  the  rods  may  not  slip  the  adhesion  of  steel  to  concrete 
must  be  equal  to  or  greater  than  the  tension  in  the  steel. 

Adhesion  Required. — Having  determined  from  the  for- 
mulae given  the  tension  in  a  reinforcing  rod  at  any  point,  we 
jnust  see  that  in  either  direction  from  that  point  the  steel  has 
sufficient  area  of  contact  that  the  total  adhesion  will  equal  or  be 
greater  than  the  tension.  If  there  is  a  deficiency  in  this  respect 
it  must  be  met  either  by  mechanical  bond  or  anchoring  of  the 
reinforcement  at  the  ends. 

Safe  values  for  adhesion  of  concrete  and  steel  are  given  in  the 
table  of  Working  Stresses  on  p.  860.  It  will  be  noted  that  all 
of  the  authorities  there  given,  except  Boston,  assume  the  ad- 
hesion to  be  the  same  as  the  shearing  resistance  of  the  concrete. 

A  safe  rule  to  apply,  without  calculation,  to  the  case  of  beams 
with  maximum  bending  moment  at  the  center  is  to  make  the 
diameter  of  the  rods  not  more  than  one  two-hundredth  of  the 
span.  Under  ordinary  conditions,  generally  speaking,  the 
length  of  rod  either  side  of  the  point  of  maximum  bending 
moment  should  be  at  least  eighty  diameters  for  plain  rods,  and 
not  less  than  fifty  diameters  for  deformed  bars.  Under  unusual 
conditions  the  adhesion  should  be  carefully  studied.  The  appar- 
ent discrepancy  between  the  first  and  second  statements  of  this 
paragraph  is  explained  by  an  allowance  made  by  the  author  to 
cover  the  fact  that  the  tension  in  the  steel  does  not  decrease 
uniformly  with  the  decrease  in  distance  from  the  supports.  The 
allowance  is  purely  arbitrary  but  is  considered  safe.  For  cases 
of  unsymmetrically  loaded  beams  the  author  believes  it  best  to 
examine  carefully  into  the  conditions. 

Separation  of  Rods. —  It  has  not  been  unusual  in  tests 
on  beams  to  have  the  concrete  split  off  at  the  under  side  of  beams 
along  the  line  of  the  reinforcement.  This  is  due,  if  not  entirely, 
at  least  in  part  to  an  insufficiency  of  concrete  between  and 


88 le  REINFORCED    CONCRETE. 

around  the  reinforcement.  To  avoid  this  the  spacing  or  separa- 
tion of  the  reinforcing  rods  in  the  cross  section  of  the  beams 
must  be  such  that  the  resistance  to  shear  of  the  concrete  at  the 
level  of  the  rods  is  at  least  equal  to  the  adhesion  of  the  concrete 
to  the  steel. 

Assuming  the  safe  values  for  shearing  and  adhesion  to  be 
equal,  the  rods  should  be  spaced  2J  diameters  on  centers  and 
two  diameters  from  the  sides  of  beams. 

Some  authorities  require  that  the  clear  distance  between  rods 
and  the  space  between  rods  and  edges  of  beams  shall  in  no  case 
be  less  than  one  and  one-half  inches;  *  and  on  the  other  hand 
the  Brooklyn  Regulations  provide  that  the  distance  need  not  be 
more  than  one  and  one-half  inches. 

Provision  against  Shear. — The  low  resistance  to  shear 
of  concrete  makes  it  generally  necessary  to  provide  metal 
stirrups  to  supply  the  deficiency.  Authorities  do  not  agree  on 
the  amount  or  the  position  of  such  web  reinforcement.  Some 
contend  that  the  stirrups  should  be  placed  vertically  and  others 
contend  they  should  be  placed  at  an  angle.  The  action  of  the 
stresses  in  the  beam  are  analogous  in  the  one  case  to  those  in  a 
Howe  truss  where  the  tensile  web  members  are  vertical  and  in 
the  other  case  to  those  in  a  Pratt  truss  where  the  tensile  web 
members  are  inclined.  In  any  case  the  stirrups  should  be  long 
enough  to  reach  to  the  top  surface  of  the  concrete. 

The  size  and  spacing  of  the  stirrups  may  be  determined  by 
the  following  formula:  f 


in  which 

a  =  sectional  area  required  in  stirrup  x{  feet  from  support. 

A  =  sectional  area  of  horizontal  reinforcement  (tension  rods). 

1  =  span  in  feet. 

xl  =  distance  from  support  of  any  stirrup. 

X2  =  distance  from  support  of  next  section  for  which  area  of 
stirrup  is  required. 

This  formula  in  the  form  given  is  applicable  where  the  sectional 
area  of  any  stirrup  is  required,  the  spacing  of  stirrups  being 
given.  When  all  the  stirrups  are  to  be  of  the  same  sectional 
area,  the  proper  spacing  may  be  determined  by  inserting  the 

*  Taylor  and  Thompson. 

t  See  Eng.  News,  April  16,  1903,  p.  348. 


DESIGN.  881/ 

given  value  for  a,  assuming  a  value  for  xl  and  then  solving 
for  x2. 

Attached  Shear  Members, — The  necessity  for  firmly 
attaching  the  stirrups  to  the  tensional  reinforcement  is  also 
still  a  matter  of  dispute.  It  is,  however,  safer  to  have  them 
attached,  as  they  will  certainly  assist  in  anchoring  the  tensional 
reinforcement. 

Different  forms  of  stirrups  and  methods  of  attachment  are 
used.  In  the  Kahn  system  (Fig.  8,  p.  867)  the  stirrups  form  a 
part  of  the  tensional  reinforcement.  In  the  Golding  system  the 
stirrup  is  a  round  rod  bent  in  the  shape  of  an  inverted  IT,  and 
secured  to  the  tension  rods  by  a  mechanical  grip  (Fig.  9,  p.  868). 
The  U  form,  either  upright  or  inverted,  is  a  very  common  form 
of  stirrup,  and  may  be  a  round  or  square  rod  or  a  flat  strap  as 
shown  in  Figs.  7,  10  and  12. 

In  some  cases  when  the  slab  and  beams  are  constructed  to- 
gether, the  slab  reinforcement  is  carried  through  the  upper  end 
of  the  stirrups  as  shown  in  Fig.  10. 

Breadth  of  Beam. — The  breadth  of  a  rectangular  beam, 
and  of  the  stem  of  a  T  beam  is  dependent  generally  on  the 
amount  of  reinforcement  necessary,  as  already  indicated,  and 
equals  the  sum  of  the  diameters  of  the  tension  rods,  of  the 
required  spaces  between  them  and  the  amount  of  concrete  out- 
side of  the  rods  needed  for  shear  or  protection  to  steel.  In  the 
case  of  beams  where  no  stirrups  are  used  is  it  also  necessary  to 
have  a  sufficient  width  of  concrete  to  take  up  the  horizontal 
shear.  This  should  be  at  least  equal  to  the  sum  of  the  perimeters 
of  the  tensional  reinforcing  rods. 

The  amount  of  concrete  to  be  provided  below  the  steel  is  fixed 
by  the  requirements  for  proper  protection  of  the  steel  against 
fire  and  corrosion.  (See  p.  SS2d). 

Compression  Rods  in  Beams. — Steel  reinforcement  in  the 
form  of  rods  is  sometimes  provided  above  the  neutral  axis 
in  beams  and  girders  for  the  purpose  of  providing  additional 
compressive  strength  where  there  is  not  sufficient  concrete  above 
the  neutral  axis  to  resist  the  total  compression.  If  steel  rein- 
forcement is  to  be  used  for  this  purpose,  the  steel  should  be 
placed  as  high  as  possible,  and  the  allowable  unit  compression 
in  the  steel  limited  to  the  actual  compression  in  the  concrete 
at  that  point  multiplied  by  the  ratio  of  the  modulus  of  elasticity 
of  the  steel  to  that  of  the  concrete,  as  in  the  case  of  columns  with 
vertical  reinforcement  The  use  of  steel  in  compression  in  beams 


8Slg  REINFORCED    CONCRETE. 

and  girders,  however,  is  not  recommended,  since  at  best  it  is 
very  uneconomical  and  there  is  a  tendency  for  the  steel  to  buckle 
and  disrupt  the  concrete. 

Columns. — Reinforced  columns  are  of  three  general  types: 
(1)  Concrete  with  vertical  reinforcement  near  the  outer  sur- 
faces; (2)  concrete  wrapped  with  spirally  wound  wire  or  with 
metal  bands;  (3)  concrete  with  a  metal  core. 

Length  of  Columns. — The  length  of  reinforced  columns 
is  variously  limited  by  different  authorities  as  follows;  the 
figures  being  in  each  case  the  ratio  of  length  to  least  lateral 
dimensions : 

New   York-Manhattan 12 

Brooklyn 13 

St.  Louis    12 

Buffalo  16 

San  Francisco 15 

Chicago 12 

National  Board  of  Fire  Underwriters 12 

Strength     of     Vertically     Reinforced     Columns. — In 

determining  the  strength  of  columns  with  vertical  reinforce- 
ment, the  steel  is  assumed  to  carry  a  load  per  square  inch 
equal  to  the  working  load  per  square  inch  on  the  concrete  times 
the  ratio  of  the  moduli  of  elasticity  of  the  steel  and  concrete. 
So,  for  instance,  in  New  York  (Manhattan)  a  load  of  350  pounds 
per  square  inch  is  allowed  on  the  concrete,  and  12  X  350  =  4200 
pounds  per  square  inch  on  the  steel,  12  being  the  ratio  of  the 
moduli  as  fixed  by  the  regulations.  The  allowable  stresses,  ratio 
of  moduli  etc.  are  given  in  Table  II,  p.  860. 

Some  authorities  do  not  allow  any  load  to  be  figured  on  the 
reinforcement,  but  instead  allow  a  higher  unit  stress  on  the 
concrete  and  provide  for  a  certain  percentage  of  vertical  rein- 
forcement, assuming  that  the  steel  merely  provides  against 
bending. 

Amount  of  Vertical  Reinforcement. — Not  less  than  one 
per  cent,  of  vertical  reinforcement  should  be  used  in  reinforced 
columns,  and  it  is  well  not  to  provide  more  than  two  and  one- 
half  per  cent. 

The  reinforcing  rods  should  be  tied  together  horizontally 
at  intervals  of  not  more  than  the  least  side  or  diameter  of  the 
column.  This  prevents,  to  a  great  extent,  the  buckling  of  the 


DESIGN.  881 A 

reinforcement  under  load  and  the  consequent  splitting  of  the 
concrete. 

The  vertical  reinforcement  to  serve  its  purpose  of  taking  up 
the  bending  in  the  column  should  be  placed  as  near  the  outer 
surfaces  of  the  column  as  possible,  consistent  with  proper  pro- 
tection of  the  steel.  (See  p.  882.) 

In  the  disposition  of  the  steel  the  same  caution  is  necessary 
as  in  the  case  of  beams,  to  avoid  getting  it  too  close  or  too  much 
of  it.  (See  p.  881c.)  As  the  concrete  in  columns  is  generally 
poured  into  the  mold  at  the  extreme  top,  it  is  particularly 
important  to  keep  the  interior  free  from  interlacing  steel  across 
the  column. 

Brooklyn  Regulations. — The  regulations  of  the  Bureau  of 
Buildings,  Borough  of  Brooklyn,  N.  Y.,  permit  unusually  high 
stresses  on  columns  as  follows : 

"The  safe  load  in  pounds-  per  square  inch  of  cross  section  on 
reinforced  concrete  columns  shall  not  exceed  six  hundred  (600) 
for  the  upper  story  columns,  six  hundred  and  twenty-five  (625) 
for  the  next  lower  story  columns,  six  hundred  and  fifty  (650)  for 
the  next  lower  story  columns,  six  hundred  and  seventy-five 
(675)  for  the  next  lower  story  columns,  seven  hundred  (700)  for 
the  next  lower  story  columns,  seven  hundred  and  twenty-five 
(725)  for  the  next  lower  story  columns  and  seven  hundred  and 
fifty  (750)  for  all  the  next  lower  story  columns.  No  allowance 
shall  be  made  for  the  steel  in  the  columns." 

Prussian  Regulations. — The  Prussian  Regulations  permit 
a  ratio  of  length  to  least  side  greater  than  eighteen,  provided 
that  in  such  cases  Euler's  formula  must  be  applied. 

In  such  columns  where  the  steel  is  considered  as  furnishing 
part  of  the  compressive  strength,  it  should  be  made  continuous 
from  the  columns  of  one  story  into  those  below,  or  some  form  of 
washer  or  base  should  be  provided  at  the  lower  end  to  properly 
distribute  the  load  on  the  steel  over  the  material  below.  The 
latter  method  should  be  avoided  as  much  as  possible,  as  these 
plates  or  washers  tend  to  form  planes  of  weakness  through  the 
concrete.  The  rods  extending  from  one  column  may  be  connected 
with  those  above  or  below  by  means  of  pipe  sleeves. 

Laterally  Reinforced  Columns.  —  In  the  wrapped  or 
hooped  column  a  much  higher  unit  strength  per  square  inch 
of  cross  sectional  area  of  column  can  be  obtained,  because  of 
the  effect  of  the  wrapping.  It  is  well  known  that  the  compressive 
strength  per  square  inch  of  any  material  increases  with  the 


88  K  REINFORCED    CONCRETE. 

area  under  compression  or  if  the  material  is  prevented  from 
spreading  laterally.  The  relation  of  this  increase  in  compressive 
strength  to  the  amount  of  wrapping  provided  has  been  investi- 
gated by  Considere  and  others.  In  the  following  formula 
developed  by  Mr.  F.  H.  Dewey  of  the  Bureau  of  Buildings, 
Borough  of  Manhattan,  N.  Y.,  this  relation  has  been  taken  into 
account. 

P=  1.5/cirr2  +  /A- "ir2  r+  1.5mfcAa, 

in  which 

P  =  safe  load  in  pounds, 

/c  =  the  safe  unit  working  stress  of  ordinary  reinforced  concrete  in 

compression, 

/&  =  the  safe  unit  tensile  stress  in  the  hoops, 
r  =  the  radius  of  the  hoops  or  wrapping  surrounding  the  concrete 

core, 

Ah  =  the  area  of  the  cross  section  of  one  hoop, 
p  =  the  pitch  of  the  hoops, 

m  =  the  ratio  of  the  modulus  of  elasticity  of  steel  to  that  of  con- 
crete, 
As  =  the  total  area  of  the  longitudinal  steel. 

The  second  part  of  the  equation  consists  of  three  terms.  The 
first  represents  the  strength  of  the  concrete  itself. 

The  second  term  is  the  increase  in  strength  of  the  concrete  due 
to  the  wrapping. 

The  third  term  represents  the  increase  in  strength  due  to  the 
vertical  reinforcement. 

The  results  obtained  with  this  formula  correspond  very  closely 
with  the  results  of  tests  on  full  sized  columns. 

Limiting  Conditions.  —  In  figuring  the  strength  of  the 
columns,  only  the  area  within  the  limits  of  the  wrapping  can  be 
considered  as  effective  area.  The  part  outside  the  wrapping  must 
be  treated  as  a  protection  of  the  steel  against  fire  and  corrosion, 
and  must  be  made  of  the  necessary  thickness  to  secure  that 
result.  (See  p.  882.) 

It  is  to  be  noted  that  the  formula  is  applicable  only  in  cases 
where  the  wrapping  or  bonding  is  circular  in  form,  and  where 
there  is  sufficient  reinforcement  to  insure  a  lateral  resistance  of  at 
least  65  pounds  per  square  inch.  This  second  condition  is  ob- 
tained when  -  -  is  equal  to  or  greater  than  — . 


DESIGN.  88 1/ 

New  York  Formula —When  /C  =  3c0,  fh=  16,000,  and 
m=  12,  the  formula  given  above  becomes,  approximately, 

P(in  tons)  =  0.8  r2  +  80~r  +  34a, 

which  is  the  shape  in  which  it  is  used  in  New  York  City  (Man- 
hattan) for  the  working  stresses  there  established. 

Details  of  Lateral  Reinforcement.— At  the  top  or  base 
of  the  columns  in  each  story,  the  wrapping  should  be  made 
to  continue  through  the  floor  construction.  Under  certain  con- 
ditions where  the  floor  construction  is  practically  solid  about  the 
column,  affording  good  lateral  support,  equal  to  the  wrapping,  it 
may  be  better  to  omit  the  wrapping  and  avoid  the  possible  com- 
plication of  steel  reinforcement  from  column,  girder,  and  floor 
construction  and  the  consequent  breaking  of  the  bond  of  the 
concrete. 

The  materials  used  for  the  wrapping  are  either  steel  wire  or 
steel  bands.  When  wire  is  used  it  is  spirally  wound  and  con- 
tinuous for  the  full  length  of  the  column.  The  ends  of  the  wire 
are  turned  into  the  column  and  turned  down  to  such  an  extent 
that  when  the  concrete  has  been  poured  and  set,  there  will  be 
sufficient  anchorage  to  resist  the  tension  in  the  wrapping  due  to 
the  outward  pressure  of  the  concrete. 

When  metal  bands  are  used,  as  in  the  Cummings  system,  care 
must  be  taken  to  make  the  ri vetted  joints  in  the  bands  as  strong 
as  the  bands  themselves. 

A  form  of  wrapping  that  has  the  merit  of  rapidity  and  ease  of 
erection  is  shown  in  the  columns  used  in  the  Bush  Terminal  Ware- 
house, Brooklyn,  New  York,  described  on  p.  882a,  in  connection 
with  fireproofing. 

Metal  Core  Columns. — The  object  of  this  type  of  column 
is  to  provide  a  construction  for  tall  or  heavily  loaded  buildings 
that  will  have  the  necessary  strength  and  yet  not  encroach  too 
seriously  oh  the  floor  space.  For  this  form  of  column  some 
engineers  advocate  placing  a  steel  core  in  the  center  of  the  con- 
crete, the  steel  taking  the  bulk  of,  if  not  the  entire,  load.  * 

For  the  McGraw  Building,  in  New  York  City,  a  column  was 
designed  by  Prof.  William  H.  Burr,  as  shown  in  Fig.  17.  The  steel 
core  is  of  sufficient  strength  as  a  column,  independent  of  any  con- 
crete, to  carry  the  entire  dead  load  coming  upon  it,  the  stresses 

*  Trans.  Am.  Soc.  C.  E.,  Vol.  XIV,  Part  E,  p.  556. 


88  lA 


REINFORCED   CONCRETE. 


in  the  steel  being  in  no  case  greater  than  those  allowed  on  steel 
columns  under  the  New  York  Building  Code,  considering  the 
ratio  of  length  to  radius  of  gyration.  Furthermore,  those  stresses 
were  not  allowed  ,to  exceed  9,000  pounds  per  square  inch  in  any 


FIG.  17. — Column,  and  Girder  and  Column  Connection,  McGraw  Building, 

N.  Y. 

case.  The  live  loads  were  provided  for  by  placing  a  sufficient 
amount  of  concrete  within  tho  steel  framework,  that  the  stress  on 
the  concrete  did  not  exceed  750  pounds  per  square  inch,  being 
one-twelfth  of  the  maximum  allowable  load  on  the  steel.  The 


DESIGN. 


881Z 


concrete  outside  of  the  steel  was  considered  only  as  protection 
against  fire  and  corrosion. 

Cast-iron  Columns. — Where  the  building  for  any  reason 
need  not  be  treated  as  a  fireproof  structure,  space  and  time  may 
be  saved  by  using  cast  iron  or  steel  columns.  In  such  cases  the 
column  connections  must  be  designed  to  get  suitable  bearing  for 
the  concrete  construction  and  a  continuity  of  that  construction; 
for  the  great  advantage  in  reinforced  concrete  construction  lies  in 
its  monolithic  character.  When  cast  iron  columns  afe  used,  the 


Granolithic  finish 
Cinder  Concrete 


Pintles  P  to  have  a  combined 
Area  equal  to  the  Area  of  the ' 
Column  they  have  to  Support, 
to  be  cast  on  at  top  of  Support- 
Basement    ing1  Column. 
Column 


FIG.   18. — Detail  of  Connection  of  Cast-iron  Column  and  Concrete  Floor 

System. 

head  of  the  column  may  be  so  cast  as  to  leave  openings  through 
which  the  reinforcement  may  pass  from  one  side  to  the  other 
Fig.  18  shows  how  this  has  been  done,  in  a  building  at  Gay  and 
Christopher  Streets,  New  York,  without  impairing  the  strength  of 
the  column  at  the  connection. 

Steel  Columns. — In  steel  columns  it  would  be  simpler  to 
provide  a  connection  of  the  reinforcing  rods  with  the  steel  shapes 
of  the  columns.  Where  the  reinforcement  does  not  go  through 
the  columns,  some  rods  should  be  placed  outside  the  columns  to 
tie  as  much  as  possible  the  concrete  on  one  side  to  that  on  the 
other. 

Eccentric  Loads. — When  the  loads  on  columns  are  eccen- 
trically placed  additional  sectional  area  must  be  provided  than  is 


881m  REINFORCED    CONCRETE. 

required  for  direct  load.  A  formula  for  eccentric  loading  is  given 
in  Chap.  XIV  on  p.  413. 

Walls. — Concrete  walls  are  generally  considered  better  than 
brick  or  stone  walls.  If  not  reinforced  they  are  generally  required 
to  be  of  the  same  thicknesses,  for  given  conditions,-  as  brick  walls. 
Under  such  circumstances  they  are  probably  not  as  economical  as 
brick  walls. 

If  reinforced  and  used  as  bearing  walls,  they  can  be  reduced  to 
about  two-thirds  the  thickness  of  brick  walls,  provided,  however, 
that  the  load  on  the  concrete  does  not  exceed  the  safe  load  per 
square  inch  permitted  on  reinforced  columns.  The  ratio  of  un- 
supported height  to  thickness  should  also  not  exceed  that  fixed  for 
columns. 

For  spandrel  walls,  supported  entirely  on  girders,  the  minimum 
thickness  should  be  eight  inches.  Such  walls  should  be  reinforced 
with  not  less  than  one-half  pound  of  steel  per  square  foot  of  Wall, 
in  the  form  of  rods  placed  vertically  and,  less  frequently,  hori- 
zontally. 

Footings. — The  principles  underlying  the  design  and  con- 
struction of  reinforced  concrete  are  the  same  as  those  applied  to 
other  types  of  footings.  In  wall,  pier  or  column  footings  the  over- 
hang or  offset  must  be  considered  as  an  inverted  cantilever  loaded 
uniformly  with  a  load  per  square  foot  equal  to  the  load  per  square 
foot  imposed  on  the  underlying  soil.  The  reinforcing  rods  will 
then  necessarily  be  placed  near  the  lower  surface  of  the  footing 
and  the  size  and  number  determined  by  formulae  given  on  p.  872. 
A  detail  often  overlooked  in  reinforced  concrete  footings  is  the 
tendency  to  shear  at  the  edge  of  the  wall,  pier  or  column  sup- 
ported. (See  Chap.  Ill,  pp.  178  and  179;  Chap.  II,  pp.  158  to  161.) 

Where  footings  would  otherwise  become  very  eccentric  canti- 
levers should  be  resorted  to,  the  same  as  for  steel  construction. 
(See  Chap.  II,  p.  174  et  seq.)  The  maximum  bending  moment  on 
the  cantilever  is  determined  and  the  concrete  girders  designed  as 
described  on  p.  872. 

Economy  of  Reinforced  Concrete  Footings.— Great 
economy  over  steel  grillage  or  other  types  of  footings  may 
often  be  effected  in  the  use  of  reinforced  concrete  footings.  The 
cost  of  the  latter  type  will  vary  from  twenty  to  forty  per  cent,  of 
the  cost  of  a  corresponding  steel  grillage  footing.  This  difference 
is  easily  accounted  for.  The  amount  of  excavation  for  the  rein- 
forced footing  is  generally  much  less  than  for  the  steel  grillage. 
A  smaller  amount  of  concrete  is  used,  and  this  concrete  is  con- 


DESIGN.  881n 

sidered  in  the  calculations  for  strength,  whereas  in  the  steel 
grillage,  the  concrete  is  chiefly  provided  for  encasing  and  pro- 
tecting the  steel.  The  amount  of  steel  is  much  less,  being  used 
only  to  supply  the  tensional  resistance  of  the  construction;  the 
compressive  strength  being  supplied  by  the  much  cheaper  ma- 
terial, concrete.  Incidently,  the  protection  of  the  steel  in  the 
reinforced  footing  is  generally  more  certain  than  in  the  steel 
grillage  footing. 

Concrete  Piles. — Concrete  piles  have  been  referred  to  in 
Chap.  II,  p.  177  and  the  principal  commercially  successful  types 
have  been  those  mentioned.  Other  types  have  been  developed, 
of  which  the  following  deserve  notice. 

The  Corrugated  Concrete  Pile,  a  cross  section  of  which 
is  shown  in  Fig.  19,  is  a  reinforced  concrete  pile,  cast  in  forms 
on  the  ground  and  after  having  hardened  sufficiently  is  driven 


FIG.  19. — Corrugated  Pile. 

by  means  of  a  water  jet  working  through  the  central  core- 
These  piles  are  made  by  the  Corrugated  Concrete  Pile  Company, 
New  York. 

The  Chenoweth  Concrete  Pile,  a  cross  section  of  which 
is  shown  in  Fig.  20,  is  constructed  without  forms  by  rolling 
up  around  a  central  mandril  a  sheet  of  expanded  metal  or  wire 
netting  upon  which  has  been  spread  a  layer  of  concrete.  Longi- 
tudinal reinforcing  rods  are  tied  to  the  expanded  metal  or  wire 
netting  at  intervals  as  shown  in  the  cut.  This  pile  may  be  driven 


'  8810 


REINFORCED    CONCRETE. 


by  either  hammer  or  water  jet.  Mr.  A.  C.  Chenoweth,  16  Court 
Street,  Brooklyn,  New  York,  is  the  patentee.  * 

Loads. — No  accepted  formula  for  the  strength  of  piles  has  as 
yet  been  offered.  The  formula  used  for  wooden  piles  (p.  154)  is 
not  applicable.  In  lieu  of  anything  more  satisfactory,  the  per- 
missible loads  on  concrete  piles  may  be  determined  in  the  same 
manner  as  the  loads  on  concrete  columns,  p.  88lg.  Concrete 
piles  should  be  driven  to  a  solid  bearing,  and  should  not  depend 
on  frictional  resistance.  A  few  test  loads  on  concrete  piles  are 
here  given. 

At  Annapolis,  Maryland,  a  Raymond  concrete  pile  6"  at  the 
point  and  about  IS"  at  the  butt,  17  J  feet  long,  was  loaded  with 
41  tons  with  a  total  settlement  at  the  end  of  one  month  of  3-32". 
Another  Raymond  pile  at  the  same  work,  driven  in  reclaimed 


Rods' 
FIG.  20. — Chenoweth  Pile. 

land  which  had  been  filled  with  sand  and  mud  three  years 
previously,  was  loaded  with  42  tons,  and  showed  a  settlement 
of  0.002  feet.  There  was  no  additional  settlement  at  the  end 
of  one  month,  f 

For  the  foundation  of  the  Produce  Exchange  Building,  Broad- 
way and  Beaver  Street,  New  York,  a  Simplex  concrete  pile  was 
loaded  with  about  43  tonsf  with  a  settlement  of  3-16"  at  the  end 
of  six  days. 

Connections. — Much  judgment  can  be  displayed  and  must 
be  exercised  in  the  design  of  details  in  the  connections.  The  great 
value  of  reinforced  concrete  construction  over  other  types  is  the 
possibility  of  securing  great  rigidity.  This  can  only  be  attained 

*  See  Eng.  News,  July  26,  1906,  p.  105. 

t  Eng.  Record,  March  4,  1905,  p.  277. 

J  Under  the  auspices  of  the  Bureau  of  Buildings. 


TYPES    OF    CONSTRUCTION.  881p 

when  the  result  is  as  nearly  monolithic  as  possible.  We  then  have 
mass  to  take  up  vibration  and  this  advantage  in  the  case  of  work- 
shops or  factories  employing  moving  machinery  is  readily  seen. 

The  reinforced  concrete  buildings  that  came  through  the  severe 
San  Francisco  earthquake  in  May,  1906  in  good  condition,  it  has 
been  found,  were  those  in  which  attention  had  been  given  to  the 
details  and  connections. 

To  secure  monolithic  character  requires  not  only  continuity  in 
the  concrete,  but  a  continuity  in  the  reinforcement.  This  often 
means  that  a  net  work  of  steel  occurs  at  the  connections.  If 
carried  to  excess,  the  bond  and  continuity  of  the  concrete  is  apt 
to  be  broken,  even  when  the  spaces  between  steel  are  thoroughly 
filled.  But  when  there  is  such  a  net  work  of  steel  it  also  acts  like 
a  sieve  and  the  spaces  are  not  readily  filled.  For  this  reason  it  is 
well  to  use  a  richer  mixture  at  the  columns  and  to  keep  the  aggre- 
gate as  small  as  possible. 

The  connections  of  floor  system  to  columns  are  particularly 
troublesome  in  this  respect,  and  partly  for  this  reason,  as  well  as  to 
provide  rigidity,  brackets  should  be  provided  under  the  girders  at 
the  columns  with  metal  reinforcement  near  the  inclined  surface  of 
the  bracket.  * 

Stairs. — Some  of  the  most  interesting  work  that  has  been 
done  in  reinforced  concrete  has  been  the  construction  of  stairs. 
The  reinforcement,  being  in  the  form  of  comparatively  small 
limber  bars,  can  be  adapted  to  most  any  shape  for  which  molds 
can  be  constructed,  and  when  a  wet,  rich  concrete  with  small 
aggregate  is  used  little  or  no  difficulty  need  be  experienced  in 
casting.  As  an  example  of  such  work,  the  stairs  in  the  residence 
of  Mr.  G.  W.  Vanderbilt,  in  New  York  City,  may  be  cited. 
When  this  stair  was  five  weeks  old  a  test  of  its  strength  was  made 
by  dropping  a  bundle  of  four  bags  of  cement  (about  380  pounds) 
from  the  floor  above  to  the  intermediate  platform,  a  distance  of 
eleven  feet.  Not  the  slightest  disturbance  occurred.  * 

Types  of  Construction. 

Mill  Construction.  —  In  localities  where  labor  is  high 
and  where  conditions  are  more  or  less  congested,  it  is  probably 
more  economical  to  use  brick  for  walls  than  concrete.  In  such 

*  For  a  detailed  description  see  Cement  hr  Jan.,  1904  and  Eng.  Record, 
Dec.  12,  1903.  For  other  examples  of  stair-work  see  Eng.  News,  June  30. 
1904. 


S8lq  REINFORCED    CONCRETE 

cases  the  type  of  construction  is  similar  to  ordinary  mill  con- 
struction. Provision  must  be  made  to  anchor  the  beams  and 
girders  which  can  be  done  by  bending  the  ends  of  the  reinforcing 
rods  so  as  to  extend  horizontally  into  the  wall  each  side. 

Skeleton  Construction.  —  The  skeleton  type  of  con- 
struction seems  to  be  the  best  form  adapted  to  reinforced 
concrete.  A  framework  of  columns,  girders,  beams  and  flooring 
is  built,  as  in  steel  construction,  the  wall  girders  and  columns, 
of  course,  being  designed  to  carry  the  weight  of  the  outside 
walls  as  well  as  such  portion  of  the  floor  and  live  loads  as  come 
on  them.  The  work,  in  this  type  of  construction,  can  progress 
more  steadily  than  in  the  mill  construction,  as  a  rule,  since  the 
concrete  work  need  not  at  any  time  be  stopped  to  wait  for  the 
brick  work  to  be  carried  up,  if  brick  is  used  for  the  walls. 

In  the  skeleton  construction  any  type  of  outside  wall  may 
be  used;  brick,  concrete,  tile,  etc.  In  some  cases  the  panels  are 
simply  filled  in  with  brick  work,  eight  or  twelve  inches  thick, 
leaving  the  concrete  columns  and  girders  showing  between  the 
brick  panels.  In  walls  situated  on  property  lines,  where  there  is 
a  likelihood  of  adjoining  buildings  this  is  not  objectionable. 
If  the  wall  remains  exposed  and  appearance  is  a  consideration, 
the  columns  and  girders  can  be  treated  architecturally  to  set 
off  the  brick  work.  Or  the  brick  work  may  be  continued  as  a 
facing  over  the  outside  of  the  columns  and  girders  as  was  done 
in  the  Bush  Terminal  Warehouses  in  Brooklyn,  New  York.  * 
To  thoroughly  secure  this  brick  facing,  galvanized  anchors 
were  placed  in  the  concrete  columns  and  girders  as  they  were 
being  erected,  projecting  sufficiently  to  bend  into  the  brick 
joints. 

In  using  concrete  for  the  panels,  the  walls,  properly  reinforced, 
may  be  six  and,  in  cases,  even  four  inches  thick  The  sides  of 
the  columns  are  cast  with  pockets,  grooves  or  recesses  to  receive 
the  panels,  which  as  in  the  case  of  brick  work,  are  most  satis- 
factorily and  most  economically  built  after  the  removal  of  the 
molds  from  the  skeleton  frame. 

In  the  Marlborough-Blenheim  Hotel,  at  Atlantic  City,  New 
Jersey,  the  panels  are  filled  in  with  hard  burned  terra  cotta  tile 
and  a  stucco  applied  on  the  outside.  This  makes  a  compara- 
tively light  construction  and  affords  good  insulation. 

The  particular  advantage  in  the  skeleton  type  of  construction, 

*  For  description  of  this  building,  see  Eng.  Record,  March,  3,  1906. 


TYPES    OF   CONSTRUCTION.  S81r 

especially  in  workshops  or  factories,  is  the  possibility  of  large 
window  areas  affording  light  and  ventilation. 

System  "  M." — A  type  of  construction  known  as  their 
"System  M"  has  been  developed  by  the  Standard  Concrete 
Company  of  New  York.  (Fig.  21.) 

It  consists  of  a  light  steel  skeleton  designed  to  carry  the  dead 
load  of  the  entire  structure  (except  that  the  columns  are  designed 
for  gross  loads)  which  is  ther  encased  in  concrete  making  ulti- 
mately a  reinforced  concrete  construction.  * 

Its  advantage  consists  in  the  ability  to  erect  and  inspect  the 
steel  reinforcement  before  even  the  centers  or  molds  are  placed. 
Under  congested  conditions,  such  as  prevail  in  large  cities, 
particularly  New  York,  it  is  a  rapid  form  of  construction.  The 
use  of  the  steel  in  this  type  is,  however,  not  economical.  In 
order  to  get  the  necessary  strength  in  the  steel  framework, 
shapes  must  be  used  which  do  not  offer  the  amount  of  adhesion 
that  should  be  had  for  the  amount  of  metal.  Furthermore  such 
shapes  must  necessarily  be  subjected  to  some  bending  which 
would  tend  to  break  the  bond  between  concrete  and  steel. 

Mushroom  System.  —  In  the  so-called  "  Mushroom "  sys- 
tem, invented  and  patented  by  Mr.  C.  A.  P.  Turner  of  Minne- 
apolis, Minn.,  an  attempt  is  made  to  eliminate  all  beams  and 
girders  and  to  construct  floor  slabs  supported  directly  by  the 
columns  and  walls.  The  columns  at  the  top  are  spread  out  into 
a  cap,  reinforced  circumferentially  and  radially.  The  principal 
slab  reinforcement  runs  diagonally  across  the  slab  from  column 
to  column,  in  two  directions.  A  secondary  reinforcement  and 
somewhat  lighter  reinforcement  runs  from  column  to  column 
along  the  outer  lines  of  each  floor  panel. 

It  will  be  seen  that  this  system  allows  the  use  of  a  shallower 
floor  construction  than  is  ordinarily  attainable.  In  erection, 
too,  it  has  the  advantage  of  a  flat  centering  for  the  entire 
floor. 

Kahn  Hollow  Tile  Construction. — In  seeking  to  mini- 
mize the  cost  of  centering,  the  floor  construction  shown  in 
Fig.  22  has  been  devised.  It  consists  of  a  series  of  reinforced 
concrete  beams  with  a  clear  space  between  them  of  the  width  of 
hollow  tile  blocks.  In  erection,  a  flat  centering  may  be  used, 
which,  however,  need  not  even  be  continuous.  Planks,  a  few 
inches  wider  than  the  concrete  beams,  are  placed  under  the 

*  For  a  full  description  see  Eng.  News,  April  25,  1907,  and  Eng.  Record 
June  22,  1907. 


881s 


REINFORCED   CONCRETE. 


TYPES    OF    CONSTRUCTION. 


881* 


location  of  the  beams,  the  tiles  are  laid  in  rows  supported  along 
their  edges  by  the  planks  and  thus  form  the  sides  of  the  molds 
for  the  beams.  The  reinforcement  is  placed  and  the  concrete 
poured  with  or  without  a  floor  plate,  as  the  necessities  of  the 
case  may  require.  Care  must  be  taken  in  pouring  the  concrete 
that  the  tiles  are  not  displaced  sidewise.  The  tile  should  also 
fit  closely  at  their  joints,  otherwise  the  finer  particles  of  the 
concrete  are  liable  to  flow  into  the  tile,  either  making  a  porous 
concrete  or  using  more  cement  and  sand  than  necessary. 


FIG.  22. — Hollow  Tile  and  Concrete  Floor. 

This  form  of  construction  offers  besides  the  economy  in  center- 
ing, the  advantages  of  a  flat  ceiling  without  the  application  of 
lath  and,  in  roof  construction  particularly,  the  avoidance  of 
condensation. 

Faber  Construction. — The  same  principle  of  construction 
is  involved  in  the  Faber  Construction  (patent  held  by  Faber 
Construction  Company,  New  York),  recently  introduced  in  the 
country  from  abroad  where  it  has  been  used  extensively.  (See 
Fig.  23.)  In  this  case,  however,  the  floor  is  reinforced  in  both 
directions,  and  the  strength  calculated  as  a  slab  supported  on 
four  sides.  (See  p.  8816.)  The  concrete  is  a  rich  mixture  of 
one  part  Portland  cement  and  three  parts  sand.  It  is  prevented 
from  running  into  the  hollow  spaces  of  the  tile  by  the  use  of  the 
cardboard  tubes  as  shown.  The  tiles  are  of  heavier  construction 
than  the  ordinary  commercial  tile,  and  are  used  in  part  in  figur- 
ing the  resistance  to  compression. 

Merrick  System. — Another  type  of  construction,  known 
as  the  Merrick  System,  controlled  by  Ernest  Merrick,  11  Broad- 
way, New  York,  is  shown  in  Fig.  24.  * 

*  See  also  chap.  XXIII,  p,  795, 


88  In 


REINFORCED    CONCRETE, 


It  consists  of  a  series  of  reinforced  concrete  beams  connected 
by  a  concrete  plate  at  the  top  and  a  ceiling  plate  at  the  bottom. 


The  size  of  the  concrete  beams  and  the  amount  of  reinforcement, 
are  dependent  on  the  span  and  loading.    The  special  features  of 


TYPES   OF  CONSTRUCTION 


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the  construction  are  the  ceiling  plate  and  the  metal  fabric  center- 
ing. The  ceiling  plate  is  made  of  cinder  concrete,  two  inches  thick 
and  offers  an  effective  fire  protection  to  the  concrete  beams.  The 
metal  cages  that  form  the  permanent  interior  centering  are  made 
of  a  stiffened  metal  fabric,  such  as  Roebling  stiffened  lath  (see 
Chap.  XXIII,  p.  827).  To  construct  the  floor,  a  temporary  flat 
wooden  centering  is  erected,  two  inches  of  cinder  concrete  are 
placed  on  the  same,  and  before  that  has  time  to  fully  set,  the 
metal  cages  are  put  in  position,  the  lower  edges  becoming  em- 
bedded in  the  concrete  of  the  ceiling  plate.  The  reinforcing  rods 
are  then  placed,  and  the  concrete  filled  in  between  and  above  the 
metal  fabric. 

Fire  Protection. 

Non-conductivity. — Concrete  is  a  poor  conductor  of  heat 
and  in  this  fact  lies  whatever  virtue  it  has  as  a  fireproof 
material.*  A  series  of  tests  made'  by  Professor  Woolson  of 
Columbia  University,  and  recently  reported  at  the  1907  meeting 
of  the  American  Society  for  Testing  Materials  show  the  following 
results : 

(1)  "That  all  concrete  mixtures  when  heated  throughout  to  a 
temperature  of  1000°  to  1500°  F.  will  lose  a  large  proportion  of 
their  strength  and  elasticity,  and  that  this  fact  must  be  well 
remembered  in  designing." 

(2)  "That  all   concretes   have  a   very  low   thermal   conduc- 
tivity, and  therein  lies  their  well  known  heat  resisting  prop- 
erties." 

(3)  "That  as  a  result  of  this  low  thermal  conductivity,  two  to 
two  and  one-half  inches  of  concrete  covering  will  protect  reinforc- 
ing metal  from  injurious  heat  for  the  period  of  any  ordinary  con- 
flagration (provided,  of  course,  that  the  concrete  stays  in  place 
during  the  fire). 

(4)  "That  reinforcing  metal  exposed  to  the  fire  will  not  convey 
by  conductivity  an  injurious  amount  of  heat  to  the  embedded 
portion." 

(5)  "That  the  gravel  concrete  was  not  a  reliable  or  safe  fire- 
resisting  aggregate."  f 

*  It  must  be  remembered  that  in  this  and  succeeding  paragraphs  on  the 
fire-resisting  properties  of  concrete,  only  such  material  as  is  used  in  re- 
inforced concrete  is  considered.  The  value  of  cinder  concrete  as  a  fireproof 
material  is  considered  in  the  previous  chapter,  p  734. 

t  Eng.  News,  Aug.  15,  1907,  p.  168. 


FIRE   PROTECTION. 


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Loss  of  Strength. — If  its  non-conductivity  were  all  that 
is  involved  in  the  fireproof  character  of  concrete,  the  minimum 
thickness  required  for  the  protection  of  the  steel  would*be  easily 
determined.  But  the  strength  of  the  concrete  is  more  or  less 
affected  when  exposed  to  the  extreme  heat  of  fire.  An  effort  has 
been  made  to  determine  this  effect  and  a  summary  of  the  results 
as  reported  by  Professor  Woolson  of  Columbia  University  *  is 
given  in  Tables  VIII  and  IX 

TABLE  IX. 

CONCRETE  BLOCKS  HEATED  ON  ONE  FACE  ONLY,  f 

Specimens  6"X6"X14"  Prisms— Proportions  1:2:4. 

Age  2  Months— Temperature  1500°  F. 


Aggregate. 

Modulus  of  Rupture  after 
heating  5  hours. 

Breaking 
Load  in 
Ibs  per  sq.  in. 

At  200  Ibs. 
per  sq.  in. 

At  400  Ibs. 
per  sq.  in. 

At  800  Ibs. 
per  sq.  in. 

Limestone 

293400 
200000 

521700 
268000 

730700 
379000 

1840 
1705 

Trap  rock  

Fire  Tests. — The  effect  of  fire  on  reinforced  concrete  has 
also  been  studied  in  a  number  of  tests  made  by  the  building 
authorities  of  New  York  City  and  Philadelphia,  and  in  some  of 
the  recent  conflagrations  in  the  country,  notably  at  San  Fran- 
cisco. 

The  test  to  which  the  sample  full  size  constructions  have  been 
subjected,  is  described  in  the  previous  chapter,  p.  745,  except  that 
there  was  no  limitation  as  to  span  or  spacing.  Of  the  nineteen 
tests  made  under  the  auspices  stated,  seven  were  failures,  the 
others  passing  in  more  or  less  satisfactory  condition. J 

The  conclusion,  from  a  study  of  the  tests  in  detail, §  shows  that 
to  a  depth  averaging  about  one  inch  the  concrete  is  seriously 
impaired  and  is  easily  washed  off  by  a  hose  stream  applied  to  the 

*  Proc.  Am.  Soc.  Testing  Materials,  Vol.  VI,  p.  433. 

t  Proc.  Am.  Soc.  Testing  Materials,  Vol  VI,  p  448. 

J  For  a  partial  lise  of  these  tests  see  Table  in  Proc.  Am,  Soc.  T.  M., 
Vol.  VI,  p.  128.  Several  tests  have  been  made  since  that  report  was  sub- 
mitted. 

§  The  detailed  reports  are  on  file  in  the  Bureau  of  Buildings,  Borough  of 
Manhattan,  N.  Y. 


FIRE    PROTECTION.  881s 

surface.  Any  stone  containing  an  appreciable  percentage  of  car- 
bonate of  lime  will  calcine  and  cause  failure.  Where  the  con- 
struction is  poorly  designed,  allowing  an  excessive  deflection,  the 
fine  cracks  in  the  concrete  below  the  steel  will  open  to  such  an 
extent  as  to  allow  the  heat  to  reach  the  metal  reinforcements 
When  the  reinforcement  is  such  as  to  produce  a  plane  of  weakness 
in  the  concrete  there  is  liable  to  be  a  flaking  off  of  concrete  and  a 
consequent  exposure  of  metal. 

Actual  Fire. — The  earliest  test  of  a  reinforced  concrete 
building  in  an  actual  fire  occurred  in  1902,  in  the  four  story 
factory  of  the  Pacific  Coast  Borax  Company,  at  Bayonne,  New 
Jersey.  The  roof  of  this  building  was  of  wood,  which,  with  the  con- 
tents of  the  building,  was  destroyed  by  the  fire.  The  only  damage 
suffered  was  a  break  in  the  top  floor  caused  by  the  fall  of  a  heavy 
tank  that  had  been  supported  by  the  roof.  At  the  same  time  an 
adjoining  building  of  unprotected  steel  posts  and  beams  was 
twisted  into  a  tangled  mass  of  metal. 

Baltimore  Fire. — In  the  Baltimore  fire  there  was  but  one 
reinforced  concrete  building  of  the  three  exposed  to  the  fire  from 
which  any  fair  conclusion  can  be  drawn.  In  one  of  the  buildings, 
the  concrete  construction  was  entirely  destroyed,  but  this  was 
probably  due  to  the  falling  walls  and  failure  of  oiher  non-fireproof 
parts.  In  a  second  building  the  heavy  floor  of  a  banking  room 
of  reinforced  concrete  came  out  practically  unharmed,  but  it 
was  not  exposed  to  severe  fire.  The  third  structure  was,  however, 
exposed  to  severe  fire.  The  contents  of  the  building  were 
destroyed,  and  a  large  part  of  the  outside  walls  fell.  The  floors, 
five  in  number,  were  all  of  reinforced  concrete  supported  on  con- 
crete columns,  having  replaced  an  old  joisted  construction.  A 
test  made  after  the  fire  showed  that  the  floors  were  still  capable 
of  sustaining  the  loads  for  which  they  were  designed,  although  the 
floor  slabs  were  cracked.  The  girders  were  cracked  longitudinally 
near  the  line  of  the  reinforcement,  and  the  columns  were  spalled 
to  such  an  extent  as  to  expose  most  of  the  reinforcement.  It 
would  have  been  difficult  to  restore  the  building  so  that  it  would 
resist  another  such  attack.  * 

San  Francisco  Fire. — The  effects  of  the  fire  on  concrete 
construction  in  the  conflagration  immediately  following  the  San 
Francisco  earthquake  in  1906,  are  summed  up  in  the  following 


*  Capt.  Sewell  in  his  report  on  this  building  draws  a  different  conclusioiii, 
See  Eng.  News,  March,  24,  1904,  p.  276. 


882  REINFORCED  CONCRETE. 

paragraph  from  the  report  of  a  committee  of  engineers  investiga- 
ting the  subject. 

"Concrete  floors  generally  had  hung  ceilings,  and,  where  thus 
protected,  were  uninjured.  Where  exposed,  the  concrete  is  in 
most  cases  destroyed,  for  instance,  in  the  Sloan,  Rialto,  and 
the  Aronson  Buildings,  and  the  Crocker  Warehouse.  The  con- 
crete is  dry,  and  while  in  many  cases  hard,  yet  all  the  water 
has  been  burned  out  and  it  may  be  said  to  be  destroyed,  even 
if  able  to  support  weights.  Floor  coverings  of  wood  invariably 
burned,  adding  to  the  destruction.  Sleepers  were  generally 
burned.  Surfaces  of  cement  mortar  fared  much  better,  the 
linoleum  covering  remaining  practically  intact."  * 

In  discussing  the  report,  Mr.  A.  L.  A.  Himmelwright,  who 
made  a  personal  inspection  of  the  ruins,  concludes  that  rein- 
forced concrete  is  inferior  as  a  fire-resisting  construction  to  any 
form  of  steel  construction  with  concrete  floors  and  concrete 
column  and  girder  protection,  but  superior  to  steel  construction 
with  terra  cotta  floor  and  terra  cotta  column  and  girder  pro- 
tection. "Where  this  method  was  used,  a  very  slight  attack  of 
fire  was  generally  sufficient  to  cause  the  rupture  of  the  concrete 
underneath  the  reinforcing  metal,  so  that  it  fell  away,  exposing 
the  metal.  There  were  comparatively  few  buildings,  however, 
in  which  this  method  of  construction  was  used."  f 

Thickness  of  Concrete  Required. — From  a  study  of  the 
tests  and  fires  just  referred  to,  a  fair  conclusion  as  to  the 
amount  of  protection  against  fire  would  seem  to  be:  In  all 
columns,  in  large  and  important  girders,  trusses  or  other  supports 
at  least  two  inches  of  concrete  outside  of  all  reinforcement; 
in  girders  and  beams  and  slabs  of  long  spans,  about  one  and 
one-half  inches  of  concrete  outside  of  all  reinforcement ;  in 
stair  work,  floor  slabs  (short  span),  walls  and  partitions  from 
three-quarter  to  one  inch  of  concrete  outside  of  all  reinforcement. 

In  footings  and  foundations  the  thickness  of  concrete  outside 
of  reinforcement  should  be  at  least  three  inches.  Not  for  fire 
protection,  but  for  protection  against  corrosion.  (See  p.  882d.) 

Fire  Underwriters'  Requirements. — The  following  pro- 
visions are  those  given  in  the  Building  Code  recommended  by  the 
National  Board  of  Fire  Underwriters.  They  are  generally 
considered,  except  by  underwriters  and  some  fire  engineers, 
as  ultra  conservative. 

*  Proc.  Am.  Soc.  C.  E.,  March,  1907,  p.  330. 
t  Proc.  Am.  Soc.  C.  E.,  August,  1907,  p.  668. 


FIRE   PROTECTION.  882a 

"The  minimum  thickness  of  concrete  surrounding  and  rein- 
forcing members  one-quarter  inch  or  less  in  diameter  shall  be 
one  inch;  and  for  members  heavier  than  one-quarter  inch  the 
minimum  thickness  of  protecting  concrete  shall  be  four  diameters 
taking  that  diameter,  in  the  event  of  bars  of  other  than  circular 
cross-section,  which  lies  in  the  direction  in  which  the  thickness 
of  the  concrete  is  measured;  but  no  protecting  concrete  need  be 
more  than  four  inches  thick  for  bars  of  any  size;  and  provided, 
further,  that  all  columns  and  girders  of  reinforced  concrete 
shall  have  at  least  one  inch  of  material  on  all  exposed  surfaces 
over  and  above  that  required  for  structural  purposes;  and  all 
beams  and  floor  slabs  shall  have  at  least  three-quarters  inch 
of  such  surplus  material  for  fire-resisting  purposes." 

Other  Forms  of  Protection. — Because  of  the  effects  pro- 
duced by  fire  on  reinforced  concrete,  as  above  described,  and 
the  difficulty  of  restoring  the  construction  where  so  affected, 
various  suggestions  have  been  made  to  protect  the  concrete 
construction  with  other  materials. 

On  account  of  its  excellent  fire-resisting  qualities  (see  p.  734), 
cinder  concrete  would  naturally  suggest  itself.  This  material  is 
out  of  the  question  where  strength  is  required.  But  its  use  may 
be  combined  with  that  of  stone  concrete,  by  placing  a  sufficient 
thickness  for  protective  purposes,  in  the  outside  of  the  reinforce- 
ment in  columns,  below  the  neutral  axis  in  beams  and  girders',  * 
and  on  the  under  surface  of  floor  slabs. 

Difficulties  are  likely  to  be  met  in  placing  two  kinds  of  con- 
crete in  the  same  mold,  but  they  are  not  insurmountable. 
But  careful  inspection  is  required  to  see  that  the  poorer  material 
is  not  put  in  place  of  the  stronger.  One  kind  of  concrete  should 
also  follow  the  other  immediately  in  order  to  secure  a  bond 
between  the  two. 

The  application  of  this  suggestion  to  column  protection  was 
satisfactorily  applied  in  the  Bush  Terminal  Warehouses  in 
Brooklyn,  serving  at  the  same  time  another  purpose.  (See 
p.  881j.) 

The  steel  wire  wrapping  for  the  columns  was  prepared  in 
sections  of  two  feet  height.  A  metal  lath  about  one-half  inch 
mesh  was  placed  outside  the  wrapping  and  secured  to  it.  This 
was  then  placed  in  a  cylindrical  wooden  mold  two  feet  high 
and  of  a  diameter  four  inches  larger  than  the  wrapping,  and 

*  Trans.  Am.  Soc.  C.  E.  Vol.  LVI,  p.  284. 


8826 


REINFORCED  CONCRETE. 


formed  the  Inner  side  of  the  mold.  The  space  between  the 
wrapping  and  the  wooden  mold  was  then  filled  with  cinder 
concrete.  When  set  and  the  mold  removed,  the  result  was  a 
hollow  cylinder  of  cinder  concrete,  two  inches  thick  and  two  feet 
height,  with  the  column  wrapping  attached  to  the  inside.  These 
cylinders  were  set  one  over  the  other  in  the  building  till  the 
proper  column  height  was  reached,  such  vertical  rods  as  were 
wanted  were  put  in  and  the  interior  filled  with  concrete.  Thus 
was  produced  a  fireproof  wrapped  column  without  the  expense 
and  inconvenience  of  column  molds  in  the  building.  (Fig.  25.) 


FIG.  25. — Fire-proofing  Shell  for  Columns. 

In  the  "Merrick  System"  (see  p.  8810  a  protection  to  the 
lower  side  of  a  floor  construction  is  sought,  giving  at  the  same 
time  what  is  often  desirable,  a  flat  ceiling. 

A  form  of  fire  protection,  advocated  by  the  National  Fire 
Proofing  Company  of  Chicago,  is  shown  in  Fig.  26.  Here  columns, 
beams  and  girders  are  completely  encased  with  hollow  tile 
blocks.  Being  either  laid  in  the  molds  or  forming  them,,  their 
rough  and  furrowed  porous  surfaces  cause  them  to  adhere 
firmly  to  the  concrete.  This  affords  as  great  protection  as  for 
steel  columns,  and  if  destroyed  the  blocks  can  be  replaced 


FIRE    PROTECTION, 


882c 


SS2d  REINFORCED  CONCRETE. 

Protection  Against  Corrosion. 

Thickness. — The  thickness  of  concrete  required  for  fire- 
proofing  has  been  found  to  be  also  ample  for  protection  against 
corrosion.  It  is  well  established  that  steel  imbedded  in  neat 
cement  will  not  corrode.  Professor  Chas.  L.  Norton  of  the  Massa- 
chusetts Institute  of  Technology  draws  the  following  conclusion 
from  a  series  of  experiments  made  in  1902  and  1903.  * 

Steel  imbedded  in  neat  cement  is  secure  against  corrosion. 

Steel  imbedded  in  a  dense  concrete  mixture  is  safe  against 
corrosion. 

To  assure  a  thorough  coating  of  the  steel  the  concrete  should  be 
mixed  wet. 

Porous  concrete,  allowing  the  admission  of  moisture  will  not 
protect  the  steel  thoroughly. 

A  coating  of  rust  is  not  a  protection  against  further  corrosion, 
as  has  been  sometimes  claimed. 

In  these  experiments  the  steel  was  encased  in  concrete  one  and 
one-half  inches  thick  on  all  sides. 

From  this  it  would  appear  that  the  steel  of  reinforced  concrete 
is  secure  against  corrosion,  provided  it  is  thoroughly  imbedded  in 
concrete. 

A  slight  coating  of  rust  on  the  steel  where  imbedded  does  no 
harm  as  the  cement  is  strongly  alkaline  and  will  counteract  the 
acidity  of  the  iron  oxide  and  prevent  further  corrosion. 

' '  In  practical  design  the  most  important  question  which  arises 
is  how  far  a*  concrete  may  be  cracked  (due  to  bending  of  beams) 
without  exposing  the  steel  to  corrosive  influences.  In  this  respect 
it  seems  to  the  writer  that  the  minute  cracks  which  appear  in  the 
early  states  of  the  tests  can  have  very  little  influence."  f  This 
means  that  within  the  safe  working  limits,  there  is  no  danger  from 
corrosion  on  account  of  the  fine  cracks  due  to  tension  in  beams 
and  girders. 

Corrosion  in  Cinder  Concrete. — Cases  of  serious  corro- 
sion of  steel  imbedded  in  cinder  concrete  are  on  record.  In  a 
report  to  the  Structural  Association  of  San  Francisco  }  the  Com- 
mittee investigating  the  subject  states  that  in  cinder  concrete 
' '  the  extent  of  the  corrosion  is  great  enough  to  seriously  endanger 

*  Reports  Nos.  4  and  9,  Insurance  Experiment  Station  of  Boston  Manu- 
facturers Mutual  Fire  Insurance  Co. 

t  Prof.  Turneaure  in  Trans.  Arn.  Soc,  Testing  Materials,  Vol.  IV,  p.  505. 
lEng.  News,  Nov.  1,  1906,  p.  458. 


PROTECTION   AGAINST  CORROSION.         882e 

the  safety  of  the  floors,  and  it  is  not  probable  that  the  floors  would 
have  supported  their  loads  more  than  one  to  three  years  longer." 
The  Committee  recommended  "that  the  Structural  Association 
try  to  amend  the  present  building  law  so  as  to  exclude  the  use  of 
cinder  concrete  in  floor  slabs  or  for  fireproofing." 

Mr.  William  H.  Fox  in  his  investigations  *  on  this  same  subject 
finds  that  "after  about  forty  days'  treatment,  the  specimens  were 
broken,  and  the  steel  carefully  examined  for  corrosion.  With  but 
one  exception,  one  or  more  of  the  three  steel  pieces  in  each  speci- 
men showed  unmistakable  signs  of  corrosion.  Apparently  it 
made  no  difference  how  the  concrete  was  mixed — wet  or  dry, 
tamped  or  untamped,  whether  the  steam  or  water  treatment  was 
used,  the  result  was  the  same — rust  streaks  and  spots  were  found; 
the  difference  in  the  amount  of  corrosion  being  imperceptible." 
He  concludes  that  "to  secure  a  dense  homogeneous  cinder  con- 
crete, a  thorough  tamping  is  necessary.  A  rich  mixture,  either 
1:1:3  or  one  in  which  the  proportion  of  cement  to  aggregate  is 
larger,  should  be  used  in  all  cases.  The  greatest  of  care  should  be 
taken  in  mixing  the  materials,  and  it  may  be  necessary  to  resort 
to  the  seemingly  impractical  method.of  coating  the  reinforcement 
with  grout  before  placing  in  the  concrete." 

On  the  question  of  the  corrosion  of  steel  in  cinder  concrete  Prof. 
Norton  concludes:  "There  is  one  limitation  to  the  whole 
question,  that  is.  the  possibility  of  getting  the  steel  properly 
incased  in  concrete.  Many  engineers  will  have  nothing  to  do  with 
concrete  because  of  the  difficulty  in  getting  '  sound '  work.  This 
is  especially  true  of  cinder  concrete,  where  the  porous  nature  of 
the  cinders  has  led  to  much  dry  concrete  and  many  voids,  and 
much  corrosion.  I  feel  that  nothing  in  this  whole  subject  has  been 
more  misunderstood  than  the  action  of  cinder  concrete.  We 
usually  hear  that  it  contains  much  sulphur  and  this  causes  cor- 
rosion. Sulphur  might,  if  present,  were  it  not  for  the  presence  of 
the  strongly  alkaline  cement;  but  with  that  present  the  corrosion 
of  steel  by  the  sulphur  of  cinders  in  a  sound  Portland  concrete  is 
the  veriest  myth,  and  as  a  matter  of  fact  the  ordinary  cinders, 
classed  as  steam  cinders,  contain  only  a  very  small  amount  of 
sulphur.  There  can  be  no  question  that  cinder  concrete  has 
rusted  great  quantities  of  steel,  but  not  because  of  its  sulphur, 
but  because  it  was  mixed  too  dry,  through  the  action  of  the 
cinders  in  absorbing  moisture,  and  that  it  contained,  therefore, 
voids;  and  secondly,  because  in  addition  the  cinders  often  contain 

*  Eng.  News,  May  23,  1907,  p.  569. 


882/  REINFORCED  CONCRETE. 

oxide  of  iron  which,  when  not  coated  over  with  the  cement  by 
thorough  wet  mixing,  causes  the  rusting  of  any  steel  which  it 
touches.  There  is  one  cure  and  only  one,  mix  wet  and  mix  well. 
With  this  precaution  I  would  trust  cinder  concrete  quite  as 
quickly  as  stone  concrete  in  the  matter  of  corrosion."  * 

In  1902  the  Pabst  Building  in  New  York  City,  an  eight-story 
steel  skeleton  construction,  was  taken  down  after  having  been 
erected  about  four  years.  The  floor  filling  between  the  steel  I 
beams  in  this  case  consisted  of  cinder  concrete  on  metal  lath,  in 
segmental  form.  (Roebling  construction.)  The  steel  work 
generally  was  found  to  be  free  from  rust,  though  it  should  be 
remembered  that  all  the  steel  had  been  painted,  t 

Taking  all  things  into  consideration  it  would  probably  be  safe 
to  use  cinder  concrete,  if  care  is  taken  to  provide  a  proper  mixture 
and  careful  and  thorough  workmanship. 

Erection. 

Forms. —  For  the  erection  of  reinforced  concrete,  it  is 
generally  necessary  first  to  construct  molds  or  centerings  for 
the  columns,  floors,  etc.  Wood  is  the  material  used  for  the 
purpose.  Sheet  metal  centering  has  been  used  with  questionable 
success  and  economy. 

In  the  selection  of  the  wood  for  the  molds  a  clean  grade  of 
dressed  pine  should  be  sought.  It  should  be  thick  enough  to 
resist  warping  and  to  resist  deflection  between  supports.  It 
must  be  coated  on  its  surface  with  soap  or  some  other  satis- 
factory substance  to  prevent  it  from  sticking  to  the  concrete. 

The  forms  or  molds  must  be  erected  carefully  to  exact  size 
of  proposed  parts  and  true  to  position  and  direction.  For  floor 
molds  sufficient  supports  must  be  provided  not  only  to  carry 
safely  the  heavy  wet  concrete,  but  also  such  materials  as  are 
liable  to  be  placed  on  the  floors  up  to  the  time  when  the  concrete 
has  set  sufficiently  to  carry  such  loads.  The  supports  must  have 
sufficient  rigidity  to  prevent  deflection  in  the  molds. 

The  molds  should  be  so  constructed  that  they  can  be  easily 
removed  when  the  concrete  has  set. 

Sharp  corners  should  be  avoided  as  much  as  possible,  as  the 
wood  is  liable  to  stick  in  them.  Where  re-entrant  angles  in  the 

*  Report  No.  9  Insurance  Experiment  Station,  Boston  Manfrs.  Mut, 
Fire  Ins.  Co. 

t  Trans.  Am.  Soc.  C,  EM  Vol.  L,  p.  297. 


ERECTION 


882j; 


finished  concrete  work  will  occur,  the  molds  should  have 
beveled  edges,  and  at  salient  edges  of  the  finished  concrete  work, 
triangular  strips  should  be  nailed  in  the  corners  of  the  molds, 
to  produce  a  beveled  edge  in  the  concrete. 

To  prevent  the  spreading  of  the  sides  of  the  molds  cleats 
are  provided  at  sufficient  intervals.  In  the  case  of  beams  and 
girders,  these  are  generally  secured  by  nailing.  In  the  case  of 
columns  and  piers  and  often  in  walls  the  cleats  are  so  notched 
at  the  ends  that  long  bolts  with  washers  may  be  used  to  hold 
them  in  place  as  shown  in  Fig.  27.  In  removing  the  form  the 


FIG.  27. — Column  Forms. 

bolts  are  loosened  and  the  cleats  and  all  are  ready  to  use  again. 
In  some  cases,  particularly  in  the  construction  of  .walls,  the 
cleats  are  held  in  place  by  wire  running  through  the  mold, 
which  becomes  imbedded  in  the  concrete.  In  removing  the 
molds  the  wires  are  cut  and  the  portions  in  the  concrete  are 
allowed  to  remain. 

The  item  of  molds  and  centering  needed  in  the  erection  of 
reinforced  concrete  buildings  form  a  considerable  part  of  the 
cost  of  construction.  Economy  in  this  respect  can  be  affected 
in  designing  and  planning  by  making  floor  panels  throughout  a 


882/1  REINFORCED  CONCRETE. 

building  uniform  in  size  and  producing  as  far  as  possible  repeti- 
tion of  parts,  such  as  piers,  walls,  etc. 

Recently  successful  attempts  have  been  made  to  dispense 
with  the  erection  of  timber  moulds  and  centering, — by  casting  the 
various  members  of  the  construction  on  the  ground  and  assemb- 
ling and  erecting  them  in  the  same  manner  as  wood  or  steel 
columns,  beams  and  floors.* 

Concrete  Mixing. — In  all  reinforced  concrete  work  the 
concrete  should  be  mixed  mechanically*  Satisfactory  hand 
mixing  can  be  obtained  and  might  be  resorted  to  in  very  small 
jobs,  where  it  would  be  uneconomical  to  set  up  a  machine  mixer. 
But  a  much  more  uniform  product  will  be  obtained  by  machine 
mixing,  and  most  types  of  mixers  are  mounted  on  wheels  so  as 
to  be  easily  moved  to  a  job. 

Mechanical  mixers  are  either  continuous  or  batch  mixers. 
In  the  continuous  mixers  the  materials  are  fed  sometimes  by 
hand  and  sometimes  mechanically,  arid  the  concrete  issues 
continuously.  The  product,  however,  is  not  likely  to  be  as 
uniform  as  in  the  batch  mixer,  for  in  the  case  of  the  latter  it  is 
under  constant  supervision,  whereas  in  the  case  of  the  former  the 
machine  is  relied  upon. 

Of  the  Batch  mixers  the  rotatory  type  is  the  one  giving  most 
general  satisfaction. 

Ransome  Mixer. — This  mixer  f  consists  of  a  cylindircal 
drum,  with  its  axis  horizontal,  made  to  revolve  about  its  axis 
by  means  of  gears.  The  materials  enter  through  an  opening 
in  the  center  of  one  end  and  are  mixed  together  by  means  of 
fixed  scoops  riveted  to  the  inside  of  the  drum.  The  batch  of 
concrete  is  dumped  without  tilting  the  drum  by  means  of  a  tilt- 
ing shute,  which  receives  the  concrete  from  the  scoops  (Fig.  28). 

These  mixers  are  made  in  four  sizes  with  capacities  of  10,  20, 
30  and  40  cu.  yds.  per  hour. 

McKelvey  Mixer. — This  mixer  {  consists  of  a  cylindircal 
drum  rotating  axially  in  which  the  materials  which  enter  through 
one  end  are  turned  over  and  over  by  means  of  curved  "shovels," 
which  pick  up  the  materials  and  then  dump  them  automatically 
by  gravity  as  the  drum  revolves.  The  mixed  concrete  is  dis- 
charged through  a  long  spout  without  the  drum  altering  its 
position  (Fig.  29) . 


*  Eng.  News,  July  4th,  1907. 

t  Made  by  the  Ransome  Concrete  Machinery  Co.,  N.  Y. 

$  Made  by  McKelvey  Concrete  Machinery  Co.,  Chicago. 


ERECTION. 


882i 


FIG.  28. — Ransome  Mixer. 


FIG.  29. — MeKelvey  Mixer. 


882f 


REINFORCED  CONCRETE. 


The  mixer  is  mounted  on  trucks  or  steel  skids,  with  or  without 
power,  and  are  built  in  the  following  sizes:  1,  J,  J,  J,  J  and  J 
yard  per  charge. 

Smith  Mixer. — This  mixer  *  consists  of  a  rotating  drum 
in  the  form  of  two  cones  having  their  bases  together  and  having 
a  common  horizontal  axis  about  which  they  are  made  to  revolve. 
The  materials  entering  the  drum  at  one  end,  are  mixed  by  means 
of  fixed  blades  on  the  inside  of  the  drum.  The  mixed  concrete 
is  discharged  through  the  end  of  the  drum  opposite  to  that  by 
which  the  materials  entered,  by  tilting  the  axis  of  the  drum 
downward  as  it  revolves  (Fig.  30) . 


FIG.  30. — Smith  Mixer. 

This  mixer  is  made  in  six  sizes,  with  capacities  of  9,  20,  30. 
39,  46  and  62  cubic  yards  per  hour. 

Paddle  Mixer. — Another  form  of  batch  mixer  that  may 
be  mentioned  is  the  paddle  mixer  consisting  essentially  of  a 
stationary  box  in  which  are  mounted  two  shafts  each  provided 
with  paddles  alternating  in  position  with  those  on  the  other, 
and  made  to  revolve  in  opposite  directions.  The  materials  are 
dumped  in  at  the  top  of  the  box,  and  after  being  thoroughly 
churned  by  the  paddles  are  allowed  to  drop  out  through  the 
bottom  into  barrows. 

*  Made  by  T.  L.  Smith  Co.,  Milwaukee,  Wis. 


ERECTION.  882/j 

Charging  the  Mixers.  —  In  charging,  the  materials  for 
each  batch,  carefully  measured,  are  dumped  into  the  mixer  and 
the  machinery  started.  After  completing  a  definite  number  of 
revolutions,  sufficient  to  thoroughly  mix  the  ingredients,  the  con- 
crete is  discharged  into  wheelbarrows  or  other  implements  for 
carrying  it  to  the  molds.  Each  batch  should  be  completed  before 
another  is  started.  To  obtain  uniform  results  the  number  of 
revolutions  in  each  operation  should  be  the  same.  It  is  not  well 
to  trust  to  the  judgment  of  the  man  in  charge  of  the  machine  as 
to  when  the  mixing  has  been  thorough.  He  should  be  instructed 
to  count  the  revolutions  each  time.  A  good  plan  is  to  attach  a 
gong  which  rings  when  the  fixed  number  of  revolutions  has  been 
completed.  The  Code  of  the  National  Board  of  Fire  Underwriters 
calls  for  "at  least  twenty-five  complete  revolutions." 

Wet  Mixture. — The  water  is  introduced  during  the  process 
of  mixing.  The  amount,  also  measured,  should  be  such  as  to 
produce  what  is  known  as  a  "wet"  mixture,  that  is,  a  mixture  of 
the  consistency  of  molasses  that  will  readily  flow  around  and 
thoroughly  encase  all  steel  to  be  imbedded.  It  may  be  necessary 
to  vary  the  amount  of  water  somewhat  in  placing  a  large  mass  of 
concrete,  as  in  walls,  since  the  water  generally  works  itself  upward 
through  the  successive  layers. 

For  transporting  the  concrete  from  the  mixer  to  the  mold,  steel 
wheelbarrows,  holding  about  two  cubic  feet,  are  generally 
employed.  A  larger  vehicle,  holding  about  six  cubic  feet,  is  made 
by  the  Ransome  Machinery  Company,  and  is  found  very  eco- 
nomical in  larger  work  (Fig.  31). 

Pouring  the  Concrete. —  Ideal  conditions  would  obtain 
if  the  process  of  placing  concrete  could  be  continuous.  This 
is  not  generally  practicable,  so  it  is  important  that  the  point  at 
which  work  is  stopped  each  day  shall  be  so  selected  and  pre- 
determined that  the  strength  of  the  construction  shall  suffer 
least.  In  smaller  buildings,  of  floor  areas  not  exceeding  about 
3000  square  feet,  is  should  be  possible  to  so  arrange  the  progress 
of  the  work  that  each  entire  floor  construction  may  be  placed  in 
one  day,  possibly  including  the  columns  of  the  story  below.  If 
the  columns  cannot  be  done  at  the  same  time,  they  should  be 
poured  the  day  before. 

In  larger  work  it  is  necessary  to  lay  off  a  certain  area  to  be  com- 
pleted within  the  time  of  concreting  for  the  day.  Work  should 
not  leave  off  across  important  beams  or  girders,  but  should  be 
made  at  the  middle  of  slabs  or  minor  floor  beams.  If  any  portion 


882Z 


REINFORCED  CONCRETE. 


of  a  floor  slab  is  considered  in  the  calculation  for  strength  of 
beams  or  girders,  it  must  be  concreted  at  the  same  time  and  as 
part  of  such  beams  or  girders. 

Ramming. — As  soon  as  the  concrete  has  been  poured  into  the 
molds,  and  during  the  process  of  pouring,  it  should  be  contin- 
ually rammed  to  secure  complete  filling  of  the  molds,  density  in 
the  finished  product,  and  thorough  adhesion  to  the  reinforcement. 
This  ramming  should  be  done,  in  wet  concrete,  such  as  is  used  for 
buildings,  with  a  flat  steel  spatula  at  the  end  of  a  handle  long 
enough  for  comfortable  manipulation.  For  column  work  the 


FIG.  31. — Ransome  Concrete  Cart. 

handle  is  lengthened  out  so  as  to  reach  to  the  bottom  of  the  forms. 
Ordinary  spades  are  sometimes  employed,  and  where  no  special 
tools  are  provided  rammers  are  sometimes  made  of  2"  x  3"  scant- 
lings rounded  off  at  the  top  end  to  make  a  handle. 

Where  a  smooth  surface  is  desired  the  spatula  rammer  should 
be  used,  particularly  at  the  sides  of  the  molds.  The  honey- 
combed appearance  that  results  from  improper  ramming  is  diffi- 
cult to  remedy  afterward  without  a  patched  appearance. 

After  having  been  placed  the  concrete  should  be  kept 
damp,  by  sprinkling  with  a  hose,  until  it  has  thoroughly 
hardened. 


ERECTION.  882m 

Removing  Forms.  —  No  fixed  rule  can  be  given  for  the 
removal  of  the  forms,  as  the  time  required  for  the  setting  of  the 
*  concrete  will  vary  with  the  consistency  of  the  mixture,  the 
climatic  and  other  conditions.  Numerous  failures  of  reinforced 
concrete  have  been  attributed  to  the  too  early  removal  of 
forms.  In  warm  weather  concrete  will  set  more  quickly  than 
in  cold.  The  setting  process  may  be  somewhat  accelerated 
after  a  day  or  two,  by  the  removal  of  the  boards  forming  the 
sides  of  beams  or  girders,  leaving  in  the  planks  on  the  under- 
side and  the  props  supporting  them.  In  cold  Weather  it  is 
well  to  warm  the  building  during  the  setting  process  by  means 
of  salamanders. 

Finish. — The  exposed  surfaces  of  concrete  walls  are  variously 
treated  in  attempts  to  produce  a  satisfactory  appearance.  Where 
no  special  provision  is  made,  the  marks  of  the  lumber  used  in  the 
forms  are  almost  certain  to  show,  and  the  lines  of  demarcation 
between  successive  layers  are  clearly  defined.  To  eliminate  these 
lines,  grooves  are  sometimes  purposely  formed,  by  tacking  on  the 
sides  of  the  molds  triangular  or  trapezoidal  strips  that  would 
produce  sunk  joints  in  the  wall,  giving  it  an  appearance  resem- 
bling dressed  stone.  The  successive  layers  of  concrete  are,  in 
such  cases,  stopped  at  these  lines  so  that  the  junction  of  the  two 
layers  is  hidden. 

In  some  cases  the  surface  is  purposely  left  rough  and  scratched 
like  the  scratch  coat  in  plastering,  and  then  stuccoed  with  a  neas 
cement  or  a  rich  cement  mortar.  In  this  form  of  finish  there  it 
always  some  danger  of  the  stucco  flaking  off. 

The  surface,  as  it  comes  from  the  mold,  is  sometimes 
hammer-dressed,  or  rather  picked  with  a  special  hammer.  This 
hammer  has  an  edge  at  right  angles  to  the  handle,  which  edge 
is  so  indented  as  to  form  a  series  of  points  along  the  edge. 
This  produces  a  roughened  face  which  in  time  attains  a  uniform 
appearance. 

Another  method  sometimes  employed  is  to  remove  the  forms 
as  soon  as  the  concrete  is  sufficiently  hard,  and  to  rub  the  surface 
with  a  plasterer's  float  using  fine  sand  between  the  float  and  the 
wall  surface  and  plenty  of  water. 

Floor  Finish. — If  the  floor  surfaces  are  not  to  be  covered 
with  a  wooden  flooring,  a  satisfactory  finish  may  be  obtained  by 
placing  over  the  surface,  before  the  concrete  has  had  time  to  set 
thoroughly,  a  mortar  finish,  one  to  one  and  a  half  inches  thick,  and 
troweling  to  get  it  smooth  and  level.  If  the  finish  is  attempted 


882??  REINFORCED  CONCRETE. 

after  the  concrete  is  set,  the  new  and  the  old  will  not  bond,  and 
there  is  always  danger  of  flaking  off  unless  the  finish  itself  is  of 
considerable  thickness. 

A  fluid  has  been  put  on  the  market  by  a  Mr.  Livingston,  of 
Baltimore,  which  is  said  to  have  some  merit  in  causing  the  bond- 
ing of  old  and  new  concrete  work.  It  is  applied  to  the  old  surfaces 
just  before  placing  the  fresh  concrete.  The  composition  is  not 
revealed  by  the  inventor. 

The  Ransome  Concrete  Company  of  New  York  controls  a  bond- 
ing process  for  securing  a  bond  between  old  and  new  concrete. 
Tests  made  by  R.  W.  Hunt  and  Company  seem  to  substantiate 
the  claim  of  efficiency.  Further  information  should  be  obtained 
from  the  above  mentioned  company  which  controls  the  patents. 

Inspection. — In  all  reinforced  concrete  work  it  is  of 
extreme  importance  to  have  competent  and  thorough  inspection 
or  superintendence.  The  inspector  should  be  familiar  with  the 
nature  and  qualities  of  the  different  materials  entering  into  the 
construction.  He  should  have  a  knowledge  of  the  underlying 
principles  of  the  design  of  reinforced  concrete  structures,  so  that 
he  may  realize  the  importance  of  carrying  out  all  the  details, 
and  particularly  of  placing  the  reinforcement  exactly  as  planned. 
He  must  be  sufficiently  alert  and  active  to  see  that  the  work  of 
the  contractor  is  progressing  properly,  so  that,  for  instance, 
work  shall  not  have  to  be  rebuilt  because  of  error  in  the  form. 

The  materials  used  in  the  construction,  particularly  the 
cement,  should  be  tested  as  the  work  progresses.  Cubes  of  the 
concrete  as  used  should  be  made  up  each  day  and  at  the  end  of 
seven  days  should  be  tested  for  compression,  and  if  necessary 
again  at  the  age  of  twenty-eight  days.  This  record  will  serve 
as  a  guide  in  the  acceptance  of  the  work,  or  in  deciding  on  the 
necessity  for  a  load  test  of  the  finished  structure.  Under  no 
circumstances,  however,  should  it  replace  or  serve  as  an  excuse  to 
omit  the  testing  of  the  cement  upon  delivery  or  before  acceptance. 

In  addition  to  the  details  discussed  in  this  chapter,  that 
require  the  attention  of  the  inspector  on  the  work,  a  few  others 
may  be  especially  mentioned  here. 

In  joining  new  work  with  that  already  in,  and  which  has 
begun  to  set,  the  surface  must  be  thoroughly  cleaned  and  wet. 
In  stopping  off  work  it  is  good  practice  where  possible,  in  a 
urface  that  will  be  joined  with  another,  to  cast  a  groove  in  it, 
so  that  when  the  work  is  afterward  continued,  a  tongue  and 
groove  junction  is  effected. 


ERECTION.  8820 

All  forms  or  molds  must  be  carefully  cleaned  out  just  before 
pouring  concrete.  The  bottoms  of  the  column  molds  must  be 
especially  watched  for  this,  as  shavings,  sawdust  and  even 
blocks  of  wood  are  liable  to  fall  into  them  unobserved.  It  is 
well  to  leave  off  a  small  piece  of  one  side  of  the  column  mold 
at  the  bottom,  for  purposes  of  observation  and  cleaning,  which 
is  closed  up  just  before  pouring  the  concrete. 

Great  care  should  be  exercised  in  pouring  and  ramming  con- 
crete in  deep  molds,  such  as  for  columns,  walls,  etc.,  to  get  the 
molds  thoroughly  filled  at  the  bottom.  In  careless  work  it  is 
not  unusual  to  find  in  such  places  very  porous  concrete,  if  not 
large  pockets.  This  is  particularly  liable  to  occur  when  there  is 
considerable  reinforcing  steel  in  the  construction. 

It  should  be  remembered  that  concrete  in  setting  shrinks. 
Hollow  spaces  at  the  tops  of  columns  are  sometimes  found  due 
to  this  cause.  As  these  are  not  always  observable  from  the  out- 
side after  the  forms  are  removed,  great  care  should  be  exercised 
to  guard  against  them.  Therefore,  in  pouring,  the  molds  should 
be  filled  to  the  top  of  deep  molds  to  overflowing. 

The  exact  position  of  the  reinforcing  steel  in  the  concrete  is 
of  such  vital  importance  that  particular  mention  is  again  made 
here.  In  loose  bar  construction  the  greatest  care  must  be 
exercised,  in  the  first  place,  to  have  the  reinforcement  carefully 
placed,  and  then  to  avoid  its  being  shifted  out  of  position  by 
the  pouring  and  the  ramming  of  the  concrete. 

The  reinforcing  steel  of  such  systems  in  which  the  advantage 
of  attached  stirrups  is  claimed,  is  often,  for  convenience  in 
shipping,  sent  with  the  stirrups  laid  flat  or  close  to  the  main  bar. 
It  is  intended  that  in  placing  them  on  the  job  the  stirrups  shall 
be  turned  up  to  their  proper  positions.  Unless  carefully  in- 
spected, this  is  liable  to  be  neglected. 

The  use  of  a  "  unit  "  type  of  construction  (see  page  869) 
practically  obviates  these  two  last  mentioned  dangers,  as  the 
entire  reinforcement  comes  framed  together,  so  that  the  relative 
positions  of  reinforcing  rods  or  bars  cannot  be  changed,  and  a 
glance  will  show  whether  the  "frame"  is  complete  or  has  been 
damaged,  and  when  placed  in  the  molds  whether  it  fits  or  not. 
In  this  type  of  construction  the  parts  are  all  assembled  in  the 
shop  from  details  carefully  drawn  and  checked,  in  much  the 
same  way  that  steel  beams,  girders,  columns,  etc.,  are  fabricated 
from  detailed  shop  drawings.  The  work  of  the  inspector  or 


882?)  REINFORCED  CONCRETE. 

superintendent  on  the  job  is  very  much  simplified,  and  hence 
the  liability  of  error  reduced  to  a  minimum. 

Load  Tests. — Load  tests  on  the  finished  structure  should 
only  be  resorted  to  when  all  reasonable  care  has  been  exercised 
to  obtain  good  results,  but,  in  spite  of  which,  some  doubt  exists 
as  to  the  results.  Such  tests,  however,  should  not  be  accepted 
in  place  of  a  strict  compliance  with  the  specifications. 

The  architect  should  know  beforehand  that  his  building  is 
correctly  designed  and  is  safe,  employing,  if  necessary,  an 
engineer  to  provide  the  design. 

The  contractor  should  understand  at  the  outset  that  the 
structure  has  been  designed  for  certain  purposes  and  loads,  and 
that  the  materials  specified  and  the  manner  of  their  application 
are  necessary  and  invariable. 

If  the  contractor  furnishes  the  design,  as  is  sometimes  done, 
(a  practice  to  be  condemned),  the  architect  should  prescribe  in 
his  specifications  that  such  design  shall  be  checked  and  approved 
by  an  engineer  appointed  by  him. 

The  New  York  Building  Regulations  provide  for  load  tests, 
when  found  necessary,  of  three  times  the  gross  load  for  which 
the  construction  was  designed,  under  which  there  should  be  no 
signs  of  distress.  This  seems  unfair  and  illogical,  as  a  working 
stress  in  the  steel  of  about  half  the  elastic  limit  is  permitted. 
Under  these  circumstances,  the  prescribed  test  load  would  stress 
the  steel  beyond  its  elastic  limit,  if  the  construction  is  economi- 
cally designed,  and  the  floor,  though  showing  novisible  defects, 
is  nevertheless  crippled  and  unsuited  for  its  working  load. 

A  fair  load  to  be  applied  in  a  test  would  be  one  and  one-half 
times  the  working  live  load  plus  one-half  the  weight  of  the  con- 
struction. The  stresses  in  the  construction  would  then  equal 
one  and  one-half  times  the  working  stresses  assumed  in  designing. 
Under  these  conditions  there  should  not  be  any  evidences  of 
distress,  and  the  deflections  should  not  exceed  one-three-hundred- 
and-sixtieth  of  the  span.  The  material  used  for  the  load  test 
should  be  so  selected  and  placed  that,  when  uniformly  distrib- 
uted, as  required,  it  will  not  arch  and  assist  the  compressive 
strength  of  the  beam  or  floor.  Pig  iron  is  a  very  good  material 
to  use.  Bricks  are  more  generally  available,  but  must  often  be 
piled  very  high  to  get  the  required  load,  consuming  much  time 
and  labor  in  making  the  test.  lu  using  bricks  they  should  be 
set  in  vertical  piles  with  spaces  of  two  or  three  inches  between 
them,  thus  avoiding  all  arching  of  the  load. 


ROOF  TRUSSES.  883 


CHAPTER  XXV. 
ROOF  TRUSSES. 

TYPES   OF   WOODEN   AND    STEEL   TRUSSES— THEIR 
LIMITATIONS  AND  REQUIREMENTS. 

WHENEVER  it  is  required  to  roof  a  hall,  room,  or  building 
with  a  clear  span  of  more  than  thirty  feet,  it  is  generally  neces- 
sary to  use  one  or  more  trusses  to  support  the  roof  and  ceiling. 

Definitions. — By  the  term  "truss"  as  used  in  this  and  the 
following  chapters,  the  author  means  "a  framework  supported 
only  at  the  ends  (or  in  the  case  of  a  cantilever,  near  the  centre), 
and  so  designed  that  it  cannot  suffer  distortion  without  either 
crushing  or  pulling  apart  one  of  the  members  of  which  it  is 
composed,  and  will  exert  only  a  vertical  pressure  on  the  walls." 
A  true  truss  does  not  depend  upon  the  rigidity  of  the  joints  to 
maintain  its  equilibrium. 

A  roof  truss  is  a  form  of  truss  designed  for  the  especial  pur- 
pose of  supporting  a  roof,  although  it  may  also  support  the 
ceiling  below  and  perhaps  a  gallery  or  one  or  more  floors. 

Roof  trusses  are  or  should  be  designed  upon  the  same  prin- 
ciple as  other  trusses,  the  difference  between  a  roof  truss  and 
a  bridge  truss  being  due  to  the  difference  in  the  shape  of  the 
truss  and  the  character  of  the  load  to  be  supported,  rather  than 
in  the  mechanical  principles  involved. 

By  wooden  trusses  is  meant  trusses  built  principally  of  wood, 
but  having  iron  or  steel  rods  for  some  of  the  tension  members, 
the  term  being  used  in  distinction  from  trusses  built  wholly 
of  steel.  The  term  "combination  truss"  is  also  sometimes 
used  to  designate  such  trusses. 

A  member  of  a  truss  is  any  straight  or  curved  piece  of  wood, 
iron,  or  steel  which  connects  two  adjacent  joints  of  a  truss,  and 
which  is  essential  to  the  stability  of  the  truss.  The  term 
"piece"  will  also  frequently  be  used  to  designate  a  particular 
member.  Every  member  of  a  true  truss  acts  either  as  a  strut 
or  a  tie. 


884 


WOODEN  ROOF  TRUSSES. 


A  tie  is  a  member  that  is  subject  to  tension;  i.e.t  a  pulling 
stress. 

A  strut  is  a  member  that  is  subject  to  a  compressive  stress. 

In  wooden  trusses,  the  struts  are  always  made  of  wood, 
but  the  ties  may  be  of  wood,  wrought  iron,  or  steel. 

A  tie-beam  is  a  tie  which  is  also  subject  to  a  transverse 
strain;  in  wooden  trusses  the  principal  tie  is  usually  called  the 
tie-beam,  even  when  it  has  no  transverse  -strain  except  that  due 
to  its  own  weight. 

A  strut  beam  is  a  strut  that  is  also  subject  to  a  transverse 
strain.  In  wooden  trusses,  the  horizontal  struts  are  some- 
times termed  " straining  beams." 

The  joints  of  a  truss  are  the  points  where  three  or  more  mem- 
bers meet,  although  two  of  the  members  may  be  formed  of  the 
same  piece  of  material. 

Purlins  are  horizontal  beams,  sometimes  trussed,  extending 
from  truss  to  truss  to  support  the  rafters  or  ceiling  joists. 

Types  of  Wooden  Trusses. 

The  simplest  truss  that  can  be  built  is  that  shown  by  Fig.  1, 

which  consists  only  of 
two  struts  or  rafters  and 
a  tie-beam. 

As  the  unsupported 
length  of  a  strut,  on  ac- 
count of  economy,  should 
not  exceed  12  feet,  such 
a  truss  is  not  suitable 
for  spans  exceeding  20 
to  24  feet,  and  even  for 
a  span  of  20  feet  there  should  be  a  centre  rod,  as  shown  by  the 
dotted  line  R,  to  support  the  tie-beam.  To  utilize  this  truss 
for  a  greater  span  than  24  feet,  it  will  be  necessary  to  brace  the 
rafters  from  the  foot  of  the  centre  rod  as  shown  by  Fig.  2. 
This  gives  us  the  king-rod  truss,  the  modern  type  of  the  old- 
fashioned  king-post  truss  shown  by  Fig.  3,  which  was  built 
wholly  of  wood  except  for  the  iron  straps  at  S  and  P. 

When  the  tie-beam  supports  a  ceiling  or  attic  floor,  rods 
should  be  inserted  at  R  R,  Fig.  2,  to  support  the  load  on  the  tie- 
beam.  By  increasing  the  number  of  rods  and  braces,  as  in 
Figs.  4  and  5,  this  type  of  truss  may  be  used  for  spans  up  to 
64  feet,  and  even  for  greater  spans,  but  it  is  not  an  economical 


WOODEN  ROOF  TRUSSES. 


885 


type  when  the  span  exceeds  60  feet,  on    account   of  the  in- 
creased length  of  the  centre  braces  and  rods.    When  there  is  no 


Fig.  2 

King-rod  Truss.     For  Spans  up  to  36  Feet. 

load  on  the  tie-beam    the  rods   R   Rt  Figs   4  and  5,  may  be 
omitted. 

Note. — The  names  given  to  the  trusses  shown  by  Figs.  4  and 
5  are  original  with  the  author.  These  trusses  are  sometimes- 
called  queen  trusses,  but  as  the  term  queen  truss  commonly 
means  a  truss  such  as  is  shown  by  Fig.  6,  the  author  has  pre- 


FOR  SPANS  FROM  25  TO  35  FT. 
Fig.  3 


fixed  the  words  "six-panel"  and  "eight-panel"  to  give  a  more' 
definite  meaning  to  the  name  of  the  truss. 

The  rise  of  the  rafter  in  any  of  the  trusses,  Figs.  1-5,  should 
never  be  less  than  6  ins.  in  12  ins,,  or  26 J°,  and  a  J  pitch,  or  a 


886 


WOODEN  ROOF  TRUSSES. 


rise  of  8  ins.  in  12  is  generally  the  most  economical.     When  the 
span  exceeds  36  feet,  it  is  generally  more  economical  to  cut  off 


Purlin 


Fig.  4 

Six-panel  Queen  Truss.     For  Spans  from  36  to  50  Feet. 

the  top  of  the  truss  as  in  Fig.  6,  which  is  the  modern  type  of  the 
ancient  queen-post  truss.      This  truss  is  quite  frequently  used 


Fig.  5 


Eight  -panel  Queen  Truss.     For  Spans  from  48  to  60  Feet. 

.for  the  support  of  deck  roofs,  although  it  may  also  be  used  for  a 
pitch  roof  with  a  ridge.     When  the  top  chord  or  straining  beam 


Fig.  6 
Queen-rod  TTUSG.    For  Spans  from  30  to  45  Feet, 


WOODEN   ROOF  TRUSSES. 


887 


is  more  than  12  feet  long,  the  size  of  the  chords  may  be  con- 
siderably reduced  by  using  a  centre  rod  and  a  pair  of  braces  as 
shown  in  Fig.  7.  The  centre  rod  will  be  especially  needed  if 


^--Top  Chord 


Fig.  7 

For  Spans  from  40  to  52  Feet. 

the  bottom  chord  or  tie-beam  is  subject  to  a  transverse  strain. 
The  centre  rod  should  never  be  used,  however,  unless  the  braces, 
B  B  are  also  added. 

Counter  Braces. — The  truss  shown  in  Fig.  6  differs  from  the 
trusses  shown  in  Figs.  1  to  5  in  one  very  important  respect.  The, 
trusses  1  to  5  are  composed  of  triangles,  while  the  centre  panel  of 
truss  6  is  a  rectangle.  Now  a  triangle  cannot  be  changed  in 
shape  without  lengthening  or  shortening  one  side,  but  a  rect- 
angle can  be  distorted  without  changing  the  length  of  the  sides* 
Thus  in  Figs.  8  and  9 
the  corresponding  sides 
have  the  same  length  in 
both  figures,  hence  a  rect- 
angle is  not  a  rigid  shape.  F'9' 8  Fig* 9 
For  this  reason  a  truss  having  a  rectangle  for  the  centre  panel 
and  built  with  pin-joints  would  not  be  stable  if  one  side  of  the 
truss  was  more  heavily  loaded  than  the  other.  Thus  if  the 
queen-rod  truss  shown  in  Fig.  6  was  loaded  with  6  tons  at  A, 
and  3  tons  at  B,  it  would  collapse  as  shown  in  Fig.  10  unless  the 
tie-beam  was  large  enough  to  resist  the  pull  from  the  rod.  To 
counteract  this  tendency  to  collapse  a  brace  should  be  placed 
in  the  centre  panel  inclined  downwards  from  the  side  that  is 
most  heavily  loaded. 

Thus,  Fig.  11  shows  the  proper  construction  for  a  queen-rod 
truss  loaded  at  one  side  only,  or  more  heavily  loaded  on  the  left- 
hand  side  than  on  the  right.  It  will  be  seen  that  this  truss  is 
composed  entirely  of  triangles. 


888 


WOODEN   ROOF  TRUSSES. 


In  practice,  the  weight  of  a  roof  is  generally  uniform  on  both 
Sides,  the  only  variation  in  the  loading  being  that  due  to  wind 
and  snow.  For  trusses  not  more  than  36  feet  span,  and  one- 
third  pitch,  the  tie-beam  will  generally  possess  sufficient  stiffness 


I 


Fig.  10 

to  resist  the  tendency  of  the  unequal  pressure  of  wind  or  snow 
to  distort  the  truss ;  but  for  larger  spans,  and  for  a  pitch  of  45°, 
two  braces  should  be  inserted  in  the  centre  panel  of  queen-rod 
trusses,  as  one  side  may  receive  the  greater  pressure  at  one  time, 
and  the  other  side  at  another  time.  Braces  put  in  to  resist  the 
effect  of  unequal  loading  are  called  counter  braces.  Under  a 


Fig.  fl 

uniform  dead  load  counter  braces  receive  no  stress  whatever. 
Every  truss  with  horizontal  top  and  bottom  chords  should  be  pro- 
vided with  counter  braces,  whenever  there  is  any  possibility  of  a 
material  variation  in  the  loading. 

When  such  trusses  support  a  floor,  they  should  always  have 
counter  braces,  because  a  floor  may  be  heavily  loaded  at  one 
point,  while  the  rest  of  the  floor  may  have  no  load  at  all.  Thus, 


WOODEN   ROOF   TRUSSES. 


889 


if  the  truss  shown  by  Fig.  7  supported  a  floor,  counter  braces 
should  be  inserted  as  shown  by  the  dotted  lines. 

Fig.  12  shows  an  ornamental  queen-post  truss  supporting  a 
portion  of  the  roof  of  the  Massachusetts  Charitable  Mechanics' 
Association  building  in  Boston  (Mr.  William  G.  Preston,  archi- 


tect). The  members,  which  are  of  Georgia  pine,  were  worked 
from  timbers  of  the  dimensions  given.  In  this  truss  posts  are 
used  instead  of  rods,  being  bolted  and  tenoned  to  the  tie-beam 
and  secured  to  the  rafters  by  iron  straps. 

The  curved  ribs  take  the  place  of  counter  braces. 


800 


WOODEN   ROOF  TRUSSES. 


Fig.  13  shows  a  queen  truss  from  the  Museum  of  Fine  Arts, 

St.  Louis,  Mo.  (Messrs.  Pea- 
body  &  Stearns,  architects), 
which  supports  the  floor  below 
by  means  of  three  rods.  The 
truss-rods  have  nuts  and 
washers  below  the  tie-beam, 
and  the  thread  on  the  rods  is 
long  enough  to  receive  turn- 
buckles  which  connect  the 
suspension  rods  with  the 
truss.  This  is  generally  the 
best  method  of  suspending 
a  floor  from  a  truss. 
Fig.  14 

DETAIL  OF  JOINT    "A."  FIG  13. 


Fig.  14  shows  the  end  joint  of  this  truss. 

Fig.  15  shows  a  combination  of  a  queen-rod  and  a  king-rod 
truss,  sometimes  used  where  it  is  desired  to  keep  the  centre 
of  the  attic  free  from  obstructions. 

In  building  this  truss  it  will  be  more  economical  to  form  the 
lower  portion  of  the  rafters  of  two  timbers,  as  shown,  than  to  make 
it  of  one  size  for  the  full  length.  This  construction  also  allows 
of  making  a  good  joint  at  B.  What  has  been  said  in  regard  to 
counter  braces  in  queen-rod  trusses  applies  also  to  this  truss, 
although  with  this  truss  the  continuous  rafter  aids  very  materi- 
ally in  resisting  distortion  from  wind  pressure,  so  that  for  ordi- 
nary construction  and  for  spans  not  exceeding  40  feet  it  will  be 
perfectly  safe  to  omit  counter  braces. 


WOODEN  ROOF  TRUSSES. 


891 


Manner  of  Supporting  the  Common  Rafters — Purlins. — Before 
describing  other  types  of  trusses,  it  may  be  well  to  consider 
the  manner  of  supporting  the  common  rafters  by  the  trusses. 


Fig.  15 

For  Spans  up  to  42. 

Occasionally  it  is  desirable  to  span  the  common  rafters  from 
truss  to  truss,  but  as  a  general  rule  it  is  better  construction  to 
support  them  by  means  of  large  beams  or  purlins  which  span 
from  truss  to  truss,  as  shown  by  Fig.  16. 


^-Purlins 

;Rafters 


Fig.  16 

The  trusses  can  be  designed  so  that  the  purlins  need  not  be 
more  than  10  feet  apart,  and  very  often  not  more  than  6  or  8  feet 
apart,  so  that  the  co'mmon  rafters  need  not  be  more  than  2'/X4" 
or  2"X6"  in  cross-section  while  the  trusses  may  be  spaced  12, 
14,  or  16  feet  on  centres.  As  a  rule  a  spacing  of  about  14  ft.  for 
the  trusses,  and  of  9  ft.  6  in.  for  the  purlins,  will  be  found  most 


892  WOODEN   ROOF  TRUSSES. 

economical.  Another  advantage  in  the  use  of  purlins  is  that 
where  the  purlins  are  placed  at  the  truss  joints  no  cross-strain 
is  brought  on  the  truss  rafters  or  chords,  and  hence  the  latter 
may  be  made  much  lighter  than  if  they  supported  the  common 
rafters.  For  wooden  trusses  of  60  feet  span  or  more,  purlins 
should  always  be  used. 

The  purlins  should  always  be  located  over  or  close  to  a  joint  of 
the  truss,  so  as  not  to  produce  a  bending-moment  in  the  truss- 
rafter  or  chord.  Purlins  may  be  placed  with  their  sides  either 
vertical  or  at  right  angles  to  the  plane  of  the  roof,  but  the  author 
prefers  placing  them  with  the  sides  vertical,  as  shown  in  Figs.  2 
and  4.  The  best  method  of  supporting  the  ends  of  the  purlins 
is  by  means  of  duplex  hangers,  described  in  Chapter  XXI ;  they 
may  also  be  supported  by  double  stirrups,  or  may  rest  on  3-inch 
plank  bolted  and  spiked  to  the  sides  of  the  trusses.  The  ceiling- 
or  floor-joists  are  usually  supported  by  the  tie-beams  of  the 
trusses.  They  may  be  framed  flush  with  the  tie-beam,  as  at  A , 
Fig.  16,  or  they  may  rest  on  top  of  the  tie-beam  as  at  B.  When 
the  joists  are  used  to  support  an  attic  floor  it  will  be  better  to 
place  them  on  top  of  the  tie-beam.  There  is  no  particular 
objection  to  imposing  a  transverse  strain  on  a  tie-beam,  as  the 
tension  in  the  beam  tends  to  straighten  it,  and  the  cross-section 
of  a  wooden  tie-beam  must  always  be  made  considerably  larger 
than  would  be  required  to  resist  the  direct  tension.  In  the  case 
of  scissors  trusses  it  is  sometimes  more  economical  to  support  the 
ceiling-joists  by  purlins,  but  for  all  trusses  with  a  horizontal  tie- 
beam  it  will  be  more  economical  to  support  the  ceiling-  or  floor- 
joists  by  the  tie-beams. 

Trusses  with  Horizontal  Chords. — For  supporting  flat  roofs, 
with  or  without  a  ceiling  below,  and  for  any  place  where  a  hori- 
zontal truss  is  practicable,  the  type  of  truss  shown  by  Figs.  17  to  19 
is  undoubtedly  the  most  satisfactory  of  any  that  can  be  devised 
for  wooden  construction,  when  the  span  does  not  exceed  80  feet, 
and  except  in  localities  where  iron  rods  are  very  expensive  it 
will  be  as  economical  as  any.  In  this  work  the  name  "Howe 
truss"  will  be  given  to  trusses  of  this  type,  as  the  truss  is  an 
adaptation  to  building  construction  of  the  Howe  bridge  truss. 
The  term  " horizontal  truss"  is  also  sometimes  applied  to  trusses 
of  this  type.  Trusses  of  this  type  can  be  made  strong  enough 
for  spans  up  to  150  feet,  but  when  the  span  exceeds  100  feet  it 
will  probably  be  cheaper  to  use  some  other  truss. 

When  a  Howe  truss  is  placed  longitudinally  of  a  flat  roof, 


WOODEN  HOOF  TRUSSES. 


893 


the  top  chord  may  be  given  the  same  inclination  as  the  roof, 
so  as  to  support  the  rafters  without  blocking,  as  shown  by 

A       Top  Chord 


Bottom  Chord 


Fig. 17 

Five-panel  Howe  Truss. 


r  Purlins 


Fig.  18 

Six-panel  Howe  Truss. 


Fig.  19 

Ten-panel  Howe  Truss. 

Fig.  20.  For  deck  roofs  the  top  chord  may  be  inclined  upwards 
toward  the  centre,  to  conform  to  the  shape  of  the  roof,  as  shown 
by  Fig.  21.  For  a  deck  and  mansard  roof  the  centre  panels 


Fig.  20 


should  have  counter  braces,  as  shown  in  Fig.  21,  to  resist  the 
wind  pressure  against  the  sides  of  the  roof,  and  any  unequal 
distribution  of  snow. 


894 


WOODEN   ROOF   TRUSSES. 


Rules  to  be  Observed  When  Designing  a  Howe  Truss—Pi  eight. 
— The  height  of  the  truss,  always  measured  from  centre  to 
centre  of  the  chords,  should  never  be  less  than  one-ninth  of 
the  span  for  spans  up  to  36  feet,  or  than'  one-tenth  of  the 
span  for  spans  from  40  to  80  feet.  As  a  general  rule  a  height 
of  from  one-seventh  to  one-sixth  of  the  span  will  be  most  eco- 
nomical. When  the  top  chord  is  inclined,  as  in  Fig.  20,  the 


Fig.  21 

height  at  X — i.e.,  at  the  shortest  rod — should  not  be  less  than 
the  limit  given  above. 

Number  of  Panels. — A  panel  is  the  space  between  two  ad- 
jacent rods  or  between  an  outer  rod  and  the  end  joint  (see  Fig. 
17).  As  a  rule,  the  number  of  panels  should  be  such  that  the 
braces  will  have  an  inclination  of  from  36°  to  60°,  an  inclina- 
tion of  about  45°  being  the  most  economical.  It  is  not  ma- 
terial whether  there  be  an  even  or  an  odd  number  of  panels. 

If  the  position  of  one  or  more  of  the  purlins  is  fixed  by  some 
special  requirement,  then  the  panels  should  be  so  arranged 
that  the  upper  end  of  a  brace  will  come  under  the  purlin,  and 
that  the  inclination  of  none  of  the  braces  will  be  less  than  36°. 

Although  it  is  generally  better  to  have  the  truss  symmetrical 
about  the  centre,  it  is  not  absolutely  necessary,  nor  is  it  neces- 
sary that  the  panels  be  of  uniform  width.  When  the  truss  is 
not  symmetrically  loaded,  however,  it  may  be  necessary  to 
reverse  the  brace  in  one  of  the  centre  panels.  This  point  is 
considered  in  Chapter  XXVI,  under  the  heading  of  "Trusses 
Unsym metrically  Loaded." 

Counter  Braces. — If  there  is  any  chance  of  the  truss  being 
more  heavily  loaded  on  one  side  of  the  centre  than  on  the  other, 
counter  braces — that  is,  braces  in  the  opposite  direction  from 
the  regular  braces — should  be  placed  in  the  centre  panels  as 
shown  by  dotted  lines  in  Fig.  18. 

When  a  load  of  much  magnitude  is  placed  on  one  side  of  a 
truss  having  an  odd  number  of  panels,  without  a  corresponding 
load  oil  the  other  side,  a  brace  will  always  be  required  in  the 


WOODEN  ROOF  TRUSSES.  895 

centre  panel,  and  the  brace  should  incline  downward  from  the 
more  heavily  loaded  side.  Thus,  if  the  truss  shown  by  Fig.  17 
were  more  heavily  loaded  to  the  left  of  the  centre  than  to  the 
right,  then  a  brace  would  be  required  from  A  to  B.  When 
the  load  on  the  truss  is  practically  uniform,  counter  braces  are 
not  necessary,  nor  is  it  necessary  to  put  a  brace  in  the  centre 
panel  of  a  truss  having  an  odd  number  of  panels. 

Spacing  of  Trusses. — The  most  economical  spacing  of  the 
trusses,  all  things  considered,  will  usually  be  from  12  to  16  feet 
for  spans  up  to  60  feet,  and  from  14  to  20  feet  for  greater  spans. 

Spacing  of  Purlins. — Purlins  should  always  be  placed  over 
the  end  of  the  braces  and  close  to  the  washers  on  the  rods;  they 
should  also  be  spaced  so  as  to  give  the  greatest  economy  in 
the  rafters,  hence  the  spacing  of  the  purlins  will  determine,  to 
a  large  extent,  the  number  of  panels.  When  the  height  of  the 
truss  is  not  more  than  one-ninth  or  one-tenth  of  the  span,  it 
will  often  be  more  economical  to  place  a  purlin  over  every  other 
joint,  as  in  Fig.  19. 

Bearing  on  Wall  or  Post. — The  point  where  the  centre  lines 
of  the  end  brace  and  of  the  tie-beam  intersect  should  always 
come  over  the  support,  and  generally  at  least  6  ins.  beyond 
the  inner  face  of  the  wall. 

Stresses. — The  strain  in  the  chords  is  always  greatest  at  the 
centre  of  the  truss,  diminishing  towards  the  supports,  while 
the  stress  in  the  rods  and  braces  is  greatest  at  the  ends. 

Table  of  Dimensions  for  Howe  Trusses. — For 
symmetrical  trusses  having  panels  of  uniform  width  and  uni- 
formly loaded,  the  stresses  in  the  different  parts  will  be  pro- 
portional to  the  span,  number  of  panels,  height  of  truss,  spacing 
of  trusses,  and  the  load  per  square  foot.  It  is  therefore  possible 
to  prepare  tables  giving  the  dimensions  of  the  parts  for  such 
trusses.  Table  I.,  computed  by  the  author,  gives  the  dimen- 
sions for  six-panel  trusses  for  heights  of  one-sixth  and  one-eighth 
of  the  span,  and  for  three  different  spacings. 

These  dimensions  are  for  a  flat  roof  of  tin,  sheet  iron  or  com- 
position, and  for  a  snow  load  of  16  pounds  per  square  foot,  which 
is  equivalent  to  about  24  ins.  of  light,  dry  snow;  aho  for  a  lath 
and  plaster  ceiling  supported  by  the  tie-beam;  the  chords  and 
braces  being  of  Norway  pine  and  the  rods  of  wrought  iron. 

These  dimensions  apply  only  when  the  rafters  are  supported 
on  purlins  placed  at  the  upper  joints,  as  in  Figs.  18  and  19. 
When  the  rafters  rest  on  the  top  chord,  as  in  Fig.  20,  the  dimen- 


896 


WOODEN   ROOF  TRUSSES. 


sions  of  the  latter  must  be  greatly  increased,  and  special  cal- 
culations should  be  made  therefor. 

The  dimensions  given  in  the  table  may  be  used  for  trusses 
having  a  greater  height  than  that  given,  but  not  for  trusses  ivith 

TABLE  I.— DIMENSIONS   FOR  SIX-PANEL   HOWE 
TRUSSES,    SYMMETRICALLY  LOADED. 

Timber,  Norway  pine,  Oregon  pine,  or  Eastern  spruce. 


p 

a 

111 

02  & 

|J 

fl 

1] 

Braces. 

Rods 
(not  upset). 

«-§ 

A. 

B. 

C. 

D. 

E. 

F. 

Ft. 

5 

Ft. 

1 

Ft.  Ins. 
6  7 
5  2 
6  8 
5  2 
6  8 
5  2 

Ins. 
6X    6 
6X   8 
6X    8 
8X   8 
6X   8 
8X   8 

Ins. 

6X  8 
6X  8 
6X  8 
8X  8 
6X  8 
8X  8 

8X  8 
8X  8 
8X  8 
8X  8 
8X  8 
8X10 

Ins. 
6X    6 
6X    6 
6X   6 
SX    6 
6X    8 
SX    8 

8X    6 
8X    6 
8X    6 

8X    8 
8X    8 
SX    8 

8X    8 
SX    8 
8X    8 
SX    8 
8X    8 
8X10 

SX   8 
8X    8 
8X   8 
SX    8 
8X10 
10  X    8 

Ins. 
6X    4 
6X    6 
6X    4 
6X    6 
6X    6 
6X    6 

8X    4 
SX    5 
8X    5 
SX    6 
SX    6 
SX    6 

SX    6 
SX    6 
SX    6 
8X    6 
8X    6 
SX    6 

SX    6 
8X    6 
8X   6 
SX   6 
SX   8 
SX   8 

Ins. 
6X    3 
6X    4 
6X    3 
6X    4 
6X   4 
6X   4 

6X   4 
SX   4 
6X   4 

SX   4 
8X   4 
SX   4 

SX   4 
SX   4 
SX   4 
SX   4 
SX   4 
SX   4 

SX   4 
SX   4 
SX   4 
8X   4 
SX   6 
SX   4 

Ins. 

in 

\1SA 

Ins. 

1 

K 
l 
l 

l 

Ins. 

5A 

•i 

I 

12J 

15 

18- 

7  7 
5  11 
7  8 
5  11 
7  8 
6  1 

8X   6 
SX   8 
SX   8 
8X   8 
8X   8 
8X10 

M 
N 

48  - 

12 
15 

8  8 
6  8 
8  8 
6  10 
8  8 
6  10 

8X   8 
8X   8 
8X    8 
8X10 
8X    8 
8X10 

8X   8 
8X   8 
8X   8 
8X10 
8X10 
10X10 

8X  8 
8X  8 
SX  8 
8X10 
8X  8 
8X10 

8X  8 
8X10 
8X  8 
8X10 
8X10 
10X10 

ii 

54- 

12  j 

15] 
tej 

9  8 
7  6 
9  8 

7  7 
9  10 

7  7 

iiM 

60  -j 

12  1 

15  j 
18- 

10  9 
8  4 
10  10 
8  4 
10  10 
8  4 

8X   8 
8X10 
8X10 
10X10 
10X10 

10x10 

8X10 
8X10 
8X10 
10X10 
10X10 
10X10 

8X   8 
8X10 
8X10 
10X   8 
10  X   8 

10x10 

SX    6 
SX   6 
SX   6 
10  X   6 
10X   6 
10X   6 

6X   6 

SX   4 
6X   6 
SX   4 
SX   6 
SX   6 

IN 

•IK 

1 

S4 
H 
H 

70  j 

12- 
15- 
18- 

12  6 
9  7 
12  6 
9  9 
12  6 
9  9 

8X10 
10X10 
10X1 
10X1 
10X1 
10X1 

8X10 
10X10 
10X10 
10X12 
10X10 
10X12 

8X10 
10  X    8 
10X    8 
10X10 

10x10 

10  X  12 

SX    6 
10X    6 
10X   6 
10  X   8 
10  X    6 
10  X   8 

6X   6 
SX   6 
SX   6 
10  X   6 
SX   6 
10X   6 

W 

1 

in 

H 

1/s 

80  J 

12- 

15  i 

18- 

14  2 
10  10 
14  2 
11  0 
14  4 
11  1 

10X1 
10X1 
10X1 
10X1 
10X1 
10X1 

10X10 
10X10 
10X10 
10X12 
10X12 
10X14 

10X10 
10X10 

10x10 

10X10 
10X12 
10X12 

10X    6 
10X    6 
10X   8 
10X   8 
10X   8 
10  X   8 

SX   6 
SX   6 
SX   6 
10X   6 
8X   6 
10X   6 

\T 

VA 

13/S 

WOODEN   ROOF  TRUSSES. 


897 


a  less  height,  as  the  less  the  height  the  greater  will  be  the  stresses 
in  the  chords  and  braces.  When  the  conditions  of  load,  span, 
height,  and  spacing  are  not  exactly  as  given  above  and  in  the 
table,  the  stresses  should  be  determined  and  the  parts  of  the  truss 
proportioned  accordingly;  but  even  in  such  cases  the  table  will 
serve  somewhat  as  a  check  upon  the  computations. 

Lattice  Trusses. — In  localities  where   lumber  is  cheap, 
and  iron  or  steel  rods  quite  expensive,  the  lattice  truss  (Fig.  22) 
will  often  be  the  most  economical  for 
supporting  flat  roofs. 

This  type  of  truss  was  designed 
by  Ithiel  Towne  for  bridges  long 
before  iron  was  used  in  this  country 
for  such  work.  Several  railroad 
bridges  were  built  on  this  principle, 
and  the  truss  has  proved  very 
efficient  in  supporting  loads.  The 
principal  objection  to  the  truss,  from 
a  mechanical  standpoint,  is  that  the 
truss  cannot  be  tightened  up,  and 
the  joints  are  not  as  satisfactory  as 
in  a  Howe  truss. 

Proportions  and  Construction. — The 
height  of  a  lattice  truss,  measured 
between  the  centre  lines  of  the  chords , 
should  be  from  one-eighth  to  one- 
sixth  of  the  span,  and  the  braces 
should  be  placed  at  an  angle  of  about 
45  degrees.  When  laying  out  a  lattice 
truss,  the  first  step  should  be  to 
determine  the  height,  and  then  the 
number  of  spaces  between  the  joints 
in  the  top  and  bottom  chords.  To 
find  the  number  of  spaces,  multiply 
the  span  by  two,  and  divide  by 
the  height,  using  the  nearest  whole 
number.  Thus,  if  the  span  is  60 
feet,  and  the  height  8  feet,  there 

should  be  — g—  =  15  spaces.    If  the 

height  is  10  feet,  there  should  be  12  spaces.  The  truss  shown 
in  Fig.  22  has  16  spaces. 


898 


WOODEN  ROOF  TRUSSES. 


Having  determined  the  height  and  number  of  spaces,  fix  the 
centre  of  the  end  joints,  and  divide  the  distance  between  into 
the  number  of  spaces  determined  upon,  thus  fixing  the  position 
of  the  braces.  The  chords  should  be  built  of  four  thicknesses  of 
plank,  two  on  each  side  of  the  truss,  and  breaking  joint  opposite 
their  centres,  using  as  long  planks  for  the  tie-beam  as  can  be 
obtained.  At  the  ends,  vertical  planks  should  be  cut  between 
the  chords,  on  each  side  of  the  bracing,  to  act  as  posts.  The 
braces  should  be  bolted  to  the  chords  and  end-posts,  and  also  to 
each  other  where  they  cross.  A  goodly  number  of  spikes  should 
also  be  used  in  the  joints,  as  indicated  in  Fig.  .24 


Fig.  23 

Vertical  Section. 


Fig.  24 

Detail  of  Joint  B. 


The  bottom  chord  should  also  be  bolted  every  two  feet  between 
the  joints,  as  this  member  is  in  tension.  The  top  chord,  being 
in  compression,  will  be  tied  sufficiently  by  the  bolts  at  the  joints, 
and  by  a  short  bolt  on  each  side  of  each  butt-joint.  The  strain 
on  the  joints  near  the  ends  of  the  truss  will  be  much  greater 
than  on  the  centre  joints.  The  first  three  joints  at  each  end 
should  have  as  many  and  as  large  bolts  as  are  given  in  the  last 
column  of  Table  II.  The  bolts  in  the  next  three  joints  may  be 
slightly  reduced  in  size,  and  those  in  the  centre  joints  still  more. 
When  the  span  of  the  truss  exceeds  40  feet,  short  pieces  of  plank 
should  be  spiked  to  the  end  braces  a  a  fitting  tightly  between 
the  other  set  of  braces,  to  give  them  additional  strength.  It 
should  be  kept  in  mind  that  the  strength  of  a  lattice  truss  is 
usually  measured  by  the  strength  of  the  joints. 

Stresses  in  a  Lattice  Truss. — The  stresses  in  a  lattice  truss  are 
computed  in  about  the  same  way  as  those  in  a  riveted  plate 
girder;  thus  the  chords  are  assumed  to  resist  the  bending- 
moment,  and  the  braces  the  shearing-stress. 

The  tension  or  compression  in  the  chords  is  greatest  at  the 
centre,  while  the  stress  in  the  braces  is  greatest  at  the  ends. 


WOODEN  ROOF  TRUSSES. 


899 


Under  a  uniformly  distributed  load,  the  maximum  stress  in 
the  chords  may  be  found  by  multiplying  the  total  load  by  the  span 
and  dividing  by  8  times  the  height,  both  in  feet. 

The  stress  in  each  of  the  end  braces  a  a  a  when  the  angle  of 
inclination  approximates  45°,  will  be  one- sixth  of  the  total  load, 
multiplied  by  1.4. 

The  following  table  gives  the  dimensions  for  lattice  trusses, 

TABLE  II.— DIMENSIONS    FOR    LATTICE  TRUSSES  OF 
FIRST  QUALITY  WHITE  PINE  OR  SPRUCE. 

To  support  a  gravel  roof  arid  plastered  ceiling,  allowing  20  pounds  per 
square  foot  for  snow. 


*o  r. 

t£  'K> 

4»"S 

-6  ' 

ft 

3  • 

I 

£ 

0) 

.s7* 

q 

03 

£ 

s  « 
§s 

a+s 

02 

|! 

o 

ll 

0)  -^  o 

ll-g 

si 

End  bra 

b 

• 

fl 
C 

Ft, 

Ft. 

Ft.  Ins. 

Inch. 

12  1 

5     6 

7     2 

16 
12 

4—  2X    6 
4—  2X    6 

4—  2X    6 
4—  2X    6 

J2X   6 

-J2X   6 

2—1 

40  -1 

14J 

5     7 
7     3 

16 
12 

4—  2X    6 
4—  2X    6 

4—  2X    8 
4  —  2X   8 

J2X    6 

|2X   6 

3—  H 

16 

5     8 

7     4 

16 
12 

4—  2X   8 
4—  2X   8 

4—  2X   8 

4—  2X    8 

•J2X   8 

J2X   6 

J3-1 

f 

6     8 

16 

4—  2X   8 

4—  2X   8 

( 

(  2X    8 

j 

12 

-(2X10 

•{    and 

•\  3  —  1 

8     8 

12 

4—  2X   8 

4—  2X   8 

1 

(  2X    6 

j 

6     8 

16 

4—  2X   8 

4—  2X    8 

( 

2X   8 

j 

50  i 

14 

^2X10 

and 

8     8 

12 

4—  2X   8 

4—  2X   8 

( 

2X    6 

1            8 

6     9 

16 

4—  2X   8 

1—2X10 

( 

2X   8 

16 

J2X10 

and 

"S  3  —  1^8 

8     8 

12 

4—  2X    8 

4—  2X    8 

1 

2X    6 

( 

[ 

12 

8     4 
10  10 

16 
12 

4—2  X  10 
4—2  X  10 

4—2  X  10 
4—2X10 

•2X10 

J2X    8 

3-lKs 

60  •{ 

14 

8     4 
10  10 

16 
12 

4—2X10 
4—2  X  10 

4—2  X  10 
4—2X10 

•2X10 

-j  2X   8 

3—1^ 

( 

16 

8     4 
10  10 

16 
12 

4—2  X  10 
4—2  X  10 

4—2  X  10 
4—2X10 

|  2X10 

-|2X    8 

J3-1H 

14 

9     5 

12     4 

16 
12 

4—2  X  10 
4—2  X  10 

4—2X12 
4—2  X  10 

•  2X10 

J2X   8 

1-2^ 

70  - 

16 

9     5 

12     4 

16 
12 

4—2  X  10 
4—2X10 

4—2X12 
4—2X10 

•  2X10 

|  2X   8 

1—2^ 

18 

9     6 
12     6 

16 
12 

4—2X12 
4—2  X  12 

4  —  2  X  12 
4—2X12 

•j  2X10 

J2X   8 

1-2H 

( 

» 

11     0 
14     0 

16 
12 

4—2X12 
4—2  X  12 

4—2X12 
4—2  X  12 

•   2X10 

-|  2X    8 

1—  2M 

( 

11     2 

16 

4—2X14 

4—2  X  14 

2X10 

80  1 

104 

2X12 

and 

1—3 

1 

14     0 

12 

4—2X12 

4—2X12 

2X   8 

( 

11     2 

16 

4—2  X  14 

4—2  X  14 

2X10 

1 

18] 

2X12 

and 

1—3 

I 

( 

14     1 

12 

4—2X12 

4—2X14 

2X   8 

Uprights  at  end  same  size  as  end  braces. 


900 


WOODEN   ROOF   TRUSSES. 


built  as  shown  in  Fig.  22,  for  five  different  spans,  and  different 
spacings  and  heights,  which  will  cover  nearly  all  of  the  conditions 
under  which  these  trusses  should  be  used.  In  localities  where 
a  fall  of  snow  two  fe^et  in  depth  is  liable  to  occur,  these  dimen- 
sions should  be  increased. 

Referring  to  Fig.  22,  it  may  be  stated  that  each  chord  of  the 
truss  is  built  of  four  2X  10's  in  10  and  20  foot  lengths,  the  braces 
aaa  are  2X 10  and  the  other  braces  2  X  8.  The  joints  at  1,  2, 3,  4, 
arid  5  have  three  IJ-inch  bolts,  the  joints  between  6  and  8  and 
7  and  9  have  two  J-inch  bolts,  while  the  other  joints  have  two 
1-inch  bolts.  There  should  also  be  two  |-inch  bolts  in  the  tie- 
beam,  in  each  space  between  the  joints,  to  assist  in  transmitting 
the  tension  from  one  plank  to  the  other. 

Wooden  Trusses  with  Raised  Tie-beams. — All  of 
the  trusses  thus  far  described  have  horizontal  tie-beams,  which 
are  the  most  desirable  as  well  as  the  most  economical,  whenever 
the  conditions  will  permit. 

In  roofing  churches,  public  halls,  etc.,  a  raised  ceiling  is  often 
desired  in  order  to  give  greater  height  to  the  room,  without  in- 
creasing the  height  of  the  walls. 

Scissors  Trusses. — For  such  roofs  some  form  of  the  scissors 
truss  (so  named  from  its  resemblance  to  a  pair  of  scissors)  is 
most  often  used.  When  correctly  designed,  with  members  of 
the  proper  size,  and  with  the  joints  carefully  proportioned  to  the 
stresses,  the  scissors  truss  makes  a  very  good  truss  for  support- 
ing the  roof  over  halls  and  churches,  up  to  a  span  of  48  feet, 

but  above  that  they 
should  be  used  with 
much  caution,  as  the 
stresses  become  very 
great,  and  the  joints 
difficult  to  make. 

Figs.  25  to  30  show 
different  forms  of  the 
truss  adapted  to  dif- 
ferent spans  and  roof 
pitches.*  None  of 
these  trusses  will  ex- 
ert a  horizontal  thrust 


Fig.  25 


*  The  dimensions  given  in  these  figures  are  for  use  in   computing  the 
roof  loads  in  the  examples  given  in  Chapter  XXVI. 


WOODEN  ROOP  TRUSSES. 


901 


if  the  members  are  of  ample  size  and  the  joints  properly  made. 
The  members  having  a  -f  sign  on  or  close  to  them  are  in  com- 
pression, while  the  others  are  in  tension. 

The  members  indicated  by  a  single  line  should  be  rods  (except 
in  the  case  of  tie-beams). 


F?g.  26 

Fig.  25  shows  the  simplest  form  of  the  scissors  truss,  which 
is  suitable  for  spans  up  to  30  feet.     When  the  span  exceeds 


Fig.  27 

30  feet,  it  will  be  more  economical  to  use  two  purlins  on  each 
side,  to  support  the  common  rafters,  and  additional   supports 


902 


WOODEN   ROOF  TRUSSES. 


will  generally  be  required  by  the  tie-beams  which  will  call  for 
the  additional  rods  and  braces  shown  in  Fig.  26. 


Fig.  28 


For  a  steep  roof  the  arrangement  shown  by  Fig.  27  is  generally 
best  adapted,  and  for  a  flatter  roof  that  shown  by  Fig.  28. 
Fig.  29  shows  a  finished  truss,  built  on  the  same  lines  as 


-32  Span.  HSUepuat 


Fig.  29 

Fig.  28,  but  with  only  one  purlin.     The  truss  shown  by  Fig.  30 
is  similar  to  that  shown  by  Fig.  27,  with  the  peak  cut  off,  and 


WOODEN  ROOF  TRUSSES. 


903 


a  straining  beam  placed  between  the  upper  ends  of  the  prin- 
cipals, and  the  centre  rod  omitted.  For  spans  exceeding  36  feet, 
Fig.  30  gives  a  more  economical  truss  than  Fig.  27;  this  truss 
can  also  be  used  where  the  roof  is  hipped.  With  this  truss  it 
will  be  better  to  use  ceiling  purlins  to  support  the  ceiling  joists 
than  to  span  them  from  truss  to  truss. 


Common  Raftersv   / 


Fig.  30 

Fig.  31  shows  the  best  way  of  making  the  joints  at  5  and  7  of 
Fig.  30. 


2-1^  Rods  <*X  C.  to  C. 
2  x  10'spiked  Each  Side 
3"x  ^"stirrup 

6x10" 


Fig.  31 

Hammer-beam  Trusses. — One  of  the  principal  char- 
acteristics of  the  Gothic  style  of  architecture  is  that  of  making 
the  structural  portions  of  the  building  ornamental,  and  exposing 
the  whole  construction  of  the  edifice  to  view.  As  the  pointed 
arch  and  steep  roof  were  developed  the  roof  truss  became 
an  important  feature  in  the  ornamentation  of  Gothic  halls 


904 


WOODEN   ROOF  TRUSSES. 


and  churches.  The  trusses  of  this  period  were  built  almost 
entirely  of  wood,  and  generally  of  very  heavy  timbers,  to  give 
the  appearance  of  great  strength. 

One  of  the  most  common  types  of  these  Gothic  trusses,  and 
also  the  most  ornamental,  was  that  of  the  "  Hammer-beam 
truss,"  which  is  still  often  used  in  Gothic  churches. 

Figs.  32  and  33  show  early  English  forms  of  this  truss,  which 
takes  its  name  from  the  horizontal  beam  H,  at  the  foot  of  the 
principal,  and  which  is  called  the  "hammer-beam." 

In    the    more    ornamental    trusses,    the    hammer-beam    was 
usually  carved  to  represent  kings 
or  angels. 

These  trusses  differ  in  princi- 
ple from  all  of  the  trusses  thus 
far  described  in  that  they  have 
no  tie-beam,  and  no  substitute 
for  one.  In  fact  the  trusses 
shown  by  Figs.  32  and  33  do  not 


SECTION  OF  SECTION  OF 

"PRINCIPAL  RAFTER  COLLAR  BEAM 


Fig.  32 

ROOF    OVER    NAVE 

CHAPEL.  SUFFOLK,  ENG. 

Span  18ft. 


come  within  the  scope  of  the  definition  for  a  truss  given  at 
the  beginning  of  the   chapter.     Although   the   rafters   or  prin- 


WOODEN   ROOF  TRUSSES. 


905 


cipals  are  connected  near  the  top  of  the  truss  by  a  short  collar 
beam,  this  would  offer  but  little  resistance  to  the  rafters  spread- 


PRINCIPAL  RAFTER 


Fig.  33 


CHANCEL  ROOF 

BEDDINGTON  CHURCH 

SURREY 


ing  at  their  lower  ends, 
hence  the  truss  must 
depend  either  upon  the 
transverse  strength  of 
the  rafter  or  the  resist- 
ance of  the  walls  to  keep 
it  intact,  and  generally 
upon  both. 

In,,  the  halls  and 
chur|hes  of  the  Gothic 
period  the  walls  were 
generally  very  thick,  and 
.usually  re-enforced  on  the 
outside  by  buttresses 
built  against  the  wall 
directly  opposite  the  roof- 
trusses.  In  most  cases  such  a  wall  possesses  sufficient  stabil- 
ity to  withstand  the  thrust  of  the  truss,  and  hence  the  tie- 
beam  may  be  dispensed  with ;  but  in  a  wooden  building  the 
walls  offer  no  resistance  whatever  to  being  thrust  out,  unless 
tied  at  the  top,  and  hence  no  truss  which  exerts  an  out- 


906 


WOODEN  ROOF  TRUSSES. 


ward  thrust  on  the  walls  should 
be  used  in  such  a  building.  It 
is  therefore  impracticable  to  use 
a  hammer-beam  truss  in  a  wooden 
building.  In  roofs  where  this 
form  of  truss  is  used,  the  ceiling 
is  generally  formed  of  matched 
sheathing  nailed  to  the  under 
side  of  the  jack-rafters  between 
the  purlins,  thus  allowing  the  lat- 
ter to  be  seen.  The  purlins  are 
generally  decorated,  and  false 


Fig.  34 

Hammer -beam  Truss. 
First  Church,  Boston. 

ribs  are  often  placed 
vertically  between 
them,  so  as  to  divide 
the  ceiling  into  panels. 
The  rafters  should 
be  made  very  large 
to  prevent  them  from 
breaking  at  the  point 
A. 

An  excellent  exam- 
ple of  a  hammer-beam  truss  adapted  to  mod- 
ern conditions  is  shown  by  Fig.  34,  which 
represents  half  of  one  of  the  trusses  in 
the  First  Church,  Boston,  Mass.  (Messrs. 
Ware  &  Van  Brunt,  architects).  The  truss 
is  finished  in  black  walnut,  and  has  the 
effect  of  being  very  strong  and  heavy. 
Fig.  35  shows  the  framing  of  the  same  truss 
without  the  casing  and  falsework.  It  should 


WOODEN   ROOF  TRUSSES. 


90? 


be  noticed  that  inside  the  turned  column  at  the  upper  part 
of  the  truss  (Fig.  34)  there  is  an  iron  rod  (Fig.  35)  which 
holds  up  the  joint  A.*' 

In  this  form  of  truss  the 
outward  thrust  of  the  arch 
enters  the  wall  just  above 
the  corbel,  K',  and,  as  the 
direction  of  the  thrust  is 
inclined  only  about  thirty 
degrees  from  a  vertical,  the 
tendency  which  it  has  to 
overthrow  the  wall  is  not 

Fig. 35 

FRAMING  OF  HAMMER" 

BEAM  TRUSS 

See  Fig.34 


SCALE  - 

5  10  15  ^ 

Span  61  feet 

DISTANCE  BETWEEN  TRUSSES 
ABOUT  15  feet 

very  great,  and  may  be  easily  resisted  by  a 
wall  twenty  inches  or  two  feet  thick,  re- 
enforced  by  a  buttress  on  the  outside. 

In  trusses  of  this  kind,  the  pieces  should  be 
securely  fastened  together  wherever  they  cross 
or  touch  each  other,  and  the  whole  truss  made 

as  rigid  as  possible.     No  dependence  for  extra  strength  should 

be  made  on  the  casings  and  panel  work. 

Fig.  36  shows  a  form  of  truss  used  in  Emmanuel  Church  at 

Shelburne  Falls,  Mass.  (Messrs.  Van  Brunt  &  Howe,  architects). 


*  The  main  rafters  of  this  truss  are  two  five-inch  by  thirteen-inch  hard- 
pine  timbers. 


90S 


WOODEN  ROOF  TRUSSES. 


This  truss  was  probably  derived  from  the  hammer-beam  truss, 
and  possesses  an  advantage  over  that  truss  in  that  it  has  in 
effect  a  trussed  rafter,  so  that  there  is  no  danger  of  the  rafter 
being  broken;  and  if  the  truss  is  securely  bolted  together 


at  all  its  joints  it  exerts  but  very  little  thrust  on  the  walls. 
The  rafters  and  cross-tie  are  formed  of  two  pieces  of  timber 
bolted  together,  and  the  small  upright  pieces  run  in  between 
them. 

The  trusses  in  the  church  at  Shelburne  Falls  have  the  hammer- 
beams  carved  to  represent  angels. 

The  action  of  the  stresses  in  hammer-beam    trusses  is  ex- 
plained in  Chapter  XXVI. 


WOODEN    ROOF  TRUSSES. 


909 


Wooden  Trusses  with  Iron  Ties. — Where  there  is  no 
ceiling  beneath  the  roof,  and  it  is  desirable  to  make  the  trusses 
as  light  in  appearance  as  possible,  wrought-iron  or  steel  rods  may 
be  used  for  the  ties,  still  retaining  the  wooden  principals  and 
struts.  Such  trusses  will  be  cheaper,  for  moderate  spans,  than 
steel  trusses,  while  they  are  just  about  as  good,  particularly 
where  the  rafters  and  purlins  are  to  be  of  wood. 


Casting 


Fig.  37 

Spans  up  to  36'. 


Figs.  37  and  40  show  forms  of  trusses  that  are  suitable  for 
many  places.  The  dimensions  given  in  Fig.  40  are  for  yellow 
pine  or  Oregon  pine  timber  and  wrought-iron  rods,  and  are 
ample  for  a  slate  roof,  the  trusses  to  be  spaced  from  12  to  14  feet 
on  centres.  Trusses  like  Fig.  37  are  sometimes  seen  with  the  rods 
C  and  D  continuous.  They 
should  not  be  made  in  this 
way,  however,  as  the  stress  in 
C  is  greater  than  that  in  D. 
The  best  way  of  making  the  con- 
nection at  joint  B  is  shown  by 
Fig.  38,  a  cast-iron  shoe  being 
fitted  to  the  end  of  the  strut  to 
receive  the  pin.  For  the  truss 
shown  by  Fig.  40,  a  shoe  made 
as  shown  in  the  detail  drawing 
will  make  a  better  connection  for  the  rods,  two  of  the  rods 


Pirn  Bolt? 
Near  Rod  G 

Fig.  38 

Detail  of  joint  B. 


Ro'dE 


910 


WOODEN  HOOF  TRUSSES. 


being  placed  outside  of  the   brackets,  and  three   between  the 

brackets. 

For  a  truss  with  a  single  strut,  a  turnbuckle  on  the  rod  E  will 

be  sufficient  to  tighten  the  rods.     When  there  are  three  struts, 

there  should  be  five  turnbuckles,  as  in  Fig.  40. 

A  cast-iron  shoe  should  be  made  to  receive  the  foot  of  the 

rafter,  and  the  rods  secured  to  a  pin  passed  through  the  shoe 

and  the  rafter.     At  the  apex  of  the  truss  shown  by  Fig.  40  there 

should  also  be  a  casting  to  receive  the  ends  of  the  rafters,  and  a 

pin  for  the  tie-bars.  The  apex 
joint  of  the  truss  (Fig.  37)  may 
be  made  either  by  crossing  the 
rods  through  a  cast  washer,  or 
the  joint  may  be  made  as  in 
Fig.  39.  The  pins  at  the  joints 
should  be  computed  for  shear- 
ing, bearing  and  bending- 
moment. 

When  it  is  desired  to  support 

a  hammer-beam  truss  on  a  clerestory  wall  without  making  the 


Fig.  39 


Fig.  40 
wall  very  thick  or  bracing  it  from  the  outside,  a  form  of  truss 


WOODEN   ROOF  TRUSSES. 


911 


like  that  shown  in  Fig.  41  may  be  used  to  advantage.     This 

truss   has   the    appear- 
ance of  a  hammer-beam 

truss,  and  when  placed 

over  a  high   nave   the 

effect  of  the  rods  is  not 

objectionable. 

The    tie-rods    should 

extend      through      the 

hammer  beams  to  their 

outer  end.     For  a  truss 

of   32-feet   span    a    1J- 

inch  square  bar  will  be 

ample,  and  it  may  be 

twisted  to  give  a  more 

pleasing  effect. 

The  curved  ribs  a,  a,  in  this  truss  are  not  in  tension  but  in  com- 
pression, and  the  braces  under  the  hammer-beams  are  necessary 

to  resist  the  vertical  component  of  the  thrust  in  the  curved  ribs. 

A  truss  similar  to  this  was  used  in  the  new  Grace  Chapel,  New 

York  city. 

Fig.  42  shows  a  form  of  truss  used  to  support  the  roof  of  the 

Metropolitan  Con- 
cert Hall,  New 
York  city,  George 
B.  Post,  architect. 
The  span  of  the 
truss  in  that  build- 
f  ing  is  about  54  feet, 
and  the  propor- 
tions are  about  as 
shown  in  Fig.  42. 
The  arch  be- 
tween the  rafter 
and  the  raised  rib 

is  ornamented  with  sawed  work.     The  truss  has  a  very  light  and 

airy  appearance,  besides  embodying  all  the  strength  that  can  be 

desired  in  it.     The  tie-rod  is  kept  from  sagging  by  a  vertical 

rod  from  the  centre  of  the  arch. 
Wooden  Arched  Ribs,  with  Iron  or  Steel  Ties.-r- 

For  roofing  large  halls  or  rooms  a  segmental  timber  arch,  with  an 

iron  or  steel  tie  for  taking  up  the  horizontal  thrust  makes  about 


912 


WOODEN   ROOF   TRUSSES. 


M »l 


the  cheapest  truss  that  can  be  built,  especially  where  there  is 

no  ceiling    to    be    sup- 
ported. 

Figs.  43  and  44  are 
good  examples  of  this 
form  of  truss.  The 
arched  ribs  support  all 
the  load  that  comes 
upon  the  truss,  and 
the  tie-rods  prevent  the 
ends  of  the  arch  from 
spreading,  as  would  be 
the  case  if  there  were 
no  tie-rods. 

The  bracing  between 
the  arched  ribs  is  sim- 
ply to  unite  them,  and 
distribute  the  stresses 
arising  from  the  load 
proportionately  over  the 
two  ribs. 

The  framework  shown 
above  the  arch  in  Fig. 
43  is  simply  to  support 
the  purlins  and  rafters, 
and  only  carries  the 
load  directly  to  the  arch. 
It  does  not  assist  the 
truss  in  any  way  in 
carrying  the  load. 

The  method  of   sup- 
porting the  roof  of  the 
11  Fifth    Avenue    Riding- 

School,  New  York  city, 

is  slightly  peculiar  and  very  ingenious ;  and,  as  it  is  an  excellent 
example  of  the  advantage  of  the  arched  form  of  truss,  we 
shall  give  a  brief  description  of  the  construction  of  the  roof  and 
its  supports.  A  plan  of  the  riding-room  is  represented  by  Fig. 
45.  The  room  is  one  hundred  and  six  feet  six  inches  long, 
and  seventy-three  feet  wide.  This  space  is  kept  entirely  clear 
of  posts  or  columns;  and  the  entire  roof  is  supported  by  two 
large  trusses,  one  of  which  is  shown  in  Fig.  44.  The  roof  be- 


WOODEN   ROOF  TRUSSES. 


913 


tween  the  trusses  and  on  either  side  is  supported  by  smaller 
trusses  resting  on  these 
large  trusses ;  but  each 
of  the  large  trusses 
eventually  carries  a 
roof  area  equal  to 
about 2, 930  square  feet, 
and  a  great  amount 
of  extra  framework. 
It  was  desired  to  pro- 
vide for  the  thrust 
of  these  large  arches 
without  having  rods 
showing  in  the  room, 
and  the  method  adopt- 
ed is  very  ingenious. 
Opposite  the  upper 
ends  of  the  iron  posts 
which  receive  the 
arched  ribs  are  oak 
struts,  which  are  held 
in  place  by  iron  tie- 
bars  and  heavy  iron 
beams,  which  together 
form  a  horizontal  truss 
at  each  end.  These  two 
trusses  are  prevented 
from  being  pushed  out 
by  two  three-inch  by 
one-inch  tie-bars  in 
each  side-wall  shown 
in  the  plan  (Fig.  45). 

The  bottoms  of  the 
two  iron  posts  are  tied 
together  by  iron  rods 
running  under  the  floor 
the  whole  length  of 
the  room.  Altogether 
this  gives  for  the  tie- 
rods  of  each  truss  two 

bars  three  inches  by  one  inch,  and  an  inch  and  a  half  iron  rod, 
which  would  be  equivalent  to  two   tie-bars  three   inches  and 


914 


WOODEN  ROOF   TRUSSES. 


three-fourths  by  one  inch.  Enlarged  sections  of  the  ribs,  up- 
rights, and  braces  are  shown  in  Fig.  44.  It  should  be  noticed 
that  the  uprights  act  both  as  struts  and  ties,  by  having  iron  rods 
through  their  centre  holding  the  two '  ribs  together. 


inuis  wvas  NOU 


o.s  wvaa  NOUI 

1        j 


•sava  aii  NO.HI 


311  NO.H! 


Fig.  46  shows  a  detail,  or  enlarged  view,  of  the  iron  skewback 
and  post  at  each  end  of  the  truss  shown  in  Fig.  44. 

Fig.  47  shows  the  method  adopted  for  supporting  the  roof  and 
gallery  at  the  City  Armory  at  Cleveland,  O.,  the  arch  being  of 
wood. 

Fig.  48  shows  one-half  of  an  arched  wooden  truss  which,  with 
seventeen  others,  was  designed  for  supporting  the  roof  over  the 


WOODEN  ROOF  TRUSSES. 


915 


15  BEAM 
STRUT 


Fig.  46 


GROUND  LINE 


1^'lRON  TIE  TO  OPP03ITE.COLUMN" 
PIER         I  106  6  DISTANT 


Fig.  48 


916 


WOODEN  HOOF  TRUSSES. 


central  bay  of  Saenger  Hall,  Philadelphia,  Messrs.  Hazelhurst 
and  Huckel,  architects.  This  building  was  erected  in  1897  for 
the  use  of  the  Eighteenth  National  Saengerf  est,  and  was  intended 


only  for  temporary  use.  With  the  dimensions  slightly  increased, 
however,  the  truss  would  be  suitable  for  permanent  use.  The 
trusses  were  spaced  20  feet  centre  to  centre.  A  description  of 
the  building  and  trusses  was  published  in  the  Engineering  Record 
of  Jan.  9,  1897. 


STEEL   ROOF   TRUSSES. 


917 


TYPES  OP  STEEL  HOOP  TRUSSES. 

Trusses  for  Pitch  Roofs. — For  ordinary  conditions  and 
for  spans  under  100  feet,  some  one  of  the  types  shown  by  Figs. 
49  to  60  will  generally  meet  the  requirements  of  strength  and 
economy.  Trusses  of  these  types  are  usually  made  with  riveted 
connections,  this  being  the  cheaper  kind  of  construction  for 
short  spans  and  small  truss  members.  There  are  cases,  how- 
ever, when  the  pin  connection  may  be  the  cheaper  or  more  ad- 
visable construction. 
Pin-connected  trusses 
may  be  more  con- 
veniently shipped,  and 
where  they  are  sup- 
ported by  brick  walls 
so  as  not  to  require 
bracing,  may  often 
be  more  economically 
erected,  especially  if 


Fig.  49 


there  is  no  other  steel  work  about  the  building  that  requires 
riveting  during  erection.  When  the  trusses  are  supported  by 
steel  columns,  and  where  there  is  a  good  deal  of  steel  work  about 
the  building  requiring  the  presence  of  iron-workers,  riveted 
trusses  will  always  be  more  economical  for  spans  up  to  80  feet. 
For  a  narrow  shed  or  shop  the  shape  of  truss  shown  by  Fig.  49 
is  the  most  economical,  the  truss  proper  being  that  portion 
inclosed  within  the  points  A,  B,  C.  This  truss  is  practically 
the  same  as  that  shown  by  Fig.  50.  For  spans  of  from  24  to 
48  feet,  and  with  an  inclination  not  exceeding  6"  to  the  foot, 
types  51  and  52  are  the  most  suitable.  The  truss  types  repre- 


Fig.  50 

Span  20'  to  36', 

sented  by  these  two  figures  has  received  the  name  of  "Fan 
truss."     The  truss  shown  by  Fig.  50  is  known  as  a     "simple 


918 


STEEL   ROOF   TRUSSES. 


Fink  truss."  The  truss  shown  by  Fig.  52  differs  from  that 
in  51  principally  in  the  inclination  of  the  braces,  the  braces 
A  and  B  in  Fig.  52  being  inserted  to  brace  the  truss  from  the 
column  to  prevent  racking  under  wind  t  pressure.  Fig.  52 


Fig.  51 

Span  36'  to  50'. 


Fig.  52 

Span  40'  to  60'. 

should  be  used  when  the  truss  is  supported  by  columns  and 
Fig.  51  when  the  truss  rests  on  brick  walls.  A  sag  tie,  as  shown 
by  dotted  line,  is  generally  inserted.  When  the  roof  construc- 
tion demands  three  purlins  on  each  side-  of  the  truss,  one  of 


Fig.  53 

Span  40'  to  80'. 

the  forms  shown  by  Figs.  53,  54,  55,  or  56  should  be  used. 
The  names  given  to  these  trusses  are  often  confounded  by 
different  writers;  many  engineers  class  the  French  and  Fan 


STEEL   ROOF  TRUSSES. 


919 


trusses  with  the  Fink  truss.  The  term  "French"  appears  to 
be  generally  given  to  those  trusses  in  which  the  tie-beam  is 
raised  in  the  centre.  The  truss  shown  by  Fig.  56  appears  to 


Fig.  54 

French  Truss.     Span  40'  to  80'. 

have  no  generally  recognized  name.  One  writer  refers  to  it 
as  an  "English"  truss.  This  truss  is  not  as  economical  as  the 
Fink  truss,  except  when  the  inclination  of  the  rafter  is  less  than 
one-fourth  pitch,  on  account  of  the  great  length  of  the  inner 
struts. 

Although  Fig.  56  somewhat  resembles  the  queen  truss, 
Fig.  5,  it  will  be  seen  that  the  diagonals  run  in  the  opposite 
direction,  the  diagonals  in  Fig.  56  being  in  tension,  and  the 
verticals  in  compres- 
sion, the  reverse  of 
the  queen  truss.  In 
designing  steel  trusses 
it  is  desirable  to  have 
as  many  members,  and 
especially  of  the  long 
members,  in  tension  as 
possible,  as  a  given 

weight    of    steel    will        _       _       _  _ 

resist  a  much  greater  F'9'  56 

stress  when  in  tension  than  when  in  compression.  The  great 
economy  of  Fink  and  Fan  trusses  lies  in  the  fact  that  most  of 
the  members  are  in  tension  and  the  struts  are  short.  Com- 
paring Figs.  55  and  56  it  will  be  noticed  that  the  inner  strut 
in  Fig.  55  is  only  J  as  long  as  the  strut  in  Fig.  56,  Another 
advantage  of  these  trusses  is  that  a  partial  load,  as,  for  instance, 
a  wind  or  snow  load,  on  one  side  of  the  truss  never  causes  stresses 
in  excess  of  those  produced  by  a  uniform  load  of  the  same 


920  STEEL   ROOF  TRUSSES. 

intensity  over  the  whole  truss.  If  the  roof  is  hipped  it  is  desir- 
able to  have  vertical  members  in  the  hip  trusses  to  receive 
the  short  trusses  or  trussed  purlins. 

Depth  of  Firik  and  Fan  Trusses. — The  depth  of  these 
trusses  at  the  centre  is  usually  determined  by  the  roofing  mate- 
rial that  is  to  be  used.  Thus,  slate  should  not  be  used  on  a 
roof  in  which  the  rise  is  not  equal  to  one-third  of  the  span,  for 
wood  shingles  the  rise  should  not  be  less  than  one-fourth  the 
span,  and  for  corrugated  iron  not  less  than  one-fifth  of  the  span. 
Steel-roll  roofing  may  be  laid  on  a  slope  of  one-twelfth  the  span. 
There  are  many  kinds  of  so-called  " ready  roofing"  put  up  in 
rolls  which  may  be  used  for  any  slope  exceeding  }"  to  the  foot. 
Tar  and  gravel  roofing  should  never  be  used  on  a  pitch  exceed- 
ing f"  to  the  foot.  Considering  the  construction  of  the  roof 
and  the  weight  of  the  trusses  the  most  economical  pitch  for  a 


Fig.  57 

Span  68', 

roof  is  about  one-fourth  the  span,  or  what  is  commonly  called 
a  quarter  pitch,  the  rise  of  the  rafters  being  6"  in  12",  or  26  degrees 
and  34  minutes.  When  the  rise  is  less  than  one-sixth  the  span 
some  other  type  of  truss  will  generally  be  required.  When  the 
inclination  of  the  roof  is  determined  almost  entirely  by  the 
question  of  economy  the  rise  is  generally  made  from  6  to  7 
inches  in  12  inches.  With  Fink  or  Fan  trusses  having  an 
inclination  for  the  rafter  not  exceeding  30  degrees  it  is  more 
economical  to  employ  a  horizontal  chord  or  tie,  since  it  obviates 
bending  of  the  laterals.  A  truss  whose  bottom  chords  has  a 
rise  of  two  or  three  feet,  as  in  Fig.  54,  presents  a  better  appear- 
ance, however,  than  one  with  a  horizontal  chord.  Raising 
the  bottom  chord  also  materially  increases  the  strains  in  the 
truss  members,  hence  it  increases  the  cost.  For  steep  roofs, 
however,  it  will  generally  be  fully  as  economical  to  raise  the 
bottom  chord,  because  of  the  shortening  of  the  members. 


STEEL   ROOF  TRUSSES. 


921 


Number  of  Struts. — The  number  of  struts  that  should 
be  used  in  each  half  of  the  truss  will  be  determined  in  a  great 
measure  by  the  construction  of  the  roof.  If  Jack  rafters  and 
purlins  are  used  then  the  distance  between  the  struts  may  be 
as  great  as  12  feet,  but  if  there  are  no  Jack  rafters  and  the 


planking  of  the  roof  is  nailed  directly  to  the  purlins,  then  the 
latter  will  not  be  placed  more  than  8  feet  apart,  and  if  the  roof 
is  covered  with  corrugated  iron  secured  to  the  purlins,  then  the 
purlins  should  not  be  more  than  5  feet  on  centres.  Whenever 
the  purlins  are  more  than  four  feet  apart  they  should  come 
over  the  end  of  a  strut  or  brace,  to  avoid  bending-moments, 
consequently  the  spacing  of  the  purlins  will  generally  deter- 


922 


STEEL  ROOF   TRUSSES. 


mine  the  number  of  struts  in  each  half  of  the  truss.  For  this 
reason  the  same  form  of  truss  may  be  required  for  a  span  of 
40  feet  as  for  a  span  of  80  feet,  but  of  course  the  members  will 
not  be  as  heavy  in  the  40-foot  truss  as  in  the  one  with  greater 
span.  The  trusses  shown  by  Figs.  50  to  60  are  mostly  drawn 
from  actual  cases,  and  give  a  pretty  good  idea  of  the  most 
economical  division  for  different  spans. 

When  the  truss  rafter  is  subject  to  a  transverse  strain,  that 
is  when  it  is  loaded  between  the  joints,  the  distance  between  the 
joints  should  not  exceed  9  feet,  and  preferably  7  or  8  feet,  depend- 
ing somewhat  on  the  distance  the  trusses  are  apart.  The  dia- 
gram shown  by  Fig.  60  represents  one-half  of  one  of  the  steel 
trusses  used  in  roofing  a  car  barn  for  the  North  Jersey  Railway 
Co.  at»Newark,  N.  J.  There  were  13  of  these  trusses  spaced 
19  feet  2J  inches  on  centres,  each  having  a  span  of  98J  feet 
between  the  centres  of  the  supporting  columns,  to  which  the  truss 
is  riveted  by  splice-plates  engaging  the  end  connection-plate  and 
the  web  of  the  column.  The  dimensions  of  the  principal  mem- 
bers of  these  trusses  are  indicated  in  connection  with  the  illus- 
trations. A  more  complete  description  of  the  truss  will  be  found 


Main  Tie  1-4.  2-5  "x    3^"x  %"  L's 

"       "  4-5.  2-3^"x2K"x5/i6"L's 

Rafter,  1-2.  2-5 "x   3K"x7/i8L's 

"      2-3.  2-5"  x   SJ|"x%"L's 

a,  a,  a,  2-2K"x.2x  %"  L's 

6,6,6,  l-2^"x2"x^"    L's 

C,  2-3  "x  2K"x  %"    L's 

d,  d,  2-3K"x  g^'xVie  L's 


Fig.  60 

Truss  over  Car  Barn,  Newark,  N.  J. 

in  the  Engineering  Record  of  June  22,  1901.  These  trusses  were 
shipped  in  four  sections,  which  were  assembled  in  a  horizontal 
plane  and  riveted  up  complete  at  the  surface  of  the  ground. 
The  bottom  chord  was  stiffened  by  lashing  a  rail  on  each  side  of 
it  for  its  entire  length,  and  a  sling  being  attached  to  the  apex  of 
the  top  chord  the  truss  was  lifted  and  set  on  top  of  the  columns 


STEEL  ROOF  TRUSSES.  923 

by  an  8X8  gin-pole  50  feet  high.  The  roofing  consists  of  corru- 
gated iron  supported  by  5-inch  I-beam  purlins,  weighing  10  Ibs. 
to  the  foot,  spanning  from  truss  to  truss  and  bolted  to  the 
rafters  with  two  bolts  at  each  end;  the  general  spacing  of  the 
purlins  being  4  feet  9f  inches.  This  may  be  considered  as  an 
example  of  an  extremely  light  roof;  the  weight  of  each  truss 
being  about  4,200  Ibs.,  and  the  entire  weight  of  the  truss,  purlins, 
bracing  of  the  lower  chord  and  the  corrugated  iron  roofing  being 
only  8  Ibs.  for  each  horizontal  foot  of  surface  covered.  The 
trusses  shown  by  Fig.  59  were  designed  for  the  roof  of  a  drill-hall 
having  a  spaa  of  80  feet,  and  with  a  spacing  between  the  trusses 
of  20  feet.  The  roof  was  to  be  constructed  with  2"X8"  rafters 
supported  by  purlins  at  points  A,  B,  C,  D,  E,  and  F.  Sash  were 
to  be  placed  in  the  rise  C  D,  to  light  the  interior  of  the  building. 
The  joint  at  X  was  located  with  reference  to  the  position  of  the 
gallery  rod ;  if  there  had  been  no  gallery  it  would  have  been  more 
economical  to  space  the  vertical  struts  uniformly  as  in  Fig.  55. 
The  plus  sign  adjacent  to  a  member  in  all  the  trusses  illustrated 
denotes  that  the  member  is  in  compression,  while  the  minus  sign 
denotes  tension.  The  members  above  the  main  rafter,  as  C  Z>, 
D  E,  and  E  F,  in  Fig.  59,  and  a  and  b  in  Fig.  60,  do  not  form  a 
part  of  the  truss  proper,  but  are  merely  a  framework  to  support 
the  elevated  roof,  and  in  drawing  the  stress  diagram  they  would 
be  omitted. 

Fink  Trusses  with  Pin  Joints. — Fig.  61  shows  one- 
half  of  a  Fink  truss  designed  for  pin  connections.  This  truss  has 
a  span  of  55  feet  4  in.  between  the  centres  of  end-pins,  and  the 
distance  between  the  centres  of  trusses  is  6  feet.  The  roof  is 
covered  with  12//X20// slate,  secured  to  J"X2£"  angle  purlins 
weighing  3  Ibs.  to  the  foot  and  spaced  8J"  on  centres.  The 
angles  span  from  truss  to  truss  and  are  bolted  to  the  deck-beam 
with  J-in.  bolts.  A  1J"X2-J"  nailing  strip  is  fastened  to  every 
third  purlin  for  securing  matched  ceiling  placed  on  the  under 
side  of  the  roof.  Complete  details  of  this  truss  were  published 
in  Architecture  and  Building  for  Jan.  18,  1890.  Fig.  62  shows 
details  of  the  cast-iron  struts.  This  truss,  being  put  together 
entirely  with  bolts  and  pins,  could  easily  be  erected  with  un- 
skilled labor. 

Trusses  for  Flat  Roofs. — For  supporting  flat  roofs  or 
roofs  having  a  fall  not  exceeding  1  inch  to  the  foot,  one  of 
the  types  shown  by  Figs.  63  to  67  will  generally  be  found 
economical,  the  choice  of  the  particular  type  depending 


924 


STEEL   ROOF  TRUSSES. 


Fig.  62 

Detail  of  Struts, 
Fig.  61. 


1 


X  Filling^ 
PlateaT 


ACBCA 


STEEL  ROOF  TRUSSES. 


925 


somewhat  on  the  span  and  whether  the  truss  is  supported 
by  columns  or  by  brick  or  stone*  walls.  For  spans  up  to  50 
feet  either  of  the  forms  shown  by  Figs.  63  or  64  will  answer 


Fig.  63 

Span  56'. 

all  practical  requirements.  The  truss  shown  by  Fig.  63  is  in- 
tended to  be  used  where  the  fall  of  the  roof  is  at  right  angles  to 
the  truss;  this  truss  can  be  built,  however,  with  an  inclination 
to  the  top  chord,  as  in  Fig.  64.  The  end  brace  in  Fig.  63  is  in 


Fig.  64 
Spans  3(y-50'. 

tension,  while  in  Fig.  64  it  is  in  compression.     The  portion  of 
the  lower  chord  between  the  end  joint  and  the  wall,  Fig.  63,  has 


Fig.  65 

no  stress  from  the  roof  load,  but  is  put  in  to  brace  the  wall 
and  to  stay  the  truss.  In  trusses  supported  by  brick  walls  this 
type  is  preferable  to  that  shown  by  Fig.  64,  while  the  latter  is 


926 


STEEL   ROOF  TRUSSES. 


more  suitable  when  the  roof  is  supported  by  columns.  The 
vertical  A,  Fig.  64,  is  inserted  to  receive  the  tension  or  com- 
pression from  brace  B,  and  would  have  no  stress  from  the  roof. 
The  truss  shown  by  Fig.  65  is  known  as  a  "Double  Warren 
Truss,"  and  is  desirable  where  it  is  important  to  make  the 
trusses  as  shallow  as  practicable ;  it  can  be  built  with  light  mem- 
bers, and  makes  a  very  stiff  roof,  being  especially  suitable  for 
roofs  supported  by  steel  columns.  Fig.  65  is  drawn  from  an 
actual  truss.  The  strength  under  unsymmetrical  loads,  as  for 
example  when  there  is  more  snow  on  one  side  than  on  the  other, 
would  be  materially  increased  by  putting  a  vertical  tie  in  the 
centre  as  shown  by  the  dotted  line;  without  this  member  the 
braces  AA  if  subject  to  any  stress  whatever  would  produce  a 
bending  in  the  bottom  chord  at  the  centre.  Fig.  66  represents 
an  actual  roof  truss  with  span  of  57  feet,  supported  by  steel 
columns.  The  entire  load  on  the  truss  is  transmitted  to  the 
columns  by  the  braces  BB  which  are  in  tension.  Fig.  67  shows 
a  truss  of  96  feet  span  over  a  pier  shed,  New  York  city,  the 
trusses  being  spaced  20  feet  apart.  They  are  about  10  feet  high 
and  weigh  1,300  Ibs.  each;  they  were  delivered  complete  from 
the  shops  and  were  raised  bodily  by  falls  suspended  from  two 
masts.  The  dimensions  of  these  trusses  are  given  in  the  En- 
gineering Record  of  Jan.  18,  1896. 


Fig.  66 

Span  57'. 


Fig.  67 

Span  96'-'.0 

The  plus  and  minus  signs  in  these  illustrations  indicate  com- 
pression and  tension  respectively  under  uniform  dead  load. 
The  plus  and  minus  signs  together  indicate  that  the  member  may 


STEEL  ROOF  TRUSSES. 


927 


be  subject  to  either  tension  or  compression  according  to  the 
direction  of  the  wind  or  to  an  uneven  distribution  of  snow.  In 
most  of  these  trusses  an  unsymmetrical  load  may  change  the 
stress  in  the  diagonals  near  the  centre  of  the  truss.  This  chang- 
ing of  stresses  due  to  unequal  loading  will  be  considered  in  the 
next  chapter.  Trusses  shown  by  Figs.  63  to  67  are  almost  in- 
variably built  with  riveted  connections  and  with  angle  or 
channel  shapes  for  all  members. 

For  horizontal  steel  trusses  intended  to  support  floor  loads, 
the  Pratt  truss,  shown  by  Figs.  68  and  69,  is  the  best  adapted, 
the  members  indicated  by  double  lines  being  in  compression  and 
those  indicated  by  single  lines  in  tension.  When  supporting 


Fig.  ( 


W 


Fig.  69 

floors  subject  to  moving  loads,  counter  ties  should  be  inserted 
as  indicated  by  dotted  lines.  For  this  truss,  pin-connections 
are  generally  employed  and  are  preferable  to  riveted  connec- 


Fig  70. 

Truss  over  Amphitheatre,  Madison  Square  Garden. 

tions.     When  properly  proportioned  this  truss  is  capable  of  sus- 
taining almost  any  load. 


928 


STEEL   ROOF  TRUSSES. 


The  Quadrangular  Truss.  —  The  truss  shown  by 
Fig.  66  is  known  as  a  quadrangular  truss,  although  the  more 
common  shape  for  this  truss  is  that  shown  by  Fig.  70,  which 
gives  the  proportions  of  the  truss  over  the  amphitheatre  of 
the  Madison  Square  Garden,  New  York.  Figs.  71  and  73  also 
show  variations  of  this  truss,  differing,  however,  from  the 
typical  truss,  in  that  the  diagonals  are  all  inclined  in  the  same 
direction,  while  in  the  typical  truss  they  are  usually  reversed 
in  the  centre  in  order  to  keep  them  in  tension. 

The  plus  and  minus  signs  indicate  the  kind  of  stress  in  the 
member  produced  by  a  uniform  dead  load.  It  should  be 

noticed  that  the  centre 
diagonals  of  trusses  71  and 
73  are  in  compression.  This 
truss  is  well  adapted  to 
steel  construction  for  spans 
up  to  180  feet.  When  the 
span  exceeds  100  feet  one 
end  of  the  truss  should  be 
supported  on  rollers  to 
allow  for  the  expansion  or 
contraction  in  the  steel.  In 
these  trusses  the  load  is 
transmitted  to  the  top  of 
the  post  by  the  end  diagonal 
which  is  always  in  tension 
and  subject  to  a  very  great 
stress,  the  truss  proper  being 
included  within  the  points 
A,  B,  C,  A  and  E,  Figs.  71 
and  72.  The  continuation 
of  the  tie-beam  to  the  post 
is  for  the  purpose  of  bracing 
the  roof  from  the  columns, 
there  being  no  stress  in  this 
member  from  a  vertical 
load  only.  In  the  truss 
shown  by  Fig.  70  the  post 
P  was  made  a  part  of  the 
truss ;  the  stress  in  this  post 
is  equal  to  the  reaction  of 
the  truss.  The  brace  £,  Fig.  70,  and  the  corresponding  member 


STEEL  ROOF  TRUSSES. 


929 


in  Figs.  71  and  72  should  be  so  constructed  as  to  resist  both 
tension  and  compression.      For    short  spans  the  lower  chord 


may  be  made  in  the  shape  of  a  semi-circle  or  semi-ellipse  so  as 
to  give  more  of  an  arch  effect. 

There  are  numerous  examples  in  this  country  of  quadrangular 
trusses  having  spans  of  from   100  to  180  feet.     For  the  wider 


930 


STEEL    ROOF   TRUSSES. 


spans  it  is  customary  to  build  the  truss  with  pin-connections, 
eye-bars  being  used  for  the  ties.  When  this  is  done  it  will 
usually  be  necessary  to  insert  counter  braces  in  two  panels  on 
each  side  of  the  truss  as  shown  by  the  dotted  lines,  Fig.  70, 
as  under  an  unsymmetrical  or  wind  load  the  stress  in  the  diago- 


XXXXXX 


•TdB 

O5   M 


o 

§ 
fi 


nals  is  generally  reversed.  When  the  span  is  less  than  100 
feet,  the  truss  may  be  built  with  riveted  connections,  in  which 
case  the  diagonals  are  generally  made  of  angles  capable  of 
resisting  both  tension  and  compression,  and,  therefore,  counter 
braces  will  not  be  required.  For  this  type  of  truss  the  stresses 


STEEL   ROOF   TRUSSES.  931 

due  to  wind  and  snow  should  be  computed  independently  of 
the  dead  load  and  the  members  computed  for  the  maximum 
stress  that  may  be.  produced  by  any  possible  combination  of 
loading. 

A  description,  with  illustrations  of  the  truss  shown  by 
Fig.  73,  which  is  a  diagram  of  one  of  the  trusses  over  the  Kansas 
City  Auditorium,  may  be  found  in  the  Engineering  Record  for 
July  22,  1899. 

ARCHED  TRUSSES. 

For  roofing  large  rooms,  such  as  railway  stations,  armories, 
and  exposition  buildings,  an  arched  truss  is  generally  the  most 
economical. 

Bowstring  Trusses. — Previous  to  the  year  1880  wrought- 
iron  trusses  of  wide  span  were  mostly  built  in  the  form  of  a 
bow,  from  which  the  term  " Bowstring"  was  derived.  Trusses 
of  this  £ype  were  built  from  88  to  211  feet  span  and  with  a  rise 
in  the  centre  of  from  one-fifth  to  one-fourth  of  the  span.  At 
that  time  this  style  of  truss  was  considered  the  most  economi- 
cal for  spans  exceeding  120  feet,  but  since  the  introduction  of 
the  braced  arch  they  have  been  comparatively  little  used. 

Fig.  74  represents  the  diagram  of  a  bowstring  truss  of 
153-feet  span.  The  trusses  in  this  particular  case  are  spaced 
21  feet  6  inches  apart.  The  arched  rafter  consists  of  a  wrought- 
iron  deck-beam  9  inches  deep,  with  a  plate  10  inches  by  1J 
inches,  riveted  to  its  upper  flange.  Towards  the  springing 
this  rib  was  strengthened  by  plates  7  inches  by  J  inch,  riveted 
to  the  deck-beam  on  each  side. 


Fig.  74 

The  struts  are  wrought-iron  I-beams  7  inches  deep.  The  tie- 
rods  have  a  sectional  area  of  6  J  sq.  ins.,  and  the  diagonal  tension 
braces  are  1|  inches  in  diameter.  These  trusses  are  fixed  at 
one  end,  and  rest  on  rollers  at  the  other,  permitting  free  ex- 
pansion and  contraction  of  the  iron  under  the  varying  heat  of 
the  sun. 


932 


STEEL   ROOF   TRUSSES. 


Fig.  75  shows  a  similar  truss  having  a  span  of  212  feet.     It 
consists   of   bowstring   principals   spaced   24   feet  apart.     The 


Fig.  75 


rise  is  one-fifth  the  span,  the  tie-rod  rising  17  feet  in  the  middle 
above  the  springing,  and  the  curved  rafter  rising  40J  feet. 
The  rafter  is  a  15-inch  wrought-iron  I-beam.  The  tie  is  a  round 
rod  in  short  lengths,  4  inches  diameter,  thickened  at  the  joints. 
The  tension  bars  of  the  bracing  are  of  plate-iron,  5  inches  to 
3  inches  in  width,  and  f  inch  thick.  The  struts  are  formed  of 
bars  having  the  form  of  a  cross. 


Fig.  76 

Braced  Arches.— Fig.  76  is  a  diagram  of  one  of  the 
three  arches  used  in  roofing  the  train  shed  of  the  Sullivan 
Square  Station  of  the  Boston  Elevated  Railway,  a  description  of 


STEEL  ROOF  TRUSSES. 


933 


Fig.  76A 


IRod 


3^  Pin 


2-1%  Plates 


which  may  be  found  in  the  Engineering  Record  for  June  15, 
1901.  These  arches  spring  from  steel  columns  and  are  provided 
with  tension  rods  which  take  up  the  thrust.  The  arch  proper 
rests  on  two  \\"  pins  at  each 
end  as  indicated  in  diagram, 
the  tie-rods  being  connected 
to  these  pins.  The  bracing 
below  the  pins  is  riveted  to 
the  column  and  the  arch 
itself  is  built  of  angles  and 
plates  with  riveted  connec- 
tions. Fig.  76  A  shows  the 
joint  at  A  where  the  tie-rods 
are  connected  and  are  held 
up  by  a  1"  suspension  rod  from  the  crown  of  the  arch.  This 
construction  is  the  same  in  principle  as  that  of  the  wooden  arch 
shown  by  Fig.  48.  It  can  hardly  be  considered  as  a  truss  in 
the  ordinary  meaning  of  the  word. 

Three-Hinged,  Braced  Arches.— The  type  of  arched 
truss  most  used  at  the  present  time  for  steel  construction  is  that 
shown  by  Figs.  78  and  79,  which  is  commonly  known  as  the 
three-hinged,  braced  arch.  This  truss  differs  from  all  other  types 
of  trusses  in  that  it  consists  essentially  of  two  separate  parts, 
each  acting  as  a  single  piece  and  depending  upon  the  opposing 
force  of  its  mate  to  keep  it  in  position.  As  usually  built,  each 
part  is  a  semi-braced  arch,  the  upper  and  lower  members  being 
so  connected  by  bracing  as  to  form  a  stiff  frame  or  curved  rafter. 

The  first  use  of  the  braced  arch  appears  to  have  been  in 
building  railway  bridges  for  French  railroads,  the  earlier  forms 
being  rigidly  connected  at  the  top. 

The  first  suggestion  for  hinging  the  ribs  at  the  crown  was 
made  by  M.  Manton,  a  French  engineer. 

The  application  of  this  principle  to  roof  trusses,  at  least  on  a 
large  scale,  the  author  believes  to  have  been  in  the  train-sheds  of 
Sa  Union  Railway  station  at  Frankfort-on-the-Main,  Germany, 
which  was  completed  in  the  year  1888.  These  trusses  have  a 
span  of  about  184  feet.  The  large  roof  of  Machinery  Hall,  of 
the  Paris  Exposition  of  1899,  was  supported  by  this  type  of  truss, 
the  span  in  this  case  being  368  feet,  exceeding  anything  hitherto 
attempted  in  a  roof  truss.  Since  then  this  truss  has  become 
quite  popular  for  roofing  large  exhibition  buildings,  train-sheds, 
armories,  etc. 


934  STEEL   ROOF  TRUSSES. 

The  three-hinged  arch-truss  proper  is  always  supported  on  a 
pin  at  the  bottom  and  usually  the  two  halves  are  pin-connected 
at  the  top,  thus  allowing  for  expansion  and  contraction.  The 
bottom  pins  are  usually  placed  below  the  ground  floor  level  and 
connected  by  tie-rods  beneath  the  floor.  These  trusses  can  be 


Ml,-. 


2-2*SquarebaE§ 


-ISi'O  — 


Fig.  77 

Half  Truss,  Manufactures  and  Liberal  Arts  Building  (Chicago). 

built,  however,  and  have  been,  without  tie-rods,  in  which  case  it 
is  necessary  that  they  rest  on  a  foundation  capable  of  resisting 
the  horizontal  thrust,  although  the  trusses  can  be  so  built  that 
the  thrust  will  not  be  very  great. 

The  special  advantages  of  this  type  of  truss  for  the  class  of 

.buildings  above  mentioned  are  economy,  maximum  clear  space 

beneath  the  truss  and  provision  for  expansion  and  contraction. 


STEEL  ROOF  TRUSSES. 


935 


Much  of  the  economy  of  the  truss  lies  in  the  fact  that  it  re- 
quires no  columns  to  support  it,  and  the  base  of  the  truss  being 
very  near  the  ground  level,  it  is  well-proportioned  to  resist  wind 
pressure. 

A  great  advantage  of  this  truss  is  the  free  movement  allowed 
under  temperature  changes  without  strain  to  the  structure,  the 


centre  rising  or  falling  freely  with  a  slight  rotation  of  the  semi- 
arches  about  the  pivots.  In  the  case  of  the  trusses  of  the  Paris 
Exposition,  it  was  estimated  that  a  range  of  temperature  of  100 
degrees  Fahr.  would  produce  a  change  in  level  of  2J  inches  at 
the  centre  pivot. 

The  arched  ribs  are  always  built  of  plates,  angles  or  channels 


936 


STEEL  ROOF   TRUSSES. 


with  riveted  connections,  and  frequently  with  a  solid  plate  web 
at  the  bottom. 

The  determining  of  the  stresses  and  detailing  of  the  members 
and  joints  will  require  the  service  of  a  competent  structural 
engineer,  but  the  illustrations  given  will  enable  the  architect  to 


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2-1  j|Sq.  Bars                          N 

5*Pin 

2^ 

& 

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-191 

^i  n-  — 

¥ 

Fig.  79 

Arched  Truss,  Machinery  Hall,  Chicago,  1890. 

decide  on  the  general  shape  of  the  truss  for  the  purpose  of  making 
preliminary  drawings  and  the  computations  and  detail  draw- 
ings can  be  made  later. 

For  spans  of  from  80  to  120  feet  this  type  is  often  put  up 
without  the  pin  connections,  as  in  Fig.  80,  the  mechanical  prin- 
ciple being  essentially  the  same  as  in  the  three-hinged  truss. 
Complete  drawings  and  details  of  the  truss  shown  by  Fig.  77 
may  be  found  in  Vol.  26  of  the  Engineering  Record,  and  of  the 
truss  shown  by  Fig.  79  in  Vol.  27.  A  description  and  details  of 
the  truss  shown  by  Fig.  78  may  be  found  in  the  Engineering 
Record  for  Dec.  3,  1899.  Table  VI,  Chapter  XXVI,  gives  the 
dimensions  and  spacing  of  a  number  of  trusses  similar  to  Figs. 
77,  78,  and  80. 

Other  examples  of  three-hinged  arched  trusses  are  given  in 
Part  III  of  the  author's  work  on  Building  Construction. 

Cantilever  Trusses. — The  term  "cantilever"  was  origi- 
nally used  to  designate  a  projecting  beam  which  served  as  a 


STEEL  ROOF   TRUSSES. 


937 


bracket;  in  mechanics  it  is  used  to  denote  a  beam  or  girder  fixed 
at  one  end,  either  by  being  built  into  a  wall  or,  most  commonly, 
by  extending  a  sufficient  distance  bej^ond  its  support  to  form  an 
anchorage  for  the  cantilever.  Thus  in  Fig.  81  we  have  a  beam 


resting  on  two  supports ;  the  portion  B  is  a  cantilever,  while  the 
part  C  forms  the  anchorage  for  it. 

(In  applying  the  cantilever  to  trusses  it  is  customary  to  inter- 
pret it  as  including  both  the  projecting  arm  and  the  balancing 
arm,  as  both  portions  form  one  piece  of  framework,  and  the  term 
will  be  so  used  in  this  work.) 

It  is  obvious  that  if  the  entire  beam  (Fig.  81)  were  uniformly 
loaded  the  post  P  would  carry  the  greater  part  of  the  weight, 
and  also  that  an  additional  load  at  W  might  produce  an  upward 
pull  on  the  post  D,  in  which  case  the  stress  on  P  would  exceed 
the  load  on  the  beam. 

Both  conditions  of  loading  occur  in  practice,  although  it 
probably  most  often  happens  that  the  outer  end  of  the  truss 
requires  anchorage  rather  than  a  support. 


938 


STEEL  ROOF  TRUSSES. 


As  applied  to  roof  construction  some  such  arrangement  as  is 
shown  in  Fig.  82  is  generally  required  to  make  this  method  of 
support  practicable;  that  is,  a  wide  centre  span,  with  shorter 
spans  or  aisles  on  each  side  of  it. 

The  projecting  or  inner  arm  of  the  cantilever  is  usually  made 
from  one-quarter  to  one-third  of  the  centre  span,  and  a  simple 
truss,  represented  by  S,  is  used  to  support  the  rest  of  the  roof,  the 
centre  truss  being  supported  by  the  arms  of  the  cantilever.  In 
all  such  cases,  therefore,  cantilever  trusses  must  be  used  in  pairs, 
one  on  each  side  of  the  building,  and  there  must  be  rooms  or  pas- 
sages outside  of  the  principal  span  to  permit  of  the  outer  or 
balancing  arm.  Such  an  arrangement  is  generally  found  in 
large  halls,  armories,  exhibition  buildings,  etc.,  and  it  might 
sometimes  be  provided  in  other  classes  of  buildings. 


Fig.  84 


Of  course,  in  a  large  building  a  simple  beam  such  as  is  shown 
in  Fig.  82  could  not  be  used,  but  the  principle  of  construction 
is  the  same  whether  the  cantilever  be  a  simple  beam  or  a  large 
truss. 

Fig.  83  shows  the  diagram  for  a  truss  to  take  the  place  of 
the  beam  CB,  Fig.  82,  the  single  lines  representing  the  tension 


STEEL   ROOF   TRUSSES. 


939 


members  and  the  double  lines  compression  members,  and 
Fig.  86  shows  the  complete  arrangement  of  the  trusses.* 

The  truss  shown  in  these  figures  may  be  extended  to  almost 
any  extent,  and  the  lower  chord  may  be  curved,  but  the  general 
outline  of  the  truss  will  be  found  best  adapted  for  all  cases 
where  a  wide  central  roof  is  to  be  supported  by  cantilevers. 

For  bridge  trusses  or  floors  the  shape  shown  in  Fig.  84  may 
be  used,  and  for  shed  and  platform  roofs  open  on  one  side  a 
truss  of  the  shape  shown  in  Fig.  85  is  about  the  only  practicable 
device.  In  this  latter  truss  the  proportions  of  the  arms  are 
such  that  a  slight  support  is  required  at  W,  thereby  bringing 
the  lower  portion  of  the  rafter  into^compression. 

It  will  be  seen  from  Figs.  83,  84,  and  85  that  the  strains  in  a 
cantilever  truss  are  directly  the  reverse  of  those  in  trusses  sup- 
ported at  both  ends,  the  upper  chord  or  rafter  in  the  cantilever 
being  in  tension,  while  in  all  other  trusses,  except  the  hinged 
arch,  it  is  in  compression. 


Fig.  86 

Suggestion  for  Wooden  Cantilever  Truss. 

Ad  vantages  an  cl  Disadvantages  of  the  Cantilever 
Truss. — The  special  advantages  possessed  by  the  cantilever 
truss  are:  A  greater  clear  height  in  the  centre  than  can  be  ob- 
tained with  any  other  type  excepting  the  three-hinged  arch, 
a  light  and  graceful  appearance,  no  horizontal  thrust,  and  con- 
sequently no  tie-rods  required.  The  particular  advantage  of 
this  truss  for  very  great  spans  is  that  it  can  be  erected  with- 


*  Suggested  by  Mr.  John  Beverly  Robinson  for  a  simple  trussed  canti- 
lever roof. 


940 


STEEL   ROOF  TRUSSES. 


out  scaffolding  under  the  centre,  and  in  bridge  work  this  is 
considered  as  its  only  advantage. 

It  is  claimed  by  prominent  engineers  that  the  cantilever  is 
not  an  economical  type  of  truss,  and  not  as  desirable  for  spans 
of  150  feet  or  more  as  the  three-hinged  arch. 

It  also  does  not  permit  of  as  readily  overcoming  expansion 
and  contraction  as  either  the  three-hinged  arch,  the  bowstring 
truss,  or  the  quadrangular  truss.  For  certain  classes  of  buildings, 
however,  and  especially  where  the  central  span  does  not  exceed 
150  feet,  it  can  perhaps  be  used  with  better  architectural  effect 
than  is  possible  with  other  types,  and  with  about  the  same 
economy.'  For  roofing  platforms,  grand-stands,  etc.,  where  an 
outer  support  is  not  desired,  it  is  the  only  type  available. 

Example  of  a  Cantilever  Truss. — Fig.  87  is  a  dia- 
gram of  one  of  the  cantilever  trusses  supporting  the  roof  of 
the  grand-stand  at  the  Monmouth  Park  (N.  J.)  racing-track, 
the  details  of  which  were  published  in  Architecture  and  Building 
in  February,  1890.  This  is  an  instance  where  the  cantilever 
was  the  only  type  of  truss  that  could  be  used,  and  the  form 
adopted  is  both  simple  and  economical. 


Fig.  87 

As  will  be  seen  from  the  drawing,  the  main  supporting  post 
extends  to  the  top  of  the  truss,  as  is  usually  the  case  with  canti- 
lever trusses,  and  the  truss  is  riveted  to  each  side  of  it.  The 
upper  and  lower  chords  were  made  of  two  angles  and  a  web- 
plate,  the  upper  chords  or  rafters  acting  as  a  tie-beam  between 
the  bracing.  The  bracing  consists  of  angle-bars  used  in  pairs 
and  varying  from  3X2X1  inches  to  3X3X/ie  inches,  the  whole 
frame  being  connected  by  rivets.  Other  examples  of  canti- 
lever roofs  are  given  in  Part  III  of  "Building  Construction." 


ROOF  LOADS.  941 


CHAPTER  XXVI. 
STRESSES  IN  ROOF-TRUSSES. 

THE  various  steps  to  be  pursued  in  designing  a  trussed  roof 
and  proportioning  its  parts  are  as  follows: 

First.  Deciding  upon  the  roof  covering  and  how  it  is  to  be 
supported  between  the  trusses. 

Second      Laying  out  the  roof  trusses  on  the  plan  and  section. 

Third.  Computing  the  truss  loads  and  determining  the 
stresses  produced  thereby. 

Fourth.     Computing  the  size  of  the  truss  members. 

Fifth.     Detailing  the  joints. 

The  kind  of  roof  covering  to  use,  on  a  pitch  roof,  will  be 
determined  largely  by  the  external  effect  sought,  and  by  the 
cost.  For  flat  roofs,  appearance  usually  cuts  no  figure,  so  that 
the  durability,  cost,  and  adaptability  to  any  peculiar  requirements 
of  the  building  are  the  controlling  elements.  The  matter  of 
incombustibility,  or  resistance  to  fire,  is  also  generally  a  point  to 
be  considered  when  steel  trusses  are  to  be  used. 

Roofing  Materials  for  Pitch  Roofs. — The  mate- 
rials suitable  for  covering  pitch  roofs  are  slate,  burnt  clay  tiles, 
metal  tiles  or  shingles,  wood  shingles,  corrugated  iron,  tin  with 
Standing  seam,  standing  seam  steel  roofing,  and  various  kinds 
of  ready  roofing. 

The  least  slope  to  which  these  materials  may  be  laid  without 
danger  of  leaks,  the  weight  per  square  foot  of  roof  and  the  com- 
parative cost  is  indicated  by  Table  I.  The  cost,  however, 
can  only  be  considered  as  approximate  as  it  will  vary  for  different 
materials,  according  to  the  locality,  and  the  scale  of  wages. 

Flat  roofs  or  roofs  having  a  fall  of  J  in.  to  f  in.  to  the  foot 
are  usually  covered  with  tar  and  gravel,  asphalt,  ready  roofing, 
or  tin  with  lock-and-solder  joint.  A  good  tin  roof  costs  about 
$8  a  square,  besides  the  painting.  The  other  kinds  will  vary 
from  $3.50  to  $4.50  a  square. 


942  STRESSES  IN  ROOF-TRUSSES, 

TABLE  I.— COVERING  MATERIALS  FOR  PITCH  ROOFS. 


Material 

Least 
Rise  of 
Rafter 
in  12 
iris. 

Comparative 
Cost  per 
Square. 

Slates,  black  

8 

$7  to  $12 

Slates,  green  . 

8 

$7  'to  $10 

Slates,  red  

8 

$12  to  $17 

Burnt  clay  tiles,  interlocking  pattern  
Tin  shingles,  painted 

7 
6 

$15  to  $25 
$8  to  $10 

Galvanized  iron  tile,  painted  .  .  . 

6 

$13  to  $15 

Cedar  shingles,  stained  or  painted  

6 

$3  80  to  $7  20 

Corrugated  iron,  painted  

3 

$4  00  to  $4  50 

Standing  seam  steel  roofing,  painted  

2 

$4  to  $4  50 

Ready  roofing  

1 

$3  50  to  $4  50 

Manner  of  Supporting  the  Roof  from  the  Trusses. 

— Wooden  roofs,  supported  by  wooden  trusses,  require  common 
or  jack  rafters  to  support  the  sheathing  or  slate,  and  generally 
purlins  to  support  the  rafters,  although  in  some  cases  it  ma}^ 
be  more  economical  to  span  the  rafters  from  truss  to  truss, 
see  p.  891. 

When  slate  or  burnt  clay  tile  are  used  pn  steel  roofs,  they 
are  usually  secured  to  steel  angles,  running  parallel  with  the 
walls  and  spaced  from  8  to  10 J  ins.  apart,  as  may  be  necessary 
to  accommodate  the  size  of  the  slate  or  tile.  If  the  span  is  not 
very  great,  the  angles  may  be  fastened  to  the  truss  rafters, 
which  will  require  that  the  trusses  be  not  more  than  6  or  7  ft. 
apart.  As  a  rule,  however,  when  slate  or  tile  are  to  be  used, 
it  will  be  cheaper  to  space  the  trusses  from  16  to  20  ft.  apart, 
and  to  use  purlins  and  jack  rafters  for  supporting  the  smaller 
angles. 

Quite  often,  wooden  rafters  and  sheathing  are  used  with 
steel  trusses;  this  is  more  economical,  but,  of  course,  increases 
the  fire  risk,  unless  there  is  a  wooden  ceiling  below,  in  which 
case  unprotected  steel  is  little  if  any  better  than  wood. 

If  corrugated  iron  is  to  be  used  for  roofing,  the  most  economi- 
cal construction  for  steel  roofs  will  be  to  space  the  trusses  from 
16  to  20  ft.  apart,  and  to  use  light  I-beams  for  purlins,  spaced 
about  4"  9"  on  centers,  as  in  Fig.  60,  Chapter  XXV,  the  cor- 
rugated iron  being  secured  to  the  purlins  by  straps.  If  warm 
air  comes  in  contact  with  the  underside  of  a  corrugated  roof 


ROOF  LOADS.  943 

the  roofing  should  be  laid  on  boards,  or  some  kind  of  anti-con- 
densation lining  provided,  otherwise  the  moisture  in  the  air  will 
condense  and  fall  011  the  floor  or  objects  below. 

Flat  roofs  will  always  require  rafters  and  sheathing,  or  fire- 
proof filling  between  the  rafters. 

Spacing1  of  Trusses. —  From  the  above  it  will  be  seen 
that  the  economical  spacing  of  the  trusses  will  depend  to  a  con- 
siderable degree  upon  the  kind  of  roofing  that  is  to  be  used, 
and  also  upon  the  span.  As  a  general  rule,  however,  the  most 
economical  spacing  will  be  about  as  follows: 

For  wooden  trusses  under  80  ft.  span,  12  to  16  ft.  C.  to  C. 

For  wooden  trusses  over  80  ft.  span,  16  to  24  ft.  C.  to  C. 

For  steel  trusses  under  80  ft.  span,  16  to  20  ft.  C.  to  C. 

For  steel  trusses  over  80  ft.  span,  20  to  40  ft.  C.  to  C. 

The  actual  spacing  of  a  number  of  steel  trusses  of  wide  span 
is  given  in  Table  VI. 

When  the  distance  between  the  trusses  exceeds  16  ft.  for 
wooden  roofs  or  20  ft.  for  steel  roofs,  it  will  generally  be  neces- 
sary to  use  trussed  purlins. 

Having  decided  upon  the  kind  of  truss  to  be  used,  the  spacing 
of  the  trusses  and  the  roof  construction,  a  section  drawing  of 
the  roof  should  be  made,  showing  an  elevation  of  the  truss,  the 
points  at  which  the  purlins  are  to  be  supported,  and  also  the 
manner  of  supporting  the  ceiling,  if  any,  and  any  other  loads 
that  are  to  be  supported  by  the  trusses. 

The  section  and  truss  drawing  with  a  knowledge  of  the  weight 
of  materials,  will  afford  the  necessary  data  for  computing  the 
loads  at  each  joint  of  the  truss. 

Until  the  stresses  have  been  determined,  the  size  of  the 
members  computed,  and  the  joints  detailed,  an  exact  drawing 
of  the  truss  cannot,  of  course,  be  made,  but  to  compute  the 
loads  and  stresses,  it  is  necessary  to  know  the  position  of  the 
joints,  and  these  can  be  indicated  with  sufficient  accuracy  with- 
out knowing  the  exact  size  of  the  members.  Chapter  XXV 
gives  sufficient  information  regarding  the  various  types  of 
trusses,  to  enable  one  to  decide  on  the  height,  and  the  number 
and  position  of  the  struts  and  ties,  and  one  can  guess  at  the 
size  of  the  members  for  the  preliminary  drawings. 


944 


STRESSES  IN  ROOF-TRUSSES. 


Roof  and  Ceiling  Area  Supported  at  any  Joint. 

Calculations  for  the  stresses  in  a  truss  are  always  based  on 
the  assumption  that  the  loads  are  transferred  to  the  joints, 
and  that  the  members  are  free  to  move  at  the  joints  as  if  hinged, 
even  although  the  actual  joint  may  be  made  with  riveted  con- 
nections. The  loads  at  the  joints  are,  of  course,  equal  to  the 
reaction  of  the  purlins,  or  of  the  tie-beams  or  principals,  if  these 
receive  the  ceiling  joists  or  rafters.  When  the  load  on  the  roof 
or  ceiling  is  uniformly  distributed,  as  is  usually  the  case,  the 
simplest  method  of  computing  the  joint  loads,  is  to  find  the 
roof  or  ceiling  area  contributory  to  the  joint,  and  multiply 
this  area  by  the  weight  or  load  per  square  foot. 

As  a  rule,  the  area  contributory  to  any  joint  is  equal  to  the 
distance  half  way  to  the  next  joint  on  each  side,  multiplied 
by  the  distance  half  way  to  the  next  truss  or  wall,  on  each  side. 
Thus  if  Fig.  1  represents  truss  1,  of  Fig.  2,  the  roof  area  contribu- 

8  +  14 
tory  to  joint  2,  is  — „ — Xa.     For  truss  2,  the  area  supported 

a 

by  the  same  joint  is  — ~ —  Xa,  or  if  we  let  D  represent  the 


Rafters  and  Ceiling  Joists  2x8"' 
16"C.  to  C. 


Fig. 


length  of  roof  or  ceiling  supported  at  each  joint,  then  the  area 
supported  by  joint  2=aXD  and  the  area  supported  by  joint 
3=2bxD.  In  the  same  way,  the  ceiling  area  supported  at 
joint  Q=cXD,  the  arrow-heads  being  half  way  between  the 
joints. 

It  makes  no  difference  in  the  joint  loads  whether  the  common 
rafters  are  supported  on  purlins  or  whether  they  rest  on  the 


ROOP  LOADS. 


945 


-y— 

i 


rafter  provided  the  purlins  come  at  or  close  to  the  joints  and 
the  load  is  uniformly  distributed. 

Thus  the  width  of  the  ceilling  contributory  to  joint  7,  Fig.  3, 
will  be  equal  to  c,  just  the  same 
as  in  Fig.  1,  but  it  makes  a  con- 
siderable difference  in  the  strain 
in  the  tie-beam.  When  the 
trusses  are  spaced  a  uniform 
distance  apart,  D,  Fig.  2,  will, 
of  course,  be  equal  to  the  dis- 
tance between  centres  of  trusses. 
When  the  trusses  are  not  spaced 
uniformly,  D  equals  one  half 
the  distance  from  the  centre  of 
the  truss  on  the  left  to  the 
centre  of  the  truss  on  the  right. 

When  the  purlin  comes  more 
than  12  ins.  from  a  joint,  or  the 
roof  area  is  not  symmetrical,  as 
is  often  the  case  at  hips  and 


Truss  2 


I 


Truss  1 


- 


J=._ 


Fig.  2 


valleys,  then  the  joint  load  must  be  determined  by  the  principle 
of  the  reaction  of  beams,  as  explained  on  pp.  274-277.     Ex- 


-K C=1Z'2- »t 

* -—12V— <- 122-- 

J 


X.  6  Rafter.8 

le'o.c. 


Fig.  3 

amples  showing   the  computation  of  joint  loads  are  given  a 
little  further  on. 


946  STRESSES  IN  ROOF-TRUSSES. 

Roof  Load  per  Square  Foot. —  By  the  term  "roof 
load"  is  meant  the  weight  of  the  materials  composing  the  roof, 
trusses,  and  purlins,  an  ample  allowance  for  snow  and  also  an 
allowance  for  wind  pressure.  The  weight  of  the  materials 
compose  what  is  called  the  dead  load.  Snow  is  generally  con- 
sidered as  a  live  load,  acting  vertically.  The  pressure  due  to 
the  wind  always  acts  normal,  or  at  right  angles  to  the  surface 
of  the  roof,  but  for  trusses  of  less  than  100  ft.  span  it  is  usually 
combined  with  the  wind  and  snow  loads  and  treated  as  a  ver- 
tical load. 

Data  for  Computing  Dead  Loads. — The  dead  load  of  any  roof 
may  be  estimated  quite  closely  from  the  following  data: 

TABLE  II.— WEIGHTS  PER  SQUARE  FOOT  OF  ROOF 
SURFACE. 

Shingles,  common,  2J  Ibs.;   18  ins.,  3  Ibs. 

Slates,  %>  in.  thick,  7J  Ibs. ;  J  in.  thick,  9.6  Ibs.  (the  common 
thickness  is%  in.  for  sizes  up, to  10"X20"). 

Plain  tiles  or  clay  shingles,  11  to  14  Ibs. 

Roman  tiles,  old  style,  two  parts,  12  Ibs.;  new  style,  one 
part,  8  Ibs. 

Spanish  tiles,  old  style,  two  parts,  19  Ibs.;  new  style,  one 
part,  8  Ibs. 

Improved  Oriental  tiles,  11  Ibs. 

Ludowici  tile,  8  Ibs. 

For  tiles  laid  in  mortar  add  10  Ibs.  per  square  foot. 

Copper  roofing,  sheets,  li  Ibs.;   tiles,  If  Ibs. 

Tin  roofing,  sheets  or  shingles,  including  one  thickness  of  felt, 
1  Ib. 

Corrugated  iron,  painted  or  galvanized,  No.  26, 1  Ib. ;  No,  24, 
1.3  Ibs.;  No.  22,  1.6  Ibs,;  No,  20,  1.9  Ibs,;  No.  18,  2.6  Ibs.;  and 
No.  16,  3.3  Ibs. 

Standing  seam  steel  roofing,  1  Ib. 

Five-ply  felt  and  gravel  roof,  6  Ibs. 

Four-ply  felt  and  gravel  roof,  5J  Ibs. 

Three-ply  ready  roofing  (elaterite,  ruberoid,  asphalt,  etc.), 
0.6  to  1  Ib. 

Skylights  with  galvanized  iron  frame,  J-inch  glass,  4|  Ibs.; 
%-in.,  5  Ibs.;  f-in.,  6  Ibs. 

Sheathing,  1  in.  thick,  3  Ibs.  per  square  foot  for  white  pine, 
spruce,  or  hemlock;  4  Ibs.  for  yellow  or  pitch  pine. 


ROOF  LOADS. 


947 


TABLE  III.— WEIGHT  OF  RAFTERS  PER  SQUARE  FOOT. 


Size  of 
Rafters, 

T           ^ 

Spruce,  Hemlock,  White  Pine, 
Spacing  in  Inches,  Centre  to 
Centre. 

Hard  Pine,  Spacing  in  Inches- 
Centre  to  Centre. 

16 

20 

24 

16 

20 

24 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

2X4 

14 

1.2 

1 

2 

1.6 

1J 

2X6 

2} 

1.8 

U 

3 

2.4 

2 

2X7 

2| 

2.1 

If 

3* 

2.8 

2J 

2X8 

3 

2.4 

1  2 

4 

3.2 

2| 

2X10 

3i 

3 

2i 

5 

4 

3J 

Wooden  purlins  will  weigh  about  2  Ibs.  per  square  foot  of  roof 
surface  when  the  span  is  between  12  and  16  ft. 

For  steel  roofs  the  size  and  weight  of  the  purlins  and  rafters 
should  be  computed  for  each  particular  case. 

For  a  rough  approximation  the  weight  of  steel  trusses,  purlins, 
and  bracing  in  a  roof  covered  with  corrugated  iron  with  no  ceiling 
will  run  from  4  to  6  Ibs.  per  square  foot  of  horizontal  surface 
covered.  The  steel  work  for  slate  roofs  with  suspended  ceil- 
ings below  will  run  about  7J  Ibs.  per  square  foot  when  the  span 
does  not  exceed  50  ft. 

Steel  roofs  supported  by  arched  trusses  will  weigh  from  8  to  12 
Ibs.  per  square  foot  of  roof  surface. 

Weight  of  Truss. — To  the  weight  of  the  roof  construc- 
tion proper  should  be  added  an  allowance  for  the  weight  of  the 
trusses.  If  trusses  could  be  built  in  exact  accordance  with 
the  theoretical  requirements  their  weight  would  be*  directly 
proportional  to  the  roof  load  and  span,  but  as  there  is  always 
some  extra  material,  it  is  impossible  to  determine  the  weight 
of  the  truss  exactly  until  the  trusses  are  completely  designed. 
Several  tables  for  the  weight  of  wooden  trusses  and  formulas 
for  steel  trusses  have  been  published,  but  hardly  any  two  of 
them  are  alike.* 

*  The  following  are  some  of  the  formulas  given  for  weight  of  steel  trusses, 
W  being  weight  per  horizontal  square  foot,  £  =  span  in  feet. 
Charles  Evan  Fowler,  C.E.,  for  Fink  trusses: 

W  =  .065 +.6  for  heavy  loads; 
T7  =  .04S  +  .4  for  light  loads. 
H.G.  Tyrrell,  C.E.: 

12 


W-.05S  + 


C.  W.  Bryan,  C.E.: 


dist.  centre  to  centre 


948 


STRESSES  IN  ROOF-TRUSSES. 


Tables  IV  and  V  compiled  by  the  author,  from  a  comparison 
of  other  tables  and  formulas,  and  from  the  weight  of  actual 
trusses,  are  sufficiently  accurate  for  the  purpose  of  determining 
stresses.  The  weights  given  are  probably  slightly  in  excess 
of  the  actual  weights  of  average  trusses,  as  the  author  prefers 
to  have  the  error,  if  any,  on  the  safe  side.  It  should  be  noted 
that  the  weights  are  for  each  square  foot  of  roof  surface,  and 
not  for  the  horizontal  area.  Table  VI  gives  the  actual  weights 
of  a  number  of  large  steel  roofs. 

TABLE    IV.— WEIGHT  PER  SQUARE  FOOT  OF   ROOF 
SURFACE  FOR  WOODEN  TRUSSES.* 


Span. 

M  Pitch. 

M  Pitch. 

\i  Pitch. 

Flat. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Up  to  36ft. 

3 

34 

3| 

4 

36  to    50ft. 

3i 

3| 

4 

44 

50  to    60ft. 

31 

4 

44 

4| 

60  to    70ft. 

3} 

41 

4f 

5| 

70  to    80ft. 

4 

5 

54 

6 

80  to    90ft. 

5 

6 

64 

7 

90  to  100  ft. 

5i 

61 

7 

8 

100  to  110ft. 

64      • 

n 

8 

9 

110  to  120  ft. 

81 

9 

10 

*  For  scissors  trusses  increase  one-third. 

TABLE  V.— WEIGHT  PER  SQUARE  FOOT  OF  ROOF 
SURFACE  FOR  STEEL  TRUSSES. 


s 

pa*n. 

Yz  Pitch. 

M  Pitch. 

M  Pitch. 

Flat. 

Up  to 

40ft. 

5.25 

6.3 

6.8 

7.6 

50  ft. 

5.75 

6.6 

7.2 

8.0 

60  ft. 

6.75 

8.0 

8.6 

9.6 

70ft. 

7.25 

8.5 

9.2 

10.2 

80ft. 

7.75 

9.0 

9.7 

10.8 

100  ft. 

8.5 

10.0 

10.8 

12.0 

120  ft. 

9.5 

11.0 

12.0 

13.20 

140  ft. 

10.0 

11.6 

12.6 

14.0 

The  data  for  the  first  seven  buildings  in  Table  VI  were  com- 
piled by  Mr.  H.  G.  Tyrrell,  C.E.,  who  states  that  all  of  the  seven 
roofs  were  proportioned  for  slate  and  plank  roofing  resting  on 
wide  rafters  2  ft.  apart,  supported  by  steel  purlins  about 
10  ft.  apart;  Spans  given  are  centre  to  centre  of  side  bearings. 


SNOW  LOAD. 


949 


Stresses  computed  for  dead  load  of  25  Ibs.,  snow  load  of  10  Ibs. 
per  square  foot  of  sloping  surface,  horizontal  wind  40  Ibs.  per 
square  foot  or  28  Ibs.  normal  pressure. 

Data  for  computing  the  weight  of  floors  and  floor  loads 
supported  by  trusses,  or  for  fireproof  construction,  may  be 
found  in  Chapter  XXI  and  XXIII. 

TABLE  VI.— WEIGHT  AND  SPACING  OF  SOME  STEEL 
ROOFS  OF  WIDE  SPAN,  INCLUDING  TRUSSES, 
PURLINS,  AND  BRACES,  BUT  NOT  ROOF  COVER- 
ING OR  RAFTERS. 


Name  of  Building. 

Type  of 
Truss. 

Span, 
Feet. 

Spacing 
C.  to  C. 
of 
Trusses. 

Wt.  per 
Sq.  Ft. 
Sloping 
Surface. 

Wt.  of 
of 
One 
Truss. 

Pawtucket  Armory  

Fig.  80* 

82 

Feet 
24 

Lbs. 

8.7 

Tons 
6.7 

Portland,  Me.,  Armory  .... 
Phoenix  Hall,  Brockton  .  .  . 
Northampton  Armory  .  ... 
Palace  Rink,  Hartford  .... 
Providence  Ex.  Hall  
Cleveland  Armory  

92 
96 
100 
104 
118 
120 

25 
24 
24 
25 
24^ 
23-25 

9.7 
8.6 
8.0 
11.8 
9.5 

9 
10 
8.5 
11.5 
12.5 

Boston  Armory  .... 

122 

30 

12.4 

21 

22d  Regt.  (N.  Y.)  Armory  .  .  . 
Brooklyn  Armory 

176 
196 

24^ 
35 

Kansas  City  Convention  Hall  . 
74th  Reg't  Armory,  Buffalo.  . 
Chicago  Coliseum  .  .  .  . 

Fig.  73* 
3-hinge  arch 
3-hinge  arch 

187Mt 
227  1 
14934f 

23^ 
28 
23-25 

*  Chapter  XXV.         t  Centre  to  centre  of  end  pins. 

Snow. — As  a  basis  for  making  an  allowance  for  snow, 
Table  VII  is  perhaps  as  good  a  guide  as  any  that  can  be  given. 
When  snow  guards  are  to  be  placed  on  a  roof,  the  same  allow- 
ance should  be  made  for  a  half  pitch  as  for  one- third  pitch. 

TABLE  VII.— ALLOWANCE  FOR  SNOW  IN  POUNDS 
PER  SQUARE  FOOT  OF  ROOF  SURFACE. 


1                       Location. 

Pitch  of  Roof. 

H 

M 

H 

V6 

^or 
less. 

Southern  States  and  Pacific  Slope  .  . 
Central  States  

tl 

0-5 
0-10 
0-10 
0-12 

u 

7-10 
10-15 
10-15 
12-18 

*  t 
0-5 
15-20 
20-25 
20-25 
25-30 

5 
22 

27 
35 
37 

5 

30 
35 
40 

45 

New  England  States  .  . 

Northwest  States  

Columns  headed  by  an  asterisk  (*)  are  for  slate,  tile,  or  metal;    those 
headed  by  a  dagger  (|)  are  for  shingle  roof. 


950 


STRESSES  IN  ROOF-TRUSSES. 


Wind  Pressure. — For  roofs  having  a  pitch  of  5  ins.  or 
more  to  the  foot,  an  allowance  must  be  made  for  wind  pressure. 
For  trusses  of  the  Fink,  Fan,  King,  or  Queen  types  the  usual 
practice  is  to  include  the  wind  pressure  with  the  vertical  loads, 
and  to  make  a  single  allowance  for  both  wind  and  snow,  as 
during  a  gale  snow  is  not  likely  to  stay  on  a  steep  roof.*  When 
the  wind  pressure  is  added  to  the  vertical  loads,  the  author 
recommends  that  the  allowance  for  wind  and  snow  combined 
be  not  less  than  indicated  in  Table  VIII. 

TABLE  VIII.— ALLOWANCE  FOR  WIND  AND  SNOW 
COMBINED  IN  POUNDS  PER  SQUARE  FOOT  OF 
ROOF  SURFACE. 


Location. 

Pitch  of  Roof. 

60° 

45° 

M 

25 
25 
25 
25 
25 

M 

30 
25 
25 
25 
25 

% 

H 

Northwest  States  . 

30 
30 
30 
30 
30 

30 
30 
30 
30 
30 

37 
35 

27 
22 
22 

45 
40 
35 
30 
20 

New  England  States  

Rocky  Mountain  States  

Central  States  

Southern  and  Pacific  States  

No  roof  truss  should  be  proportioned  for  a  total  load  of  less 
than  40  Ibs.  per  square  foot,  except  flat  roofs  in  warm  climates. 

For  trusses  having  a  span  exceeding  100  ft.  (except  horizontal 
trusses)  and  for  trusses  in  which  a  partial  load  may  produce 
maximum  stresses,  or  call  for  counter  bracing,  as  is  the  case  in 
quadrilateral  trusses,  and  trusses  with  curved  chords  the  stresses 
for  all  the  different  loadings  should  be  found  separately  and 
each  member  of  the  truss  proportioned  to  the  maximum  stress 
to  which  it  may  be  subject  under  any  possible  combination 
of  the  load. 

For  determining  the  stresses  due  to  wind  pressure  alone 
the  force  of  the  wind  is  usually  assumed  to  act  in  a  direction 
normal,  i.e.,  at  right  angles  to  the  slope  of  the  roof.  This 
force  is  commonly  based  on  a  horizontal  wind  pressure  of  30  Ibs. 

*  Mr.  Bryan,  the  designing  engineer  of  the  Edgemoor  Bridge  Works,  states 
that  "  in  Fink  trusses  a  partial  load  due  to  wind  or  snow  never  causes  any 
maximum  stresses,  so  that  it  is  customary  to  calculate  these  trusses  for  a 
uniform  load  over  the  entire  truss,  the  wind  and  snow  loads  combined  being 
usually  assumed  at  SOlbs.persq.  ft. of  areacovered;  i.e.  .horizontal  surf  ace." 


WIND  PRESSURE. 


951 


per  square  foot,  although  quite  often  it  is  taken  at  40  Ibs.  per 
square  foot,  depending  somewhat  upon  the  exposure  and  the 
shape  of  construction  of  the  roof  and  truss. 

The  normal  and  horizontal  pressure  per  square  foot  of  roof 
surface  corresponding  to  a  horizontal  pressure  of  30  Ibs.  against 
a  vertical  surface  is  given  in  Table  IX. 

TABLE  IX.— NORMAL  AND  HORIZONTAL  WIND  PRES- 
SURE ON  ROOFS  FOR  30  POUNDS  HORIZONTAL 
PRESSURE  AGAINST  A  VERTICAL  SURFACE. 


Inclination, 

Norm 

Hor. 

Inclination. 

Norm. 

Hor. 

5°. 

Ibs. 
3.9 

Ibs. 
0.3 

30°  .  . 

Ibs. 
19.9 

Ibs. 
10.0 

10°  

7.2 

1.2 

33°-41'  (K  pitch)  .  . 

22.0 

12.0 

15°  .  . 

10.5 

35°  

22.6 

18°-26'  (K  pitch)  .  .  . 

13  0 

4  0 

40° 

25.1 

15.9 

20°  ... 

13.7 

4.5 

45°  (\i  pitch)  

27.1 

19.0 

21°  48'  (y~  pitch).  .  .  , 

15  0 

6  0 

50°  .  . 

28.6 

21.9 

25°  .  . 

16.9 

55°  

29.7 

26°-34'  {\i  pitch)    . 

18  0 

8  0 

60°  

30.0 

25.5 

For  horizontal  wind  pressure  of  40  Ibs.  per  square  foot  the 
pressure  given  above  should  be  increased  one-third. 

Variations  in  Loading*  for  which  Stresses  should 
be  Found. — To  determine  the  maximum  stresses  under 
any  possible  condition  of  loading,  stresses  should  be  found  for 
the  following  cases: 

(1)  Stresses  due  to  permanent  dead  loads. 

(2)  Snow  covering  only  one  side  of  roof. 

(3)  Snow  covering  entire  roof. 

(4)  Wind  on  side  of  truss  nearer  the  expansion  end. 

(5)  Wind  on  side  of  truss  nearer  the  fixed  end. 

It  is  generally  assumed  that  the  maximum  wind  pressure 
and  the  snow  load  cannot  act  on  the  same  half  of  the  truss  at 
the  same  time,  hence  the  combinations  for  maximum  stress 
will  be  either  cases  1  and  3  or  cases  1,  2,  and  4  or  5. 

If  the  trusses  are  supported  on  iron  columns  instead  of  walls 
the  wind  force  is  transferred  to  the  foundations  through  the 
columns,  producing  a  bending  moment  in  the  columns.  The 
strains  in  the  columns,  trusses,  and  knee-braces  should  there- 
fore be  determined  for  the  horizontal  wind  pressure  against 
the  side  of  the  building  and  roof.  This  pressure  is  obtained 
by  multiplying  the  area  of  the  vertical  surfaces  by  the  full 


952  STRESSES  IN  ROOF-TRUSSES. 

pressure  per  square  foot  and  the  elevation  of  the  roof  by  the 
horizontal  component,  given  in  Table  IX. 

For  the  trusses  supporting  the  roof  of  the  Kansas  City  Audi- 
torium (see  Fig.  73,  Chapter  XXV)  stresses  were  computed 
for  the  following  conditions:  First,  full  dead  and  live  load  on 
both  galleries  and  the  roof-garden  and  wind  pressure  due  to  a 
velocity  of  45  miles  an  hour;  second,  full  dead  load,  snow  load, 
and  gallery  live  load,  wind  pressure  10  Ibs.  and  no  load  on  roof- 
garden  floor;  third,  full  dead  load  and  50  Ibs.  wind  pressure; 
fourth,  full  dead  load  and  wind  pressure  at  45  miles  an  hour, 
and  full  live  loads  on  gallery  and  roof-garden  on  one  side  only. 

Snow  loads  throughout  were  taken  at  one-third  of  the  dead 
load.  Examples  showing  manner  of  combining  the  stresses  due 
to  different  conditions  of  loading  are  given  on  pp.  1023  and  1034. 

Examples  of  the  Computation  of  Roof  jLoads, 

(All  loads  considered  as  acting  vertically.) 

1.  For  the  first  example  we  will  take  the  roof  and  truss 
shown  by  Fig.  1  (p.  944),  which  we  will  assume  represents  truss 
2  of  Fig.  2.  We  will  assume  that  the  timber  is  to  be  common 
white  pine  and  that  the  roof  is  to  be  covered  with  ^-inch  slate 
of  medium  size  on  J-inch  sheathing. 

The  ceiling  to  consist  of  lath  and  plaster. 

The  dead  load  of  roof  and  truss  per  square  foot  of  roof  sur- 
face will  be  made  up  as  follows: 

For  slate 7i  Ibs. 

For  sheathing 3       " 

For  rafters 3       " 

For  purlins 2 

For  truss 3       " 

Total 18J  Ibs. 

For  wind  and  snow  load  combined  we  should  allow  about 
28  Ibs.  (the  pitch  being  about  40  degrees),  which  would  make  a 
total  roof  load  of  46^  Ibs.  To  avoid  fractions,  however,  we 
will  take  48  Ibs.  per  square  foot. 

As  the  distance  to  truss  1,  Fig.  2,  is  14  ft.,  and  to  truss  3 
12  ft.,  the  length  of  roof  supported  by  the  truss  will  be  13  ft. 
The  roof  area  supported  by  the  purlins  at  joint  2  will  be  equal 
to  the  distance  a  multiplied  by  13  ft.,  and  a  will  be  one-half  of 
the  distance  from  the  wall  plate  to  the  next  purlin,  or  22'  8/f-s-2 


COMPUTATIONS  OF  ROOF  LOADS.      953 

=  11'  4",  or  11 J  ft.     Hence  the  roof  area  supported  at  joint  2 
will  be  11JX13,  or  147J  square  feet. 

The  roof  area  supported  by  the  purlins  at  joint  3  will  be 
26X13  ft.,  or  12'  4"X13'=160J  square  ft. 

Multiplying  the  roof  areas  by  the  load  per  square  foot  (48), 
we  have  7,072  Ibs.  for  the  load  at  joint  2  and  7,696  Ibs.  for  the 
load  at  joint  3.  The  load  at  joint  4  will  be  equal  to  that  at  2, 
as  the  truss  is  symmetrical. 

We  must  now  compute  the  ceiling  loads  at  joints  6  and  7. 
The  ceiling  area  supported  at  joint  6=cXl3  ft.,orSiXl3=107i 
sq.  ft.  The  area  supported  at  joint  7=8f  X13>=114|  sq.  ft. 

The  actual  weight  of  the  ceiling  per  square  foot  will  be  3  Ibs. 
for  the  joists  and  10  Ibs.  for  lath  and  plaster;  but  where  there 
is  a  large  attic  space  it  is  liable  to  be  used  for  storing  odd  articles, 
so  that  it  is  always  well  to  make  a  small  allowance,  say  5  Ibs. 
per  square  foot,  for  any  extra  weight  that  might  be  placed  in 
the  attic.  We  will,  therefore,  allow  18  Ibs.  per  square  foot  for 
the  weight  of  the  ceiling,  which  would  make  the  weight  at 
joints  6  and  8  107JX18,  or  1,930  Ibs.,  and  the  weight  at  joint  7 
114|X18=2,067  Ibs. 

As  soon  as  computed,  the  roof  and  ceiling  loads  should  be 
marked  on  a  truss  diagram,  as  in  Fig.  10.  The  roof  and  ceiling 
loads  at  joint  1  are  transmitted  directly  to  the  wall  and  need 
not  be  taken  into  account  in  determining  the  stresses. 

EXAMPLE  2. — To  compute  the  joint  loads  for  the  truss  shown 
by  Fig.  3,  p.  945,  all  timber  to  be  of  spruce  and  the  roof  to  be 
covered  with  shingles  on  1-inch  sheathing;  the  ceiling  to  be 
of  lath  and  plaster. 

For  the  dead  load  per  square  foot  we  have 

Weight  of  shingles 2J  Ibs. 

Weight  of  sheathing 3       " 

Weight  of  rafters 2J     " 

Weight  of  purlins 2       " 

Weight  of  truss 3       " 

Total  dead  load  per  square  foot .  .  .  12f  Ibs. 

Allowance  for  wind  and  snow 30    Ibs. 

Total  roof  load  per  square  foot ....  42}     " 
For  the  weight  of  the  ceiling  it  will  be  well  for  a  truss  of 
this  kind  to  allow  at  least  20  Ibs.  per  square  foot. 

We  will  assume  that  the  trusses  are  to  be  spaced  uniformly 
15  ft.  centre  to  centre. 


954 


STRESSES  IN  ROOF-TRUSSES. 


Then  the  roof  area  supported  at  joint  2  will  be  9'  10"X15', 
or  147  J  square  feet,  and  the  load  at  this  joint  6,306  Ibs.  The  purlin 
at  joint  3  supports  the  roof,  from  a  point  midway  to  joint  2, 
to  the  ridge,  or  b=4f  11"  +  8'  5",  or  13'  4".  The  roof  area 
supported  at  this  point  is  13'  4"  XI 5',  or  200  sq.  ft.,  and  the 
load  8,550  Ibs. 

The  loads  at  joints  4  and  5  will  be  equal  respectively  to  those 
at  3  and  2. 

For  the  ceiling  loads  at  joints  7  and  8  we  have  an  area  to  be 
supported=12'  2"X15',  or  182J  sq.  ft.,  which  multiplied  by  20 
gives  3,650  Ibs. 

EXAMPLE  3. — For  this  example  we  will  take  the  church 
roof  shown  in  section  by  Fig.  4.  In  this  roof  the  trusses  take  the 


Fig,  4 

place  of  the  rafters  and  ceiling  beams,  the  sheathing  spanning 
from  truss  to  truss  and  the  laths  for  the  ceiling  being  nailed 
to  1J"X2J"  furring  strips  spaced  12  or  16  ins.  on  centres. 
Assuming  that  the  parts  of  the  trusses  will  have  the  dimen- 
sions indicated  in  the  figure,  and  that  the  wood  is  to  be  white 
pine,  the  actual  weight  of  one  truss  will  be  about  1,200  Ibs. 
The  roof  area  supported  by  one  truss  is  170  sq.  ft.,  hence  the 
weight 'of  the  trusses  will  be  about  7  Ibs.  per  square  foot  of 


COMPUTATIONS  OF  ROOF  LOADS.      955 

roof  surface.  (Note.  It  will  be  seen  that  this  weight  is  more 
than  twice  that  given  in  Table  IV,  owing  principally  to  the 
trusses  being  so  close  together  and  the  members  of  small  di- 
mensions.) The  weight  of  the  sheathing  and  shingles  will 
be  about  5J  Ibs.,  and  we  will  allow  30  Ibs.  for  wind  pressure. 
(The  roof  is  too  steep  for  snow  to  lodge  on  it.) 

This  gives  us  a  total  roof  load  of  42  J  Ibs.  per  square  foot  of 
sloping  surface.  For  the  weight  of  the  ceiling  12  Ibs.  .per  square 
foot  will  be  ample,  as  no  load  other  than  its  own  weight  is  likely 
to  come  upon  it. 

The  roof  area  supported  at  joint  2=10|'X2i',  or  27  sq.  ft. 
The  area  supported  at  joints  4  and  5  is  equal  to  12J/X2J/=31 
sq.  ft.  for  each.  Ceiling  area  supported  at  joint  3=14i'x2J', 
or  35J  sq.  ft.  Multiplying  the  joint  areas  by  the  correspond- 
ing loads  per  square  foot  we  have  1,148  Ibs.  for  the  load  at 
joint  2,  1,318  Ibs.  for  the  load  at  joints  4  and  5,  and  426  Ibs. 
for  the  load  at  joint  3. 

EXAMPLE  4. — Roof  corrugated  iron,  supported  by  a  steel 
truss  of  the  shape  shown  by  Fig.  60  of  Chapter  XXV.  This 
truss  supports  nothing  but  the  corrugated  iron  and  the  purlins 
and  the  pressure  due  to  wind  and  snow,  the  purpose  for  which 
the  building  is  used  being  such  that  there  will  be  no  occasion 
for  suspending  any  load  from  the  trusses. 

In  figuring  the  dead  loads  for  such  a  roof,  the  size  of  the 
purlins  and  the  gauge  of  the  iron  should  first  be  definitely  fixed, 
so  that  the  weight  per  square  foot  of  roof  may  be  accurately 
determined.  In  this  instance  the  purlins  are  5- inch  I  beams 
spaced  4'  9"  centre  to  centre  and  weighing  10  Ibs.  per  lineal 
foot. 

The  weight  of  the  purlins  per  square  foot  of  roof  is  therefore 
equal  to  10  Ibs.  divided  by  4f,  or  2.1  Ibs. 

For  a  span  of  4'  9"  the  corrugated  iron  should  be  No.  20 
gauge  (see  Corrugated  Iron,  Part  III),  weighing  1.9  Ibs.  per 
square  foot. 

For  the  weight  of  the  truss  and  bracing  we  will  take  the 
weight  given  in  Table  V  for  a  span  of  100  ft.  and  i  pitch,  10.8 
Ibs.*  This  will  give  us  a  total  dead  load  of  14.8  Ibs.  per  square 
foot  of  sloping  surface. 

For  wind  and  snow  we  should  allow  22  Ibs.  per  square  foot 

*  The  actual  weight  of  this  truss  and  bracing  was  4  Ibs.  per  square  foot 
of  sloping  surface,  which  is  remarkably  small. 


956 


STRESSES  IN  ROOF-TRUSSES. 


if  the  building  is  situated  in  the  Central  States,  making  the 
total  roof  load  36.8  Ibs.  per  square  foot.  It  is  quite  generally 
recommended,  however,  that  no  roof  should  be  designed  for 
a  less  load,  all  told,  than  40  Ibs.  per  square  foot;  therefore  the 
joint  loads  should  be  computed  on  that  basis. 

The  only  loaded  joints  in  this  truss  are  under  the  purlins,  and 
as  the  trusses  are  spaced  19'  2^"  centre  to  centre,  and  the 
purlins  4'  9"  centre  to  centre,  the  roof  area  supported  at  each 
upper  joint  is  91  sq.  ft.  Hence  the  joint  loads  should  be  figured 
at  3,640  Ibs.  (Note.  Even  for  the  locality  in  which  it  was 
built,  this  is  a  very  light  roof  and  would  hardly  be  safe  in  the 
more  Northern  or  Western  States.) 

EXAMPLE  5. — Flat  roof  (Fig.  5).  Timber  to  be  of  spruce  I 
five-ply  gravel  roof  and  plastered  ceiling. 


9-8*-—  — ->!  , 2"x  e'Raf ters 


Fig.  5 

For  the  dead  load  we  have 

Weight  of  roofing 6  Ibs. 

"  sheathing 3  " 

"        "  rafters 2J  " 

"        "  purlins 2  " 

"        "  truss,  say 4J  " 

Total  dead  load 17J  Ibs.  per  sq.  ft. 

No  allowance  will  be  required  for  wind  pressure,  but  the 
snow  load  will  be  a  considerable  item  in  any  of  the  Northern 
States,  as  indicated  in  Table  VII.  Assuming  that  the  building 
is  located  in  one  of  the  Central  States,  we  should  allow  30  Ibs. 
per  square  foot  for  snow,  making  the  total  roof  load  47J  Ibs. 
The  plaster  ceiling  and  the  ceiling  joists  will  weigh  about  12|  Ibs., 
and  a?  the  roof  space  is  not  likely  to  be  used  for  storage,  13  Ibs. 
per  square  foot  will  be  a  sufficient  allowance  for  the  ceiling. 


COMPUTATIONS  OF  ROOF  LOADS.      957 

Assuming  that  the  trusses  are  to  be  uniformly  spaced,  14  ft. 
centre  to  centre,  the  roof  area  supported  at  joint  2  will  be 
9i'  X 14',  or  133  sq.  ft ,  and  the  area  supported  at  joint  4,  9§'  X 14', 
or  135J  square  feet. 

The  ceiling  area  supported  at  joint  3  will  be  9J'X14',  or 
130|  sq.  ft.,  and  at  joint  5,  9'Xl4',  or  126  sq.  ft. 

Multiplying  these  areas  by  the  corresponding  loads  per  square 
foot,  we  have  6,317  Ibs.  for  the  load  at  joint  2,  6,428  Ibs.  at 
joint  4,  1,699  Ibs.  at  joint  3,  and  1,638  Ibs.  at  joint  5. 

In  practice  it  is  hardly  worth  while  to  try  to  compute  the  t 
stresses  closer  than  100  Ibs.,  so  that  the  loads  may  as  well  be 
put  down  at  an  even  50  or  100  Ibs.  above  the  load  obtained  by 
computation.  When  the  roof  is  supported  by  purlins,  there  are 
often  some  joints  of  the  truss  which  have  no  load.  Thus  for 
the  truss  shown  by  Fig.  19,  Chapter  XXV,  there  would  be  no 
loads  on  joints  2,  6,  and  10. 

The  roof  area  supported  at  joint  4  (Fig.  19)  is  equal  to  one-half 
the  distance  OB  multiplied  by  the  distance  halfway  to  the  truss 
on  each  side.  If  the  lower  chord  supports  ceiling  joists,  then 
there  will  be  a  load  at  each  of  the  joints  3,  5,  7,  9,  etc.  Stress 
diagrams  can  be  drawn  for  any  arrangement  of  loads,  the  im- 
portant point  being  to  compute  the  loads  exactly  as  they  will 
be  imposed  on  the  truss.  These  five  examples  illustrate  fairly 
well  the  method  of  computing  the  loads  on  a  truss.  Special 
cases  of  loading  should  be  computed  on  the  same  principle. 

Determining  the  Stresses. 

To  determine  the  stresses,  a  diagram  of  the  truss,  composed 
of  single  lines  representing  the  centre  line  of  the  truss  members, 
should  first  be  carefully  drawn  to  a  scale  and  the  loads  at  the 
different  joints  indicated  by  arrows  and  numbers  as  in  Figs.  10 
and  12.  If  the  centre  lines  of  the  members  as  they  are  actually 
placed  do  not  intersect  at  common  points,  they  must  be  made 
to  do  so  in  the  diagram,  as  the  stresses  can  be  computed  only 
on  the  assumption  that  the  centre  lines  of  all  members  meeting 
at  any  point  intersect  at  a  common  point. 

In  wooden  trusses  it  is  not  always  practicable  to  place  the 
braces  so  that  their  centre  line  will  pass  through  the- centre  of 
the  joints,  but  they  should  come  as  near  to  it  as  practicable, 
and  in  steel  trusses  the  joint  connections  should  be  made  so  that 
the  centre  lines  of  all  members  meeting  at  a  joint  will  intersect 
at  the  same  point. 


958 


STRESSES  IN  ROOF-TRUSSES. 


Stresses  Obtained  by  Direct  Computations. 

As  a  general  rule,  the  stresses  in  a  roof  truss  can  be  deter- 
mined much  more  readily  by  the  graphic  method  than  by 
mathematical  computations  and  with  as  close  a  degree  of 
accuracy  as  is  necessary.  There  are  a  few  forms  of  trusses, 
however,  for  which  the  stresses  can  be  quite  easily  determined 
by  computation  provided  the  truss  is  perfectly  symmetrical 

TABLE   X.— COEFFICIENTS    FOR   DETERMINING   THE 

STRESSES  IN   SIMPLE   FINK  AND    FAN   TRUSSES 

When  panel  loads  are  all  equal. 


3= Span 
|P=2.5  W. 

To  find  the  stress  in  any  member  multiply  its  factor  by  panel  load  W. 
SIMPLE    FINK    TRUSS. 


Member. 

Kind  of 

Stress. 

-  =  3. 

^.  =  3.464 

,=4. 

^-  =  5. 

=  30°. 

A 

Comp. 

2.71 

3.00 

3.35 

4.04 

B 

u 

2.15 

2.50 

2.91 

3.66 

D 

(i 

0.83 

0.87 

0.89 

0.93 

F 

Tension 

2.25 

2.60 

3.00 

3.75 

G 

•       u 

1.50 

1.73 

2.00 

2.50 

K 

n 

0.75 

0.87 

1.00 

1.25 

SIMPLE    FAN   TRUSS. 


A 

Comp. 

4.50 

5.00 

5.59 

6.73 

B 

3.53 

4.00 

4.55 

5.58 

C 

3.39 

4.00 

4.70 

5.98 

D 

0.93 

1.00 

l.OS 

1.21 

E 

0.93 

1.00 

l.OS 

1.21 

F 

Tension 

3.75 

4.33 

5.00 

6.25 

G 

2.25 

2.60 

3.00 

3.75 

K 

1.50 

1.73 

2  .  00 

2.50 

STRESSES  IN  FINK  AND  FAN  TRUSSES.        959 


and  the  joint  loads  all  alike,  as  is  quite  frequently  the  case  with 
simple  steel  roofs  having  no  ceiling  load. 

Tables  X  to  XIII  give  constants  by  which  the  stresses  in 
Fink  and  fan  trusses  may  be  readily  computed  simply  by  mul- 
tiplying the  constant  by  the  panel  or  joint  load.  These  tables 
only  apply,  however,  when  the  rafter  is  divided  by  the  struts 
into  uniform  spaces,  giving  uniform  panel  loads.  For  any 

TABLE  XI.—  COEFFICIENTS  FOR  DETERMINING  THE 
STRESSES  IN  EIGHT-PANEL  FINK  TRUSS 
When  panel  loads  are  all  equal. 


S =Span 

|P  =  3.5  W. 
To  find  the  stress  in  any  member  multiply  its  factor  by  panel  load  W. 


Member. 

Kind 
of 

Stress. 

1=3. 

|  =  3.464 
=  30°. 

5  -4 
H~ 

S-5 
H~5- 

A 

Comp. 

6.31 

7.00 

7.83 

9.42 

B 

5.75 

6.50 

7.38 

9.05 

C 

5.20 

6.00 

6.93 

8.68 

D 

4.65 

5.50 

6.48 

8  31 

E 

0.83 

0.87 

0.89 

0.93 

F 

1.66 

1.73 

1.79 

1.86 

G 

0.83 

0.87 

0.89 

0.93 

I 

Ten  ion 

0.75 

0.87 

1.00 

1.25 

K 

0.75 

0.87 

1.00 

1.25 

L 

1.50 

1.73 

2.00 

2.50 

M 

2.25 

2.60 

3.00 

3.75 

N 

5.25 

6.06 

7.00 

8.75 

O 

4.50 

5.19 

6.00 

7.50 

P 

3.00 

3.46 

4.00 

5.00 

960 


STRESSES  IN  ROOF-TRUSSES. 


other  conditions  the  stresses  should  be  computed  by  the  graphic 
method.  Tables  XIV  and  XV  give  formulas  for  computing 
the  stresses  in  Howe  trusses.  These  formulas,  unlike  the 

TABLE  XII.— COEFFICIENTS  FOR  DETERMINING  THE 

STRESSES  IN  CAMBERED  FINK  AND  FAN  TRUSSES 

When  panel  loads   are   all   equal    and   the    camber  equals   one- 

sixth  the  rise. 


u s-a 

|p=1.5W.  |P=2.5W. 

Fig.  A  Fig.  B 

To  find  the  stress  in  any  member  multiply  its  factor  by  panel  load  W. 

TRUSS    LIKE    FIG.    A. 


Kind 

S 

8 

a 

8 

Member. 

of 

—      o. 

H 

—  =4. 

—  =  5. 

Stress. 

or  30°. 

U 

A 

Comp. 

3.64 

4.13 

4.70 

5.78 

B 

tt 

3.09 

3.63 

4.25 

5.41 

D 

" 

0.83 

0.87 

0.89 

0.93 

F 

Tension 

3.07 

3.62 

4.24 

5.40 

G 

it 

1.80 

2.08 

2.40 

3.00 

K 

1.43 

1.69 

1.98 

2.52 

TRUSS    LIKE    FIG. 


A 

Comp. 

6.09 

6.88 

7.83 

9.64 

B 

4.89 

5.63 

6.48 

8.10 

C 

4.96 

5.88 

6.93 

-     8.89 

D 

1.04 

1.15 

1.26 

1.49 

E 

1.04 

1.15 

1.26 

1.49 

F 

Tension 

5.12 

6.03 

7.07 

9.01 

G 

2.70 

3.12 

3.60 

4.50 

K 

2.66 

3.13 

3.67 

4.69 

STRESSES  IN  FINK  TRUSSES. 


961 


constant,  in  Tables  X  to  XIII,  may  be  used  for  unequal 
panel  loads  provided  that  the  truss  is  symmetrical  about  a 
vertical  line  drawn  half  way  between  the  supports. 

For  the  young  architect  or  engineer  these  tables  will  be  found 
useful  in  affording  a  check  upon  stresses  determined  by  the 
graphic  method. 


TABLE  XIII.— COEFFICIENTS  FOR  DETERMINING  THE 
STRESSES  IN  EIGHT-PANEL  CAMBERED  FINK 
TRUSS. 

When   panel   loads   are   all  equal   and  camber  equals  one-sixth 
the  total  rise. 


11. 


I  P=3.5  W. 
To  find  the  stress  in  any  member  multiply  its  factor  by  panel  load  W, 


Member. 

Kind  of 

Stress. 

I-. 

|=3.464 
or  30°. 

5-4 
H~ 

S  -5 
H~' 

A 

Comp. 

8.49 

9.63 

10.96 

13.49 

B 

7.94 

9.13 

10.51 

13.11 

C 

7.39 

8.63 

10.06 

12.74 

D 

6.83 

8.13 

9.61 

12.37 

E 

0.83 

0.87 

0.89 

0.93 

F 

1.66 

1.73 

1.79 

1.86 

G 

0.83 

0.87 

0.89 

0.93 

I 

Tension 

1.02 

1.21 

1.41 

1.80 

K 

1.02 

1.21 

1.41 

1.80 

L 

2.87 

3.37 

3.96 

5.04 

M 

3.89 

4.58 

5.37 

6.85 

N 

7.17 

8.44 

9.90 

12.61 

0 

6.15 

7.23 

8.48 

10.81 

P 

3.60 

4.16 

4.80 

6.00 

962 


STRESSES  IN  ROOF-TRUSSES. 


TABLE   XIV.— STRESSES   IN   TRUSS,    FIG.   C,   DUE  TO 
ROOF   LOADS   ONLY.     RAFTERS   AND   TIE-BEAMS 
DIVIDED  INTO  FOUR  EQUAL  SPACES. 
TF  =  load  at  each  upper  joint. 


Fig.  C 

COMPRESSION  IN  STRUTS. 
Stress  in  FH=   -^  X™-- 

Stress  in  EI=    W  X^F*. 
tin 

Stress  in  M-?£x2* 

TENSION  IN  VERTICAL  TIES. 

W 
Stress  in  EH=—;     Stress  in  £>/  =  TP;     Stress  in  C  B= 

COMPRESSION  IN  RAFTER. 
Stress  from  C  to  D  =    2W  X^g-. 

Stress  from  D  to  #  =  2JTF  X  ^-. 
Stress  from  ^  to  .F  =   3TFX^B  • 

Stress  from  F  to  /I  =  3 J FT X ^D". 
TENSION  IN  HORIZONTAL  TIE. 

4  R 

Stress  from  J5  to  7 


Stress  from  /  to  #=   STfX^rg  - 
Stress  from  //  to  A  =  3%W  x4£. 


STRESSES  IN  HOWE  TRUSSES. 


963 


TABLE  XV.  —  STRESSES  IN  SIMPLE  QUEEN  ROD 
TRUSS.  TRUSS  SYMMETRICAL  AND  SYMMETRIC- 
ALLY LOADED. 

w  w 


HJO  W  ^ 

Tension  in  R=w. 
Compression  in  B=  (w+W)  X  77-* 

& 

Tension  'n  N  and  M  =  (w  +  TF)X-Tj. 

Compression  in  D=  tension  in  N. 

NOTE. — The  distance  a  has  no  effect  on  the  stresses,  except 
as  it  increases  the  loads  w  and  W. 

TABLE  XVI.— STRESSES  IN  FOUR-PANEL  HOWE 
TRUSS.  TRUSS  SYMMETRICAL  AND  SYMMETRIC- 
ALLY LOADED. 


Tension  in  Rl  =  w. 


n          .     A     w  +  W  .    A 
Comp.  in  A  =  — ^ —  X  -77. 


Tension  in  N=  (^ 

-      <«     M=  tension  ^+[ 
Compression  in  D  =  tension  in 


,B_ 

b 


*  Meaning  length  of   B  divided  by  height  H,  both  in  the  same  unit  of 
measurement. 


964 


STRESSES   IN  ROOF-TRUSSES. 


TABLE  XVII.  —  STRESSES  IN  FIVE-PANEL  HOWE 
TRUSS.  TRUSS  SYMMETRICAL  AND  SYMMETRIC- 
ALLY LOADED. 


Tension  in  Rv  =  w. 


Compression  in  A  =  (w  +  W)  X  vr. 

ti 


B 


Tension  in  N= 

"  M  and  0=tension  in  N+ 

Compresion  in  D=  tension  in  AT. 
"  "  E  =  tension  in  M, 


TABLE  XVIII.  —  STRESSES  IN  SIX-PANEL  HOWE 
TRUSS.  TRUSS  SYMMETRICAL  AND  SYMMETRIC- 
ALLY LOADED. 


Tension  in  Rl  =  w. 


Compression  in  A  =  (\w  +  JW)  X  -^. 

12 


B=  (Jw  +wl 


»>x|. 


STRESSES  IN  HOWE  TRUSSES. 


965 


Tension  in  N 

"        "  M=  tension  in  N+ 

"  O=  tension  in  M  + 

Compression  in  D  =  tension  in  N, 
"  "  E=  tension  in  M. 


~. 


TABLE  XIX.— STRESSES  IN  SEVEN-PANEL  HOWE 
TRUSS.  TRUSS  SYMMETRICAL  AND  SYMMETRIC- 
ALLY LOADED. 


Compression  in  A  =  (w  +  W)  X  77 


Tension  in  N^ 

"        "  M  =  tension  in  N  + 

"  O  and  P=  tension  in 

Compression  in  D  =  tension  in  N. 
"  "  E=  tension  in  M. 

"  "  F=  tension  in  0. 


-g  .] 


966  STRESSES  IN  ROOF-TRUSSES. 


Examples  Showing  Application  of  Tables. 

EXAMPLE    I.  —  Simple    fan   truss    of    36    ft.    span.     Distance 

Q 

between  centres  of  trusses  12  ft.     Height  of  truss  9  ft.  or  77  =4. 

Total  load  per  square  foot  of  roof  40  Ibs.: 
Length  of  rafter  20  ft.,  nearly. 

20 
Panel  load  W=  =^  X  12'  X  40  =3,200  Ibs. 

o 

Then  from  Table  X: 

Stress  in  bottom  of  rafter  =3,  200X5.  59  =  17,888  Ibs. 
Stress  in  ends  of  main  tie  (F)  =3,200X5.00  =16,000  Ibs. 
Stress  in  centre  of  main  tie  =3,200X3.00  =9,600  Ibs. 
Stress  in  braces  D  and  #=3,200X1.08=3,456  Ibs. 
Stress  in  tie  K  =3,200X2  =6,  400  Ibs. 

EXAMPLE  II.  —  Truss  shown  in  Fig.  5,  p.  956  (four-panel 
Howe  truss).  //  =  68  ins.,  a  =  108  ins.,  6  =  116  ins.  Length 
of  inner  braces  (measured  from  centres  of  joints),  127J  ins. 
Length  of  outer  braces,  134  ins.  From  p.  957,  w  =  1,640; 
Wi  =  1,700;  TF=6,430,  and  1^=6,320^8.  Then  by  means 
of  the  formulas  in  Table  XVI  we  find  stress  in  centre  rod  = 
1,640  Ibs. 


Stress  in  outer  rods  =          +  ~-  +  1,700=5,735  Ibs. 

1640  +  6430  ^  127J 

Stress  in  inner  braces  =  -  ^  -  X  -—•*  =7,536  Ibs. 

£  08 


Tension  in  end  panels  of  tie-beam 

=  (^-  +  ^TT-+  1,700+6,320)  x^  =  19,028  Ibs. 

\     Z  Z  I         uo 

Compression  in  top  chord  =  19,028  Ibs. 

The    Graphic    Method    of    Determining   the 
Stresses  in  Roof  Trusses. 

The  "Graphic  Method"  is  the  simplest  and  in  most  cases 
the  quickest  method  (provided  the  tools  are  at  hand)  of  deter- 
mining the  stresses  in  a  roof  truss,  and,  besides  these,  it  has 
the  additional  advantages  that  it  can  be  used  for  any  true 
truss  and  for  any  arrangement  of  loads.  There  is  also  less 


PRINCIPLES  OF  GRAPHIC  STATICS.  967 

chance  of  making  a  mistake  in  the  graphic  method  than  by 
numerical  computations,  as  an  error  in  the  graphical  analysis 
almost  always  becomes  manifest. 

Stress  diagrams  can  be  very  quickly  drawn  when  once  the 
principle  is  understood,  and  without  the  aid  of  books  or  tables. 
For  the  forms  of  trusses  in  common  use,  the  method  of  drawing 
the  stress  diagrams  is  quite  simple,  and  a  careful  study  of  the 
following  examples  supplemented  by  a  little  practice  in  draw- 
ing the  diagrams  should  enable  any  architect,  draughtsman, 
or  builder  to  grasp  the  principle. 

Principles  upon  which  the  Graphic  Method  is  based. — To 
thoroughly  understand  this  method,  a  knowledge  of  the  com- 
position and  resolution  of  forces  as  explained  in  Chapter  VI 
is  essential,  and  before  studying  this  subject  the  student 
should  read  carefully  pp.  231-233.  Propositions  I,  III,  and 
IV  on  those  pages  form  the  basis  of  graphic  statics.  In  the 
graphic  method  all  forces,  including  the  loads,  are  repre- 
sented by  straight  lines,  and  the  direction  of  the  force  must 
be  constantly  kept  in  mind,  and  often  it  is  of  assistance  to  indi- 
cate the  direction  by  an  arrow-head  as  explained  on  p.  232. 
The  direction  in  which  a  force  acts  also  tells  whether  it  is  a 
pushing  or  pulling  force,  or  whether  the  member  in  which  the 
force  or  stress  acts  is  in  compression  or  tension.  This  is  more 
fully  explained  on  the  following  pages,  and  also  in  connection 
with  several  of  the  stress  diagrams. 

Forces  which  Act  In  and  On  a  Truss. — Every  stress  diagram 
represents  three  sets  of  forces,  viz.,  the  external  loads,  the  sup- 
porting forces,  and  the  stresses  in  the  truss  members. 

Supporting  Forces. — For  a  truss  to  stand  in  place,  the  supports 
of  the  truss,  taken  together,  must  be  capable  of  offering  a 
reaction  equal  to  the  total  load  on  the  truss,  including  the 
weight  of  the  truss  itself.  Each  of  these  reactions  must  be 
represented  as  one  of  the  forces  acting  on  the  truss  when  drawing 
the  stress  diagram;  they  will  be  hereinafter  referred  to  as  the 
supporting  forces. 

When  the  loads  are  symmetrical  on  each  side  of  the  centre 
of  the  span,  the  supporting  forces  will  be  equal,  and  each  will 
be  equal  to  one-half  of  the  total  load  on  the  truss.  When 
the  loads  are  not  symmetrical  about  the  centre,  either  as  regards 
point. of  application  or  magnitude,  the  supporting  forces  will 
be  unequal  and  in  most  cases  must  be  determined  before 
the  stress  diagram  can  be  drawn.  The  supporting  forces  for 


968 


STRESSES  IN  ROOF-TRUSSES. 


unsymmetrically    loaded    trusses    may    be    computed    by    the 
method  explained  on  pp.  275-277. 

Application  of  Graphic  Statics  to  Simple  Trian- 
gular Frames  Having  but  One  External  Load. 

The  simple  triangular  frame  is  much  used  in  building  con- 
struction, and  many  forms  of  roof  trusses  are  simple  combina- 
tions of  such  triangles.  It  is  therefore  worth  while  to  show 
how  easily  the  above  principles  may  be  used  to  determine  the 
stresses  in  such  a  frame. 

In  Diagram  1,  Fig.  6,  we  have  two  struts  abutting  at  the  top 


Fig.  6 

and  held  both  vertically  and  horizontally  at  the  bottom  by  a 
tie-beam.  The  vertical  component  of  the  thrust  in  the  strut, 
however,  merely  passes  through  the  tie-beam  and  is  resisted  by 
the  support  below. 

We  will  assume  that  a  load  of  100  Ibs.  is  applied  at  the  apex 
and  disregard  the  weight  of  the  frame  itself.  Now,  if  at  2  we 
draw  a  vertical  line  w,  1  in.  long  (scale  of  100  Ibs.  to  the  inch) 
and  from  the  upper  end  draw  a  line  parallel  to  A ,  and  from  the 
lower  end  a  line  parallel  to  B,  until  the  lines  intersect,  then 
the  length  of  the  line  a,  measured  to  the  scale  of  100  Ibs.  to 
the  inch,  will  give  the  compressive  force  in  A  and  the  line  b 
the  compressive  force  in  B.  Further,  if  from  the  intersection 
of  a  and  b  we  draw  a  horizontal  line  (parallel  with  the  tie-beam) 
intersecting  the  line  w,  then  the  length  of  the  line  c  will  give 
the  horizontal  stress  in  the  tie-beam  produced  by  the  load  of 
100  Ibs.  Moreover,  the  line  c  will  divide  the  line  w  in  the  pro- 
portion of  the  reactions  of  the  supports.  Thus  the  portion  p 
will  be  the  amount  of  reaction  at  P  and  pf  the  reaction  of  P'. 

All  of  these  conditions  remain  true  whatever  the  inclination 
of  the  struts,  whether  equal  or  unequal,  and  also  if  the  tie- 


PRINCIPLES  OF  GRAPHIC  STATICS.  969 

beam  is  inclined,  provided  that  the  lines  a,  6,  and  c  are  drawn 
parallel  to  the  pieces  A,  B,  and  C  of  the  frame. 

Moreover,  the  stresses  will  be  proportional  to  the  load  at  the 
apex.  Thus  for  200  Ibs.  the  stress  in  each  part  will  be  just 
twice  what  it  is  for  100  Ibs. 

In  Fig.  7  we  have  a  load  supported  by  two  ties  instead  of 
two  struts,  the  effect  on  the  rod  w 

being   the  same  as  if   the  load      ^ 1 c ^ 

were  suspended  from  the  bottom. 

If  we  let  the  vertical  line 
1-2  represent  the  load  W,  then 
the  lines  a  and  6,  drawn  parallel 
to  A  and  B  respectively,  will 
represent  the  stress  or  tension 
!  in  the  two  parts  of  the  rod,  and 
a  horizontal  line  drawn  from  c 
to  the  vertical  line  will  represent 
the  compression  in  the  strut  C,  9>  7 

and  p'  will  be  the  reaction  at  Pr  and  p  the  reaction  at  P.     The 
stress  in  the  post  S  will  be  equal  to  W. 

The  direction  in  which  the  forces  act  are  determined  as 
follows:  Dead  loads  always  act  downward  (hence  are  repre- 
sented by  vertical  lines),  and  consequent!}-  the  arrow-head  on 
line  1-2  must  point  down. 

The  forces  in  b  and  a  must  also  act  in  the  direction  of  the  arrow- 
heads, i.e.,  around  the  figure,  in  order  to  preserve  equilibrium. 
Now  the  lines  a,  6,  and  w  represent  the  three  forces  acting  at 
o,  and  we  see  that  the  arrow-heads  in  a  and  b  point  away  from 
the  joint,  hence  these  pieces  are  in  tension.  The  arrow-head 
on  w  points  towards  the  joint,  hence  S  is  in  compression. 

In  Fig.  8  we  have  a  crane  supporting  a  load  W. 

If  we  draw  the  vertical  line  dc  to  represent  the  load,  and 
I  from  the  lower  end,  or  c,  a  line  parallel  to  AC,  and  from  the 
upper  end  a  line  parallel  to  BC,  the  two  lines  intersecting  at  e, 
then  a  will  represent  the  stress  in  A  C  and  b  the  stress  in  BC. 

Considering  the  forces  as  acting  at  C,  the  direction  in  which 
the  forces  act'  are  as  indicated  by  the  arrow-heads. 

The  arrow-head  on  a  points  away  from  C,  hence  AC  is  in 
tension;  the  head  on  6  points  towards  C,  hence  BC  is  in  com- 
pression. 

We  will  next  consider  the  forces  which  act  at  the  point  A. 
Of  these  three  forces  we  have  the  force  in  AC  represented 


970 


STRESSES  IN  ROOF-TRUSSES. 


by  the  line  a.     If  from  e  we  draw  a  line  parallel  to  AE,  inter- 
secting w  at  of  then  eo  will  represent  the  stress  in  AE,  and  oc 


e  "    a 


Fig.  8 


Piece  in  .Tension 

Piece  in  Compression 

Fig.  9 


the  stress  in  AB.  In  the  triangle  eco,  the  arrow-heads  will 
point  in  the  opposite  direction  from  what  they  do  in  ecd,  show- 
ing that  AE  is  in  tension  and  AB  in  compression. 

[NOTE. — If  two  boys  pull  on  the  two  ends  of  a  rope  so  as 
to  just  balance  each  other,  the  stress  in  the  rope  will  be  just 
the  force  with  which  one  boy 
pulls,  and  each  end  of  the  rope 
will  pull  away  from  the  boy 
holding  it  by  the  same  force 
that  he  exerts.  Thus  if  each 
boy  exerts  a  force  of  100  Ibs., 
then  the  stress  in  the  rope  will  be  100  Ibs.,  and  each  end  of  the 
rope  will  be  pulling  away  with  a  force  of  100  Ibs.  If  the  boys 
were  pushing  against  the  two  ends  of  a  piece  of  timber  with 
a  force  of  100  Ibs.,  then  the  timber  would  push  against  each 
boy  with  a  force  of  100  Ibs.,  although  the  entire  stress  in  the 
timber  would  be  but  100  Ibs. 

Consequently  a  stress  line  with  arrow-heads  pointing  toward 
each  other,  as  at  A,  Fig.  9,  denotes  tension,  and  a  stress  line 
with  arrow-heads  pointing  in  opposite  directions,  as  at  B,  de- 
notes compression.  In  other  words,  the  stress  in  any  member 
of  a  truss  acts  in  opposite  directions  at  the  two  ends  of  the  piece. 
This  is  an  important  truth  to  remember  in  drawing  stress 
diagrams.] 

Stress  Diagrams  for  Vertical  Loads. 

Trusses  Symmetrically  Loaded. — Before  the  stress  diagram 
for  a  truss  can  be  drawn,  it  is  necessary  to  make  a  skeleton 
drawing  of  the  truss,  representing  the  centre  lines  of  the 
members  as  explained  on  p.  957.  This  diagram  (which  will 


LETTERING  TRUSS  DIAGRAMS.  971 

be  hereinafter  designated  as  the  "Truss  Diagram")  should  be 
drawn  on  the  same  sheet  of  paper  as  the  stress  diagram  for 
convenience  in  drawing  the  latter.  The  truss  diagram  should 
also  have  all  of  the  loads  which  come  on  the  truss  indicated  by 
arrows  and  figures  as  in  Fig.  10,  which  is  the  truss  diagram  for 
the  truss  represented  by  Fig.  1,  and  for  which  the  loads  were 
computed  on  p.  953. 

Combining  the  Ceiling  Loads  with  the  Roof  Loads. —  It  should 
be  noticed  that  in  the  truss  diagram,  Fig.  10,  the  ceiling  loads 
found  on  p.  953  are  added  to  the  roof  loads.  This  is  done 
to  simplify  the  stress  diagram.  As  far  as  the  stresses  in  the 
struts  and  tie-beams  are  concerned  it  makes  no  difference 
whether  the  ceiling  loads  are  considered  as  applied  at  the  top 
or  bottom  of  the  truss,  but  the  stresses  in  the  rods  will  be  in- 
creased by  just  the  amount  of  the  ceiling  load.  The  +2070  Ibs. 
opposite  the  centre  rod  is  put  on  the  truss  diagram  as  a  re- 
minder to  add  this  load  to  the  stress  afterwards  determined. 
The  rods  from  2  to  6  and  4  to  8,  Fig.  10,  receive  no  stress  from 
the  roof  loads  and  are  therefore  omitted  or  dotted  in  the  truss 
diagram,  the  latter  being  lettered  as  though  there  were  no  rods 
there.  The  stress  on  these  rods  is  simply  that  of  the  ceiling 
load  at  6  and  8. 

Whenever  the  ceiling  loads  are  carried  directly  to  the  top  by 
vertical  rods  or  ties  it  is  much  simpler  to  add  them  to  the  roof 
loads,  as  above  described,  but  when  the  ties  are  not  vertical 
the  ceiling  loads  must  be  indicated  at  their  point  of  application. 

Supporting  Forces. — The  supporting  forces  should  also  be 
indicated  on  the  truss  diagram  as  in  Fig.  10.  These  forces  are 
computed  as  explained  on  p.  967. 

Lettering  the  Truss  Diagram. — After  the  truss  diagram  is 
drawn,  it  should  be  lettered  after  a  particular  method  known 
as  "Bow's  Notation,"  which  enables  a  ready  comparison  of 
the  truss  and  stress  diagrams  and  also  aids  the  student  in 
drawing  the  stress  diagram  and  in  tracing  the  stresses.  The 
essential  principle  of  this  method  of  lettering  is  to  letter  the 
space  each  side  of  every  force  or  piece  of  the  truss  so  that 
on  the  truss  diagram  a  piece  or  force  is  denoted  b}^  the  letters 
on  each  side  of  it.  When  the  stress  diagram  is  drawn  it  will  be 
found  that  the  same  letters  come  at  the  end  of  the  corresponding 
lines. 

Fig.  10  shows  the  truss  diagram  of  the  truss  represented  in 
Fig.  1,  properly  drawn,  lettered,  and  figured,  ready  for  drawing 


972  STRESSES  IN  ROOF-TRUSSES. 

the  stress  diagram.  The  supporting  force  at'  the  left  is  A0> 
the  bottom  of  the  main  rafter  AE,  the  left  portion  of  the  tie- 
beam  EO,  etc.  The  loads  acting  at  joints  2,  3,  and  4  are 
designated  as  AB,  BC,  and  CD  respectively.  It  makes  no  par- 
ticular difference  what  letters  are  used,  except  that  it  is  better 
to  letter  the  outside  spaces  consecutively  and  then  the  inside 
spaces. 

Stress  Diagram. — The  stress  diagram  is  drawn  by  taking  the 
forces  acting  on  the  joints  in  consecutive  order,  commencing 
at  one  of  the  supports.  The  author  considers  it  more  natural 
and  convenient  to  start  with  the  support  at  the  left,  or  at  joint  1. 

[NOTE. — In  actual  computations  it  is  not  necessary  to  number 
the  joints,  but  in  order  to  refer  to  them  in  the  description  it  is 
necessary  to  number  them  in  the  illustrations.] 

Commencing  at  joint  1,  then,  the  first  step  of  the  stress  dia- 
gram is  to  draw  a  vertical  line  to  a  scale  of  pounds  to  the  inch 
to  represent  the  supporting  force  OA.  This  line  is  the  line  oa, 
Fig.  10  A,  which  is  here  drawn  to  the  scale  of  16,000  Ibs.  to  the 
inch.*  It  is  best  to  use  a  scale  as  large  as  convenient  and  not 
have  the  diagram  too  large.  An  engineer's  scale,  one  divided 
to  lOths,  20ths,  30ths,  etc.,  of  an  inch,  will  be  found  most  con- 
venient for  these  drawings. 

The  small  letter  o  should  be  placed  at  the  bottom  of  the  line 
and  the  letter  a  at  the  top.  Next  from  a  draw  a  line  parallel 
to  the  rafter  AE  and  from  o  a  line  parallel  to  the  tie-beam  OE. 
The  two  lines  meet  at  e,  and  ae  represents  the  stress  in  AE  and 
oe  the  stress  in  OE.  As  the  supporting  force  acts  up,  the  arrow- 
head will  be  at  the  top  of  oa,  and  the  others  must  follow  in  ro- 
tation, showing  that  ae  acts  toward  the  joint  and  the  piece  is  in 
compression,  and  eo  acts  from  the  joint  and  the  piece  is  in 
tension. 

We  next  consider  the  stresses  at  joint  2.  Commencing  at 
the  bottom  of  the  joint  and  going  around  to  the  left  the  first 
stress  that  we  know  is  the  stress  in  ae,  which  we  have  just 
determined.  As  this  stress  acted  downward  at  1,  it  will  act 
upward  at  2,  as  the  stresses  in  the  two  ends  of  a  strut  or  tie  act 
in  opposite  directions,  as  explained  on  p.  970.  The  stress  ae  we 
determined  in  Diagram  10A,  and  for  convenience  in  explana- 
tion we  will  consider  it  redrawn  in  Fig.  10s.  The  next  force 

*  The  original  of  this  drawing  was  at  a  scale  of  8,000  pounds  per  inch, 
the  drawing  being  reduced  one  half  in  making  the  cut. 


STRESS  DIAGRAMS— VERTICAL  LOADS. 


973 


is  the  load  AB  =9,000  Ibs.,  which  we  measure  to  our  scale  from 
a  downward  (as  the  loads  acts  down),  which  gives  us  the  point 
b.  The  stresses  in  BF  and  EF  we  do  not  know,  so  from  b 
(Fig.  10,  B)  we  draw  a  line  parallel  to  BF,  and  from  our  starting- 
point,  e,  a  line  parallel  to  EF,  and  we  obtain  the  lines  bf  and  fe, 
which  represent  the  stresses  in  BF  and  FE  respectively.  The 
arrow-heads  should  follow  as  indicated,  all  of  the  parts  being 


Roof  7700 
Ceiling  2070 
Total  9770 


7070 

1930 

"8000" 


in  compression.  At  joint  7  we  now  know  the  stresses  in  OE 
and  EFt  leaving  three  unknown  forces  and  as  we  can  only 
determine  two  forces  we  must  go  to  joint  3,  where  there  are 
but  two  unknown  forces.  The  first  force  which  we  know  at  3 
is  the  stress  /&,  which  now  acts  up;  we  then  have  the  load  BC 
of  9,770  Ibs.,  which  we  measure  off  from  b  (Fig.  10,  C)  to  our 
scale,  which  gives  us  the  point  c.  From  c  we  draw  a  line  parallel 
to  CG,  and  from  /  a  line  parallel  to  FG,  and  we  have  the  lines 
eg  and  fg,  which  represent  the  stresses  in  CG  and  FG  respec- 
tively. The  arrow-heads  follow  as  shown,  gf  acting  downward 
or  from  the  joint  3,  and  hence  indicating  tension.  As  the  truss 
is  symmetrical,  we  now  have  determined  the  stresses  in  all  of 


974 


STRESSES  IN   ROOF-TRUSSES. 


the  parts,  but  we  can  continue  the  process  if  we  wish,  when 
we  will  obtain  the  stresses  shown  by  the  dotted  lines,  the  dia- 
gram being  symmetrical  about  the  line  eo.  The  letter  h  will 


Roof  Load  48  Ibs. 


Fig.   II 

come  opposite  e,  the  stresses  in  the  two  parts  of  the  tie-beam 
being  equal. 

In  practice  the  stresses  are  all  drawn  on  one  diagram,  as  in 
Fig.  10,  C,  the  three  diagrams  being  used  here  only  to  show  the 
different  steps. 

We  now  apply  our  scale  to  the  different  lines  of  the  last  dia- 
gram and  obtain  the  values  indicated  on  the  corresponding 
lines  of  the  truss  diagram,  Fig.  11.  To  fg  should  be  added  the 
ceiling  load  of  2,070  Ibs. 

By  Using  the  +  sign  before  the  figures  we  can  show  that  the 
piece  is  in  compression,  while  the  —  sign  denotes  tension.* 

The  truss  diagram,  as  figured  in  11,  now  gives  all  of  the  data 
required  to  determine  the  size  of  the  parts,  and  when  these  are 
determined  they  should  also  be  marked  on  the  diagram  so  as 
to  have  a  complete  record  of  the  whole  computation. 

In  practice  diagrams  Figs.  10  and  11  would  be  combined 
in  one  drawing,  they  being  shown  separately  merely  to  indicate 
the  progressive  steps  in  lettering  and  figuring. 

EXAMPLE  2  (Fig.  12). — The  upper  diagram  in  Fig.  12  repre- 
sents the  centre  lines  of  the  truss  shown  by  Fig.  3,  and  the 
loads  indicated  are  those  found  in  Example  2,  p.  953.  The 
counter  braces  in  the  centre  panel  are  indicated  by  dotted  lines 

*  There  is  no  uniformity  in  the  use  of  these  signs  by  different  writers,  some 
using  +  to  denote  tension;  hence  the  notation  should  be  looked  up  in  each 
work. 


STRESS  DIAGRAMS— VERTICAL  LOADS.         975 

in  the  truss  diagram,  because  under  a  symmetrical  load  there 
is  no  stress  in  these  members,  and  hence  they  cannot  be 
represented  in  the  stress  diagram. 

As  in  the  foregoing  example,  the  ceiling  loads  are  added  to 
the  roof  loads  and  treated  as  one  load. 

As  the  truss  is  symmetrically  loaded  each  supporting  force 
will  be  equal  to  one-half  of  the  total  load,  or  18,500  Ibs. 

To  draw  the  stress  diagram,  first  draw  a  vertical  line  oa 
equal  to  the  supporting  force,  then  from  the  upper  end  a  line 
parallel  to  AE,  and  from  the  lower  end  a  line  parallel  to  OE, 
the  two  lines  intersecting  at  e.  We  will  thus  have  the  triangle 
oae  representing  the  three  forces  acting  at  the  joint  1.  As 
the  supporting  force  always  acts  up,  the  arrow-head  on  oa  will 
be  at  a,  on  ae  at  e,  and  on  eo  at  o,  showing  that  AE  is  in  com- 


SJRESS  DIAGRAM 


pression  and  EO  in  tension.  Next  find  the  stresses  acting  at 
joint  2.  We  already  have  the  stress  in  AE,  represented  by  the 
line  ea,  and  as  the  stress  will  act  in  the  opposite  direction  at 
joint  2  from  what  it  does  at  joint  1,  it  will  now  act  up.  The 
next  force  is  the  load  of  6,300  Ibs.,  which  must  act  downward 
from  a.  We  obtain  the  point  b  by  measuring  from  a  a  distance 
=to  6,300  Ibs.  (at  the  same  scale  as  was  used  in  drawing  oa). 
There  now  remain  two  stresses  to  be  found,  viz.,  the  stresses  in 
BF  and  FE.  From  the  point  of  beginning  e,  draw  a  line  parallel 


976  STRESSES  IN  ROOF-TRUSSES. 

to  EF,  and  from  b  a  line  parallel  to  BF,  the  two  lines  intersecting 
at  /.  Then  the  figure  eabf  will  represent  the  four  forces  acting 
at  joint  2,  and  the  stresses  will  act  in  the  directions  indicated 
by  the  letters,  or  all  act  toward  the  joint.  We  may  next 
obtain  the  forces  acting  at  either  joints  3  or  7,  as  there  are  but 
two  unknown  forces  at  either  joint. 

Considering  the. forces  acting  at  joint  3,  we  already  have  the 
force  in  FB,  represented  by  the  line  /6,  which  acts  up  then  the 
load  of  12,200  Ibs.,  which  takes  us  to  o,  where  we  also  put  the 
letter  c  to  conform  with  the  lettering  on  the  truss  diagram. 
From  c  draw  a  horizontal  line  (parallel  to  CH),  and  from  the  point 
of  beginning,  /,  a  line  parallel  to  FH,  the  two  lines  intersecting 
at  h.  ch  will  represent  the  stress  in  CH  and  Jh  the  stress  is 
FH. 

[NOTE. — Although  the  line  ch  lays  over  the  line  oe,  it  should 
be  considered  as  a  separate  line  representing  a  distinct  stress.] 

We  have  now  determined  the  stresses  in  all  of  the  truss  members 
except  in  the  piece  OH.  This  we  find  by  considering  the  forces 
acting  at  joint  7.  At  this  joint  we  have  the  stress  in  OE, 
represented  by  oe,  next  the  stress  ef,  also  fh,  and  the  line  ho 
must  complete  the  figure;  hence  ho  denotes  the  stress  in  HO, 
and  as  it  acts  from  the  joint,  HO  must  be  in  tension.  The  line 
ch  acts  toward  joint  3,  hence  HC  is  in  compression.  Scaling 
the  lines  in  the  stress  diagram  we  obtain  the  figures  shown  by 
the  side  of  the  lines,  which  represent  pounds,  the  +  sign 
denoting  compression  and  the  —  sign  tension.  The  line  hf 
scales  3,250  Ibs.,  but  to  this  must  be  added  the  load  at  joint  7, 
3,650  Ibs.,  which  gives  6,900  Ibs.  as  the  true  stress  in  the  rod. 

Remark. — The  two  foregoing  examples  illustrate  as  clearly 
as  can  be  shown  in  print  the  method  of  drawing  the  stress 
diagram  for  simple  symmetrical  trusses  symmetrically  loaded. 
The  student  should  draw  the  truss  diagrams  in  accordance 
with  the  measurements  given,  but  to  a  scale  of  not  less  than 
J  inch  to  the  foot,  and  then  draw  the  stress  diagram,  line  by 
line,  in  accordance  with  the  foregoing  directions  and  compare 
the  results  obtained  with  those  given  in  the  figures.  A  varia- 
tion of  100  or  even  200  pounds  may  be  expected,  but  a  greater 
variation  will  indicate  either  that  sufficient  care  has  not  been 
exercised  in  drawing  the  stress  lines  exactly  parallel  with  the 
corresponding  lines  of  the  truss  diagram  or  that  an  error  has 
been  made  in  drawing  the  truss  diagram  or  in  scaling  the  lines 
of  the  stress  diagram. 


STRESS  DIAGRAMS—  VERTICAL  LOADS.         977 


After  these  two  examples  have  been  worked,  a  number  of 
the  following  examples  should  be  worked  until  the  entire  prin- 
ciple is  fully  understood. 

EXAMPLE  3.  —  Fig.    13   represents  the   truss  diagram  of   the 


12,240 


15,600        12j000       15)600 
P  =41,040  Fig.  13 


Fig.  13  A 

truss  shown  by  Fig.  13,  Chap.  XXV,  the  loads  indicated  being 
approximately  those  due  to  the  roof  and  the  suspended  floor 
below. 

The  loads  being  symmetrically  disposed,  each  supporting 
force  will  be  equal  to  one-half  of  the  total  load,  or  41,040  Ibs. 
The  counter  braces  CC,  shown  in  Chap.  XXV,  are  omitted  from 
the  truss  diagram  because  they  have  no  stress  when  the  truss 
is  uniformly  loaded. 

To  draw  the  stress  diagram,  first  draw  the  vertical  line 
oa  =41,040  Ibs.  =P,  then  ab  and  ob  parallel  to  AB  and  OB 
and  representing  the  stresses  acting  at  joint  1.  At  joint  2 
we  have  the  line  ba  representing  the  stress  in  BA,  and  from 
a  measure  down  ac=  7,200  Ibs.,  then  draw  cd  and  bd,  bacdb 
representing  the  forces  acting  at  joint  2. 

At  joint  3  we  have  three  unknown  forces,  and  as  we  cannot 
find  three  unknown  forces  in  one  polygon,  we  must  go  next 
to  joint  4,  where  we  already  have  dc  and  the  load  CF. 


978  STRESSES  IN  ROOF-TRUSSES. 

[NOTE. — In  Fig.  13  the  bottom  loads  are  not  shown  added  to 
the  top  loads,  but  they  should  be  so  added  before  drawing 
the  stress  diagram.] 

Measuring  off  the  force  c}= 27,840  Ibs.,  we  have  only  the 
stresses  in  FE  and  DE  to  determine,  which  we  obtain  by  draw- 
ing a  line  from  /  parallel  to  FE,  and  a  line  from  d  parallel  to 
DE,  the  two  lines  intersecting  at  e.  Now,  going  to  joint  3, 
we  have  ob,  bd,  and  de  (which  we  already  know),  and  draw  eg 
and  og  to  close  the  figure.  In  this  case  the  point  g  happens 
to  come  at  the  point  6,  so  that  one  lays  over  the  other.  At 
joint  5  we  have  gef  ef,  fi  (equal  12,000  Ibs.),  and  draw  ih  and 
gh  to  close  the  figure.  There  would  be  no  strain  on  the  central 
rod  other  than  the  direct  pull  of  12,000  Ibs.,  which  it  carries 
from  the  floor  below.  It  should  also  be  remembered  that  the  tie 
de  has,  besides  the  stress  shown  in  the  diagram,  a  direct  pull  of 
15,600  Ibs.  from  the  weight  of  the  floor  suspended  from  it,  so 
that  the  two  should  be  added  to  show  the  total  pull  in  the  rod. 
The  stresses  in  pounds,  in  the  various  pieces  are  given  in  numbers 
on  the  corresponding  lines  in  the  stress  diagram  (Fig.  13  A). 

EXAMPLE  4. — Take  the  skeleton  truss  represented  in  Fig.  14, 
loaded  as  there  shown  (by  the  weight  of  the  roof  above  and  a 
ceiling  below). 

To  draw  the  stress  diagram,  first  draw  the  supporting  force 
°1  C^ig-  14  A)  =46,620  Ibs.  Then  for  convenience  measure  off 
from  jj  ik,  equal  to  the  sum  of  the  weights  at  joints  o  and  1 
(13,320  Ibs.),  kl  =  13,320,  lm  =  13,320,  and  mn  =  13,320.  Then 
draw  the  lines  ja  and  oa  and  we  have  the  stresses  at  the  support. 
At  joint  1  we  know  aj  and  jk,  and  draw  kc  and  ac  to  close  the 
figure.  There  will  be  no  line  in  the  stress  diagram  correspond- 
ing to  AB,  for  there  is  no  stress  in  that  tie  excepting  the  direct 
pull  of  3,000  Ibs.  At  joint  2  we  have  oa  and  ac,  and  draw  cd 
and  od  to  close  the  figure.  At  joint  3  we  have  dc,  ck,  and  kl, 
and  draw  le  and  de.  At  joint  4  we  already  have  od  and  de, 
and  find  ef  and  of  by  drawing  lines  from  e  and  o  parallel  to  the 
respective  pieces  in  Fig.  14.  At  joint  5  we  have  }e,  el,  and  Im, 
and  draw  mg  and  fg.  We  must  next  go  to  joint  7;  for  at  joint 
6  we  would  have  three  stresses  to  find,  and  by  the  graphic  method 
we  can  find  only  two  at  a  time.  At  joint  7  we  have  gm  and 
mn  (13,320  Ibs.),  and  draw  nh  and  gh  to  close  the  figure.  This 
completes  the  stresses  in  all  the  pieces  for  one-half  of  the  truss, 
and  of  course  the  stresses  for  each  half  are  the  same. 

EXAMPLE   5       (Eight  panel   Howe  Truss).  —  For    the  next 


STRESS   DIAGRAMS— VERTICAL  LOADS. 


979 


example  we  will  take  a  Howe  truss  whose  centre  lines  give  the 
diagram  shown  by  Fig.  15.  This  truss  is  for  a  span  of  sixty- 
four  feet,  and  supports  a  flat  roof  and  plaster  ceiling  below 


the  tie-beam,  and  also  a  gallery  below  on  each  side.  The  loads 
at  the  different  joints  would  be  about  as  indicated  in  Fig.  15. 
To  draw  the  stress  diagram  (Fig.  15  A)  lay  off  the  loads  on  a 


980 


STRESSES  IN   ROOF-TRUSSES. 


vertical  line,  commencing  first  with  the  loads  nearest  the  support. 
Thus  ab  equals  load  at  joints  1  and  2,  be  equals  load  at  joints 
3  and  4,  cd  equals  load  at  joints  5  and  6,  and  do  and  oe  each 
equals  one-half  of  loads  at  7  and  8,  because  one-half  of  this 
load  is  borne  by  each  support. 

Next,  commencing  at  joint  o,  we  have  the  supporting  force  oa, 
the  stress  in  the  rafter  ap,  and  the  stress  in  the  tie  po,  closing 
the  figure.  At  joint  1  we  know  pa  and  ab,  and  draw  bn  and  pn, 
closing  the  figure.  At  joint  2  we  know  op  and  pn  already,  and 
draw  nm  and  om.  At  joint  3  we  know  mn,  nb,  and  be,  and  draw 


4,800  4,800  4,800  4,800  4,800 


00  2,400  2, 


FIG.  15, 


00  2,400 


FIG.  15  A 


; 

J  f\ 

1 

/§ 

l                                      /        34,200 

i7 
aT 

X                 52,200 

y7  i 

/                           63,000 

V_j£               S 

/ 

/                                   66,600 

*X  Tc                m                             p 

\                                                                                                        63,000 

/ 

cl  a,nd  ml  The  stresses  at  joints  5  and  6  are  found  in  the  same 
way  as  those  at  3  and  4;  and  at  joint  7  we  know  the  stresses  hi, 
id,  and  de,  and  draw  ef  and  hf.  The  centre  rod  HH  has  no  stress 
excepting  the  direct  pull  of  2,400  Ibs.,  so.it  cannot  be  represented 
in  the  stress  diagram. 

The  stresses,  in  pounds,  in  the  various  members  of  the  truss 
are  given  on  the  stress  diagram.  These  stresses  can  be  checked 
by  means  of  the  formulas  given  for  a  six-panel  truss  (Table 
XVIII)  carried  one  step  further. 


STRESS  DIAGRAMS— VERTICAL  LOADS.        981 


EXAMPLE  6. — Howe  Truss  loaded  at  alternate  joints  (Fig.  16). 
This  example  has  been  selected  to  show  how  to  proceed  when 
there  is  no  load  at  one  or  more  of  the  joints.  Fig.  16  represents 
the  centre  lines  of  a  truss  of  50  ft.  span  and  only  5  ft.  in  height, 


5CCO 

I* 


I 


p- 10,000 


5 — ^Y 5 — iff? 

O          Centre 


FIG.  16 


10,000 


j  h  f  d 

bg  =  20,000;  ~6/^  25,000;   oj  —  ck  =  30,000 

FIG.  16  A 

In  order  to  give  the  braces  an  inclination  approximating  45° 
the  truss  is  divided  into  ten  panels,  but  purlins  are  placed  over 
every  other  joint,  as  in  Fig.  19  of  Chap.  XXV.  The  loads  from 
these  purlins  would  be  about  5,000  Ibs.  The  stresses  at  joint  1 
are  found  in  the  same  manner  as  in  the  previous  examples, 
always  starting  with  the  supporting  force. 

At  joint  2  we  have  the  stress  line  da,  and  as  there  is  no  load 
at  this  joint  we   draw  from  a  a  1  ne   parallel  to  AE  (A  covers 
the  entire  space  from  joint  1  to  joint  4),  and  from  d  a  line  parallel 
to  DE    the  two  lines  intersecting  at  e.     At  joint  3  the  stress 
lines  are  od,  de   ef,  and  fo: 
Stresses  at  joint  4,  fe,  ea,  ab,  bg,  and  gf. 
11      "     5,  of,  fg,  gh,  and  ho. 
"      "     6,  hg,  gb,  bi,  and  ih. 
"         "      "     7,  oh,  hi,  ij,  and  jo 

"  "  8,  ji,  ib,  be,  and  ck,  the  latter  line  bringing  us 
to  the  point  of  beginning,  showing  that 
there  is  no  stress  in  kj. 

At  joint  9  the  only  stresses  are  oj  and  lo,  for  as  there  is  no  stress 
in  JK,  there  can.  lie  none  in  Kl/. 


982 


STRESSES  IN  ROOF-TRUSSES. 


There  would  also  be  no  stress  in  the  centre  rod.  Although 
these  members  have  no  stress  it  is  advisable  to  insert  them  in 
the  truss  to  stiffen  the  top  and  bottom  chords,  but  they  can 
be  made  very  light,  say  J  inch  for  the  rods  and  3X6  for  the 
braces. 

EXAMPLE  7. — Howe  Truss  with  slanting  top  chord.  In  order 
to  give  a  slope  to  the  roof  it  is  often  desirable  to  incline  the 
top  chord  of  a  Howe  truss  as  in  Fig.  20,  Chap.  XXV.  Fig.  17 
shows  the  truss  diagram  for  such  a  truss,  and  Fig.  17  A  the 

Loads  in  Tons' 


FIG.  f  7  A 


stress  diagram.  The  latter  is  drawn  in  the  same  way  as  the 
stress  diagram  in  example  5,  but  because  the  top  chord  is  not 
level,  the  stress  diagram  will  not  be  symmetrical.  When  the 
stress  diagram  is  not  symmetrical  it  is  necessary  to  complete 
the  entire  diagram,  so  as  to  show  the  stress  in  every  member  of 
the  truss;  the  stress  lines  for  joint  9  are  om,  mn,  nr,  and  ro. 
This  leaves  only  the  line  rf  to  complete  the  diagram,  and  if 
the  diagram  has  been  correctly  drawn,  a  line  joining  r  and  / 
will  be  exactly  parallel  to  RF.  There  will  be  no  stress  in  the 
centre  rod. 

EXAMPLE  8. — Truss  with  inclined  ties  (Fig.   18).     This  truss 
has  the  same  dimensions  as  the  truss  shown  by  Fig.  14,  but  the 


STRESS  DIAGRAMS—  VERTICAL  LOADS.        083 


diagonals  incline  in  the  opposite  direction  and  are  in  tension, 
and  the  verticals,  except  at  the  centre,  are  in  compression. 

This  form  of  truss  is  sometimes  used  in  wooden  construction 
to  avoid  the  long  centre  braces  which  occur  in  Fig.  14.  Long 
ties  being,  as  a  rule,  more  economical  than  long  struts. 

For  this  truss  we  cannot  add  the  ceiling  loads  to  the  roof 
loads,  because  the  effect  on  the  ties  is  greater  than  the  amount 
of  the  loads. 


10,320 


-  /   V   3|/  5|/  7|/          ;   81 

!f — 10- — ^ — lo1^ — ^IOL-^ — 10--^-  g 

O  3000  P  3000  Q  3000  R  3000 
P  =  i6,620 


FIG.  18 


To  draw  the  stress  diagram  (Fig.  ISA),  first  draw  oa=to 
the  supporting  force  (46,620  Ibs.)  and  from  a  and  o  draw  lines 
parallel  to  AF  and  OF,  intersecting  at  /.  The  triangle  oaf  is 
the  same  as  in  Fig.  14 A,  showing  that  the  maximum  stresses 
in  rafter  and  tie-beam  are  the  same  as  in  the  truss,  Fig.  14. 
Having  found  the  forces  at  joint  1,  we  proceed  to  joint  2,  where 
we  have  fa  acting  up,  ab=  10,320  Ibs.,  and  draw  bg  and  fg. 
The  arrow-head  on  gf  points  up,  or  towards  the  joint,  showing 
that  FG  is  in  compression.  Next  go  to  joint  3.  The  first 
force  which  we  know  at  this  joint  is  the  load  of  3,000  Ibs.  As 
weights  must  always  be  represented  by  a  vertical  line  acting 
down,  and  as  the  bottom  of  the  line  in  this  case  must  be  at  o, 
we  measure  upwards  from  o  3,000  Ibs.  and  mark  the  point 
thus  obtained  p.  Our  polygon  of  forces  for  joint  3,  then,  com- 
mences at  p,  and  we  have  po,  of,  and  fg.  Then  from  p  draw 
a  line  parallel  to  PH,  and  from  g  a  line  parallel  to  GH,  the  two 
intersecting  at  h.  Then  po,  of,  fg,  gh,  and  hp  represent  the 


984  STRESSES  IN  ROOF-TRUSSES. 

forces  acting  at  joint  3.     gh  and  hp  both  act  from  the  joint, 
and  hence  are  in  tension. 

The  stresses  at  joint  4  are  hg,  gb,  be,  ci,  and  ih. 
11         "        "      "     5  are  qp,  ph,  hi,  ij,  and  jq. 
"        "      "     6  are  ji,  ic,  cd,  dk,  and  kj. 
"         "         "      "     7  are  rq,  qj,  jk,  kl,  and  Ir. 

The  stress  in  LM  will  be  only  that  produced  by  the  load 
which  it  directly  supports,  viz.,  3,000  Ibs.,  and  it  need  not  be 
represented  in  the  stress  diagram,  unless  we  wish  to  complete 
the  diagram  so  as  to  show  the  stresses  in  the  other  half  of  the 
truss.  To  show  the  stress  in  LM  draw  sr=3,000  Ibs.;  we 
have  rl,  and  from  I  draw  a  vertical  line,  and  from  s  a  horizontal 
line,  the  two  intersecting  at  m.  If  we  complete  the  stress  diag- 
gram  for  the  entire  truss,  it  will  be  symmetrical  about  a  line 
drawn  half  way  between  s  and  r. 

The  student  should  compare  the  stresses  figured  on  Fig.  ISA 
with  those  on  Fig.  14A  and  note  the  effect  of  changing  the 
direction  of  the  braces.  Fig  14  will  require  a  very  much  larger 
rod  in  the  centre  than  is  required  for  KL  and  MN  in  Fig.  18 
while  the  centre  rod  in  Fig.  18  may  be  made  very  light. 

Fig.  18,  however,  requires  special  cast  washers  for  the  rods 
to  make  a  good  job. 

The  manner  of  laying  off  the  ceiling  loads  in  Fig.  18 A  applies 
to  all  trusses  where  the  loads  are  not  carried  directly  to  the 
top  by  means  of  vertical  rods  or  ties. 

EXAMPLE  9. — Simple  Fan  Truss  (Fig.  19).  In  Fig.  19  we 
have  the  skeleton  of  a  simple  fan  truss  with  inclination  of  30° 
and  the  rafters  divided  into  three  equal  panels,  so  that  the  loads 
are  all  alike. 

The  stress  diagram  is  drawn  on  the  same  principle  as  those 
previously  explained  and  involves  no  unusual  points.  As 
the  loads  are  all  alike,  the  stresses  in  this  truss  may  be  readily 
figured  by  means  of  Table  X,  and  the  student  should  compare 
the  stresses  thus  obtained  with  those  obtained  by  scaling  the 
stress  diagram. 

EXAMPLE  10. — Cambered  Fink  Truss  (Fig.  20).  Inclination 
of  rafters  30°.  Distances  between  trusses  20  ft  Loads  are 
for  slate  roof  on  boards  or  angle-iron  purlins.  Commence  the 
stress  diagram  by  drawing  a  vertical  line  equal  to  the  supporting 
force  P,  or  56,350  Ibs.,  and  lettering  the  bottom  o  and  the  top  a, 
as  these  are  the  letters  on  each  side  of  the  supporting  force  at 
joint  0.  Draw  an  and  on  parallel  to  A N  and  NO.  At  joint  1 


STRESS   DIAGRAMS— VERTICAL  LOADS.        985 

we  have  na  acting  up;  measure  off  aZ>=16,100  Ibs.,  draw  bm 
and  nm  parallel  to  BM  and  NM.  At  joint  2  we  have  on  and 
nm,  and  draw  ml  parallel  to  ML,  the  stre.ss  polygon  being 
on,  nm,  ml,  and  lo. 

At  joint  3  we  meet  a  condition  which  we  have  not  found  in  any 
of  the  preceding  examples,  and  which  is  peculiar  to  this  truss, 


Loads  in  Tons 


FIG.  19  A 


viz.,  three  unknown  forces  apparently.  From  a  study  of  the 
truss  diagram,  however,  we  see  that  ML  and  Kl  act  as  belly- 
rods  to  take  up  the  thrust  in  the  struts  at  joints  2  and  5,  and 
as  the  loads  at  joints  1  and  6  are  equal  and  NM  and  IH  are 
of  the  same  length,  the  stress  in  KI  must  be  the  same  as  the 
stress  in  ML,  which  we  already  know.  This  reduces  the  number 
of  unknown  forces  at  joint  3  to  two. 

The  first  force  which  we  know  at  this  joint  is  Im,  the  next  mb, 
the  next  bc=  16,100  Ibs.,  and  from  c  draw  a  line  parallel  to  CI, 
and  from  /,  the  point  of  beginning,  a  line  parallel  to  LK.  Now 
between  these  two  lines  we  must  have  a  line,  ik,  parallel  to  IK 
and  equal  in  length  to  ml;  this  line  we  obtain  by  means  of  the 
dividers  and  a  parallel  ruler,  or  triangle.  If  correctly  drawn, 
the  point  i  will  be  found  in  line  with  nm.  The  stress  polygon 
for  joint  3,  then,  is  Im,  mb,  be,  ci,  ik,  and  kl. 

At  joint  4  the  stress  lines  are  ol,  Ik,  kg,  and  go. 
"  "  5  "  "  "  "  gk,ki,ih,sindhg. 
"  "  6  "  "  "  "  hi,  ic,  cd,  and  dh. 

If  the  stress  diagram  is  accurately  drawn  a  line  from  d  parallel 
\>  the  rafter  will  pass  through  the  point  h.  The  vertical  tie  GG, 


986 


STRESSES  IN  ROOF-TRUSSES. 


Fig.  20,  has  no  stress  and  its  only  duty  is  to  prevent  the  hori- 
zontal tie  from  sagging. 

EXAMPLE  11   (Fig.  21). — Same  Truss  as  in  Fig.  20,  carrying 
two    additional   loads.     Steel    trusses    of    this    shape    are    often 

16,100 


16,100 


E    16,100 


16,100 


SPAN  SO  FT.  PITCH  30° 

Fig.  20 


56350 


required  to  support  loads  from  below.  In  Fig.  21  we  have 
two  loads  of  4  tons  each,  supported  at  joints  5  and  9,  in  addition 
to  the  roof  loads. 

The   stress  diagram  is   drawn   in   exactly  the   same  way  as 
Fig.  20 A,  except   that  at  joint  5  the  first  known  force  is  RO, 


STRESS  DIAGRAMS-VERTICAL  LOADS.        987 

4  tons,  and  we  lay  off  above  o  a  distance  equal  to  4  tons,  which 
gives  us  the  point  r.  We  then  have  at  this  joint  ro,  ol,  Ik, 
and  draw  kg  and  rg  to  close  the  figure. 

It  should  be  noticed  that  the  stresses  in  NM,  IH,  ML,  KI, 
and  LK  are  the  same  as  the  stresses  in  the  corresponding  mem- 


bers  of  Fig.  20,  as  these  are  not  affected  by  the  ceiling  load.  All 
of  the  other  stresses,  however,  are  increased  because  of  the 
increase  in  the  supporting  forces,  the  greatest  increase,  however, 
being  in  KG  and  EG. 

EXAMPLE  12. — Simple  Scissors  Truss  (Fig.  22).  Fig.  22  is  the 
truss  diagram  of  the  truss  shown  by  Fig.  25,  Chap.  XXV, 
which  is  the  simplest  form  of  the  scissors  truss.  The  truss 
diagram  is  drawn  by  commencing  with  the  line  oa  equal  to 
the  supporting  force  (9,600  Ibs.)  and  drawing  ad  and  od  parallel 
to  AD  and  OD.  Next,  at  joint  2  we  have  da  acting  up;  measure 
off  ab=  5,800  Ibs.  and  draw  be  and  de  parallel  respectively  to 
BE  and  DE.  Next  go  to  joint  3.  Here  we  have  eb  acting  up; 
measure  off  bc=  5,200  Ibs.  and  draw  cf  and  ef  parallel  to  CF 
and  EF.  We  now  have  the  stresses  in  one  half  of  the  truss  and 
the  stresses  in  the  other  half  will  be  ttfe  same.  If  we  wish 
to  complete  the  diagram,  measure  off  above  o,  ro  equal  to 
the  load  at  joint  4,  2,400  Ibs.,  and  draw  rg  and  fg  parallel  to 
RG  and  FG.  The  stress  polygon  for  joint  4  is  ro,  od,  de,  ef, 


988 


STRESSES  IN   ROOF-TRUSSES. 


fg,  and  gr.  For  the  stresses  at  joint  5,  measure  down  from 
c  a  distance=  5,800  Ibs.  and  draw  a  line  parallel  to  the  rafter 
which  should  pass  through  the  point  g.  The  completed  figure 


FIG.  22  A 


should  be  symmetrical  about  a  horizontal  line,  half  way  between 
r  and  o. 

EXAMPLE  13. — Scissors  Truss  like  Fig.  26,  Chapter  XXV. 
Fig.  23  is  the  truss  diagram  of  the  truss  shown  in  Fig.  26,  Chap. 
XXV,  with  the  loads  figured  about  as  they  would  be  for  a 
slate  roof  and  wooden  ceiling  with  trusses  spaced  12  ft.  on 
centres. 

Commence  the  stress  diagram  by  drawing  the  line  oa=to 
the  supporting  force  at  joint  1  (14,750  Ibs.).  The  stress  poly- 
gons for  the  different  joints  are  as  follows: 

At  joint  1 :  oa,  ae,  eo. 

"  "  2:  ea,  ab,  &/.  and  fe. 

"  "  3:  oe,  ef,fh,  and  ho. 

"  "  4:hf,fb,bk,sindkh. 

"  "  5:  r0=l,100  Ibs.,  oh,  hk,  kl,  and  Ir. 

"  "  6:  Ik,  kb,  bc=  5,400  Ibs.,  cm,  and  ml 

"  "  7:  me,  cd=  5,700  Ibs.,  dn,  and  nm. 

The  student  should  notice  how  much  the  stresses  in  the  prin- 
cipal members  of  this  truss  exceed  the  supporting  forces  or 
loads,  and  particularly  the  great  stress  in  the  centre  rod. 

For  this  reason  this  is  not  an  economical  type  of  truss  for 
spans  exceeding  36  ft. 


STRESS  DIAGRAMS— VERTICAL  LOADS.        989 

EXAMPLE  14. — Scissors  Truss  like  Fig.  4.  Fig.  24  is  the 
truss  diagram  of  the  truss  shown  by  Fig.  4,  p.  954,  and  for 
which  the  roof  and  ceiling  loads  are  computed  in  Example  3, 
p.  954.  The  truss  shown  by  Fig.  4  is  built  of  planks  spiked 
and  bolted  together,  but  the  stresses  would  be  found  in  pre- 


RG.  23  A 


cisely  the  same  way  if  the  truss  were  made  of  heavy  timbers 
and  supported  a  greater  roof  area.  It  should  be  remembered 
that  only  the  shape  of  the  truss  and  the  loads,  including  their 
point  of  application,  affect  the  stress  diagram. 

The  stresses  at  joints  1  and  2  are  readily  found  commencing 
with  oa=P.  At  joints  3  and  4,  however,  we  have  three  un- 
known forces.  We  cannot  obtain  the  stresses  at  joint  4  until 
we  have  drawn  those  acting  at  joint  3.  The  known  forces  at  3 
are  the  load  0/2=430  Ibs.  and  the  stresses  acting  in  OE  and 
EF,  and  the  unknown  forces  those  acting  in  FH,  HK,  and  KR. 
Now  both  HK  and  KR  are  in  tension  and  both  serve  to  hold 
joint  3  from  falling  down  and  outwards.  Either  one  (but  not 
both)  could  be  omitted,  and  the  greater  the  stress  in  one  the 
less  will  be  the  stress  in  the  other.  The  only  way  in  which  we 
can  complete  the  stress  polygon  for  joint  3  is  to  fix  the  amount 


990 


STRESSES  IN   ROOF-TRUSSES. 


of  one  of  the  unknown  stresses  arbitrarily.  The  most  satis- 
factory analysis  seems  to  be  to  make  the  stress  in  HK  equal 
to  that  in  KR.  This  is  done  as  follows:  The  first  known  force 


36'lO- 


at  joint  3  is  the  load  represented  by  ro  (the  point  r  being 
obtained  by  measuring  upwards  from  o  430  Ibs.),  next  the 
lines  oe  and  ef.  From  /  draw  a  line  parallel  to  FH,  and  from  r 
a  line  parallel  to  KR.  These  two  lines  must  be  connected  by 
a  third  line  parallel  to  HK.  This  line  should  be  drawn  so 
that  its  length  will  be  equal  to  kr,  which  can  be  done  by  means 
of  dividers.  Lettering  the  ends  of  this  line  h  and  k  we  have  the 
completed  stress  polygon  for  joint  3,  viz.,  ro,  oe,  ef,  }h,  hk, 
and  kr.  Knowing  the  stress  in  FH,  we  have  but  two  unknown 
forces  at  the  joint  4,  which  are  readily  found. 

The  stress  polygon  for  joint  5  is  Ic,  cd,  dm,  and  ml.  Compar- 
ing this  stress  diagram  with  Fig.  23 A,  we  see  that  the  stress 
in  the  centre  rod  is  much  less  in  proportion  to  the  loads  in 
Fig.  24A  than  it  is  in  Fig.  23 A,  this  reduction  being  due  to 
the  horizontal  tie  RK.  For  light  trusses  built  of  planks  spiked 
or  bolted  together  the  form  of  truss  shown  by  Fig.  24  is  prefer- 
able to  that  shown  in  Fig.  23. 

EXAMPLE  15. — Scissors  Truss  like  Fig.  30,  Chap.  XXV. 
Fig.  25  is  the  truss  diagram  of  the  truss  shown  by  Fig.  30  of 
Chapter  XXV.  The  line  EF  in  Fig.  25  does  not  correspond 


STRESS  DIAGRAMS— VERTICAL  LOADS.        991 

with  the  centre  line  of  the  strut  in  Fig.  30,  because  the  inner 
end  of  the  latter  is  dropped  slightly  on  account  of  the  detail 


EIG.  25  A 


of  the  joint,  but  in  the  truss  diagram  all  lines  must  go  from  joint 
to  joint,  otherwise  the  stress  diagram  could  not  be  drawn. 
There  is  no  stress  in  the  upper  portion  of  the  tie-beams  under 
a  symmetrical  vertical  load,  hence  they  are  shown  by  dotted 
lines  in  Fig.  25.  There  are  no  complications  in  drawing  the 
stress  diagram  of  this  truss,  therefore  a  detailed  description 
is  unnecessary. 

The  stress  polygons  for  the  different  joints  are  as  follows: 

For  joint  1 :  oa,  ad,  do. 

I"       "2:  TO,  od,  de,  er. 
"       "     3:  ed,  da,  ab,  bf,fe. 
"       "4:  fb,  be,  ch,  hf. 
"       "5:  sr,re,ef,fh,smdhs. 

hs  and  he  coincide,  showing  that  the  tension  in  HS  is  equal 
to  the  compression  in  CH.  The  plus  and  minus  signs  on  Fig.  25 
denote  compression  and  tension  respectively. 

EXAMPLE  16. — The  Hammer-beam  Truss.  As  this  truss  is  so 
frequently  used  by  architects  for  supporting  the  roofs  of  churches 
and  large  halls,  we  have  devoted  considerable  space  to  it. 


992  STRESSES  IN  ROOF-TRUSSES. 

As  generally  constructed,  hammer-beam  roof  trusses  exert 
a  more  or  less  horizontal  pressure  upon  the  walls  supporting 
them,  requiring  that  the  walls  shall  be  heavy  and  re-enforced 
by  buttresses  on  the  outside.  In  churches  where  the  walls 
are  low,  this  horizontal  thrust  of  the  truss  is  easily  taken  care 
of;  but  in  many  cases  it  is  desirable  to  do  away  with  it  entirely 
if  possible.  In  order  better  to  understand  the  action  of  the 
stresses  in  this  truss,  we  have  presented  first  a  truss  (Fig.  26) 
which  has  all  the  features  of  the  hammer-beam  truss,  excepting 
the  lower  braces,  and  yet  exerts  no  horizontal  thrust  against 
the  wall. 

The  truss  is  supposed  to  be  built  like  the  ordinary  hammer- 
beam  truss,  excepting  the  omission  of  the  lower  braces,  and 
putting  in  strong  timber  ties,  HO  and  PO,  in  place  of  the  orna- 
mental curved  pieces  usually  employed.  In  this  particular 
example  we  have  assumed  the  span  of  the  truss  as  60  ft.,  the 
rise  as  35  ft.,  and  the  distance  between  centres  of  trusses  15  ft, 
This  would  make  the  loads  at  different  joints  about  as  is  in- 
dicated in  Fig.  26. 

To  draw  the  stress  diagram,  lay  off  the  supporting  force  P 
on  a  vertical  line  oa,  =  42,000  Ibs.  Now  at  joint  1  we  have  the 
stresses  oa,  af,  and  /o;  at  joint  2,  fa,  ab,  bg,  and  }g;  at  joint  3, 
of,  fg,  gh,  and  oh,  oh  acting  from  h  to  g,  and  hence  is  a  pulling 
stress.  At  joint  4  we  have  hg,  gb,  be,  ci,  and  hi  to  close  the 
figure;  hi  is  also  in  tension.  At  joint  5  we  have  ic,  cd,  dk,  and 
ik.  At  the  top  joint  6  the  stresses  are  kd,  de,  el,  and  kl,  which 
completes  the  stress  diagram  for  one-half  of  the  truss,  which, 
of  course,  is  all  that  is  needed.  Examining,  now,  the  diagram, 
we  find  that  the  stresses  are  in  general  much  larger  than  would 
be  the  case  if  there  were  a  horizontal  tie  across  the  truss;  still, 
if  we  make  the  pieces  large  enough  to  withstand  these  stresses, 
the  truss  will  be  stable  and  exert  no  outward  thrust  on  the  walls. 

Looking  at  Fig.  26  we  see  that  OF,  H,  Pt  and  R  form  a  con- 
tinuous tie,  only  it  is  pulled  up  in  the  centre  in  the  form  shown. 
In  Fig.  26A  we  see  that  the  stress  in  the  tie-rod  KL  is  very  great, 
and  this  is  because  the  rod  has  to  hold  up  the  inclined  ties  HO 
and  PO.  If  we  imagine  the  tie  KL  to  be  cut  in  two  just  above 
the  joint,  the  main  rafters  would  break  at  the  joints  4  and  9, 
and  the  bottom  portion  immediately  slide  outwards,  straightening 
out  the  main  tie  and  allowing  the  top  of  the  truss  to  fall  through. 

Having  seen  that  a  hammer-beam  truss  could  be  built  in  which 
there  is  no  horizontal  thrust,  we  will  now  consider  the  hammer- 


STRESS  DIAGRAMS— VERTICAL   LOADS.        993 


- 42 ,000 


SPAN  60  FT.        RISE  35  FT.  Q 

Fig  26 


Fig.  26  A 


994  STRESSES  IN  ROOF-TRUSSES. 

beam  truss  as  usually  built,  in  which  a  horizontal  thrust  is 
expected.  The  diagram  of  such  a  truss  is  shown  in  Fig.  27,  in 
which  the  curved  braces  usually  built  in  the  centre  of  the  truss 
are  not  shown,  as  they  are  considered  to  be  purely  ornamental 
and  have  no  stresses  in  them.  The  brace  OM  is  drawn  as 
though  it  were  straight;  but  a  curved  brace  can  be  used  as 
well,  without  altering  the  diagram,  for  the  reason  that  the 
stress  in  the  curved  piece  acts  in  a  straight  line  connecting  the 
centres  of  each  end  of  the  brace. 

To  draw  the  stresses  in  this  truss  we  must  first  find  the  hori- 
zontal thrust  of  the  truss  against  the  wall. 

To  do  this  we  have  to  consider  that  all  the  pieces  from  joints  0 
to  joint  4  simply  form  a  framed  brace  supporting  the  upper 
portion  of  the  truss  at  joint  4,  or  that  a  single  brace,  shown 
by  the  broken  line  04,  Fig.  27,  would  have  the  same  effect 
on  the  wall  as  all  the  pieces  put  together  in  the  framed  strut; 
that  is,  we  may  consider  the  truss  to  have  the  same  horizontal 
thrust  as  the  truss  shown  in  Fig.  27A.  The  load  at  joint  4  would 
evidently  be  12,000  Ibs.  plus  load  at  joint  5,  plus  half-load  at 
joint  6  and  half-load  at  joint  2,  making  in  all  36,000  Ibs.  To 
draw  the  horizontal  thrust  and  stresses  we  proceed  as  follows: 

Lay  off  ab  (Fig.  275)  =  load  at  joint  2,  6c=load  at  joint  4, 
cd=load  at  joint  5,  and  de=load  at  joint  6.  Then  the  load  at 
joint  4  (Fig.  27A)  =  %ab  +  bc  +  cd  +  %de;  and  if  we  draw  from  x 
a  horizontal  line  to  the  left,  and  from  the  centre  of  ab  a  line 
parallel  to  04  (Fig.  27 A),  these  two  lines  will  intersect  at  m, 
and  mx  will  be  the  horizontal  thrust  exerted  on  the  wall  at  the 
point  0. 

Having  obtained  this  thrust,  it  is  easy  to  determine  the 
stresses  in  the  pieces. 

At  joint  0  we  have  the  thrust  mx,  the  vertical  supporting  force 
xa,  and  the  stresses  ao  and  mo  closing  the  figure.  At  joint  1 
we  have  oa,  af,  and  of,  as  the  stresses  in  OA,  AF,  and  FO. 

At  joint  3  the  stresses  are  mo,  of,  fg,  and  mg;  at  joint  2  they 
are  fa,  ab,  bg,  and  <//;  at  joint  4  the  stresses  are  mg,  gb;  be 
and  ci  closing  the  figure.  It  will  be  noticed  that  the  figure 
closes  without  allowing  any  line  to  be  drawn  parallel  to  MI] 
hence  there  is  no  tensional  stress  in  MI  under  purely  vertical 
loads.  Under  a  wind  stress  there  would  be  some  compression 
in  MI,  and  in  practice  a  tie-beam  is  necessary. 

At  joint  5  we  have  the  stresses  ic,  cd,  dk,  and  ki,  and  at  joint 


STRESS  DIAGRAMS— VERTICAL  LOADS.        £95 


6  we  have  kd,  de,  el,  and  kl,  which  completes  the  stresses  for 
one-half  of  the  truss,  which  is  all  we  need. 


Fig.  27  A 

Comparing,  now,  the  diagram  of  stresses,  Fig.  27B,  with 
Fig.  26A,  we  find  that  in  general  the  stresses  in  the  truss,  Fig.  27, 
are  much  less  than  in  the  truss,  Fig.  26;  while,  on  the  other 
hand,  the  latter  truss  exerts  no  outward  thrust  on  the  walls, 
as  is  the  case  in  Fig.  27. 

By  building  a  truss  like  Fig.  27,  and  putting  in  curved  ties 
from  joints  3  and  11  to  joint  12,  we  can  relieve  the  brace  OM 
of  part  of  the  load  without  straining  the  other  timbers  as  much 
as  is  the  case  in  Fig.  26. 


996 


STRESSES  IN   ROOF-TRUSSES. 


The  truss  shown  in  Fig.  36,  Chap.  XXV,  combines  the  ad- 
vantages of  both  the  forms  of  hammer-beam  trusses  which  we 
have  considered,  though  it  may  not  be  quite  so  pleasing  to 
the  eye. 

EXAMPLE  17. — Suspended  Pratt  Truss,  Symmetrically  Loaded. 
Let  Fig.  28  be  the  truss  diagram  of  a  suspended  Pratt  truss, 
uniformly  loaded  at  top  and  bottom,  with  2  tons  at  each  joint. 

The  stress  diagram  is  drawn  in  exactly  the  same  way  as  for 


A B  C  D 


s.d. 


FIG.  28  A 


a  Howe  truss,  except  that  the  diagonals  run  in  the  opposite 
direction.     The  stresses  should  be  drawn  for  the  joints  in  the  . 
order  in  which  they  are  numbered.     In  this  truss  the  verticals 
are  in  compression  and  the  diagonals  in  tension. 

EXAMPLE  18.— Truss  like  Fig.  63,  Chap.  XXV.  Fig.  29 
is  the  truss  diagram  of  a  light  iron  truss  of  32  ft.  span  intended 
to  support  a  tar-and-gravel  roof,  the  slope  oT  the  roof  being 
at  right  angles  to  the  line  of  the  trusses. 

The  stress  diagram  is  drawn  as  in  the  previous  examples, 
taking  the  joints  in  the  order  in  which  they  are  numbered. 

EXAMPLE  19.— Double  Warren,  or  Lattice  Truss.  The  truss 
diagram  shown  by  Fig.  30  is  best  analyzed  by  considering 
it  as  built  up  of  two  Warren  trusses,  laid  one  over  the  other, 
the  full  lines  indicating  a  truss  such  as  is  shown  in  Fig.  31, 
and  the  dotted  lines  a  truss  like  Fig.  32.  Three  of  the  seven 


STRESS  DIAGRAMS— VERTICAL  LOADS.        997 

loads  would  come  on  the  first  truss  and  four  on  the  second. 
The  stresses  are  found  for  each  truss  separately  and  then 
combined  for  the  top  and  bottom  chords. 

Thus  the  stress  in  the  top  chord,  from   1  to  3,  Fig.  30,  would 
be  that  in  AD,  Fig.  31,  or  3  tons;  from  3  to  5  it  would  be  equal 


FIG.  29  A 

to  the  stress  in  AD,  Fig.  31,  plus  that  in  BE,  Fig.  32,  or  9  tons; 
from  5  to  7  it  would  be  equal  to  stress  in  BFt  Fig.  31,  plus 
stress  in  BE,  Fig.  32,  or  13  tons,  and  so  on,  the  stress  in  the 
bottom  chord  being  found  in  the  same  way.  The  diagonal 
struts  and  ties  act  independently  of  each  other,  and  the  stresses 
are  those  indicated  on  the  stress  diagrams.  The  plus  signs 
denote  compression  and  the  minus  signs  tension. 

In  Fig.  32  the  stress  polygon  for  joint  7  is  fe,  eb,  be,  and  cf, 
which  closes  without  any  room  for  a  line  parallel  to  FF,  show- 
ing that  there  is  no  stress  in  the  two  inner  diagonals  except 
that  due  to  the  weight  of  the  bottom  chord. 

This  truss  can  be  extended  indefinitely  by  giving  it  sufficient 
height  for  the  span.  It  is  usually  built  of  steel  angles  with 
riveted  joints. 

EXAMPLE  20.— Truss  like  Fig.  66,  Chapter  XXV.  Fig.  33 
is  the  truss  diagram  of  a  truss  similar  to  that  shown  by  Fig.  66, 
p.  926,  the  panel  loads  being  taken  at  2  tons  each,  the  analysis 
being  the  same  for  any  other  loads.  The  stress  diagram  is 
drawn  exactly  as  in  the  previous  examples,  commencing  with 


998 


STRESSES  IN  ROOF-TRUSSES. 


the  supporting  force  =oa  and  taking  the  joints  in  the  order 
in  which  they  are  numbered.  In  this  truss  the  diagonal  web 
members  are  all  in  tension  and  the  verticals  in  compression. 
It  will  be  noticed  that  the  diagonals  in  the  two  panels  nearest 


the  centre  incline  in  the  opposite  direction  from  those  in  the 
outer  panels.  This  is  due  to  the  inclination  of  the  top  chord, 
which  would  cause  the  inner  diagonals  to  be  in  compression 
if  they  inclined  the  other  way.  The  stress  in  LMt  howeverv 


STRESS  DIAGRAMS— VERTICAL  LOADS.        999 


is  so  small  that  a  single  angle  would  resist  either  a  compressive 
or  tensile  stress. 


Fig.  33 

The  truss  shown  by  Fig.  34  is  very  similar  to  that  shown  in 
Fig.  33,  the  principal  difference  being  that  the  slope  of  the 
top  chord  is  less  in  the  former  than  in  the  latter.  In  Fig.  34, 
only  the  diagonals  in  the  two  centre  panels  incline  from  the 


-  —  6  r--^--6— 1|* — 6--*  —  6--* 
P=s9-T0ns  FIG.  34 


Centre) 


centre,  and  the  stress  in  these  diagonals  is  very  small.  With 
a  still  less  inclination  to  the  top  chord,  the  stress  in  NR  would 
become  0,  and  with  a  horizontal  top  chord  the  stress  in  NR 
would  become  reversed,  or  to  keep  it  in  tension,  the  direction 


1000 


STRESSES  IN  ROOF-TRUSSES. 


should  be  changed,  as  in  the  Pratt  truss,  Fig.  28.  Comparing 
the  stresses  in  these  two  trusses,  it  will  be  seen  that  while  the 
stresses  in  the  end  panels  are  less  in  Fig.  34  A  than  in  Fig.  33 A, 
yet  the  stresses  in  the  chords  at  the  centre  are  considerably 
greater.  As  a  rule,  the  less  the  height  of  a  truss  in  proportion 
to  the  span  the  greater  will  be  the  stresses  in  the  chords,  espe- 
cially at  the  centre  of  the  truss. 

EXAMPLE  21. — Fig.  35  is  a  truss  diagram  similar  to  the  truss 
shown  in  Fig.  73,  Chap.  XXV.  The  truss  diagram  is  drawn 
as  in  the  previous  examples,  except  that  in  this  case  the  bottom 
chord,  having  different  inclinations  in  the  different  panels, 
the  stress  lines  do  not  lie  over  each  other,  but  all  radiate  from 
o,  the  lines  in  the  stress  diagram  being  parallel  to  the  corre- 
sponding lines  in  the  truss  diagram. 


FIG.  35  A 


In  this  truss  the  stresses  in  the  diagonal  web-members  re- 
verse in  the  two  panels  nearest  the  centre.  Thus  the  stress 
polygon  for  joint  6  is  nm,  me,  cd,  dp,  and  pn,  the  stress  pn 
acting  from  the  joint  and  hence  denoting  tension.  At  joint  8 
the  stress  polygon  is  rp,  pd,  de,  es,  and  sr,  the  latter  line  acting 
towards  the  joint,  and  hence  denoting  compression. 

Under  irregular  loading,  the  stress  in  SR  would  probably 
be  reversed,  so  that  the  piece  would  be  in  tension  instead  of 
compression.  Trusses  like  Figs.  33,  34,  and  35  should  always 
be  computed  for  snow  on  one  half  of  the  truss  only,  and  also 
for  wind  pressure. 

EXAMPLE  22. — In  Fig.  36  we  have  the  diagram  of  the  truss 
shown  by  Fig.  72,  Chapter  XXV.  This  truss  is  similar  to 


STRESS  DIAGRAMS—VERTICAL  LOADS.       1001 

that  shown  by  Fig.  34,  except  for  the  secondary  bracing  in 
the  panels  and  for  the  curved  tie-beam.  The  stress  diagram 
presents  no  difficulties.  In  drawing  the  lines  from  o  parallel 
to  the  bottom  chord  the  latter  should  be  considered  as  made 
up  of  straight  lines  joining  the  joints;  thus  om  is  drawn  parallel 
to  an  imaginary  straight  line  connecting  joints  4  and  8.  As 
there  is  no  load  over  the  centre  of  the  panels  next  the  centre, 
there  will  be  no  stress  in  XX'  and  X'X".  If  the  bottom  chord 
was  straight,  as  in  Fig.  34,  there  would  be  no  stress  in  the  tie 
YZ,  but  as  the  chord  is  curved,  it  requires  a  certain  amount 

2000 


FIG.  33  A. 


of  tension  in  YZ  to  hold  it  up,  the  stress  being  indicated  by  yz 
(Fig.  36 A).'  If  the  diagram  were  completed  for  the  entire  truss, 
it  would  be  symmetrical  about  a  horizontal  line  drawn  through  o. 
There  is  one  point  in  which  this  example  differs  from  all 
of  the  preceding,  viz.,  in  the  load  AB  over  the  support.  As 
a  matter  of  fact,  there  would  be  such  a  load  over  the  support 
for  all  of  the  trusses,  but  as  the  load  does  not  act  on  the  truss, 
but  only  on  the  support,  it  has  been  neglected  in  the  previous 
examples. 


1002 


STRESSES  IN  ROOF-TRUSSES. 


When   trusses   are   supported   by    columns    this   outer   load 
should  be  taken  into  account  in  computing  the  load  on  the 


column.     In  representing  the  load  AB,  in  the  stress  diagram, 
we  first  measure  off  on  a  vertical  line,  oa,  equal  to  the  support- 


STRESS  DIAGRAMS— VERTICAL  LOADS.      1003 

ing  force  P,  which  acts  up,  then  measure  down  ab,  equal  to 
load  AB\  then  draw  bj  and  oj.  The  load  AB  has  no  effect  on 
the  stresses  in  the  truss,  because  if  it  is  omitted  the  value  of 
P  would  be  just  that  much  less. 

EXAMPLE  23. — Iron  Bowstring  Truss.  Span  of  truss,  90  ft.; 
distance  between  trusses  from  centres,  20  ft.;  rise  of  arched 
rafter,  20  feet. 

The  form  of  truss,  represented  by  Fig.  37,  is  one  of  the  most 
economical  of  trusses  for  very  great  spans. 

In  such  cases  as  the  present  example,  the  rafter,  or  curved 
principal,  is  the  only  piece  that  is  in  compression,  and  all  the 
others  are  in  tension.  Under  a  steady  load  only,  such  as  the 
weight  of  the  roof  itself,  one  set  of  braces  placed  as  shown  in 
Fig.  37  would  be  all  that  would  be  needed;  but  under  a  severe 
wind  pressure  blowing  against  one  side  of  the  roof  only,  it  is 
necessary  to  have  another  set  of  braces,  as  shown  by  the  dotted 
lines  in  the  figure. 

These  "  counter-braces/'  as  they  may  be  called,  have  no  stress 
on  them  at  all  when  there  is  only  a  vertical  load  to  be  supported 
by  the  trusses;  so  we  must  leave  them  out  in  drawing  the 
diagram  of  stresses. 

To  draw  the  stress  diagram,  lay  off  the  loads  on  a  vertical 
line,  as  in  all  the  previous  examples,  and  remember  that  the 
point  o  should  be  half-way  between  e  and  /  (Fig.  37 A);  then  oa 
will  be  the  supporting  force  at  joint  1.  In  drawing  the  stresses 
at  the  different  joints,  draw  first  those  at  joint  1  and  then 
those  at  joints  2,  3,  4,  5,  etc.,  in  the  order  in  which  they  are 
numbered  (Fig.  37). 

To  commence  the  stress  diagram,  we  have  oa  equal  to  the 
supporting  force  at  joint  1,  and  from  a  draw  a  line  parallel  to 
AG,  and  from  o  a  line  parallel  to  OG.  These' two  lines  intersect 
at  g.  (In  drawing  lines  parallel  to  the  curved  lines  of  the  truss, 
draw  the  stress  line  parallel  to  a  line  connecting  the  two  ends 
of  the  curved  chord.  Thus  ag  should  be  drawn  parallel  to  1-3, 
and  og  parallel  to  1-2.)  At  joint.  2  we  already  have  og,  and  from 
g  draw  a  line  parallel  to  GH,  and  from  o  a  line  parallel  to 
j  OH  (2-4):  this  gives  the  lines  oh  and  gh. 

At  joint  3  we  have  hg,  ga,  and  the  load  ab,  and  draw  bi  and 
hi  from  b  and  h. 

At  joint  4  we  now  have  oh  and  hi,  and  draw  ik  and  ok.  The 
stress  lines  for  joints  0  and  8  are  drawn  in  a  similar  way,  and 
those  for  5,  7,  and  9  simila  *ly  to  those  at  joint  3.  After  drawing 


1004  STRESSES  IN   ROOF-TRUSSES. 

the  stresses  at  joint  9,  go  to  joint  10;  and  after  drawing  the 
lines  for  that  joint  all  the  stresses  in  the  truss  will  have  been 
obtained.  The  stresses  in  this  particular  example  are  given 
in  pounds  on  the  respective  lines  in  the  stress  diagram.  It 
will  be  noticed  that  the  stress  is  very  severe  on  the  top  and 
lower  chords,  but  very  slight  on  the  bracing.  It  is  in  fact  so 
slight  that  it  will  be  about  as  well  to  make  all  the  diagonal 
braces  of  the  same  size  sufficient  to  resist  the  stress  on  IH, 
where  the  stress  is  the  greatest;  or  IH  and  KL  might  be  the 
same  size  and  MN  and  PR  a  smaller  size. 

The  vertical  or  radiating  pieces  might  be  all  of  a  sectional 
area  capable  of  resisting  the  stress  in  NP. 

The  great  advantage  of  this  truss  lies  in  the  fact  that  all  its 
parts  are  in  tension  excepting  the  upper  chord,  which,  of  course, 
is  in  compression.  We  might  analyze  the  way  in  which  the 
stresses  act,  by  saying  that  the  upper  chord  carries  all  the  load, 
like  an  arch,  and  is  prevented  from  spreading  out  at  the  ends 
by  the  lower  tie.  The  object  of  the  bracing  and  vertical  pieces 
is  only  to  keep  the  tie  in  its  curved  position,  and  not  permit  it  to 
come  down  flat,  and  thus  allow  the  ends  of  the  arch  to  spread 
out. 

Trusses  Uiisymmetrically  Loaded. — In  all  of  the 
preceding  examples  the  loads  have  been  symmetrically  dis- 
posed each  side  of  the  centre  of  the  truss,  so  that  each  support- 
ing force  is  equal  to  one  half  of  the  total  load.  It  very  often 
happens,  however,  that  the  loads  are  not  symmetrically  dis- 
posed, and  in  all  such  cases  it  is  necessary  to  first  compute  the 
supporting  forces  and  then  to  draw  the  stress  diagram  for 
the  entire  truss,  as  the  diagram  will  not  be  symmetrical.  Other- 
wise the  process  is  the  same  as  described  for  the  foregoing 
examples.  The  following  examples  will  illustrate  sufficiently 
the  method  of  computing  the  supporting  forces  and  drawing 
the  stress  diagrams: 

EXAMPLE  24. — Fig.  38  represents  the  diagram  of  a  truss 
similar  to  that  shown  in  Fig.  1,  but  of  a  greater  span  and  having 
a  gallery  supported  from  it  at  one  side  only.  The  approximate 
roof  and  ceiling  loads  are  indicated  by  the  figures  near  the 
arrows,  and  the  weight  coming  on  one  truss  from  the  gallery 
would  be  about  9,000  Ibs. 

The  first  step  towards  drawing  the  stress  diagram  is  to  com- 
pute the  reactions  at  the  two  ends  of  the  truss,  which  will  give 
the  supporting  forces.  This  is  most  readily  done  by  the  method 


VERTICAL  LOADS   NOT  SYMMETRICAL.       1005 

of   moments   explained   on   pages   274-277.     In    this   example 
we  will  take  the  moments  about  joint  1. 

As  the  loads  at  joints  2  and  3  have  the  same  arm,  we  will 
add  them  together  before  multiplying  by  the  arm,  also  the 
loads  .at  joints  4  and  5,  and  6  and  7.  The  moments  about 
joint  1  will  then  be: 

(8,000  +  4,500  +  9,000)  =21 ,500X  12J  =    268,750  ft.-lbs. 
(8,000  +  4,500)  =12,500X25   =    312,500      " 

(8,000  +  4,500)  =12,500X37i=    468,750      " 

Total  moments  =  1,050,000  ft.-lbs. 

This  moment  must  be  balanced  by  the  supporting  force  P2, 
which  has  an  arm  equal  to  the  distance  between  Pl  and  P2, 
or  50  ft.  Knowing  the  arm  the  force  is  obtained  by  dividing 
the  total  moment  of  the  loads  by  the  span.  Dividing  1,050,000 
by  50  we  have  21,000  Ibs.  as  the  reaction  or  supporting  force 
at  joint  8,  and  Pl  must  equal  the  difference  between  the  sum 
of  the  loads  and  P2.  The  sum  of  the  loads  is  46,500  Ibs.,  and 
subtracting  21,000  we  have  25,500  as  the  value  of  Pr  We 
are  now  ready  to  draw  the  stress  diagram,  Fig.  38A.  First 
draw  a  vertical  line  oa  =Pi=  25,500 , Ibs.  From  a  and  o  draw 
lines  parallel  respectively  to  AE  and  OE,  which  gives  the  point 
e.  For  the  stress  lines  at  joint  2  we  measure  up  from  o  a 
distance  equal  to  the  load  at  that  joint,  13,500  Ibs.,  which 
gives  the  point  r,  and  from  e  and  r  draw  lines  parallel  to  EF 
and  RF,  which  intersect  at  /.  At  joint  3,  the  stress  polygon 
is  fe,  ea,  ab,  bg,  and  gf.  Draw  the  stress  polygons  for  joints  4, 
5,  and  6  in  the  order  in  which  they  are  numbered.  At  joint 
6  the  stress  polygon  is  ih,  he,  cd,  dj,  and  }%.  If  the  diagram 
has  been  correctly  drawn,  the  line  ij  will  be  just  equal  to  the 
load  at  joint  7.  The  stress  polygon  for  joint  7  is  te=4,500 
Ibs.,  si,  ij,  and  jt,  the  only  line  to  be  drawn  being  jt,  which 
must  be  parallel  to  JT,  consequently  j  must  be  exactly  oppo- 
site t,  or  the  polygon  will  not  close.  The  distance  dt  should  be 
equal  to  P2. 

In  this  example  we  have  taken  the  ceiling  and  roof  loads 
separately,  and  hence  the  full  stress  in  the  vertical  members 
is  shown  by  the  stress  diagram.  It  is  simpler,  however,  to 
add  the  ceiling  loads  (including  the  weight  from  the  gallery 
to  the  roof  loads)  and  then  draw  the  stress  diagram  as  though 
the  loads  were  applied  at  joints  3,  4,  and  6. 


1006 


STRESSES  IN  ROOF-TRUSSES. 


The   stress  diagram,   Fig.   38J5,   is  drawn   in   that  way.     In 
this    diagram   the   rods  EF  and  //  are  not  represented,  he- 
ft 


FIG.  38  A 


cause  they  have  no  stress  when  the  loads  are  all  at  the  top. 
In  drawing  Fig.  38B,  the  last   line  drawn  is   di,  which  must 


VERTICAL  LOADS  NOT  SYMMETRICAL.       1007 

start  from  d  and  be  parallel  to  JD.  If  it  does  not  pass  through 
the  point  i,  previously  found,  then  the  diagram  has  not  been 
correctly  drawn,  or  else  an  error  has  been  made  in  computing 
the  supporting  forces. 

Comparing  Figs.  38A  and  B,  it  will  be  seen  that  the  inclined 
lines  and  also  the  lines  representing  the  stresses  in  different 
parts  of  the  tie-beam  are  of  the  same  length  in. both  diagrams, 
but  the  line  gh  in  Fig.  385  is  less  in  length  than  the  corre- 
sponding line  in  Fig.  38A.  This  difference  should  be  just 
equal  to  the  load  at  joint  5,  consequently  if  we  draw  the  stress 
diagram  as  in  Fig.  38  £,  we  must  add  to  the  stress  obtained 
by  scaling  the  line  gh,  the  load  at  joint  5.  The  stresses  in 
the  rods  EF  and  1J  are  just  equal  respectively  to  the  loads 
at  joints  2  and  7,  as  the  only  purpose  of  these  rods  is  to  transmit 
the  loads  at  2  and  7  to  the  joints  above. 

Wlien  these  rods  are  inclined  from  a  vertical,  the  ceiling  loads 
must  be  treated  separately  as  in  Fig.  38A. 


FIG.  39 


EXAMPLE  25.— Fig.  39  is  the  diagram  of  a  wooden  roof  truss 
designed   by  the   author   for   a  certain    building.      The   actual 


1008 


STRESSES  IN  ROOF-TRUSSES. 


loads  were  about  as  given  on  the  diagram.  Purlins  occurred 
at  joints  3  and  5  only,  and  the  ceiling  below  was  suspended 
by  rods  from  joints  4  and  7,  joint  4  being  fixed  by  the  framing 
of  the  ceiling. 

The  moments  of  the  loads  about  joint  1  are: 

3,200  X  8J=  27,200  ft.-lbs. 

5,500Xl5i  =  85,250     " 

4,100X19   =  77,900     " 

5,500X24   =132,000     " 

Sum  of  moments  =322,350  ft.-lbs. 

Dividing  the  sum  of  the  moments  by  the  distance  between 
supporting  forces,  we  have  9,768  Ibs.  as  the  value  of  P2.  The 
sum  of  the  loads  is  18,300  Ibs.  Subtracting  9,768,  we  have 
8,532  as  the  value  of  Pr 

To  draw  the  stress  diagram  start  with  oa=  8,532  lbs.=P1, 


and  draw  ae  and  oe.    Assume  that  the  load  at  7  is  transferred 
to  joint  2,  then  the  stress  polygon  for  joint  2  is  ea,  ab,  bf,  and 


HOWE  TRUSSES  UNSYMM  ETHICALLY  LOADED.  1009 

fe.  At  joint  3  we  have  }b,  measure  down  &c  =  5,500  Ibs.,  and 
draw  eg  and  fg.  At  joint  4,  start  by  measuring  upwards  from 
o  4,100  Ibs.,  giving  point  o',  and  draw  gh  and  o'h.  At  joint  5 
we  have  hg,  gc,  measure  down  cd  =  5,500  Ibs.,  and  a  line  from 
d  drawn  parallel  to  DH  should  pass  through  h,  which  completes 
the  diagram.  The  stress  in  rod  2-7  will  be  the  load  at  joint  7. 

EXAMPLE  26. — Fig.  40  is  the  truss  diagram  of  another  truss 
used  in  the  same  building  as  the  truss  shown  by  Fig.  39.  Taking 
moments  about  joint  1,  we  have  for  the  sum  of  the  moments 
406,050  ft. -Ibs.,  and  dividing  by  33  ft.,  we  have  12,304  as  the 
value  of  P2.  The  sum  of  the  loads  is  28,600  Ibs.,  which  leaves 
16,296  Ibs.  for  the  value  of  P,. 

The  stress  diagram  is  drawn  in  the  same  manner  as  Fig.  39.A, 
starting  with  oa  =  Pr  ab  is  drawn  equal  to  the  sum  of  the 
loads  at  joints  2  and  3,  and  the  actual  stress  in  EF  is  3,400  Ibs. 
plus  the  length  of  the  line  ef.  If  the  stress  diagram  is  correctly 
drawn  a  line  through  d  parallel  to  KD  will  pass  through  the 
point  k,  previously  obtained.  The  character  of  the  stresses 
is  indicated  by  the  plus  and  minus  signs  on  Fig.  40,  +  denoting 
compression. 

If  we  compare  the  stress  diagrams  in  the  last  three  examples 
with  those  for  symmetrically  loaded  trusses  of  similar  shape 
we  shall  find  that  while  the  stress  diagrams,  Figs.  38^1,  39 A, 
and  4QA,  are  unsymmetrical,  they  are  of  the  same  general 
character,  and  the  stresses  are  all  of  the  same  kind  as  when 
the  supporting  forces  are  equal.  This  condition  holds  true 
for  most  triangular  trusses,  but  for  trusses  with  horizontal 
or  curved  chords,  unsymmetrical  loading  will  usually  cause 
a  reversal  of  the  stress  in  kind  in  one  or  more  of  the  braces 
or  verticals,  and  if  the  truss  contains  any  four-sided  panels 
an  additional  brace  will  generally  be  required.  This  is  par- 
ticularly true  of  the  Howe  truss,  and  as  this  truss  is  very  ex- 
tensively used  by  architects  and  builders,  we  will  now  con- 
sider at  some  length  the  effect  of  unsymmetrical  loading. 

Howe   Trusses  Un symmetrically  Loaded. 

When  a  Howe  truss  is  loaded  symmetrically  each  side  of  the 
centre,  all  of  the  braces  will  incline  downward  from  the  centre, 
as  in  Figs.  17-20,  Chap.  XXV,  and  if  there  are  an  odd  number 
of  panels,  the  centre  panel  will  need  no  brace. 

When  a  load  of  much  magnitude  is  placed  on  one  side  of  a 
truss  having  an  odd  number  of  panels  without  a  corresponding 


1010 


STRESSES  IN  ROOF-TRUSSES. 


load  on  the  other  side,  a  brace  will  always  be  required  in  the 
centre  panel  and  the  brace  should  incline  downward  from 
the  side  which  is  most  heavily  loaded. 

When  the  truss  has  an  even  number  of  panels,  an  unsym- 
metrical  load  will  cause  a  greater  stress  in  the  braces  on  one 
side  of  the  truss  than  on  the  other,  and  if  there  is  a  sufficient 
difference  between  the  loads  on  one  side  of  the  truss  from  those 
on  the  other,  it  will  cause  a  compression  stress  in  one  or  more 
of  the  rods  and  a  tensile  stress  in  one  or  more  of  the  braces. 
Now,  as  this  truss  is  especially  designed  with  the  idea  of  having 
the  braces  in  compression  and  the  verticals  in  tension,  when- 
ever the  loading  would  cause  tension  in  a  brace,  or  a  com- 
pression in  a  rod,  then  the  direction  of  the  brace  should  be 
reversed,  which  will  cause  it  to  be  in  compression  again. 

For  instance,  take  the  truss,  Fig.  41,  having  6  equal  panels 


FIG.  41 


and  loaded  with  4  tons  at  each  of  the  upper  joints  and  9  tons  at 
the  second  lower  joint.  Without  the  bottom  load  of  9  tons  the 
brace  in  the  third  panel  should  incline  downward  from  the 
centre  joint,  as  shown  by  dotted  line  at  B,  but  when  the  load 
of  9  tons  is  added  it  will  cause  a  tensile  stress  in  B  and  a  com- 
pression stress  in  R.  To  avoid  this,  the  direction  of  the  brace 
is  reversed  as  shown  by  the  full  line,  and  the  brace  is  then  in 
compression,  and  the  vertical  R  has  no  stress  except  the  direct 
load  of  9  tons.  The  same  thing  would  occur  if  the  load  of 
9  tons  was  applied  at  the  joint  directly  above,  instead  of  at 


FIG.  42 


the  lower  joint,  although  in  that  case  there  would  be  no  stress 
at  all  on  R,  except  the  weight  of  the  tie-beam.     If  the  load  of 


HOWE  TRUSSES  UNSYMMETRICALLY  LOADED.  1011 

9  tons  were  reduced  to  6  tons,  then  no  brace  at  all  would  be 
required  in  the  third  panel,  and  when  the  bottom  load  is  less 
than  6  tons,  then  a  brace  in  the  normal  direction  is  required, 
as  shown  in  Fig.  42. 

In  the  five-panel  truss,  shown  by  Fig.  43,  a  load  of  7.5  tons 
at  A  would  require  the  arrangement  of  braces  shown  by  the 
full  lines,  and  if  the  load  at  A  were  increased  to  more  than  15 
tons,  then  the  brace  R  would  need  to  be  reversed,  as  shown 
by  the  dotted  line. 


FIG.  4.3 


The  stress  diagram  will  always  show  in  which  direction  any 
brace  should  be  placed  to  be  in  compression,  but  it  may  also 
be  determined  by  the  following: 

Rule. — When  the  sum  of  the  loads  to  the  left  of  any  section 
taken  between  P,  and  the  centre  is  greater  than  the  reaction 
at  Plf  then  the  direction  of  the  brace  cut  by  that  section  must 
be  reversed  from  its  normal  direction.  When  the  sum  of 
the  loads  is  less  than  Pv  then  the  brace  should  be  in  its  normal 
position.  When  the  sum  of  the  loads  (to  the  left  of  the  section) 
is  just  equal  to  Plt  then  no  brace  at  all  will  be  required.  For 
example,  take  a  section  at  X,  Fig.  43;  here  the  sum  of  the 
loads  to  the  left  is  10.5,  which  is  less,  than  Pv  and  consequently 
the  brace  should  be  in  its  normal  direction. 

If  we  take  a  section  at  Y,  the  sum  of  the  loads  to  the  left 
is  13.5  or  greater  than  Pt;  hence  a  brace  will  be  required  slant- 
ing downward  from  the  heavier  loaded  side. 

Taking  a  section  at  X,  Fig.  41,  the  load  to  the  left  is  4,  which 
is  less  than  Pj  hence  the  brace  in  that  panel  should  be  in  its 
normal  position.  Taking  a  section  at  Y,  the  sum  of  the  loads 
is  greater  than  Pv  and  hence  the  brace  in  that  panel  must  be 
reversed. 

Taking  a  section  at  F,  Fig.  42,  the  sum  of  the  loads  to  the 
left  is  less  than  Pt;  hence  the  brace  should  be  in  its  normal 
position.  By  the  rule  above  given,  one  can  always  tell  in 
which  direction  the  brace  in  any  panel  should  be  placed,  no 


1012 


STRESSES  IN  ROOF-TRUSSES. 


matter  how  complicated  the  loading,  or  whether  or  not  the 
panels  are  of  equal  width;  but  to  apply  the  rule,  it  is  first  neces- 
sary to  determine  the  supporting;  forces,  which  can  be  done 
by  the  method  of  moments  explained  in  Example  24. 

EXAMPLE  27. — As  an  example  of  an  unsymmetrical  Howe 
truss  unsymmetrically  loaded,  we  will  take  the  truss  repre- 
sented by  the  diagram,  Fig.  44.  This  truss  is  supposed  to 
support  a  ceiling  over  a  hall,  a  flat  roof,  and  a  wooden  tower 
located  as  shown.  The  position  of  the  tower  necessitates  a 
division  of  the  panels  as  indicated,  so  that  the  truss  is  quite 
unsymmetrical. 

We  will  assume  that  the  weight  of  the  ceiling,  roof,  snow, 
and  tower  will  give  the  loads  at  the  upper  joints  indicated  by 
the  figures  which  are  supposed  to  represent  tons.  Multiplying 
each  load  by  its  distance  from  the  support  P2  and  adding 
together  the  products  we  have  1,475  foot-tons  as  the  total 
moment.  Dividing  by  the  distance  between  P^  and  P2  (62), 
we  obtain  23.8  as  the  value  of  Pr  The  total  load  is  45.5  tons; 
hence  P2  will  equal  21.7  tons. 


FIG.  44  A 


The  only  panels  of  this  truss  in  which  there  would  be  any 
question  as  to  the  direction  of   the  braces  are  the  third  and 


HOWE  TRUSSES  UNSYMMETRICALLY  LOADED.  1013 

fourth.  Taking  a  section  at  X,  the  sum  of  the  loads  to  the 
left  is  greater  than  Pjj  hence  the  brace  should  be  placed  as 
drawn.  A  section  taken  through  C  would  give  the  sum  of 
the  loads  to  the  left  less  than  Px,  and  hence  the  brace  should 
be  in  its  normal  position.  The  stress  diagram  of  this  truss 
is  readily  drawn,  starting  with  oa=Pl  and  going  from  joint 
to  joint  as  in  previous  examples.  The  completed  stress  dia- 
gram is  shown  by  Fig.  44/1.  To  the  stresses  on  the  verticals 
obtained  from  the  diagram  44A  should  be  added  the  ceiling 
loads  which  they  support. 

Counter  Braces. — These  are  extra  braces  that  are  put  in  a 
truss  to  counteract  the  effect  of  a  load  which  may  be  applied 
for  a  time  and  then  removed.  For  illustration,  let  us  consider 
the  truss  represented  by  Figs.  41  and  42.  Here  we  have  already 
seen  that  when  the  load  at  A  is  less  than  6,  the  brace  in  the 
third  panel  should  be  in  the  position  shown  by  Fig.  42,  while 
when  the  load  is  greater  than  6,  the  brace  should  be  in  the 
position  shown  by  the  full  line,  Fig.  41.  Now,  if  the  load  at 
A  represented  the  weight  of  a  gallery  with  people  in  it,  or  a 
hoist  for  raising  heavy  loads,  or  in  fact  almost  any  live  load, 
it  is  evident  that  when  the  live  load  was  absent  the  brace  in 
the  third  panel  would  need  to  be  in  its  normal  position,  and 
when  the  full  load  is  present  a  brace  is  needed  in  the  opposite 
direction,  and  as  it  is  not  practical  to  move  the  brace  to  suit 
the  condition  of  loading,  it  is  necessary  to  put  in  two  braces, 
only  one  of  which,  however,  would  come  in  action  at  any  given 
time. 

The  stresses  in  a  Howe  truss,  therefore,  that  are  subject  to  a 
variable  and  unsymmetrical  load  should  be  computed  for 
at  least  two  conditions  of  loading,  viz.:  a,  when  the  maximum 
load  is  applied;  and,  6,  when  the  variable  load  is  removed 
and  the  truss  proportioned  to  resist  both  conditions.  Snow 
is  a  variable  load,  to  which  such  trusses  are  often  subjected, 
but  as  it  is  nearly  uniformly  distributed  over  the  roof,  it  would 
not  change  the  stress  (in  kind)  in  any  of  the  members;  hence 
if  the  truss  is  designed  for  the  maximum  snow  load,  it  will 
be  more  than  strong  enough  when  there  is  no  snow.  More- 
over, the  transverse  strength  of  the  chords  is  usually  sufficient 
to  resist  any  slight  inequality  in  the  loading. 

The  principal  variable  loads,  therefore,  to  which  a  roof  truss 
may  be  subjected  that  would  require  counter  braces  are  those 
due  to  the  weight  of  people,  merchandise,  etc.,  these  either 


1014  STRESSES  IN   ROOF-TRUSSES. 

befog  suspended  from  the  truss  by  rods  or  brought  upon  the 
truss  by  a  floor  supported  by  the  tie-beam.  The  truss  shown 
in  Fig.  44  is  also  an  instance '  of  such  loading.  The  weights 
given  by  the  figures  indicate  merely  the  combined  dead  and 
snow  loads.  During  a  high  wind  the  weight  on  the  leeward 
side  of  the  tower  would  be  much  increased  and  lessened  on 
the  windward  side,  so  that  with  the  wind  blowing  from  the 
right,  the  load  at  4  would  be  much  greater  than  indicated, 
and  less  at  8,  while  with  the  wind  in  the  opposite  direction 
the  load  would  be  increased  at  8  and  lessened  at  4.  This  would 
require  counter  braces  in  both  the  third  and  fourth  panels. 

As  counter  braces  can  do  no  harm,  even  if  they  are  never 
brought  into  action,  it  is  always  well  to  use  them  in  the  centre 
panels  wherever  the  loads  are  at  all  variable. 

Simple  Cantilever  Trusses. 

Cantilever  trusses  may  be  considered  as  unsymmetrically 
loaded  trusses,  for  although  the  loads  may  be  symmetrical 
in  relation  to  the  truss,  they  are  usually  unsymmetrical  in 
relation  to  the  supports. 

The  method  of  computing  the  supporting  forces  and  drawing 
the  stress  diagram  is  quite  clearly  shown  by  the  following 
examples : 

EXAMPLE  28. — Fig.  45  is  the  diagram  of  a  cantilever  truss 
such  as  might  be  used  to  support  the  roof  over  a  grand-stand 
or  depot-platform,  and  could  be  constructed  either  of  wood 
or  steel,  although  steel  would  be  preferable. 

The  first  step  towards  determining  the  stresses  is  to  find 
the  supporting  forces. 

For  this  purpose  we  have  taken  the  panel  loads  at  1,000  Ibs., 
all  of  the  panels  being  of  equal  width,  as  this  illustrates  the 
method  as  well  as  actual  loads  and  simplifies  the  problem. 

In  cantilever  trusses  the  loads  at  the  ends  of  the  trusses 
should  be  taken  into  account  as  well  as  the  intermediate  loads. 
These  end  loads  are  each  equal  to  one  half  of  the  panel  loads. 

To  find  the  supporting  forces,  take  moments  about  joint  13. 
The  sum  of  the  moments  will  be  found  to  be  147,000  ft.-Ibs. 
This  moment  must  be  resisted  by  the  force  Pv  which  acts  with  a 
lever  arm  of  24'.  Dividing  147,000  by  24,  we  have  6,125  as 
the  value  of  Pv  and  as  the  total  load  is  7,000  Ibs.,  P2  must  be 
875  Ibs. 


SIMPLE  CANTILEVER  TRUSSES. 


1015 


The  stress  diagram  may  be  commenced  either  with  the  forces 
at  joint  1  or  those  at  joint  13,  but  as  we  have  commenced  at 
the  left  in  all  preceding  examples  we  will  continue  in  this  order. 

Commencing  then  with  joint  1,  we  lay  off  on  a  vertical  line 
the  load  oa  =  500  Ibs.,  which  acts  down,  and  from  o  and  a  draw 
lines  parallel  respectively  to  01  and  AI.  The  forces  act  from 
o  to  a,  a  to  i  (from  the  joint),  and  from  i  to  o  (towards  the  joint), 
showing  that  A I  is  in  tension  and  OI  in  compression,  the  re- 
verse of  a  truss  supported  at  both  ends. 

Next,  at  joint  2,  we  have  the  stress  ia,  and  measure  down 
a6  — 1,000  Ibs.;  then  draw  ij  and  bj,  IJ  being  in  compression. 


Next  draw  the  forces  for  joint  3 
and  for  the  remaining  joints  in 
the  order  in  which  they  are  num- 
bered. At  joint  6,  the  first  force 
which  we  know  is  the  supporting 
force  Pv  which  we  represent  by 
measuring  down  from  o,  6,125  Ibs. 
(although  the  force  acts  up),  giving 
the  point  o' .  The  polygon  of 
forces  will  then  be  o'o,  om,  mn, 
and  no'.  It  will  be  noticed  that 
the  stress  in  MN  is  equal  to  the 
supporting  force,  which  is  evident 
from  the  truss  diagram.  In  prac-  v< 
tice,  Pl  would  probably  be  a 
post,  which  would  be  continued 
to  the  apex  of  the  truss.  Jl 

At  joint  12  we  have  the  stresses  vu,  uf,  fg=  1,000  Ibs.,  and 


1016 


STRESSES  IN 


gv  must  close  the  polygon.  It  will  be  noticed  that  gv  acts 
toward  the  joint;  hence  the  rafter  in  the  end  panel  is  in  com- 
pression. If  a  line  drawn  from  g  parallel  to  the  rafter  passes 
through  v,  then  the  stress  diagram  must  be  correct;  if  it  does 
not  pass  through  v,  then  either  the  stress  diagram  has  not  been 
drawn  with  sufficient  accuracy  or  an  error  has  been  made 
in  computing  the  supporting  forces.  In  drawing  the  stress 
diagram  for  cantilever  trusses,  it  is  important  to  keep  the 

1000 


direction  in  which  the 
forces  act  in  mind  in 
order  to  tell  which 
members  are  in  com- 
pression and  which  in 
tension. 

EXAMPLE  29. — Fig. 
46  is  the  diagram  of 
a  truss  similar  in  out- 
line to  Fig.  45,  but 
with  the  diagonal 
braces  inclined  in  the 
opposite  direction,  so 
as  to  cause  them  to  be 
in  compression  and  the 
verticals  in  tension. 
The  supporting  forces 
are  found  in  the  same 
way  as  in  Example 
28,  and  the  stress  dia- 
gram is  also  drawn  in 
the  same  way  as  Fig.  45A.  In  this  truss,  however,  the  stress 


SIMPLE  CANTILEVER  TRUSSES.  1017 

in  the  vertical  post  MN  is  considerably  less  than  the  reaction  Pp 
because  a  large  portion  of  the  loads  is  transmitted  to  joint  6  by 
the  struts  LM  and  NR.  It  will  also  be  noticed  that  in  this  truss 
three  sections  of  the  rafter  on  the  right  side  are  in  compression 
and  three  sections  of  the  tie-beam  in  tension,  owing  to  the  fact 
that  in  this  truss  the  projection  of  the  overhang  in  proportion 
to  the  anchor  span  is  less  than  in  Fig.  45.  It  may  be  noticed 
that  when  the  stress  lines  pass  to  the  left  of  the  load  line  (Fig. 
46.4)  the  stresses  are  reversed  in  kind. 

This  truss  is  better  adapted  to  wooden  construction  (with 
vertical  rods)  than  is  the  truss  shown  by  Fig.  45. 

EXAMPLE  30  (FiG.  47) . — In  this  example  we  have  a  truss  with 
an  anchorage  at  the  outer  end  to  hold  it  down,  so  that  Pl  acts 
downward.  To  obtain  the  value  of  the  supporting  forces 
take  moments  about  joint  6  as  follows: 

Moments  of  loads  to  the  right  of  joint  7: 
(5X8)  +  (5X16)  +  (5X24)  +  (12.5X32)  =640,000  *  ft.-lbs. 
Moments  of  loads  to  the  left  of  joint  7: 

(2.5X24)  +  (5X16)  +  (5X8)  =180,000  ft.-lbs. 

As  these  moments  act  in  opposite  directions,  we  must  sub- 
tract the  smaller  from  the  larger,  and  we  have  an  unbalanced 
moment  of  640,000-180,000=460,000,  tending  to  turn  the 
truss  down  on  the  right  or  to  lift  the  left-hand  end.  This 
moment  must  be  resisted  by  the  reaction  Plf  which  has  an 
arm  of  24  ft.  Dividing  460,000  ft.-lbs.  by  24  ft.,  we  have 
19,250  Ibs.  as  the  reaction  at  P,,  or  it  will  require  a  weight 
of  this  amount  to  hold  the  truss  in  place. 

As  the  support  P2  must  resist  this  pull  as  well  as  the  loads, 
P2  will  equal  the  sum  of  the  loads  plus  the  pull  at  Pp  or  45,000 
+  19,250=64,250  Ibs. 

Having  obtained  the  value  of  the  supporting  forces  we  pro- 
ceed to  draw  the  stress  diagram  by  laying  off  on  a  vertical 
line  oa  =  19,250  Ibs.  =PV  remembering  that  it  acts  down.  The 
next  force  is  the  load  of  2,500  Ibs.,  which  also  acts  down,  and 
which  gives  the  point  6;  then  from  b  draw  a  line  parallel  to  BI 
and  from  o  a  line  parallel  to  01,  and  we  obtain  the  point  i. 


Note  that  loacjs  are  in  thousands  of  pounds. 


1018 


STRESSES  IN  ROOF-TRUSSES. 


bi  acts  from  the  joint  and  io  towards  it,  showing  that  BI  is 
in  tension  and  IO  in  compression.     The  remainder  of  the  stress 


— 8--4— 8--^— 8--^ sL 


$=  64,250 


Jc  n 


FIG.  47  A 


diagram  is  drawn  in  the 
same  way  as  diagrams 
Figs.  45 A  and  46A.  At 
joint  6  we  must  start  with 
the  force  P2,  which  acts 
up,  and  the  upper  end'  of 
which  must  be  at  o;  conse- 
quently we  obtain  o'  by 
measuring  down  from  o, 
64,250  Ibs.;  the  stress  poly- 
gon for  this  joint  being  o'o,  om,  mn,  and  no'.  After  we  have 
measured  off  gh=load  at  joint  13,  the  remaining  distance  ho' 
should  be  just  equal  to  the  load  at  joint  14,  or  12,500  Ibs.  If 
P!  and  P2  have  been  correctly  computed  and  the  stress  dia- 
gram accurately  drawn  the  points  s,  u,  and  w  will  come  in  the 
line  o'n. 


THREE-HINGED  ARCHED   TRUSSES.          1019 

In  the  last  three  examples  we  have  considered  vertical  loads 
only.  Cantilever  roof  trusses,  however,  should  always  be 
computed  for  wind  loads  as  well  as  for  vertical  loads  and  should 
be  braced  from  the  supports. 

Three-hinged  Arched  Trusses. 

Several  examples  of  this  type  of  truss  are  illustrated  in 
Chapter  XXV. 

For  computing  the  stresses  each  half  truss  is  considered  as 
an  entire  truss  itself.  Considering  the  half  arch,  Fig.  48,  it 
is  evident  that  a  horizontal  pressure  must  be  exerted  at  the 
top  to  prevent  the  arch  from  falling  down,  and  this  horizontal 
thrust  takes  the  place  of  one  supporting  force,  the  other  being 
exerted  on  the  bottom  pin.  In  the  actual  truss  this  hori- 
zontal thrust  is  provided  by  the  opposite  arch,  each  half  arch 
holding  up  the  other. 

In  accordance  with  the  mechanical  principle  that  for  a  body 
to  be  in  equilibrium  the  algebraic  sum  of  the  forces  acting 
in  any  given  direction  on  the  body  must  equal  zero,  to  main- 
tain the  half  arch,  Fig.  48,  in  equilibrium,  a  horizontal  resistance 
must  be  exerted  on  the  bottom  pin  equal  to  the  horizontal 
reaction  on  the  top  pin,  and  the  two  horizontal  forces  must 
act  in  opposite  direct  ons.  In  practice  the  horizontal  re- 
sistance at  the  bottom  is  usually  provided  by  rods  or  eye-bars 
connecting  the  pins  of  the  two  half  arches,  although  the  re- 
sistance may  be  provided  by  an  abutment  as  with  a  masonry 
arch. 

In  Fig.  48  the  horizontal  reactions  are  represented  by  the 
arrows  H,  H . 

The  vertical  stress  diagram  for  this  truss  is  very  readily 
drawn  after  the  reactions  are  determined.  These  reactions 
consist  of  a  vertical  resistance,  Pv  equal  to  the  entire  load  on 
the  half  arch,  and  a  horizontal  resistance  H.  To  compute  the 
horizontal  resistance,  obtain  the  algebraic  sum  of  the  moments 
of  the  loads  about  the  bottom  'joint  and  divide  by  the  vertical  dis- 
tance between  the  pins.  In  obtaining  the  sum  of  the  moments, 
those  which  tend  to  turn  the  truss  to  the  right  should  be  marked 
plus,  and  those  which  tend  to  turn  the  truss  to  the  left  minus. 

EXAMPLE  31. — The  moments  of  the  loads  in  Fig.  48  about 
the  bottom  pin  are  as  follows,  commencing  with  the  load  at 
joint  5. 


1020  STRESSES  IN  ROOF-TRUSSES. 

5001bs.X   3'  6"=  -1,750 

1,000  "  X   7'  6"  =+7,500 

1,000  "   X18'  §"=--  18,500 

1,000  "  X29'  6"  =   29,500 

1,000  "  X40'  6"  =  40,500 

1,000  "  X51'  6"  =  51,500 

1,000  "  X62'  6"  =  62,500 

1,000  "  X73'  6"  =  73,530 

Total  moment = 283,500  - 1 ,750  =  281 ,750 
#=281,7504-72.5=3,886,  or  say  3,890  Ibs. 
Pl=sum  of  the  loads  =7,500  Ibs. 

Having  obtained  Pl  and  H,  commence  the  stress  diagram 
by  drawing  the  vertical  line  oa=Pl  and  a  horizontal  line  from 
o  =  3,890.  The  stress  lines  for  the  bottom  joint  will  then  be 
so,  oa,  a/,  and  js.  Both  aj  and  js  act  towards  the  joint,  hence 
both  of  these  members  are  in  compression.  At  joint  1  the 
stress  lines  are  ja,  ak,  and  kj,  the  point  k  being  obtained  by 
drawing  a  line  from  /  parallel  to  JK.  At  joint  2  the  stress 
lines  are  sj,  jk,  kl,  and  Is.  jfc  and  kl  act  from  the  joint  and. 
Is  towards  the  joint,  hence  JK  and  KL  are  in  tension  and  LS 
in  compression. 

At  joint  3  the  stress  lines  are  Ik,  ka,  am,  and  ml,  am  acting 
from  the  joint,  showing  that  AM  is  in  tension.  At  joint  4 
the  stress  lines  are  si,  Im,  mn,  and  ns.  At  joint  5  we  have 
nm,  ma,  measure  down  a6=500  Ibs.,  and  draw  bp  and  np, 
parallel  respectively  to  lines  BP  and  NP.  Continue  in  the 
same  way  at  all  of  the  joints  in  the  order  in  which  they  are 
numbered.  In  this  example  the  point  c  happens  to  come  very 
close  to  the  point  k,  but  it  is  merely  a  coincidence.  The  line 
xy  is  also  very  short,  barely  long  enough  to  indicate  the  direc- 
tion in  which  the  stress  acts. 

At  joint  20  the  stress  lines  are  sd',  d'e',  and  e's.  Now  if 
the  horizontal  resistance  H  was  correctly  computed  and  the 
stress  diagram  has  been  drawn  with  great  accuracy,  a  line 
through  o  parallel  to  IE'  will  just  pass  through  e' '.  Owing 
to  the  fact  that  the  lines  of  the  truss  are  at  so  many  different 
angles,  it  is  more  than  likely  that  when  the  stress  diagram  is 
completed  the  line  oe'  will  not  quite  pass  through  e',  and  it 
may  be  necessary  to  go  over  the  diagram  a  second  time  with 
great  accuracy  to  make  it  come  out  right. 

In  drawing  the  stress  diagram  for  a  truss  of  this  kind  it  wil] 


THREE-HINGED  ARCHED  TRUSSES. 


1021 


be  necessary  to  keep  in  mind  the  direction  in  which  the  stresses 
act  at  each  joint,  in  order  to  tell  which  members  are  in  com- 
pression and  which  in  tension,  as  a  slight  change  in  the  pro- 


-11-0     >n     1-1-0 

I 
I 

1 

I 


L-l-O^Uk — l-i-o"  ^     1-lV-  >k    1-1-0— 

*l        J 


portions  of  the  arch  or  the  location   of  the  joints  may  change 
the  character  of  the  stress  in  the  braces. 

EXAMPLE  32. — Fig.  49  represents  the  truss  diagram  of  one 
of  the  three-hinged  arches  used  in  the  Liberal  Arts  Building 
of  the  Columbian  Exposition  at  Chicago,  1893,  the  diagram 
being  taken  from  one  published  in  the  Engineering  Record  of 
July  9,  1892.  The  trusses  were  spaced  50  feet  apart,  with 
trussed  purlins  supported  at  every  other  joint,  as  shown  by 


1022 


STRESSES  IN  ROOF-TRUSSES. 


the  arrows,  Fig.  49.  The  horizontal  roof  area  supported  at 
each  of  joints  11,  15,  19,  etc.,  was  therefore  50'X38',  or  1900 
square  feet.  The  dead  load  was  assumed  at  42  Ibs.  per 
horizontal  square  foot  (snow  12  Ibs.,  steel  and  wood  30  Ibs.), 
which  multiplied  by  950  gives  the  loads  indicated  for  joints  11, 


lO-O'-^r-lO-O— »k-19-0— ^-19-0^-4-19-0-^-1^0-^ 


|  g, 

^|— --J-- {-  —  - f|---- 

'ift: 


H  =  171,000  '       STRESS  DIAGRAM 


J 


-t- 


FIG.  40 


15,  etc.  The  loads  at  joints  9  and  26  would  obviously  be  one 
half  of  the  loads  at  intermediate  joints.  There  are  also  dead 
loads  at  joints  1  and  5,  due  to  the  weight  of  outside  walls  and 
galleries.  The  total  moments  of  the  loads  about  the  bottom 
joint,  remembering  that  the  moments  for  the  loads  at  joints  1, 
5,  and  7  are  negative,  is  35,158,500  Ibs. 

Dividing  this  moment  by  the  vertical  distance  between  pins 
(206'  4"),  we  have  170,400  Ibs.,  or  say  171,000. 

The  sum  of  the  loads  is  457,750  lbs.=Pr     The  stress  dia- 


THREE-HINGED  ARCHED  TRUSSES. 


1023 


gram  is  drawn  in  the  same  way  as  explained  for  Fig.  48A,  and 
presents  no  difficulties  except  in  drawing  the  lines  exactly 
parallel  to  the  corresponding  members  of  the  truss.  It  will 
be  noticed  that  the  line  UU  has  no  stress  because  there  is  no 
load  or  other  force  to  produce  a  stress  where  it  joins  the  rafter. 
It  was  doubtless  inserted  to  stiffen  the  rafter  between  joints  9 
and  11.  The  character  of  the  stress  in  the  different  members 
is  indicated  by  the  plus  and  minus  signs,  +  in  all  cases  de- 
noting compression.  It  will  be  noticed  that  the  stress  in  AJ 
and  JK  is  very  small  under  a  dead  load,  due  to  the  inclination 
of  A  J  and  JS.  In  the  stress  diagram  published  in  the  Engineer- 
ing News,  the  line  aj  comes  on  the  other  side  of  the  load  line, 
the  difference  being  due  either  to  the  truss  diagram,  Fig.  49, 
not  being  exactly  right  or  possibly  to  what  appears  to  be  an 
additional  load  at  joint  o.  It  will  be  noticed  that  if  the  line 
JS  was  but  a  very  little  steeper  it  would  bring  the  point  /  on 
the  other  side  of  the  load  line.  The  stress  diagram  in  Fig.  49 
is  correct  for  the  truss  as  drawn  and  for  the  loads  given. 

Necessity  for  Determining  Wind  Stresses  in  Three-hinged 
Arches. — The  stresses  produced  by  the  wind  in  trusses  of  this  kind 
will  in  many  instances  greatly  exceed  those  due  to  the  dead  load, 
and  will  also  in  many  cases  be  of  the  opposite  kind,  so  that  it 
is  absolutely  necessary  to  compute  stresses  for  the  wind  in 
both  directions  (see  pages  1024  and  1029).  To  show  how  the 
stresses  vary  for  dead  and  wind  loads,  we  give  below  the  stresses 
for  several  members,  as  published  in  the  Engineering  Record: 


Member. 

Dead  Load. 

Wind  Left. 

Wind  Right. 

AJ 

-    11,000 

+  290,000 

-  78,000 

JS 

+  498,000 

-228,000 

+  183,000 

JK 

+     2,500 

-  86,000 

+   24,000 

BK 

-   34,000 

+  277,000 

-   75,000 

KL 

-168,000 

+  208,000 

-   97,000 

LS 

+  612,000 

-389,000 

+  254,000 

LM 

+   95,000 

-119,000 

+   55,000 

With  wind  to  the  right,  piece  AJ  would  have  a  total  tensile 
stress  of  89,000  Ibs.,  and  with  wind  from  the  left  a  compressive 
stress  =  290,000 -11, 000,  or  279,000  Ibs.  Piece  LS  would  be  sub- 
ject to  a  compressive  stress  of  866,000  Ibs.  when  wind  is  from 
the  right  and  223,000  Ibs.  when  wind  is  from  the  left. 


1024  STRESSES  IN  ROOF-TRUSSES. 

Wind  Load  Stresses. 

Thus  far  we  have  considered  the  stresses  due  to  vertical 
loads  only,  the  pressure  of  the  wind  being  combined  with  the 
dead  load  and  considered  as  acting  vertically.  For  triangular 
and  Fink  trusses  this  method  is  sufficiently  accurate,  as  the 
wind  pressure  never  causes  a  maximum  stress  in  excess  of  that 
obtained  by  the  method  explained  in  connection  with  the 
foregoing  examples.  For  trusses  with  curved  chords,  and 
in  fact  for  almost  all  forms  of  steel  trusses  except  the  Fink 
and  fan  types,  it  is  not  safe  to  consider  wind  pressure  as  acting 
vertically,  because  the  wind  acts  in  a  direction  at  right  angles 
to  the  roof  surface,  and  upon  but  one  side  of  the  roof  at  a  given 
time,  thus  loading  the  truss  unsymmetrically  and  often  causing 
stresses  of  an  opposite  kind  from  those  produced  by  a  vertical 
load.  Braces  which  are  inactive  under  a  vertical  load  may 
therefore  be  necessary  to  resist  the  force  of  the  wind  or  the 
total  stress  due  to  wind  and  vertical  load  combined  may  be 
greater  than  it  would  be  if  the  wind  pressure  were  considered 
as  a  vertical  load.  To  design  a  roof  truss  correctly,  therefore, 
it  is  necessary  to  determine  the  stresses  due  to  vertical  loads 
and  wind  loads  separately  and  then  combine  them  so  as  to 
get  the  greatest  stress  that  may  be  produced  under  any  probable 
conditions. 

In  the  calculation  of  trusses  with  curved  chords  it  is  the  usual 
practice  to  find  the  stresses  for  the  following  different  loadings 
and  then  combine  them  to  obtain  the  maximum  stress: 

Stresses  due  to  wind  on  the  side  of  the  truss  nearer  the  ex- 
pansion end,  and  for  the  wind  on  the  side  of  the  truss  nearer 
the  fixed  end. 

Stresses  due  to  permanent  dead  load. 

Stresses  due  to  snow  covering  the  entire  roof  or  only  one 
half,  and  even  in  special  cases  only  a  small  area  on  one  side. 

It  is  generally  assumed  that  the  maximum  wind  pressure 
and  the  snow  load  can  not  act  on  the  same  half  of  the  truss  at 
the  same  time.  Fig.  50  (from  " Modern  Framed  Structures"), 
which  is  a  half  diagram  of  the  roof  trusses  of  the  St.  Louis 
Exposition  Building,*  shows  the  different  stresses  as  figured 
for  those  trusses.  All  loads  and  stresses  are  given  in  thousands 
of  pounds.  The  letters  in  connection  with  the  stresses  have 
the  following  significance: 

jD,  permanent  dead  load  at  20  Ibs.  per  square  foot;  S,  uniform 

*   Erected  saveral  years  ago. 


WIND  LOAD  STRESSES. 

& 


1025 


•— ao'o- 


--15;0- 

—  —  — t.  — .  _  _ 

^>3.7 


* 


&          Jj 

— lO.-TlS^ i>i 

-_- iag 


1026  STRESSES   IN  .ROOF-TRUSSES. 

snow  load  at  20  Ibs.;  SL,  snow  load  on  left  side  only;  SR,  snow 
load  on  right  ride  only;  WF,  wind  from  fixed  end;  WR,  wind 
from  roller  end.  The  total  maximum  stresses  are  marked 
M  (for  each  kind). 

In  the  table  on  p.  1023  is  given  the  stresses  in  a  few  of  the 
members  in  the  three-hinged  arch,  Fig.  49,  due  to  vertical 
load,  and  wind  left  and  right. 

For  trus  es  w'.th  straight  rafters  it  will  generally  be  sufficient 
to  find  the  stresses  due  to  permanent  dead  load,  and  to  the 
wind  from  both  directions,  disregarding  the  snow  load  when 
the  pitch  of  the  roof  is  45°  or  greater.  For  the  Northern  States 
when  the  pitch  is  less  than  30°  it  is  well  to  consider  that  a 
heavy  sieet  may  be  on  both  sides  of  the  roof  at  the  time  of  a 
heavy  w'nd  and  to  add  about  10  Ibs.  per  square  foot  of  roof 
surface  to  the  dead  load  to  a  low  for  sleet. 

In  localities  where  heavy  snowfalls  may  be  expected  the 
stresses  due  to  fu'.l  snow  load  should  also.be  found,  as  these 
combined  with  the  permanent  dead  load  may  exceed  those 
due  to  dead  load,  sleet,  and  wind  pressure. 

Wind.  Stress  Diagrams. — These  are  affected  by  the 
manner  in  which  the  truss  is  supported.  If  both  ends  of  the 
trus  are  fixed,  the  wind  reactions  are  parallel  to  the  resultant 
wind  load;  if  one  end  is  free  to  move,  i.e.  on  rollers  or  supported 
on  a  rocker,  the  reaction  at  the  roller  end  is  vertical  and  that 
at  the  fixed  end  will  be  inclined.  "If  one  end  be  fixed  and 
the  other  merely  supported  upon  a  smooth  iron  plate,  the 
reaction  at  the  free  end  may  have  a  horizontal  component 
equal  to  the  vertical  component  multiplied  by  the  coefficient 
of  friction,  which  is  about  one-third." 

Wooden  trusses  may  be  considered  as  fixed  at  the  ends. 

Steel  trusses,  when  supported  on  masonry  walls,  should  have 
one  end  fixed  and  the  other  free  to  move  and  when  the  span 
exceeds  70  feet  the  free  end  should  be  supported  on  rollers  to 
permit  of  expansion  or  contraction. 

When  steel  trusses  are  supported  by  steel  posts,  as  in  steel 
mill  buildings,  the  trusses  are  rigidly  attached  to  the  columns 
and  no  provision  is  made  for  expansion.  In  such  buildings 
the  wind  pressure  produces  a  bending  strain  in  the  columns 
which  must  be  provided  for. 

EXAMPLE  33. — To  draw  the  wind-stress  diagram  for  a  truss 
with  fixed  ends.  Wind  pressure  is  usually  assumed  to  be  applied 
uniformly  over  one  side  of  the  roof  and  to  act  at  right  angles 


WIND  LOAD  STRESSES. 


1027 


to  the  surface  of  the  roof.  The  joint,  or  panel,  loads  will  therefore 
be  proportional  to  the  roof  areas  supported.  When  the  joints 
divide  the  rafter  into  panels  of  equal  length,  then  the  joint 
loads  will  be  uniform,  except  for  the  joints  at  the  edges  of 
the  roof.  The  actual  wind  pressure  is  obtained  by  multiplying 
the  roof  surface  by  the  values  given  in  Table  IX. 

For  this  example  we  will  take  the  triangular  truss  shown  in 
outline  by  Fig  51  and  assume  that  the  span  and  spacing  of 
the  truss  are  such  as  will  give  a  load  of  1,000  Ibs.  at  joints  2 
and  4.  The  loads  at  joints  1  and  5  would  be  only  one  half  of 
those  at  2  and  4. 

To  find  the  supporting  forces  or  reactions,  draw  a  line  repre- 
senting the  resultant  of  the  loads,  cutting  the  bottom  chord 
at  X.  As  the  loads  are  symmetrical  the  resultant  must  act 
at  the  centre  of  the  rafter  and  at  right  angles  to  it. 

The  reactions  will  be  proportional  to  the  two  segments  into 
which  a  horizontal  line  joining  the  points  of  support  is  divided 
by  the  resultant,  or  in  this  case  to  IX  and  X7,  the  larger  re- 
action being  at  joint  1.  The  sum  of  the  reactions  must  be 
equal  to  the  sum  of  the  loads.  To  find  the  reactions  graph- 
ically, draw  a  line  from  joint  1,  at  any  angle,  say  from  30°  to 
45°,  and  measure  off  a  distance  equal  to  the  total  load. 

In  Fig.  51  the  line  1-8  represents  3,000  Ibs.  Join  7  and  8, 
and  from  X  draw  a  line  parallel  to  7-8,  intersecting  1-8  at  X'. 


FIG.  51  A 


Then  X'-8  will  be  the  reaction  at  joint  1  and  X'-l  the  reaction 
at  joint  7. 

To  draw  the  stress  diagram,  Fig.  51  A,  first  draw  the  load 
line  ae  equal  to  the  sum  of  the  loads  (in   this  case   3,000  Ibs.) 


1028  STRESSES  IN  ROOF-TRUSSES. 

and  perpendicular  to  the  rafter  1-5,  and  divide  it  so  that  ao 
=X/-8.  Then  at  joint  1  we  have  oa  equals  the  supporting 
force,  a&=500  Ibs.,  and  from  b  and  o  di-aw  lines  parallel  re- 
spectively to  BF  and  OF,  intersecting  at  /.  The  stresses 
act  in  the  direction  oa,  ab,  bf,  and  /o,  showing  that  BF  is  in 
compression  and  FO  in  tension. 

At  joint  2  the  stress  lines  are  fb,  be  — 1,000  Ibs.,  eg,  and  gf. 
The  stress  lines  at  joint  3  are  of,  fg,  gh,  and  ho.  At  joint  4, 
hg,  gc,  cd,  di,  and  ih.  At  joint  5,  id,  de,  ek,  and  ki.  (Note.  If 
the  load  line  has  been  correctly  divided  at  o,  and  the  stress 
lines  drawn  exactly  parallel  to  the  lines  of  the  truss,  the  point 
k  will  be  exactly  above  the  point  i.) 

At  joint  6  the  stress  lines  are  oh,  hi,  ik,  and  as  the  figure 
must  close  by  a  horizontal  line  through  o,  it  is  evident  that 
the  line  KK  of  the  truss  diagram  cannot  be  represented,  and 
therefore  there  can  be  no  stress  in  this  member  when  the  wind 
is  from  the  left.  At  joint  7  we  have  the  reaction  eo,  acting  up, 
ok  and  ke  must  close  the  figure,  showing  that  the  line  ke  repre- 
sents the  stress  in  the  entire  length  of  the  rafter  to  the  right, 
and  that  there  is  no  stress  in  the  bracing  on  that  side  of  the 
truss  when  the  wind  is  from  the  left.  If,  however,  either  the 
lower  tie  or  the  rafter  were  not  straight,  some  of  the  braces  on 
that  side  would  come  into  action. 

By  following  the  direction  of  the  stresses  in  Fig.  51.4,  it 
will  be  found  that  the  different  members  of  the  truss  have 
the  same  kind  of  stress  as  is  produced  by  a  vertical  load. 

As  the  wind  may  blow  from  either  direction,  it  is  evident 
that  both  sides  of  the  truss  must  be  made  alike. 

This  example  illustrates  the  method  of  drawing  the  stress 
diagram  for  any  truss  with  a  straight  rafter  when  both  ends 
of  the  truss  are  fixed. 

EXAMPLE  34. — To  draw  the  wind-stress  diagrams  for  a  truss 
having  one  end  fixed  and  the  other  end  on  rollers.  When 
one  end  of  the  truss  is  free  to  move,  the  reaction  at  that  end 
must  always  be  practically  vertical,  and  this  condition  gives 
a  considerable  variation  of  stress  when  the  wind  is  on  different 
sides  of  the  roof,  so  that  it  is  necessary  to  draw  two  wind- stress 
diagrams,  one  for  wind  from  the  left,  marked  WL,  and  one 
for  wind  from  the  right,  marked  WR.  It  is  customary  with 
authors  when  writing  on  this  subject  to  consider  that  the  rollers 
are  always  under  the  right-hand  support,  and  we  shall  follow 
this  custom.  In  practice  the  rollers  may  be  placed  under 


WIND  LOAD  STRESSES. 


1029 


either  end,  as  both  sides  of  the  truss  are  usually  proportioned 
to  the  maximum  stresses. 

For  this  example  we  will  take  the  same  truss  diagram  that 
was  used  in  Fig.  51,  illustrating  it  again  in  Fig.  52,  which  is 
drawn  to  show  wind  from  the  left.  Lay  off  the  load  line  1-8 
and  divide  it  at  X't  as  in  Example  33,  and  draw  a  line  at  aet 


R       1000 


W.R. 


perpendicular  to  the  rafter  and  equal  to  1-8,  and  divided  in 
the  same  proportions.  Through  xr  on  ae  draw  a  horizontal 
line,  and  through  e  a  vertical  line,  the  two  intersecting  at  o. 
Then  eo  will  represent  the  vertical  reactions  at  joint  7  and 
oa  the  reaction  at  joint  1. 

The  stress  lines  at  joint  1  are:  oa,  a6=500  Ibs.,  &/,  and  Jo. 
At  joint  2:  fb,  be,  eg,  and  gf.  The  remainder  of  the  diagram 
(WL}  is  completed  exactly  as  described  for  Fig.  51  A,  the  only 
difference  in  the  two  diagrams  being  in  the  location  of  point  o, 
which  increases  the  stress  in  the  tie-beam. 


1030  STRESSES  IN  ROOF-TRUSSES. 

Fig.  53  represents  the  same  truss  with  wind  from  the  right. 
To  draw  the  stress  diagram  WR,  start  with  td,  perpendicular 
to  the  rafter  and  equal  to  the  total  load  (3,000  Ibs.).  Divide 
the  line  at  x'  in  the  same  proportion  as  the  line  1-8,  Fig.  52,  the 
longer  portion  being  at  the  top.  To  find  the  reactions  draw  a  hori- 
zontal line  through  x'  and  a  vertical  line  through  t,  the  two  lines 
intersecting  at  o.  Then  ot  is  the  reaction  at  joint  10,  and  od.the 
reaction  at  joint  1.  For  this  diagram  it  will  be  better  to  start 
with  joint  10  and  take  the  forces  in  the  reverse  order  from  that 
in  which  we  have  taken  them  before.  The  stress  lines  for  joint  10 
are  ot,  ts  =  500  Ibs.,  sn,  and  no.  At  joint  9,  ns,  sr,  rm,  and  mn. 
At  joint  8,  on,  nm,  ml,  and  lo.  At  joint  7,  Im,  mr,  re,  ek,  and  kl. 
At  joint  5,  ke,  ed,  di,  and  ik.  (Note  that  if  the  work  has  been 
correctly  done  the  point  i  will  come  exactly  above  the  point  k.) 

Comparing  the  two  figures  WL  and  WR,  we  see  that  the 
stress  lines  for  the  rafter  and  braces  are  of  the  same  length 
(and  also  of  the  same  kind)  in  both  diagrams,  but  that  the 
stress  in  the  tie-beam  is  considerably  less  with  wind  from  the 
right.  This  condition  does  not  apply  to  all  trusses,  however, 
so  that  it  is  best  to  draw  the  stress  diagrams  for  wind  from  both 
directions. 

EXAMPLE  35. — Wind-stress  diagram  for  wooden  queen-rod 
truss.  Fig.  54  represents  the  outline  of  a  queen-rod  truss 
for  a  roof  having  a  rise  of  14J"  in  12".  As  the  truss  is  of  wood 
we  will  consider  the  supports  fixed.  Joint  2  divides  the  rafter 
into  two  equal  parts,  consequently  the  wind  load  at  this  joint 
will  be  twice  that  at  joints  1  or  4.  For  convenience  we  will 
assume  that  the  wind  load  at  joint  2  is  1,000  Ibs.,  and  at  joints 
1  and  4,  500  Ibs.  The  resultant  will  be  2,000  Ibs.  and  will  act 
through  joint  2  and  intersect  the  tie-beam  at  X.  To  find  the 
supporting  forces,  draw  the  line  1-8=2,000  Ibs.  and  connect  7 
and  8.  From  X  draw  a  line  parallel  7-8  intersecting  1-8  at 
X'.  Then  X'-&  is  the  supporting  force  at  joint  1  and  1-X' 
the  supporting  force  at  joint  7. 

Begin  the  stress  diagram  (Fig.  54 A)  by  drawing  the  line 
ad  at  right  angles  to  the  rafter  1-4,  and  equal  in  length  to  1-8. 
By  means  of  dividers  locate  the  point  o  so  that  ao  will  equal 
X'-8.  Then  the  stress  lines  for  joint  1  will  be  oa,  ab,  be,  and  eo. 
At  joint  2,  eb,  be,  cf,  and  fe.  At  joint  3,  oe,  ef,  fh,  and  ho.  At 
joint  4,  hf,  fc,  cd,  dk,  and  kh.  It  wi.l  be  seen  that  we  cannot 
close  the  figure  at  joint  4  without  the  brace  hk,  because  we 
started  at  ht  and  a  horizontal  line  through  d  will  not  pass  through 


WIND   LOAD   STRESSES. 


1031 


h.  Therefore  a  queen-rod  truss  requires  braces  in  the  centre 
panel  to  resist  the  wind  stress.  With  the  wind  from  the  right, 
a  brace  will  be  required  from  joint  3  to  joint  6. 


FIG.  54 


At  joint  5  the  stress  lines  are  oh,  hk,  klt  and  lo.  It 
should  be  noticed  that  lo  acts  towards  the  joint,  showing  that 
OL  is  in  compression.  At  first  it  would  seem  as  though  this 
could  not  be  true,  but  if  we  glance  at  joint  7  we  see  that  Pl 
is  thrusting  in  on  the  joint,  and  that  a  strut  is  required  to 
keep  the  joint  in  position.  This  condition  is  true  only  when 
the  inclination  of  the  rafter  is  greater  than  45°.  When  the 
inclination  of  the  rafters  is  exactly  45°,  -there  will  be  no  stress 
in  OL,  and  when  the  inclination  is  less  than  45°,  OL  will  be 
in  tension. 

The  stress  lines  for  joint  6  are  Ik,  kd,  and  dl.  If  no  errors 
have  been  made,  a  line  through  d  parallel  to  DL  will  just 
pass  through  the  point  I,  previously  obtained.  A  very  slight 
inaccuracy  in  getting  the  point  X',  or  in  drawing  the  stress 
diagram,  however,  w'll  cause  the  line  through  d  to  pass  to 
one  side  or  the  other  of  point  /,  and  if  this  happens,  it  shows  that 
there  has  been  some  inaccuracy  somewhere.  In  practice,  a 
slight  divergence  will  not  materially  affect  the  stresses.  At 
joint  7  the  stress  polygon  is  ol,  Id,  and  do=Plt  the  lines  being 
already  drawn. 

EXAMPLE  36. — For  the  purpose  of  showing  how  the  stresses 
due  to  wind  and  vertical  loads  are  combined  we  will  take  the 
truss  diagram  shown  by  Figs.  55  and  56,  being  the  same  as 
shown  by  Fig.  12,  and  representing  the  truss  shown  by  Fig.  3. 


1032 


STRESSES   IN  ROOF-TRUSSES. 


We  will  first  determine  the  stresses  due  to  the  weight  of  the 
roof  and  ceiling  and  an  allowance  of  10  Ibs.  per  square  foot 
for  sleet. 

On  page  954  the  roof  area  supported  at  joint  2  was  found 
to  be  147J  sq.  ft.,  and  at  joint  3,  200  sq.  ft.  On  page  953  the 
weight  of  the  roof  was  estimated  at  12|  Ibs.  per  square  foot, 
and  allowing  10  Ibs.  for  sleet,  we  have  22  f  Ibs.  as  greatest  dead 
load  under  a  heavy  wind,  which  gives  3,360  Ibs.  for  the  load 
at  joint  2  and  4,550  Ibs.  for  the  load  at  joint  3.  The  ceiling 
loads  would,  of  course,  be  the  same  as  in  Fig.  12. 

Fig.  55  shows  the  loads  due  to  weight  of  materials  and  sleet 

IJI8    CeUingJLpad    ff5<> 
82pO  ^8200" 

C  L 


FIG.  55  A 


as  computed  above,  the  ceiling  loads  being  added  to  the  roof 
loads  for  convenience  in  drawing  the  stress  diagram.  Fig.  55 A 
is  the  stress  diagram  for  these  loads,  with  the  stresses  indicated 
by  figures.  (This  diagram  is  drawn  exactly  in  the  same  way 
as  the  stress  diagram  in  Fig.  12.) 

Wind  Stresses. — The  inclination  of  the  roof  is  very  close  to 
45°,  and  from  Table  VIII  we  find  the  normal  wind  pressure 
for  that  angle  to  be  27  Ibs.  Multiplying  the  roof  area  at  joints 
2  and  3  by  27,  we  have  the  wind  loads  indicated  in  Fig.  56. 
We  must  also  figure  the  wind  load  at  joint  1.  The  roof  area 
supported  at  this  joint,  allowing  17  ins.  for  eave  projection  (see 
Fig.  3)  is  6J'X15'=95  sq.  ft.  which  would  make  the  wind  load 
2,565  Ibs.  The  next  step  will  be  to  find  the  point  at  which 
the  resultant  of  these  loads  would  cut  the  rafter.  As  the  loads 


WIND  LOAD  STRESSES. 


1033 


are  not  symmetrical  or  uniform  on  the  rafter,  we  must  obtain 
the  point  through  which  the  resultant  would  act  by  means 
of  moments  about  joint  1.  The  arms  of  the  loads  at  joints  2 
and  4  are  figured  on  the  truss  diagram  (Fig.  56).  The  moments 
are 

3,990 X  9T5S  =  37,572 

5,400X18i  =  98,550 

Total  moment  =  136,122  ft.-lbs. 

The  resultant  will  be  the  sum  of  all  the  loads,  or  11,955  Ibs., 
and  the  distance  of  its  point  of  application  from  1  is  found 
by  dividing  the  total  moment  by  the  resultant,  136,122 
divided  by  11,955  =  11.4  ft.  Measuring  off  11.4  ft.  on  the 
rafter  from  joint  1  and  drawing  a  line  at  right  angles  to  it 
intersecting  the  tie-beam  we  obtain  the  point  X.  From  1 
draw  the  line  1-8  at  any  angle  equal  in  length  to  the  sum  of 
the  loads,  11,955  Ibs.,  and  connect  7  and  8.  From  X  draw  a 
lice  parallel  to  7-8,  intersecting  1-8  at  X'.  Then  X'-&  will 
be  the  supporting  force  at  joint  1. 


FIG.  56  A 


Supporting  Forces  Computed  by  Moments. — The  supporting 
forces  can  also  be  computed  by  moments.  The  moments  of 
the  loads  about  joint  1  tend  to  rotate  the  truss  from  left  to 
light.  To  prevent  this  rotation  we  have  the  supporting  force 
Pt  acting  at  joint  7.  To  just  maintain  equilibrium,  the  mo- 
ment of  Pl  about  joint  1  must  just  equal  the  moments  of  the 
loads  about  the  same  point,  which  we  found  above  to  be 


1034 


STRESSES   IN   ROOF-TRUSSES. 


136,122  ft.  Ibs.  The  arm  of  Pt  is  the  perpendicular  distance 
between  its  line  of  action  and  joint  1.  Continuing  Pt  above 
the  truss  we  obtain  the  dotted  line  at  p,  and  the  distance  from 
1  to  p  is  26.5  ft. 

Knowing  the  arm,  the  value  of  P^  is  obtained  by  dividing 
the  moments  of  the  loads  136,122  by  the  arm,  or  26.5  ft ,  which 
gives  5,137  Ibs.  As  the  sum  of  P  and  P±  must  equal  the  total 
load,  P  =  ll,955-5,137  =6,818.  The  distance  l-X'  and  X'-& 
should  scale  reasonably  close  to  these  figures.  Knowing  the 
Lupporting  forces,  the  stress  diagram,  Fig.  56A,  is  drawn  exactly 
as  described  for  Fig.  54A.  As  the  inclination  of  the  rafters  is 
a  little  greater  than  45°,  OL  is  in  compression,  but  the  stress 
is  very  small.  The  figures  on  Fig.  56 A  indicate  the  stresses 
in  pounds.  We  are  now  prepared  to  tabulate  the  stresses, 
which  should  be  done  as  in  the  following  table. 

In  tabulating  the  wind  stresses,  it  should  be  remembered 
that  the  wind  may  blow  against  either  side  of  the  truss,  and 
the  greatest  stress  liable  to  occur  should  be  put  in  the  table. 


STRESSES  FOR  TRUSS  (Fias.  12,  55,  AND  56). 


Member.* 

Dead  Weight 
and  Sleet. 

Wind 

Stresses. 

Total. 

Stresses 
(Fig.  12). 

A-E 

+  16,150 

+  4,900 

+  21,050 

+  25,640 

B-F 

+  13,800 

+  4,900 

+  18,700 

+  21,400 

C-K 

+   9,600 

+  3,400 

+  13,000 

+  14,900 

E-F 

+   2,350 

+  3,950 

+    6,300 

4,400 

H-K 

0 

+  5,000 

+    5,000 

0 

F-H 

-   5,410 

-3,550 

-   8,960 

-   6,900 

E-0 

-11,200 

-5,900 

-17,100 

-17,800 

H-0 

-   9,600 

-3,250 

-12,850 

-14,900 

*  Members  are  lettered  according  to  Fig.  56. 

Thus  the  stress  in  the  rafter  LC  is  greater  than  in  the  rafter 
on  the  other  side,  and  this  stress  acts  through  the  entire  length 
of  the  rafter;  hence  the  stress  for  AE  and  BF  should  be  entered 
as  4,900  Ibs.  (the  stress  hi  LC).  In  the  same  way  the  stress 
in  the  rod  KL  is  greater  than  in  FH;  hence  the  stress  in  KL 
should  be  tabulated.  The  stress  in  LO  would  slightly  reduce 
the  tension  due  to  dead  load,  but  as  the  stress  in  EO  increases 
it,  the  stresses  in  EO  and  HO  should  be  tabulated. 

Both  sides  of  the  truss  shoud  of  course  be  made  alike,  and 


WIND  LOAD  STRESSES.  1035 

two  braces  should  be  inserted  in  the  centre  panel.  In  the 
fifth  column  of  the  table  we  have  given  the  stresses  due  to  the 
ceiling  load  and  a  vertical  load  on  the  roof  of  42|  Ibs.  per  square 
foot,  as  obtained  from  the  stress  diagram,  Fig.  12.  Comparing 
the  stresses  in  the  fourth  and  fifth  columns,  we  see  that  except 
for  the  brace  EF,  and  for  the  two  rods,  the  stresses  obtained 
by  combining  snow  and  wind  and  adding  to  the  dead  weight 
are  greater  than  the  totals  due  to  wind,  dead  weight,  and  sleet. 
Vertical  loads,  of  course,  give  no  stress  for  the  braces  in  centre 
panel,  and  unless  the  wind  stresses  are  drawn,  it  will  be  neces- 
sary to  guess  at  the  sizes  of  these  braces.  The  stress  in  these 
braces,  however,  is  so  small  that  it  will  not  require  a  very 
large  piece  of  timber. 

The  stresses  given  in  the  fourth  column  are  unquestionably 
nearer  what  the  real  stresses  are  likely  to  be  than  those  in 
the  fifth  column.  If  the  roof  were  to  be  erected  in  a  warm 
climate  where  there  would  be  no  sleet,  then  these  stresses 
could  be  further  reduced  by  omitting  the  10  Ibs.  per  square 
foot  added  for  sleet. 

If,  on  the  other  hand,  the  inclination  of  the  roof  was  less 
than  30°,  the  stresses  produced  by  a  heavy  fall  of  snow  with- 
out wind  will  generally  exceed  the  sum  of  those  due  to  dead 
weight,  sleet,  and  wind,  and  for  such  roofs  the  stresses  due 
to  maximum  snow  load  should  always  be  computed. 

Reactions. — It  will  be  noticed  that  the  reactions,  or  supporting 
forces  in  Fig.  56,  are  very  much  inclined  from  a  vertical.  As 
the  dead  load  is  always  acting  on  the  truss,  however,  the  real 
reaction  would  never  have  such  an  inclination,  but  would  be 
more  nearly  vertical,  and  when  there  is  no  wind  the  reactions 
will  be  exactly  vertical.  The  theoretical  reaction,  due  to 
both  wind  and  dead  load,  will  be  the  diagonal  of  a  parallelo- 
gram formed  with  the  reactions  for  dead  and  wind  loads  as 
two  of  its  sides.  Thus  if  7 -a,  Fig.  56,  represents  P,  at  a  smaller 
scale,  and  7-6  the  vertical  reaction  to  the  same  scale,  then 
PR  will  be  the  resultant  reaction,  which  will  be  modified  some- 
what by  friction. 

Examples  33,  K4,  and  35  serve  to  show  the  general  method 
of  drawing  wind-stress  diagrams,  and  are  sufficient  to  enable 
the  student  to  draw  those  diagrams  for  most  trusses  with 
straight  rafters.  For  trusses  with  curved  rafters  the  diagrams 
become  more  complicated,  and  the  reader  is  referred  to"  Graph- 
ical Analysis  of  Roof  Trusses/'  by  Prof.  Charles  E.  Greene, 


1036  STRESSES  IN   ROOF-TRUSSES. 

also  to  "  Steel  Mill  Buildings,"  by  Prof.  Milo  S.  Ketchum,  for 
explanations  regarding  wind-stress  diagrams  for  such  trusses. 
The  latter  work  also  takes  up  in  detail  stress  diagrams  for 
trusses  supported  and  braced  from  steel  columns,  and  will 
be  found  of  valuable  assistance  in  designing  steel  mill  buildings. 


MEMBERS  OF  WOODEN  TRUSSES.  1037 


CHAPTER  XXVII. 
ROOF-TRUSSES  (Continued), 

Proportioning   the  Members  and  Detailing   the 
Joints. 

Proportioning  the  Members  to  the  Stresses. — The 

size  or  sectional  area  of  the  different  members  of  a  truss  cannot 
be  proportioned  with  any  accuracy  until  the  stresses  which 
the  maximum  loads  will  produce  have  been  found.  When  the 
stresses  are  known,  however,  the  size  of  the  truss  members 
can  be  readily  computed  by  the  rules  and  tables  for  the  strength 
of  materials. 

Every  member  of  a  truss  must  be  either  a  tie  or  a  strut.  If 
either  is  also  subject  to  a  transverse  load,  as  is  often  the  case 
with  rafters  and  tie-beams,  then  the  member  becomes  a  tie-beam 
or  strut-beam  according  as  it  is  in  tension  or  compression.  We 
therefore  have  four  kinds  of  members  (regardless  of  material) 
to  be  considered  in  trusses,  viz.,  simple  ties,  simple  struts; 
tie-beams  and  strut-beams. 

Rules  and  data  for  computing  the  sectional  area  of  simple 
ties  of  any  shape  or  material  are  given  in  Chapter  XI.  Struts 
may  be  computed  by  the  rules  and  tables  given  in  Chapter  XIV, 
and  directions  for  proportioning  steel  tie-  and  strut-beams 
to  the  load  and  stress  are  given  on  pages  511  and  512,  and  for 
wooden  strut-  and  tie-beams  on  pages  568  and  569. 

To  more  fully  show  the  application  of  the  rules,  however, 
we  will  compute  the  size  of  members  for  three  or  four  trusses. 

EXAMPLE  1. — To  compute  the  size  of  the  members  in  the 
truss  shown  by  Fig.  1. 

This  is  the  same  truss  as  is  represented  by  Figs.  3,  12,  55, 
and  56  of  Chapter  XXVI. 

For  the  stresses  we  will  use  those  given  in  the  fourth  column 
of  the  table  on  p.  1034,  and  which  are  tabulated  below.  The 
members  RR  are  to  be  wrought-iron  rods,  not  upset,  and  all 
other  members  are  to  be  of  a  good  quality  of  white  pine. 


1038 


TRUSS   MEMBERS  AND  JOINTS. 


None  of  the  members  of  this  truss  are  subject  to  a  trans- 
verse strain,  so  that  we  have  to  consider  only  simple  ties  and 
simple  struts. 


Rafters 
16'fO..O. 


xl2" 

i"J 


Fig.  I 


Rods. — The  tension  in  each  of  the  two  rods  (see  table  below) 
is  8,960  Ibs.  As  a  considerable  portion  of  the  stress  is  due 
to  wind -pressure  we  can  safely  use  a  unit  stress  of  12,500  Ibs. 
to  the  square  inch.  From  the  table  on  p.  340  we  find  that 
the  safe  strength  of  a  1J"  rod,  not  upset,  at  12,500  Ibs.  to  the 
square  inch  is  8,570  Ibs.,  and  of  a  1J"  rod  11,060  Ibs.  The 
1J"  rod  is  not  quite  strong  enough  and  we  will  use  a  1J"  rod, 
or  we  might  use  a  1J"  steel  rod. 

STRESSES   AND  DIMENSIONS  FOR   TRUSS  I. 


Member. 

Stress.,  Lbs. 

Dimensions. 

A 

+  21,050 

6X8,  white  pine 

B 

+  18,700 

6X8,  white  pine 

C 

+  13,000 

6X8,  white  pine 

D 

+   6,300 

4X6,  white  pine 

E 

+   5,000 

4x6,  white  pine 

N 

-17,100 

3  2"X8"  f"  bolts,  2'  centre  to  centre 

M 

-12,850 

3  2"X8"  J"  bolts,  2'  centre  to  centre 

R 

-  8,960 

1   y  rod,  wrought  iron,  not  upset 

MEMBERS  OF  WOODEN  TRUSSES.  1039 

Rafter.— The  stress  in  the  rafter  is  21,050  Ibs.  at  A  and  18,700 
Ibs.  at  B,  but  as  it  should  be  of  the  same  size  for  its  entire  length 
we  will  proportion  it  to  the  stress  at  A.  The  clear  length 
between  joints  is  about  9  ft.  From  the  table  for  white-pine 
posts,  p.  412,  we  see  that  a  6X8  timber  is  more  than  strong 
enough,  while  a  6X6  is  hardly  sufficient.  We  will  therefore 
make  the  rafter  6X8. 

Strut-beam  (C).— The  stress  in  this  member  is  13,000 
Ibs.  and  it  is  about  12  ft.  long  between  bearings.  From  the 
same  table,  p.  412,  we  see  that  a  6X6  timber  would  do  for  this 
member,  but  on  account  of  making  a  better  joint  we  will  make 
it  of  the  same  size  as  the  rafter,  or  6X8. 

Braces. — The  stress  in  the  brace  D  is  6,300  Ibs.  From 
the  table,  p.  412,  we  see  that  a  4x6  timber  will  have  ample 
strength.  The  stress  in  the  braces  EE  is  5,000  Ibs.  and  the 
length  about  17  ft.  As  the  braces  stiffen  each  other  at  the 
intersection,  however,  we  can  safely  make  them  4"X6",  notch- 
ing each  brace  1  in.  where  they  pass,  so  that  the  total  thick- 
ness at  the  intersection  will  be  6",  and  bolting  them  together 
with  a  J"  bolt  in  a  J"  hole  to  give  a  little  play.  Brace  D  had 
better  be  set  flatways  and  the  braces  E  edgeways. 

Tie-beam. — The  maximum  tension  in  the  tie-beam  is 
12,850  Ibs.  The  tensile  strength  of  white  pine  is  given  on  p.  322 
at  1,400  Ibs.  per  square  inch,  therefore  the  tie-beam  must  have 
a  net  sectional  area  at  N=  12,850-^-1,400  or  9.2  sq.  ins.  A 
2"X6"  plank  if  continuous  from  end  to  end  of  the  truss  and 
without  holes  would  therefore  resist  the  stress,  but  to  make 
good  joints  with  the  rafters  and  braces,  the  tie-beam  must  be 
as  wide  as  the  rafters. 

We  must  also  allow  for  the  holes  where  the  rods  pass  through 
and  for  a  slight  notch  at  joints  7  and  8.  A  6X6  timber  in 
one  length  will  have  ample  strength,  but  as  this  may  be  diffi- 
cult to  obtain,  we  can  build  it  up  of  three  2"X8"  planks  bolted 
together,  using  24-ft.  and  14-ft.  lengths  and  lapping  the  long 
pieces  so  that  there  will  be  10  ft.  between  the  joints. 

The  centre  planks  will  be  cut  so  nearly  in  two  by  the  rods 
that  they  will  have  little  strength,  and  the  stress  in  the  centre 
will  practically  have  to  be  borne  by  one  plank. 

The  planks  should  be  bolted  together  by  f "  bolts  2  ft.  on  centres. 
We  now  have  the  dimensions  for  all  members  of  the  truss,  and 
they  should  be  entered  in  the  table  opposite  the  stresses. 

Note.     In  this  example  we  have  an  excess  of  strength  in  the 


1040 


TRUSS  MEMBERS  AND  JOINTS. 


timber,  but  as  none  of  the  timbers  are  large,  nothing  to  speak 
of  would  be  gained  by  trying  to  cut  them  down.  When  the 
stresses  are  four  or  five  times  as  great  as  in  this  truss,  requiring 
large  timbers,  then  the  size  may  be  figured  more  closely,  as  the 
cutting  at  the  joints  is  not  as  much  in  proportion  to  the  sec- 
tional area  in  large  timbers  as  in  small  ones. 

EXAMPLE  2. — For  this  example  we  will  take  the  truss  shown 
by  Fig.  2,  which  is  the  same  truss  as  is  shown  by  Figs.  4  and 
24  of  Chapter  XXVI.  The  stresses  produced  by  a  vertical  dead 
load  of  42J  Ibs.  per  square  foot  of  roof  for  wind  and  snow  are 
figured  on  the  stress  diagram,  Fig.  24A,  Chapter  XXVI,  and 
reproduced  in  the  following  table. 

The  rafters  and  tie-beams  of  this  truss  also  sustain  a  trans- 
verse load  which  is  uniformly  distributed.  In  computing  the 
joint  loads  for  this  truss  (see  Example  3,  Chapter  XXVI), 
we  allowed  12  Ibs.  per  square  foot  for  the  weight  of  the  ceiling, 
which  will  give  the  transverse  loads  for  S  and  B  indicated  in 
the  following  table. 

The  transverse  loads  for  the  rafters  A  and  B  are  figured  at 
42J  Ibs.  per  square  foot. 

STRESSES   AND  DIMENSIONS  FOR  TRUSS  2. 


Member. 

Stress,  Ibs. 

Dimensions,  Material 
White  Pine. 

A 

j  Compression,  8,000 
{  Transverse,      1,000 

[2  if'xs" 

B 

(  Compression,  6,600 
}  Transverse,      1,320 

j-2    If'xS" 

D 

Compression,  1,890 

1    2X8 

E 
F 

Compression,      750 
Tension,           4,350 

1    2X8  or  2X10 

2    1X8 

H 

Tension,           2,530 

2    1X6 

S 

(Tension,           1,875 
1  Transverse,         470 

ll    2X10 

T 

j  Tension,           5,400 
(  Transverse,         384 

j-1    2X8 

TI 

Tension,           1,875 

1    2X8 

We  will  assume  that  the  truss  is  to  be  built  of  a  good  quality 
of  white  pine,  spiked  and  bolted  at  the  joints. 

Rafter. — The  compression  in  the  bottom  of  the  rafter  A 
is  greater  than  at  B,  but  as  the  length  of  B  is  considerably 
greater  than  A,  and  the  transverse  load  is  also  greater  on  B 


MEMBERS  OF    WOODEN  TRUSSES. 


1041 


if  the  rafter  is  strong  enough  to  resist  the  strains  at  B,  it  will 
be  strong  enough  to  resist  those  at  A. 


Fig.  2 

We  will  first  find  the  dimensions  necessary  to  resist  the  trans- 
verse load.  As  the  rafter  is  inclined  its  strength  as  a  beam 
is  considerably  greater  than  if  horizontal;  we  therefore  will 
use  for  the  span  9  ft.,  which  is  about  an  average  of  the  real  length 
and  the  horizontal  projection. 

To  support  1,320  Ibs.  with  a  span  of  9  ft.  will  require  a 
lf"X8"  joist  (formula  11,  p.  564).  Considering  the  re- 
sistance to  compression,  it  should  be  remembered  that  the 
sheathing  is  nailed  to  the  rafters,  and  hence  they  cannot  bend 
sideways.  The  depth  of  the  rafter  can  therefore  be  considered 
as  the  breadth,  so  that  the  ratio  of  length  to  breadth  will  be 
i|i  =  18  (the  clear  distance  between  the  joints  should  be  taken 
for  the  length  as  a  strut). 

By  formula  (5),  p.  410,  we  find  that  the  safe  resistance  for  a 
white-pine  strut  with  a  ratio  of  length  to  breadth  of  18  is 
517  Ibs.  per  square  inch,  hence  it  will  require  13  sq.  ins.  to 
resist  6,600  Ibs.  This  is  equivalent  to  If  X8.  Therefore  two 
pieces  each  lf"X8"  will  be  strong  enough  for  the  rafters. 


1042  TRUSS  MEMBERS  AND  JOINTS. 

Tie-beams. — These  should  preferably  be  of  single  planks 
spiked  between  the  rafters. 

The  transverse  load  on  S  is  470  Ibs.  and  the  span,  say,  15'  6". 
Assuming  a  depth  of  10  ins.  the  breadth,  from  formula  (11), 
p.  564,  should  be  f  in.,  or  a  j"XlO"  board  would  support  the 
transverse  load.  The  sectional  area  required  to  resist  the 
tension  equals  }fj§  or  less  than  1J  sq.  ins.;  hence  a  1J''X10" 
board  will  be  strong  enough  for  S,  but  it  would  not  be  stiff 
enough  to  resist  the  compression  at  E,  so  we  will  make  it  2"  X 10". 

For  T  we  will  try  a  depth  of  8  ins.,  as  the  piece  is  inclined 
and  the  span  is  not  as  great.  The  transverse  load  is  384  Ibs. 
and  we  will  call  the  span  12  ft.  Then  with  a  depth  of  8  ins. 
we  shall  require  a  breadth  of  f". 

To  resist  the  tension  we  shall  require  a  sectional  area  =f|JJ, 
or  3£  sq.  ins.,  equivalent  to  about  J"X8";  therefore  a  2"X8" 
plank  will  answer  for  T  and  7\. 

We  will  now  see  if  it  will  answer  for  D.  As  this  piece  is 
free  to  bend  in  either  direction  we  must  divide  the  length,  in 
inches,  by  2,  to  get  the  ratio  of  length  to  breadth.  The  length 

is  about  86  ins.,  therefore  ^-  =  43.    The  safe  resistance  per  square 

inch  of  a  white-pine  strut  for  this  ratio  is,  formula  (5),  p.  410, 
367  Ibs. ;  hence  we  shall  require  a  little  more  than  5  sq.  ins.  to 
resist  1,890  Ibs.  A  2X8  strut  is  therefore  ample. 

Ties  F  and  H. — For  F  we  shall  require  a  sectional  area 
=  f  Jf  g,  or  3J  sq.  ins.,  and  for  H  f £§§,  or  1.8  sq.  ins.  As  it  would 
be  impossible  to  secure  the  ends  of  such  small  pieces,  we  will 
make  the  tie  F  of  two  lX8's  and  HH  of  two  lX6's,  so  as  to 
have  plenty  of  room  for  nailing. 

(Note.  Wooden  ties  must  always  be  much  larger  than  the 
sectional  area  required  by  the  formula  for  tension,  to  provide 
means  for  making  a  satisfactory  joint.)  We  have  now  com. 
puted  the  dimensions  for  all  parts  of  the  truss,  as  indicated 
in  the  table.  By  continuing  the  boards  F  to  the  tie  S,  so  as 
to  shorten  the  span,  we  could  reduce  S  to  2"X8". 

EXAMPLE  3. — For  this  example  we  will  take  the  Howe  truss, 
shown  by  Fig.  3.  The  trusses  are  supposed  to  be  uniformly 
spaced  15'  8"  centre  to  centre  and  the  rafters  and  ceiling  joists 
span  from  truss  to  truss  and  rest  directly  on  the  chords. 

Allowing  30  Ibs.  for  snow  and  6  Ibs.  for  tar  and  gravel  roofing, 
the  dead  load  per  square  foot  of  roof  will  be  46 J  Ibs.,  and  for 
the  ceiling  we  will  allow  16  Ibs.  per  square  foot.  This  would 


MEMBERS  OF  WOODEN  TRUSSES. 


1043 


make  the  roof  load  5,885  Ibs.  at  joint  2  and  5,704  Ibs.  at  joints 
4  and  6.  The  ceiling  load  at  joint  3  would  be  1,984  Ibs.  and 
at  joints  5  and  7  1,968  Ibs.  Fig.  4  shows  the  dimensions  of 
the  truss  on  centre  lines,  the  loads  and  the  stresses  that  would 
be  produced  thereby. 

The  figures  above  the  chord  lines  preceded  by  the  letter  W 
denote  the  transverse  loads.  All  loads  and  stresses  are  in 
pounds. 

Rods. — The  diameter  of  the  rods  may  be  found  directly  by 
means  of  Table  III,  p.  340.  We  will  assume  that  they  are  to  be 
of  wrought  iron,  not  upset,  and  allow  a  unit  stress  of  12,500  Ibs. 
per  square  inch.  Then  from  ihe  table  (p.  140)  we  see  that  it 
will  require  a  If"  rod  at  joint  2,  a  1"  rod  at  joint  4,  and  a  TV' 
rod  at  the  centre.  As  the  last,  however,  would  look  very  light 
we  will  make  it  f"  in  diameter. 


Fig.  3 

Top  Chord, — The  load  on  one  of  the  centre  spans  of  the 
top  chord  is  5,704  Ibs.  and  the  span  is  about  7J  ft.  Assuming 
a  depth  of  10  ins.  we  find  the  breadth  required  to  resist  this 
load  (by  formula  (11),  p.  564,  the  wood  being  white  pine) 


Fig.  4 

=  3.7  ins.  The  compression  in  the  centre  panels  is  43,260  Ibs. 
From  Table  V,  p.  412,  we  see  that  a  10"XlO"  post  8  ft.  long 
will  support  62,500  Ibs.  Therefore  to  support  43,260  Ibs.  will  re- 


1044  TRUSS  MEMBERS  AND  JOINTS. 

quire  a  7"X  10"  timber.  Adding  together  the  thickness  require.] 
for  the  transverse  load  and  for  the  compressive  stress,  we  have 
10. 7"  X 10"  as  the  required  size,  which  will  require  using  a 
12"X10"  timber.  As  the  timber  will  be  stronger  if  placed  ver- 
tically, we  will  make  the  top  chord  10"  X  12",  and  build  it  of 
five  2"X12"  planks,  bolted  together.  Between  the  end  joints 
and  the  wall  the  chord  can  be  reduced  to  6"X12". 

Tie-beam. — The  transverse  load  on  centre  panel  is  1,968  Ibs. 
Assuming  a  depth  of  10  ins.,  it  will  require  a  thickness  of  1J" 
to  sustain  the  transverse  load.  To  resist  the  direct  tension  will 

require  a  net  sectional  area=  i  7r)rr  =  35  sq.  iris.,  or  3J"XlO". 

Between  the  joints  this  must  be  increased  by  1J"  to  resist  the 
transverse  strain,  so  that  a  beam  4|"X10"  is  the  least  that 
would  answer  for  a  solid  tie-beam,  i.e.,  a  single  stick  of  timber. 
As  it  would  be  impracticable  to  obtain  such  a  timber  in  most 
localities,  it  will  be  best  to  build  the  beam  of  2"X10"  planks 
bolted  together,  and  on  account  of  the  reduction  in  net  area 
due  to  splicing,  it  will  be  necessary  to  use  at  least  five  planks 
so  that  the  tie-beam  will  be  10"XlO".  Even  then  it  will  be 
necessary  to  lay  out  the  beam  with  care,  so  as  to  get  the  re- 
quired strength  between  the  end  joints  of  the  planks.  See 
p.  1058. 

Braces. — As  the  chords  are  to  be  10  ins.  wide,  the  braces 
1-2  and  3-4  should  be  of  the  same  width.  Brace  5-6  may 
be  reduced  to  8  ins.  wide.  The  length  of  the  braces  is  about 
9  ft,  From  Table  V,  p.  412,  we  see  that  a  6X10  is  not  quite 
strong  enough  for  the  outer  brace,  and  is  a  little  stronger  than 
necessary  for  the  second  brace.  Therefore  we  will  use  a  10"  X  8" 
timber  for  brace  1-2  and  a  10  X  6  for  brace  3-4.  For  the  inner 
braces  a  3X6  would  answer,  except  that  it  would  not  give 
sufficient  support  to  the  top  chord,  and  it  will  therefore  be 
better  to  use  either  an  8X4  or  an  8X3  timber. 

Proportioning1  the  Members  of  Steel  Trusses. 

EXAMPLE  4. — Fig.  5  is  the  diagram  of  one  half  of  a  light  steel 
truss  built  some  years  ago  for  supporting  the  roof  of  a  machine- 
shop  in  New  York  State.  The  trusses  were  spaced  8  ft.  centre 
to  centre.  The  roof  consisted  of  3''  plank,  spiked  to  a  3X6 
bolted  to  the  rafters  of  the  truss,  and  covered  with  a  patent 
roofing  similar  to  ruberoid.  The  actual  weight  of  the  roof 


MEMBERS  OF  STEEL  TRUSSES. 


1045 


is  therefore  very  small,  but  as  it  is  quite  steep  it  would  be  well 
to  allow  40  Ibs.  per  square  foot  of  roof  surface  for  obtaining 
the  stresses.  As  the  roof  area  supported  at  each  joint  is  49J 
sq.  ft.,  this  would  make  the  panel  loads  1 ,973  Ibs.,  or  say  2,000  Ibs. 
The  stresses  due  to  these  loads  are  indicated  on  the  diagram, 
Fig.  5.  For  a  roof  construction  such  as  this,  it  is  more  eco- 
nomical to  divide  the  rafter  into  uniform  panel  lengths,  as  in 
Fig.  5.  When  this  is  done,  the  stresses  in  the  four  web-braces, 
as  BD  and  GL,  are  equal,  also  in  the  two  ties  DE  and  EL,  so 
that  it  is  only  necessary  to  compute  the  size  for  one  strut  and 
one  tie. 

As  the  stresses  in  the  rafters  are  comparatively  small,  it 
will  also  be  more  economical  to  make  the  rafter  of  the  same 
section  for  its  entire  length. 

The  tie-beam  we  will  make  of  one  section  from  A  to  F,  and 
reduce  it  in  the  center  panel. 

For  convenience  in  computing  the  size  of  the  members  we 
will  tabulate  the  maximum  stresses  for  the  different  members, 
omitting  duplicates,  also  the  length  of  the  members. 

(Note.  In  figuring  length  of  struts,  some  reduction  can  be 
made  from  the  exact  distance  between  joints,  on  account  of 
the  riveting.)  As  the  section  of  the  ties  is  not  affected  by  the 
length,  the  latter  is  omitted  for  those  members. 


STRESSES  AND   SIZES   (Fia.  5). 


Member. 

Stress,  Lbs. 

Ap. 
Length, 
Inches. 

Net  Area 
of 
Section 
Re- 
quired.* 

Section  Selected. 

A  -F 

—  16,900 

Sq.  Ins. 
1.13 

2,  2^X2Xi  L's    Net  area  1  76 

F-M 

-    9,200 

0.55 

sq.  ins. 
2    2X2Xi  L's.     Net  area  1  52 

F-K 

—  7  700 

0  52 

sq.  ins. 
1    2  X  2  X  i  L         Net  area  076 

D-E 

—   3  070 

0  21 

sq.  in. 
1    2X2Xi  L         Net  area  0  76 

A-K 

+  20,200 

72 

sq.  in. 
2,  2X2Xi    L's.       1     10"  Xi" 

2,000t.  1. 

web-plate      r  —  31 

B-D 

+    1,900 

72 

1,  2X2Xi    L      r  —  039       Safe 

E-F 

+   5,000 

144 

strength  4,000  Ibs. 
2,  2X2Xi  L's      Cross-  section 

r  =  0.94.  Safe  stgth.l  0,980  Ibs. 

*  At  15,000  Ibs,  per  square  inch. 


1046 


TRUSS  MEMBERS  AND  JOINTS. 


Dimensions  of  Tension  Members. — For  these  mem- 
bers we  can  safely  use  a  working  strength  of  15,000  Ibs.  per 
square  inch  of  net  section.  Dividing  the  stresses  by  15,000  Ibs., 
we  obtain  the  required  net  sectional  areas  given  in  the  fourth 
column  of  our  table.  We  must  next  select  angles  having  a 
sectional  area  slightly  in  excess  of  these  figures. 


For  the  main  tie,  AF,  it  is  necessary  to  use  two  angles  in 
order  to  make  satisfactory  joints.  For  AF,  then,  we  will  use 
two  angles  each  having  a  sectional  area  slightly  in  excess  of 

1  13 

—^—,  or  .57  sq.  in.     The  sectional  areas  for  angles  of  all  sizes 
z 

are  given  on  pp.  302-311.  On  p.  311  we  find  that  a  2//X2//XTV 
angle  has  a  sectional  area  of  .72,  which  would  be  large  enough 
for  our  purpose,  but  it  is  a  good  rule  not  to  use  anything  less 
than  J"  in  thickness,  and  for  the  principal  tie  of  a  truss  two 
2J"X2"Xi"  angles  are  about  the  least  that  should  be  used; 
therefore  we  will  use  that  joint  for  the  tie  from  A  to  F.  From 
F  to  the  corresponding  joint  on  the  other  side  we  will  use  two 
2"  X2"Xi"  angles. 

For  the  ties  FK,  DE,  and  EL  we  will  use  single  2"X2"Xi" 
angles.  (Note.  A  2"X2"  angle  is  the  smallest  size  that  it  is 
practicable  to  use  in  roof-trusses,  although  they  are  frequently 
used  only  fg"  thick.) 

The  sizes  of  angles  selected  and  the  net  sectional  areas  should 
be  put  in  the  table,  The  net  sectional  area  is  obtained  by 


MEMBERS  OF  STEEL  TRUSSES.  1047 

subtracting  from  the  area  given  in  the  tables  the  amount  cut 
out  by  one  rivet-hole,  which  may  be  obtained  from  Table  I, 
on  p.  640.  For  this  truss,  as  the  members  are  all  small,  we  will 
use  f  "  rivets. 

Compression  Members.  —  For  the  main  rafter  we  will  use 
two  angles  and  a  web-plate,  as  in  Fig.  6,  as  this  is  an  economical 
section  for  »  strut-beam,  and  a  good  section  for  making  joint 
connections. 

We  will  proportion  the  section  so  that  the  plate  will  be 
capable  of  resisting  the  transverse  strength  and  the  angles  the 
compressive  stress. 

We  will  assume  a  depth  for  the  plate  of  10  ins.  and  find  the 
necessary  thickness.  This  may  be  computed  by  the  same 
formula  as  given  for  wooden  joists,  formula  (11),  p.  564,  using 
888  Ibs.  for  A.  The  transverse  load  on  each  panel  is  2,000  Ibs. 

6'  X  2  000 

Then  ^==2X1QOX888=='07  m'}  °T  leSS  than  T^;  but  Jt  would 
not  do  to  use  a  plate  less  than  J  in.  thick,  therefore  we  will 
make  the  web-plate  10"X}". 

To  find  the  size  of  angles  required  to  resist  the  compressive 
stress,  we  must  assume  some  size,  then  find  the  radius  of  gyra- 
tion of  the  entire  section,  and  then  the  strength  as  a  strut. 

To  find  the  radius  of  gyration,  we  must  first  find  the  centre 
of   gravity   of   the   section,    then   the   moment 
of  inertia,  and  finally  the  radius  of  gyration. 

The  distance  X  of  centre  of  gravity  from  axis 
AB  (see  p.  240) 

=  area  of  plate  X  d"  +  area  of  both  angles  Xd' 
area  of  entire  section 

As   the   stress   in   the    rafter  is    comparatively 

small  we  will  try  2"x2"Xi"  angles,  having  a  total  area  of 

1.88  sq.  ins. 

The  distance  d  we  find  from  the  table,  p.  311,  to  be  .59,  so 
that  d'=10-.59  =  9.41".  d",  of  course,  =5".  Then  x= 

—  —  6.9.     The  moment  of  inertia  of  the  section 


about  C—  g  is  found  by  the  rule  on  p.  282,  as  follows: 


Moment  for  plate  1        12 

2.5X1.  92=9.025 


1048  TRUSS  MEMBERS  AND  JOINTS. 

.  t  j       2X   .35  (p.  311)  =     .70 

Moment  for  angles  j  1>88x2-51,  =  1L84 

Moment  for  entire  section  =42.36 

The  radius  of  gyration  is  found  by  dividing  the  moment  of 

inertia  by  the  area  of  the  section  and  taking  the  square  root 

of  the  quotient  (see  p.  289).    42.36  divided  by  the^area  of  the 

section=9.67,  and  the  square  root  of    this  is  3.1  =  r.     As    the 

I     72 
length  of  each  section  of  rafter  may  be  taken  as  6  ft.,  — = 5-^  = 

23.2.  From  Table  XI,  p.  463,  we  see  that  when  l+r  is  less  than 
30,  we  should  use  12,000  Ibs.  per  square  inch  in  computing  the 
strength  of  the  strut.  Multiplying  the  area  of  the  two  angles 
(1.88)  by  12,000,  we  have  22,560  Ibs.  as  the  safe  resistance  to 
compression,  and  as  this  is  in  excess  of  the  stress,  we  will  use 
this  section  for  the  entire  length  of  the  rafter. 

(Note.  The  above  process  for  finding  size  of  rafter  seems 
long  and  tedious,  but  there  is  no  shorter  way  of  rinding  the 
strength  of  a  strut  of  this  section  with  any  degree  of  accuracy.) 

The  other  struts,  being  simply  in  compression,  can  be  pro- 
portioned directly  by  means  of  the  tables  in  Chapter  XIV. 
Thus  for  the  strut  BD,  which  is  72  ins.  long,  we  find  from  the 
table,  p.  469,  that  a  single  2x2Xj-in.  angle  has  a  strength 
greater  than  the  stress,  and  we  will  therefore  make  the  four 
short  struts  of  single  2X2  angles.  For  the  strut  EF,  which 
is  long,  but  not  very  heavily  strained,  we  will  use  two  angles 
riveted  together  by  plates,  so  that  the  cross-section  will  be 
in  the  shape  of  a  cross.  At  the  bottom  of  p.  470,  we  find  that 
a  strut  of  this  section  formed  of  two  2x2Xi-in.  angles  has  a 
strength  of  10,980  Ibs.  for  a  length  of  12  ft.,  or  twice  the  stress 
in  the  member;  therefore  we  will  use  that  section.  For  mem- 
bers in  compression  it  is  not  customary  to  deduct  for  rivet- 
holes.  We  have  now  determined  the  sizes  for  all  members 
of  the  truss,  as  indicated  in  the  table. 

EXAMPLE  5. — Fig.  7  is  the  diagram  of  one  half  of  a  steel 
truss  designed  and  built  by  the  Berlin  Iron  Bridge  Co.  for 
the  Elerslie  Coal  and  Coke  Co.,  at  Winifrede  Junction,  W.  Va. 
The  roof  is  covered  with  slates  fastened  to  angle-iron  purlins 
running  from  truss  to  truss  and  spaced  10 J  ins.  c.  to  c.  The 
stresses  indicated  on  the  diagram  are  those  that  would  be  due 
to  a  vertical  load  of  34  Ibs.  per  square  foot  of  roof  surface,  with 
trusses  spaced  8  ft.  on  centres.  The  author  does  not  know 


MEMBERS  OF   STEEL   TRUSSES. 


1049 


for  what  loads  the  truss  was  actually  computed,  but  they  were 
probably  somewhat  in  excess  of  those  assumed.  In  the  truss 
as  actually  built  all  of  the  members  are  formed  of  pairs  of 
angles,  except  ties  CD  and  DF,  which  are  single  angles. 

To  facilitate  determining  the  size  of  angles  to  be  used  for 
the  different  members,  the  stresses  and  length  of  struts  are 
given  in  the  following  table.  The  lengths,  however,  are  not 
the  actual  lengths,  but  are  what  may  be  termed  the  distance 
between  centres  of  bearings,  considering  each  member  as  end- 
ing at  the  joints. 

The  loads  marked  1. 1.  are  the  transverse  loads  on  the  rafter. 

DATA  FOR  PROPORTIONING  MEMBERS  OF  TRUSS 

(Fio.  7). 


Member. 

Stress. 

Length. 

Net  Sec- 
tional 
Area 
Re- 
quired.* 

Angles  Selected. 

Net 
Sec. 

AC 

-21,800 

Sq.  In. 
1.46 

2,  3   X2}XJ 

Sq.  In. 
2   18 

CE 

—  18  700 

1.25 

2    2JX2JXJ 

1  94 

EH 

-  12,500 

0.84 

2,  2^X2  Xi 

1  68 

EF 

-   6,250 

0.42 

2,  2  X2  Xi 

1  44 

FG 

-  9,300 

0.62 

2,  2   X2   Xi 

1  44 

CD 

-   3,050 

0.21 

1,  2   X2  X% 

0  56 

AD 

/+  23,500 

[    8'  6" 

2    5   X3JX| 

DG 

\        2,320  1.  1. 
|  +21,600 

!•    8'  6" 

2,  5   X3iX^ 

BC 

{        2,320  1.  1. 
-f   2325 

I 
3'0" 

2    2   X2   Xj 

DE 

+   4,650 

6'  6" 

2,  2   X2   Xi 

*  At  15,000  Ibs.  per  sq.  inch. 

Tension  Members. — First  find  the  net  sectional  areas 
required  for  these  members  by  dividing  the  stresses  by  15,000 
Ibs.,  the  allowed  stress  per  square  inch,  and  put  them  in  the 
fourth  column.  Then,  by  means  of  the  tables  on  pp.  306-311, 
select  the  angles  having  sectional  areas  a  little  in  excess  of  the 
required  area  and  put  the  sizes  in  the  fifth  column.  It  is  also 
a  good  idea  to  put  down  the  net  areas  of  the  angles  selected 
for  the  tension  members,  which  are  obtained  by  deducting 
from  the  actual  area  the  allowance  for  one  f-inch  rivet,  p.  640. 

Kai'ter. — As  the  rafter  has  a   transverse   load,   it   will  be 


1050 


TRUSS  MEMBERS  AND  JOINTS. 


necessary  to  assume  some  section  and  then  compute  its  strength 
as  a  strut-beam,  and  if  its  strength  is  not  equal  to  the  combined 
stress  and  load,  we  must  try  a  larger  section. 


For  the  rafter  from  A  to  D  we  will  try  two  5"  X  3J"  X  f " 
angles.  From  the  table  on  p.  529  we  find  the  coefficient  for 
one  angle  to  be  12.21  tons,  or  24,420  Ibs.,  and  dividing  by  the 
span  8.5  ft.,  we  have  2,873  Ibs.  as  the  safe  transverse  load, 
with  long  leg  vertical,  and  two  angles  would  support  5,746  Ibs. 
The  actual  load  is  2,320  Ibs.,  or  44  per  cent,  of  the  strength  of 
the  angles. 

From  the  table  on  p.  470  we  find  the  strength  as  a  strut  of 
two  angles  of  this  size,  8'  6"  long,  to  be  about  30.9  tons,  or 
61,800  Ibs.  The  actual  stress  is  23,500  Ibs.,  or  only  38  per  cent, 
of  the  strength  of  the  section.  As  it  requires  44  per  cent,  to 
resist  the  transverse  load,  it  will  require  82  per  cent,  to  resist 
both,  and  as  a  smaller  section  would  probably  not  be  strong 
enough  we  will  use  two  5X3}Xf"  angles  for  the  rafter  from 
A  to  D.  For  the  upper  half  of  the  rafter  we  will  try  the  same 
size  of  angles  with  a  thickness  of  %" '.  The  coefficient  for 
this  thickness  is  (p.  530)  10.34  tons,  or  20,680  Ibs.,  and  dividing 
by  the  span  we  have  2,433  Ibs.  as  the  safe  strength  of  one  angle. 
Therefore  it  will  require  about  50  per  cent,  of  the  strength  of 
two  angles  to  support  the  actual  load. 

The  resistance  to  compression  of  two  SXSJX/ie"  angles 
is  not  given  in  the  table,  p.  470,  but  we  find  the  difference 
between  the  loads  given  for  f  and  f  thicknesses  to  be  for  8  ft. 
length  28.96  tons,  which  would  be  4.83  tons  for  each  }£  in. 
in  thickness,  so  if  we  subtract  5  tons  from  the  safe  load  for 


JOINTS  OF   WOODEN  TRUSSES.  1051 

the  f-in.  thickness,  we  will  have  the  safe  load  for  %  in.  Mak- 
ing the  subtraction  we  have  26.66  tons  as  the  safe  load  for 
length  of  8  ft.,  and  to  obtain  the  strength  for  8'  6",  we  should 
subtract  about  .62  ton,  which  would  give  the  safe  strength,, 
say  26'  tons,  or  52,000  Ibs.,  for  a  length  of  8'  6".  As  the  stress 
is  only  21,600  Ibs.,  we  shall  utilize  only  42  per  cent,  of  the 
strength  of  the  strut,  and  as  we  require  50  per  cent,  to  resist 
the  transverse  load,  we  require  92  per  cent,  in  all;  therefore 
this  section  is  strong  enough  for  the  upper  portion  of  the  rafter. 

Struts. — These  we  can  find  directly  from  the  table  on 
p.  470.  For  all  three  of  the  struts  we  will  use  two  2X2Xi" 
angles,  which,  while  they  have  considerable  excess  strength, 
are  as  light  as  should  be  used. 

The  actual  size  of  angles  used  in  this  truss  are  indicated 
on  Fig,  28. 

Joints  of  Wooden  Trusses. 

It  is  probably  safe  to  say  that  the  joints  in  wooden  trusses, 
taking  them  as  they  are  found  throughout  the  States,  are  the 
weakest  portion  of  the  truss,  and  especially  the  joints  at  the  ends 
of  wooden  ties.  For  example,  a  6"X6"  timber  of  Georgia 
pine  would  require  a  force  of  288,000  Ibs.  to  pull  it  apart,  but 
it  is  practically  impossible  to  secure  the  end  of  such  a  timber 
so  as  to  develop  its  full  tensile  strength.  The  splicing  of  tie- 
beams  also  is  often  a  weak  place  in  many  trusses. 

The  joints  of  any  truss  should  be  proportioned  with  as  much 
care  as  the  size  of  the  members,  so  that  the  truss  will  be  equally 
strong  in  all  its  parts.  The  principles  by  which  the  strength 
of  joints  on  which  a  pulling  stress  is  exerted  are  explained  at 
length  on  pp.  382-397,  and  illustrated  by  a  few  examples. 
To  explain  the  subject  still  further,  we  will  show  how  the  joints 
of  the  trusses  illustrated  by  Figs.  1  and  3  (of  this  chapter) 
should  be  made. 

The  first  and  most  important  joint  of  the  truss  shown  by 
Fig.  1  is  joint  1,  where  the  truss  rests  on  the  wall.  There  are 
several  ways  in  which  this  joint  may  be  made,  the  simplest 
being  a  bolt  joint  like  that  shown  by  Fig.  8.  In  trusses  having 
a  horizontal  wooden  tie-beam,  the  tie-beam  almost  invariably 
extends  over  the  support,  and  the  rafter  or  principal  strut 
bears  on  top  of  it.  The  correct  method  of  properly  portion- 
ing a  joint  such  as  is  shown  by  Fig  8  is  explained  on  pp  392-39$. 


1052 


TRUSS  MEMBERS  AND  JOINTS. 


In  this  case  the  thrust  in  the  rafter  is  21,050  Ibs.,  and  to  find 
the  theoretical  stress  in  the  bolt,  we  should  first  make  a  drawing 
of  the  joint  at  a  scale  .of  about  1  in.  to  the  foot,  giving  the  rafter 
its  correct  inclination,  and  locating  it  on  the  tie-beam,  so  that 
the  point  where  the  central  lines  of  the  tie-beam  and  rafter 
intersect  will  be  at  least  6  ins.  in  011  the  wall.  Then  draw  the 


Fig.  8 

Joint  1  of  Fig.  1. 

notch  so  that  the  toe  of  the  rafter  will  be  about  2J  ins.  deep, 
and  a  little  to  one  side  draw  a  line  ab  parallel  and  equal  to 
the  stress  in  the  rafter,  to  a  scale  of  pounds,  and  from  the  upper  , 
end  a  a  line  at  right  angles  to  the  seat  of  the  rafter,  and  from  the 
lower  end  b  a  line  at  right  angles  to  the  rafter,  and  parallel  to  the 
bolt.  Then  the  line  be,  measured  by  the  scale  with  which  ab  is 
drawn,  gives  the  stress  in  the  bolt.  In  this  case  the  line  be  scales 
31,250  ibs.  To  find  the  diameter  of  the  bolt  necessary  to  resist 
this  stress  we  should  use  table  IX,  p.  384.  From  that  table  we 
find  that  to  resist  31,250  Ibs.  will  require  a  If"  bolt.  The 
bolt  should  be  placed  at  right  angles  to  the  rafter,  and  should 
have  a  good-sized  washer  at  each  end  (see  Washers,  p.  1064). 
It  will  not  do  to  cut  into  the  tie-beam  sufficient  to  get  a  proper 
bearing  for  so  large  a  bolt,  therefore  we  must  either  put  a  wooden 
block  under  the  truss,  as  in  Fig.  8,  or  use  a  cast-iron  washer, 
as  in  Fig  33 ,  p  394  For  light  trusses  the  wooden  block 
answers  the  purpose  as  well  as  the  cast  washer  and  will  generally 
be  cheaper.  To  prevent  the  block  from  sliding,  notches  should 


JOINTS  OF  WOODEN    TRUSSES. 


1053 


be  cut  in  the  top  of  the  block  and  the  bottom  of  the  tie-beam 
and  1"  or  f"  square  iron  bars  driven  in.  The  bolster  should 
also  be  well  spiked  to  the  tie-beam  before  the  bolt  is  put  in 
place. 

As  a  rule,  it  is  a  good  idea  to  place  the  wall  plate  which  re- 
ceives the  common  rafters' just  above  the  tie-beam  of  the  truss, 
the  wall  being  built  around  the  truss.  This  affords  an  oppor- 
tunity for  getting  at  the  nut  on  the  bolt  to  tighten  it  in  case 
the  wood  shrinks. 

The  bearing  of  a  truss  on  the  wall  should  always  be  con- 
sidered, and- a  plate  or  heavy  stone  provided  which  will  reduce 
the  pressure  to  within  the  limits  given  on  page  399.  In  this 
case  we  will  use  a  16"X  14"  XH"  cast-iron  plate,  which  reduces 
the  pressure  on  the  brickwork  to  82J  Ibs.  per  square  inch. 

Joint  1  of  Fig".  3. — This  joint  might  be  made  in  the 
manner  shown  by  Fig.  35,  p.  396,  but  if  the  tie-beam  is  to  be 
cased,  the  projection  of  the  cast-iron  washers  below  the  tie- 
beam  is  objectionable.  Fig.  9  shows  another  method  of  making 


Fig.  9 
Detail  of  Joint  1,  Fig.  3. 

the  bearing  joint  of  a  wooden  truss  which  avoids  the  use  of 
large  bolts  and  projecting  bolt-heads.  This  is  a  strong  joint, 
especially  serviceable  for  heavy  stresses,  and  where  the  in- 
clination of  the  rafter  is  less  than  45  degrees.  The  points  to 
be  computed  in  this  truss  are:  Area  of  bent  plate,  height  at 
toe,  and  the  distance  X.  The  sectional  area  of  the  plate  (which 
should  be  of  wrought  iron)  after  deducting  for  the  bolt-holes 


1054  TRUSS  MEMBERS  AND  JOINTS. 

at  Y  should  be  equal  to  the  tension  in  the  tie-beam  divided 
by  12,500  Ibs.,  and  the  thickness  of  the  plate  should  never  be 
less  than  f". 

27,350 

In  this  case  we  would  require  a  net  sectional  area=  = 

iZjoOO 

2.2  sq.  ins.,  but  as  the  plate  must  be  10"  wide  and  f"  thick 
it  will  give  a  net  area  considerably  in  excess  of  this.  The 
height  H  for  the  toe  of  the  rafter  should  be  equal  to  the  tension 
in  the  tie-beam  divided  by  the  breadth  of  the  rafter  multiplied 
by  1,000  for  white  pine,  1,200  for  spruce,  1,350  for  oak  and 
Oregon  pine,  and  1,500  for  long-leaf  yellow  pine. 

In  this  case  the  breadth  of  the  rafter  is  10  ins.  and  the  wood 

is   white   pine;   therefore  H   should   equal    — --         r\—^i    ms- 

-LU  X  1  jUUU 

The  distance  X  should  be  sufficient  to  resist  the  tendency  of 
the  plate  to  shear  off  the  top  of  the  tie-beam,  and  is  found  by 
dividing  the  tension  in  the  tie-beam  by  the  breadth  of  the 
beam  multiplied  by  the  resistance  to  longitudinal  shearing, 
given  on  p.  361,  increased  by  20  per  cent,  on  account  of  the 
additional  resistance  to  shearing  caused  by  the  vertical  pressure 
of  the  strut.  The  answer  will  be  in  inches. 

27  350 

In  this  case  X  should  equal  ,  '  =28^  ins.  In  the  draw- 
ing X= 30  ins. 

Bolts. — At  least  two  bolts  are  always  required  for  this 
joint,  one  at  Z  and  one  at  Y,  and  when  the  breadth  of  the  tie- 
plate  exceeds  6  ins.,  there  should  be  two  bolts  at  Y.  The  bolt 
at  Z  need  not  exceed  1"  when  the  tension  in  the  tie-beam  is 
less  than  50,000. 

The  diameter  of  the  bolts  at  Y  should  be  in  proportion  to  the 
thickness  of  the  plate,  and  the  bolts  should  always  be  placed 
.against  the  lug  on  the  plate.  When  a  joint  like  Fig.  9  is  under 
pressure  there  is  a  decided  tendency  for  the  lug  on  the  plate  to 
spring  up  out  of  the  wood,  and  in  an  actual  test  the  spring  in 
the  plate  was  sufficient  to  break  the  head  off  of  a  V  bolt.  The 
bolt,  however,  was  placed  about  2  ins.  back  from  the  notch. 
The  author  knows  of  no  way  by  which  the  stress  in  the  bolts 
at  Y  can  be  computed.  In  his  judgment,  however,  two  f" 
bolts  will  be  sufficient  for  a  f"  plate,  two  1"  bolts  for  a  \"  plate, 
and  two  1J"  bolts  for  a  f"  plate  10  ins.  wide.  If  the  plate  is 
12  ins.  wide  three  bolts  should  be  used. 


JOINTS  OF  WOODEN  TRUSSES. 


1055 


Joint  2  of  Fig".  1. — Where  a  brace  abuts  against  a  rafter, 
as  in  this  joint,  the  end  of  the  brace  should  be  notched  into 
the  rafter  sufficient  to  give  it 
a  good  "hold."  In  this  case 
a  notch  of  -J"  will  be  sufficient. 
To  support  the  purlin,  a  3" 
plank  may  be  bolted  to  rafter 
and  brace,  as  in  Fig.  10,  or 
the  rafter  may  be  hung  in 
duplex  hangers  let  into  the 
rafter.  For  purlins  larger  than 
8"X10"  the  duplex  hangers 


Fig.  10 

Detail  of  Joint  2  of  Fig.  1. 


are  to  be  preferred. 

In  the  truss  shown  by  Fig.  1 , 
there  is  no  rod  at  joint  2,  but  as  there  very  often  is  a  rod  at 
this  joint,  one  is  shown  in  Fig.  10.  If  the  rod  does  not  exceed 
\y  in  diameter,  a  round  hole  may  be  bored  in  the  top  of  the 
rafter  to  form  a  seat  for  a  cast-iron  washer. 


%  Wrought 
Iron  Plate 


Fig.  II 

Joint  at  Apex  of  King-rod  Truss. 

Fig.  11  shows  the  joint  at  the  top  of   a  king-rod  truss,  with 
a  duplex  hanger  for  supporting  the  purlin.      For  heavy  trusses 

a    cast-iron    cap-plate    such   as    is 
2"  Thick   ghown  by  Fig>  12  is  preferable  to 

the  bent  plate,  unless  the  latter  is 
made  very  heavy  and  lag-screwed 
to  the  rafters.  The  rafters  should 
butt  square  against  each  other. 

Joint     3    of   Fig.    1.— This 
should  be  made  as  shown  by  Fig. 
13.     In  place  of  the  cast  washer  a 
bent  plate  of  wrought  iron  is  often  used. 


1056 


TRUSS   MEMBERS  AND  JOINTS. 


Fig.  14  shows  how  joint  2  of  Fig.  3  should  be  made,  this  detail 
applying  also  to  any  of  the  upper  joints  of  a  Howe  truss, 
except  that  at  the  centre  of  the  truss,  where  two  braces  come 
together,  it  is  better  to  spike  a  block  to  the  bottom  of  the  top 
chord  for  the  braces  to  butt  against,  as  in  Fig.  3,  as  this  does 
not  weaken  the  truss,  and  also  where  counter-braces  are  re- 
quired it  is  better  to  insert  a  hard- wood  block  as  in  Fig.  16, 
so  that  each  brace  will  bear  against  the  chord  independent  of 
the  other. 


-IX  Rod 

I 

Fig.  13 

Detail  of  Joint  3  of  Fig.  1. 


Fig.  14 
Detail  of  Jdint  2  of  Fig.  3. 


For  joints  such  as  that  shown  by  Fig.  14  a  double  notch  is 
often  made,  as  shown  by  the  dotted  lines.  In  the  opinion  of 
the  author  this  does  not  make  as  strong  a  joint  as  the  single 
notch,  for  the  reason  that  with  a  double  notch  it  is  very  difficult 
to  fit  the  end  of  the  brace  so  that  it  will  bear  evenly  in  both 
notches,  while  with  a  single  notch  the  full  bearing  must  neces- 
sarily be  brought  on  the -toe. 

As  it  is  important  not  to  cut  into  the  chords  of  a  Howe  truss 
for  the  braces  more  than  is  really  necessary,  the  depth  of  the 
notch  should  always  be  proportioned  to  the  horizontal  component 
of  the  stress  in  the  brace.  The  latter  can  be  readily  measured 
from  the  stress  diagram.  Thus,  Fig.  15  is  the  stress  diagram 
of  the  truss  shown  by  Fig.  3,  0-2  is  the  horizontal  component 
of  the  stress  in  the  end  brace,  2-4  the  horizontal  component  of 
brace  3-4,  and  4-6  the  horizontal  component  of  brace  5-6, 
the  horizontal  component  of  the  stress  in  the  end  brace  being 
always  equal  to  the  tension  in  the  tie-beam  of  the  end  panel. 
To  avoid  splintering  or  crushing  of  the  wood,  the  depth  of  the 


JOINTS  OF  WOODEN   TRUSSES. 


1057 


notch  d  (Fig.  14)  multiplied  by  the  breadth  of  the  strut  should 
be  equal  to  the  horizontal  component  in  pounds  divided 
by  the  values  given  on  p.  1054  for  finding  the  height  H.  For 


Fig.  15 

the  truss  shown  by  Fig.  3,  this  rule  would  require  a  depth  d 
for  the  outer  brace  of  2J",  If"  for  the  next  brace,  and  J"  for 
the  inner  brace.  A  depth  of  J  inch,  however,  is  about  the 
minimum  that  should  be  made.  As  the  stress  is  the  same  at 
both  ends  of  a  brace,  the  notch  in  the  tie-beam  should  be  of 
same  depth  as  is  the  top  chord. 

Fig.  16  is  a  detail  of  joint  7  of  Fig.  1.  The  block  between 
the  braces  affords  a  bearing  for  the  stirrup  and  also  a  good  bear- 
ing for  the  braces,  and 
does  not  weaken  the  tie- 
beam  as  much  as  if  the 
block  were  omitted  and 
the  braces  notched  into 
the  tie-beam  beyond  the 
stirrup.  When  a  block 
is  inserted  between  the 
ends  of  two  braces,  and 
especially  when  the  braces 
are  not  subject  to  the  same 


6  x  6  x  &  Washer 


Fig.  16 

Joint  7  of  Fig.  1. 

stress,  the  block  should  be  notched  into  the  tie-beam  or  chord 
about  1  in.,  otherwise  the  brace  having  the  greater  stress  might 
push  the  other  brace  along.  In  the  case  of  the  two  centre  struts 
of  Fig.  3  the  block  between  their  upper  ends  need  only  be 
spiked  to  the  top  chord,  because  the  two  braces  would  nearly 
always  have  the  stame  stress  and  three  or  four  good  spikes 
would  be  fully  capable  of  resisting  any  difference  in  the  stresses 
that  might  arise  through  unequal  loading  of  the  truss. 


1058 


TRUSS  MEMBERS  AND  JOINTS. 


\i  crr 


Nr 


r 

* 


-I 


,;v 


Detail  of  Tie-beam,Fig.  3. 

— Fig.  17  shows  a  little  more  than 
one  half  of  the  tie-beam  as  it  should 
be  laid  out  in  practice  except  that 
the  scale  should  be  increased  to 
at  least  J  inch  to  the  foot. 

In  Fig.  17  the  breadth  of  the 
tie-beam  in  plan  is  drawn  out  of 
scale  in  order  to  more  clearly  show 
the  different  planks. 

The  first  step  in  making  such  a 
drawing  is  to  locate  the  rods  and 
braces,  with  the  proper  notches  for 
the  latter.  It  then  remains  to 
show  the  splices.  In  this  truss  the 
tie-beam  is  to  be  built  up  of  2"  X 10" 
planks  five  layers  in  thickness,  and 
the  problem  is  how  to  break  joints, 
and  how  many  bolts  are  required 
to  give  the  necessary  tensile  strength 
to  the  chord.  The  correct  method 
of  building  up  such  a  tie-beam  is 
fully  explained  under  Case  1,  p.  385; 
therefore  we  will  consider  this  ex- 
ample as  briefly  as  possible.  For 
convenience  the  tensile  stress  in  the 
tie-beam  for  each  panel  and  the 
net  sectional  area  required  is  given 
above  the  beam,  Fig.  17. 

Two  planks  will  be  amply  strong 
to  resist  the  tensile  stress  even  in 
in  the  central  panel.  The  centre 
layer  of  the  beam  we  will  consider 
merely  as  filling.  The  problem  is 
to  bolt  the  other  four  layers  together 
so  as  to  form  a  continuous  tie  hav- 
ing the  necessary  tensile  strength. 
The  two  outer  layers  we  will  make 
of  two  planks  each — two  planks 
A'  26'  0"  long,  and  two  A  23'  4" 
long  (the  beam  being  49'  6"  long). 
This  will  bring  the  joints  in  these 


JOINTS  OF  WOODEN  TRUSSES.  1059 

layers  at  Y  and  Z.  In  the  next  layers  we  will  use  planks 
28'  long  in  the  centre  of  the  beam,  with  planks  10'  8"  long 
at  each  end,  bringing  the  joints  in  the  second  and  fourth 
layers  at  X  and  the  same  distance  from  the  other  end. 

As  the  planks  B  and  B'  reach  beyond  the  centre  panels  on 
each  side,  they  will  carry  the  entire  stress  in  those  panels,  so 
that  we  need  only  figure  on  transmitting  the  stress  in  the  second 
panel. 

We  can  safely  assume  that  the  plank  B  will  transmit  one  half 
of  the  stress,  or  21,630  Ibs.  This  stress  must  be  transmitted  to 
A  by  bolls  having  a  combined  resistance  of  this  amount  and 
these  bolts  must  be  located  between  the  joints  X  and  Y.  From 
Table  VII,  p.  383,  we  find  that  the  resistance  of  a  J-in.  bolt 
in  white  pine  is  880  Ibs.  per  inch  of  length,  hence  in  a  2-in. 
plank  it  is  1,760  Ibs.  21, 630 -f- 1,760=  12+. 

As  we  will  have  four  bolts  between  Y  and  Z,  twelve  bolts  will 
be  ample  between  X  and  Y.  Two  of  these  bolts  should  be 
placed  5i"  from  Y  and  two  the  same  distance  from  X  (see  last 
column  of  Table  VII,  p.  353),  leaving  eight  to  be  spaced  between, 
which  will  make  the  distance  c.  to  c.  15§  ins.  As  the  planks 
A  and  A'  extend  to  the  end  of  the  tie-beam,  it  is  only  necessary 
to  use  enough  bolts  from  X  to  the  end  to  hold  the  planks  well 
together;  f"  bolts,  2  ft.  c.  to  c.,  will  be  ample  for  this  purpose. 
Wherever  an  end  joint  comes  in  a  tie-beam,  two  bolts  should 
be  placed  each  side  of  the  joint  as  at  X,  Y,  and  Z. 

As  the  centre  layer  will  offer  some  assistance  in  transmitting 
the  stress,  the  tie-beam  will  probably  have  some  excess  of 
strength  even  with  a  good  factor  of  safety;  but,  on  the  other 
hand,  some  of  the  bolts  may  not  fit  perfectly  and  the  planks 
may  not  be  full  2  ins.  thick,  so  that  it  is  well  to  be  on  the  safe 
side. 

Wall  Joint  of  Scissors  Trusses. — In  scissors  trusses 
the  joint  over  the  wall  formed  by  the  rafter  and  tie-beam  should 
always  be  carefully  proportioned  to  the  stress  in  the  tie, 
otherwise  the  joint  is  liable  to  open  and  allow  the  wall  to  be 
pushed  out.  Much  greater  strength  is  required  in  this  joint 
than  in  the  wall  joint  of  a  king-rod  truss  of  the  same  span,  be- 
cause the  stresses  in  a  scissors  truss  are  usually  at  least  twice 
and  sometimes  three  or  four  times  as  great  as  in  a  truss  with  a 
horizontal  tie-beam.  For  a  scissors  truss  built  of  planks  as 
in  Fig.  2  a  J"  bolt  through  the  centre  of  each  joint,  with  as 


1060 


TRUSS  MEMBERS  AND  JOINTS. 


many  spikes  as  can  be  driven,  will  ordinarily  give  sufficient 
strength. 

For  trusses  like  those  shown  by  Figs.  27-30  of  Chapter  XXV 
the  author  has  found  that  the  best  method  of  making  the  wall 
joint,  unless  the  roof  is  quite  flat,  is  that  shown  by  Fig.  18, 
which  is  the  detail  of  an  actual  joint  used  by  the  author  where 
the  stress  in  the  tie-beam  was  25,000  Ibs. 

It  should  be  noticed  that  the  wrought-iron  strap  is  secured 
to  the  tie  by  lag-screws  instead  of  bolts.  The  author  has  found 


.13,  %"  x  tyflJSSs  Screws 

Potted  lines  show  screws 

on,  other  side. 


Fig.  18 

Wall  Joint  of  Scissors  Truss. 

that  it  is  practically  impossible  to  bolt  a  strap  to  each  side  of 
a  beam  so  as  to  get  a  good  bearing  for  all  of  the  bolts,  owing  to 
the  difficulty  in  boring  the  holes  straight,  and  if  the  holes  are 
bored  a  little  large  some  bolts  may  bear  on  the  wood  and  some 
may  not. 

With  lag-screws  each  screw  is  bound  to  get  a  good  bearing 
in  the  wood.  The  holes  in  the  two  sides  of  the  strap  must,  of 
course,  be  staggered,  so  that  they  will  not  come  opposite  each 
other. 

The  net  sectional  area  of  the  strap  should  at  least  be  equal  to 
the  stress  in  the  tie-beam  divided  by  20,000  Ibs. 

The  number  of  lag-screws  (for  both  sides)  is  found  by  dividing 
the  stress  in  the  tie-beam  by  the  resistance  of  one  screw.  For 
the  safe  resistance  of  lag-screws  used  in  this  way  the  author 
recommends  the  values  given  in  Table  I. 


JOINTS  OF   WOODEN  TRUSSES. 


1061 


In  the   joint  shown  by  Fig.  18  the  stress  in  the  tie-beam  is 
25,000  Ibs.  and  the  wood  is  Oregon  pine. 

The   above   rules   therefore   require   a   sectional   area   in   the 
25,000 


strap= 


'  ins-  anc* 


3/,  . 

I     lag-screws. 


TABLE  I.—  SAFE  RESISTANCE  OF  LAG-SCREWS  WHEN 
USED  AS  IN  FIG.  18. 


Safe  Resistance  in  Pounds. 

Minimum 

Size  of  Screw. 

Oak. 

White 
Pine. 

Oregon 
Pine. 

Georgia 
Pine. 

Thickness 
of  Strap. 

Dia.        Length. 

1     X     3J 

800 

600 

700 

800 

i 

i     X     4 

1400 

1000 

1100 

1200 

i 

I     X     4 

2000 

1500 

1650 

1800 

ft 

f      X     4J 

2500 

1800 

2100 

2400 

ft 

1X5 

3000 

2400 

2800 

3000 

1 

With  a  thickness  of  f  in.,  the  width  of  the  strap  necessary 

i  ^^ 
to   give   a   sectional   area   of   1.25   sq.   ins.  =  ^=^=3J   ins.     To 

.OiO 

this  should  be  added  the  diameter  of   one  lag-screw  to  obtain 


Casting, 


Fig.  19 

Wall  Joint  of  Scissors  Truss. 

the  working  width,  3  J  +  •$  =  4  fa  ins.     The  strap  used  was  4"  X  f ", 
as  some  additional  strength  was  obtained  by  the  bolt  at  X, 


1062  TRUSS  MEMBERS  AND  JOINTS 

which  it  is  necessary  to  insert  to  hold  the  timbers  together 
while  the  truss  is  being  raised  into  position,  and  also  to  bring 
them  tightly  together  before  fitting  the  strap. 

Fig,  19  shows  another  method  of  making  this  joint  which 
may  be  used  with  advantage  when  the  inclination  of  the  rafter 
is  less  than  45  degrees.  This  joint  has  the  advantage  that  if 
the  truss  is  erected  one  piece  at  a  time  the  tie-beams  may  be 
put  up  first  and  a  seat  is  provided  to  receive  the  rafters.  The 
strap  prevents  the  end  of  the  rafter  from  springing  up.  The 
diameter  of  the  bolt  should  be  proportioned  to  the  horizontal 
component  of  the  stress  in  the  rafter  using  the  value  for 
strength  given  in  Table  IX,  p.  384.  Fig.  20  shows  a  good  form 
of  joint  to  use  at  joint  5  of  Fig.  30,  p.  903,  when  it  is  desired 
to  substitute  a  wooden  tie  for  the  rods  shown  in  Fig.  30. 


Fig.  20 

The  sectional  area  of  the  strap  and  number  of  lag-screws 
should  be  proportioned  by  the  rule  given  for  Fig.  18. 

Washers. — When  designing  roof  trusses  it  is  important  to 
proportion  the  washers  on  the  rods  and  large  bolts  so  that  they 
will  not  crush  the  timber  (see  p.  414).  As  the  softwoods  crush 
under  a  less  pressure  than  the  harder  woods,  washers  cannot 
be  proportioned  according  to  the  size  of  the  bolt  or  rod,  but 
must  be  proportioned  according  to  the  stress  in  the  rod  and 
the  kind  of  wood%against  which  they  bear. 

Table  II  gives  the  maximum  stress  which  round  and  rec- 
tangular washers  will  resist  without  sinking  into  the  wood. 

The  diameters  of  the  round  washers  are  those  of  the  standard 
sizes  of  cast-iron  washers  given  in  Table  III.  Comparing  the 
values  given  in  Table  II  for  round  washers  with  the  strength 
of  the  rods  for  which  they  are  intended,  it  will  be  seen  that  the 
bearing  resistance  of  the  washers  on  white  pine  and  spruce  is 


JOINTS  OF  WOODEN  TRUSSES. 


1063 


only  about  one  half  the  working  strength  of  the  rod,  conse- 
quently for  white  pine  and  Oregon  pine  the  standard  size  of 
washers  is  not  large  enough  for  the  strength  of  the  rod. 


TABLE   IL— SAFE   BEARING   RESISTANCE 
WASHERS  IN  POUNDS. 

ROUND   WASHERS. 


OF 


Diameter. 

White  Pine 
and  Spruce. 

Oregon 
Pine. 

Georgia 
Pine. 

Oak. 

2f 

1,350 

2,160 

2,700 

3,240 

3 

1,760 

2,820 

3,520 

4,230 

3* 

2,070 

3,300 

4,140 

4,970 

3| 

2,760 

4,400 

5,520 

6,620 

4 

3,140 

5,020 

6,280 

7,530 

4J 

4,430 

7,080 

8,860 

10,630 

6 

7,060 

11,400 

14,100 

16,960 

6i 

7,660 

12,260 

15,300 

18,400 

7i 

10,300 

16,500 

20,600 

24,700 

8i 

12,900 

20,700 

25,800 

31,100 

•9i 

16,250 

26,000 

32,500 

39,000 

10* 

20,000 

32,000 

40,000 

48,000 

RECTANGULAR   WASHERS. 


Size. 

4X6 

6,000 

9,600 

12,000 

14,400 

4X8 

8,000 

12,800 

16,000 

19,200 

6X6 

9,000 

14,400 

18,000 

21,600 

6X7 

10,500 

16,800 

21,000 

25,200 

6X8 

12,000  ' 

19,200 

24,000 

28,800 

6X9 

13,500 

21,600 

27,000 

32,400 

6X10 

15,000 

24,000 

30,000 

36,000 

8X8 

16,000 

25,600 

32,000 

38,400 

8X9 

18,000 

28,800 

36,000 

43,200 

.  8X10 

20,000 

32,000 

40,000 

48,000 

8X12 

24,000 

38,400 

48,000 

57,600 

10X10 

25,000 

40,000 

50,000 

60,000 

10X11 

27,500 

44,000 

55,000 

66,000 

10X12 

30,000 

48,000 

60,000 

72,000 

10X14 

35,000 

56,000 

70,000 

84,000 

12X12 

36,000 

57,600 

72,000 

86,400 

12X14 

42,000 

67,200 

84,000 

100,800 

12X16 

48,000 

76,800 

96,000 

115,200 

14X14' 

49,000 

78,400 

98,000 

117,600 

14X16 

56,000 

89,600 

112,000 

134,400 

As  a  rule  for  the  rods  of  wooden  trusses  it  is  best  to  use 
rectangular  washers  cut  from  steel  plates,  cutting  the  washers 
to  the  required  size.  It  is,  of  course,  not  really  dangerous  to 


1064 


TRUSS  MEMBERS   AND  JOINTS. 


use  smaller  washers  than  would  be  required  by  Table  II,  as  a 
little  crushing  of  the  timber  will  not  en- 
danger the  safety  of  the  truss,  but  it  is  best 
to  keep  within  the  limits  of  Table  II  when 
practicable. 

Very  large  washers  should  be  made  of  cast 
Fig.  21  iron  with  brackets,  as  in  Fig.  21.     The  rod 

in  Fig.  16  has  a  stress  of  8,960  Ibs.,  and  as  the  wood  is  white 
pine,  we  see  from  Table  II  that  a  6"  X  6"  washer  will  be  required. 


TABLE    III.—  PROPORTIONS   OF 
STANDARD  CAST  WASHERS. 

For  sizes  not  given  below. 
Diameter  of  bolt=<£. 


All  dimensions  in  inches. 


•fir 


Standard  Cast  Washer. 


Diameter 
of 
Bolt=d. 

A. 

B. 

c. 

D. 

Weight 
in 
Pounds. 

* 

2f 

if 

% 

f 

i 

f 

3 

if 

% 

f 

f 

3f 

21 

% 

H 

J 

3J 

ty 

% 

i 

li 

i 

4 

2| 

1% 

it 

2J 

H 

4| 

21 

We 

H 

3 

H 

6 

3 

We 

'if 

5J 

li 

6i 

3i 

If 

i| 

6 

H 

7i 

3J 

If 

if 

9* 

2 

8* 

*i 

2J 

2 

17} 

2* 

9} 

4| 

2S 

2i 

20 

21 

10i 

5} 

2f 

2J 

27J 

2f 

Hi 

Si 

2J 

2J 

36 

3 

12| 

6i 

3* 

3 

46 

Riveted  Joints   of  Steel   Trusses. 

Trusses  with  riveted  joints  are  invariably  made  with  angle- 
bars  for  the  web  members  and  generally  for  the  chords,  al- 
though the  latter  are  sometimes  made  of  a  pair  of  channels 


RIVETED  JOINTS  OF  STEEL  TRUSSES.       1065 

or  of  two  angles  and  a  web-plate.  The  members  are  connected 
at  the  joints  by  means  of  gusset-plates,  to  which  all  of  the  mem- 
bers are  riveted.  Typical  examples  of  riveted  joints  in  roof 
trusses  are  shown  by  Figs.  24  to  34.  When  the  rafter  or  chord 
has  a  web-plate,  as  in  Fig.  26,  the  web  members  are  riveted 
to  this  plate  and  a  gusset-plate  is  not  required  except  at  the 
end  joint  and  apex. 

In  order  that  there  shall  be  no  twisting,  it  is  necessary  that 
the  principal  members  of  the  truss  be  double  so  that  the  gusset- 
plate  may  be  riveted  between  them.  Where  single  angles  are 
used  for  web  members  and  two  such  members  come  at  one  joint 
they  should  be  riveted  to  opposite  sides  of  the  gusset-plates  as 
in  Fig.  31.  The  thickness  of  the  gusset-plates,  as  a  rule,  should 


Fig.  22 

be  twice  the  thickness  of  the  angles  that  are  connected  to  it. 
In  laying  out  the  joints,  which  should  be  done  to  a  scale  of  not 
less  than  1  in.  to  the  foot,  the  members  should  be  arranged, 
when  practicable,  so  that  the  lines  passing  through  their  centre 
of  gravity  will  coincide  with  the  lines  of  the  truss  diagram,  and 
thus  meet  at  a  single  point,  as  in  Fig.  22.  This  is  not  always 
practicable,  but  the  principle  should  be  followed  as  closely  as 
possible.  For  small  angles  the  rivet  lines  of  the  members  may 
be  considered  as  passing  through  the  centre  of  gravity  of  the 
section  without  serious  error. 

The  number  of  rivets  required  for  each  member  must  be 
determined  according  to  the  stress  in  the  members,  the  re- 
sistance of  the  rivets  being  considered  both  for  shearing  and 
bearing. 

The  method  of  determining  the  number  of  rivets  in  a  joint 
is  explained  on  pp.  363-370,  but  to  show  more  clearly  the 
application  to  truss  joints  we  will  illustrate  by  one  example, 


1066  TKUSS  MEMBERS  AND  JOINTS. 


Fig.  23 

Diagram  of  Light  Steel  Truss  supported  by  Brick  Walls. 


Fig.  24 
Detail  of  Joint  A  of  Fig.  23.     All  Rivets  f  inch. 


RIVETED  JOINTS  OF  STEEL  TRUSSES.       1067 


1 

PLAN 

Fig.  25 

Detail  of  Joint  D  of  Fig.  23. 


,«'«" 

c  -         11  3" 

-n" 

tq% 

^Vfr 

,5"!                   .*'*•       • 

<•         'Ilia 

' 

<616T:     ' 

/              

irzzr_:rr^zt4 

>    < 

>--!-< 

HH 

S*^;—  d 

/•                            g 

»                 ~i  i 

i  T"                        "I 

/                                           ' 

L_ 

Fig.  26 
Detail  of  Joint  S  of  Fig.  23,     All  rivets  ^  inch. 


1068 


TRUSS  MEMBERS  AND  JOINTS. 


EXAMPLE. — To  find  the  number  of  rivets  required  in  the  joint 
shown  by  Fig.  32,  the  stresses  in  the  members  being  as  follows: 
A,  -6,250  Ibs.;  B,  -3,050  Ibs.;  C,  +2,325  Ibs.;  andD,  -9,300 


Fig.  27 
Detail  of  Joint  K  of  Fig.  23. 


Fig.  28 

Diagram  of  Light  Steel  Truss  of  68  Feet  Span. 

Ibs.     The  dimensions  of  the  members  as  previously  determined 
are  given  in  the  figure. 

We  will  use  a  gusset-plate  f "  thick. 


RIVETED  JOINTS  OF   STEEL  TRUSSES.      1069 

Number  of  Rivets  Required  for  B. — As  there  is  but 
one  angle  the  rivets  will  be  in  single  shear,  and  as  the  leg  of 
the  angle  is  only  2"  wide  we  must  use  f"  rivets.  From  the 
table  on  p.  372  we  find  the  resistance  of  a  f"  rivet  to  single 
shear  to  be  3,060  Ibs.  The  bearing  resistance  on  a  %>"  plate 
(the  thickness  of  the  angle)  is  not  given,  but  it  is  jths  the  re- 
sistance for  a  J"  plate,  or  2,100  Ibs.;  therefore  the  strength 
of  the  rivet  is  governed  by  its  resistance  to  bearing.  As  the 


Fig.  29 
Joint  A  of  Fig.  28. 

stress  is  3,050  Ibs.  it  will  require  1J  or  2  rivets.  Four  rivets  are 
shown  in  the  drawing,  probably  to  give  additional  stiffness,  as 
but  one  leg  of  the  angle  is  riveted. 

Rivets  in  C.— This  member  is  composed  of  two  angles, 
consequently  the  rivets  are  in  double  shear,  and  their  resistance 
to  shearing  is  6,120  Ibs.  each.  The  minimum  bearing  is  on 
the  |"  gusset-plate.  The  bearing  resistance  of  a  f "  rivet  on  a 
§"  plate  is  4,210  Ibs.,  which  governs  the  strength  of  the  rivet. 
As  the  stress  is  only  2,325  Ibs.  only  one  rivet  would,  theoretically, 


1070 


TRUSS  MEMBERS  AND  JOINTS. 


be  required  to  resist  the  stress,  but  two  rivets  is  the  least  that 
should  ever  be  used  in  the  end  of  a  truss  member,  no  matter 
how  small  the  stress. 

Rivets  in  D. — This  member  is  also  double,  and  as  the 
combined  thickness  of  the  angles  is  greater  than  the  thickness 
of  the  gusset-plates  the  strength  of  the  rivets  will  be  governed 
by  the  resistance  to  bearing  on  a  f "  plate,  or  4,210  Ibs.  As  the 
stress  is  9,300  Ibs.,  it  will  require  three  rivets  to  resist  it  and 
two  rivets  for  A.  For  such  small  stresses  more  rivets  are 


Fig.  30 

Joint  B  of  Fig.  28. 

generally  used  than  are  theoretically  required,  but  when  the 
stresses  are  large,  only  as  many  rivets  as  are  theoretically  re- 
quired are  generally  used. 

The  above  example  illustrates  the  process  to  be  pursued  in 
determining  the  number  of  rivets  in  any  joint. 

For  Angles  in  Tension,  both  legs  should  be  connected 
by  rivets,  as  in  Fig.  33,  unless  the  sectional  area  of  the  angle  is 
very  much  greater  than  would  theoretically  be  required,  as  is 
the  case  with  the  brace  B  in  the  last  example. 

Cooper,  in  his  "  Specifications  for  Iron  and  Steel  Bridges," 
requires  that  "Angles  subject  to  direct  tension  must  be  con- 


RIVETED  JOINTS  OF  STEEL  TRUSSES.      1071 

nected  by  both  legs  or  the  section  of  one  leg  only  will  be  con- 
sidered as  effective." 

When  two  rows  of  rivets  are  used  in  a  tension  member,  the 
rivets  should  be  staggered  as  in  Fig.  34,  so  that  any  cross- 
section  will  be  weakened  by  only  one  rivet-hole. 

Stay-rivets. — Struts  composed  of  a  pair  of  angles  should- 
be  riveted  together,  with  a  washer  between  the  angles,  about 


Fig.  31 

Joint  D  of  Fig.  28. 

every  eighteen  inches  for  2"  angles,  24"  for  2J"  angles,  and  30" 
for  3 J"  angles,  and  from  30"  to  3  ft.  for  tension  members.  Stay- 
rivets  are  shown  in  Figs.  30  and  34. 

For  locating  the  rivet  lines  on  angles,  or  the  "pitch,"  as  it 
is  called  in  bridge-shops,  the  distances  given  in  the  table  on 
p.  551  should  be  used. 

Figs.  24-27  show  the  details  of  several  of  the  joints  in  the 
truss  shown  by  the  diagram,  Fig.  23,  and  Figs.  29-33  several 
of  the  joints  of  the  truss  shown  in  Fig.  28.  The  engravings 
were  made  from  the  actual  working  drawings  prepared  by  the 


1072 


TRUSS  MEMBERS  AND  JOINTS. 


Berlin  Iron  Bridge  Co.,  and  are  very  good  examples  of  riveted 
joints  in  roof-trusses. 

\  /D 


Fig.  32 
/Joint  F  of  Fig.  28. 


Fig  33. 

Joint  G  of  Fig.  28. 

The  solid  black  circles  indicate  holes  for  bolts  to  be  put  in 


PURLINS  AND  PURLIN  CONNECTIONS.       1073 

place  in  the  field,  the  truss  being  shipped  in  four  parts  and 
assembled  at  the  building. 

Fig.  34  was  engraved  from  the  working-drawing  made  by  the 


!        I  .  /  X'X --'- {•£/ 


Fig.  34 

New  Jersey  Steel  and  Iron  Co.  of  Trenton,  N.  J.,  and  represents 
joint  1  of  Fig.  60,  p.  922. 

Purlins  and  Purlin  Connections. 

Where  the  roofing  is  supported  directly  on  the  purlins,  as 
is  generally  the  case  in  light  steel  roofs,  the  purlins  and  trusses 
are  generally  spaced  so  close  together  that  simple  shapes  may 
be  used  for  the  former. 

For  spans  between  trusses  of  8  or  10  feet,  angles  are  com- 
monly used,  and  for  greater  spans  Z  bars,  channels,  and  I  beams. 

Wooden  purlins  are  also  frequently  used  with  steel  trusses. 


1074 


TRUSS  MEMBERS  AND  JOINTS. 


If  the  purlins  support  wooden  rafters  or  plank  roofing,  a  strip 
of  wood  is  bolted  to  the  I  beam  or  channel  purlin,  as  shown  by 
Figs.  36  and  37,  to  form  nailings  for  the  rafters  or  plank. 


Fig.  35 

Purlin-clips. 


Fig.  36 

Purlin  Connections. 

When  the  distance  between  trusses  is  more   than  about  15  ft., 
a  line  of  f "  rods  should  be  run  from  the  ridge  through  the  pur- 
lins to  prevent  them  from  sagging  in  the  plane  of  the  roof. 
Purlin  Connections. — Angle,  channel,  and  Z-bar  pur- 
lins, and  also  wooden  purlins,  are  fastened 
to  the  rafters  of  the  truss  by  angle-clips 
as  in  Figs.  35,  36,  and  37.      These  clips 
should    be    riveted    to   the  truss  at   the 
shop,  the   purlins   being   secured  to   the 
clips  by  bolts. 

I-beam  purlins  are  usually  bolted  di- 
rectly to  the  rafter  by  a  bolt  in  each 
side  of  the  flange.  12"X15"  I  beams 
and  channel  are  sometimes  braced  as  in 

Fig.  37,  the  necessity  for  bracing  depending  largely  upon  the  in- 
clination of  the  roof. 


Fig.  37 


WIND  BRACING  OF  BUILDINGS.  1075 


CHAPTER  XXVIII. 

WIND    STRESSES    AND    BRACING  IN  TOWERS 
AND  HIGH  BUILDINGS. 

THE  stresses  produced  by  the  force  of  the  wind  acting  against 
high  structures  are  often  of  great  magnitude  and  must  be 
provided  for  as  much  as  those  produced  by  vertical  loads. 

Brick  or  stone  structures,  if  the  walls  are  well  built  and  of 
proper  thickness,  are  able  to  withstand  these  stresses  without 
bracing,  but  framed  structures  require  bracing  and  additional 
sectional  area  in  the  posts;  the  amount  of  bracing  and  in- 
crease in  sectional  area  depending  largely  upon  the  height 
and  width  of  base,  and  the  character  of  the  construction. 

The  method  of  determining  the  wind  stresses  can  best  be 
shown  by  means  of  examples. 

EXAMPLE  1. — We  will  assume  that  Fig.  1  is  an  elevation  of 
one  side  of  a  tower  48  ft.  high,  12  ft.  8  ins.  wide,  and  25  ft.  4  ins. 
long.  The  tower  to  be  built  with  wooden  posts  and  girts  and 
braced  with  rods,  the  latter  being  in  the  same  plane  as  the 
posts  and  girts.  The  spaces  between  the  posts  to  be  filled 
with  studding,  and  the  entire  tower  to  be  sheathed  and  cov- 
ered with  some  suitable  material.  In  regard  to  its  resistance 
to  wind  pressure,  such  a  frame  is  in  effect  a  cantilever  truss 
fixed  at  one  end,  i.e.,  at  the  ground  (either  by  bolts  or  by  its 
own  weight),  and  uniformly  loaded  over  its  entire  length,  and 
the  stresses  may  be  found  exactly  in  the  same  way  as  for  a 
cantilever  truss. 

The  wind  pressure  is  considered  as  acting  horizontally  and 
applied  at  the  joints  the  same  as  the  loads  on  a  truss. 

In  a  tower,  the  two  sides  parallel  with  the  direction  of  the 
wind  are  assumed  to  resist  the  stress,  so  that  the  frame  shown 
by  Fig.  1  has  to  resist  only  one  half  of  the  total  pressure. 

Assuming  the  wind  to  act  from  the  left,  the  rods  should  be 
placed  as  in  the  figure. 

The  wind  load  at  joint  o  will  equal  half  the  height  of  the 


1076  WIND  BRACING  OF  TOWERS. 

panel  multiplied  by  half  the  width  of  the  structure,  and  the 
product  by  the  pressure  per  square  foot. 

For  enclosed  towers,  the  wind  pressure  should  be  taken  equal 
to  40  Ibs.  per  square  foot  of  vertical  elevation,  at  least,  and 
if  the  tower  is  in  a  very  exposed  situation,  it  will  be  safer  to 
assume  a  pressure  of  50  Ibs.* 

Assuming  a  pressure  of  40  Ibs.,  we  have  for  the  loads  at 
joints  o  and  8,  of  Fig.  1,  6'X12'  8" X 40= 3,040  Ibs.,  or  say 
3,000  Ibs.,  and  at  joints  2,  4,  and  6  twice  this  amount,  or  6,000 
Ibs.  To  draw  the  stress  diagram,  Fig.  IA,  we  will  commence 
with  joint  1,  Fig.  1  being  lettered  as  for  a  truss  diagram  (see 
p.  971).  The  pressure  exerted  at  o  is  transmitted  by  the  top 
girt  directly  to  joint  1,  and  we  may  therefore  consider  the 
force  as  acting  at  that  joint.  Then  at  joint  1  we  have  a  hori- 
zontal force  of  3,000  Ibs.,  which  is  represented  by  the  line  ab 
drawn  to  a  scale,  and  the  force  acts  in  the  direction  indicated. 
Besides  this  force  we  have  the  stresses  in  BF  and  FA,  which 
we  obtain  by  drawing  a  vertical  line  from  a,  and  a  line  from  b, 
parallel  to  the  diagonal  B'F,  the  two  lines  intersecting  at  /. 
The  triangle  of  forces  for  joint  1,  then,  is  ab,  bf,  and  fa.  The 
arrow-head  on  bf  points  from  the  joint,  and  on  fa,  towards  the 
joint;  hence  B'F  is  in  tension  and  FA  in  compression.  (Note. 
It  will  be  seen  that  the  order  of  rotation  is  from  right  to  left, 
and  this  order  must  be  followed  at  all  of  the  joints.) 

At  joint  2  we  have  the  stress  in  FB',  which  must  act  from 
the  joint,  next  the  load  of  6,000  Ibs.,  which  we  lay  off  from 
b  to  c,  to  the  same  scale  as  ab  (theoretically  there  will  be  no 
stress  in  BB').  Then  draw  eg  and  fg  to  represent  the  stresses 
in  CG  and  FG  respectively.  The  arrow-head  on  eg  points  from 
the  joint,  hence  CG  is  in  tension.  At  joint  3  we  have  the 

*  In  a  paper  read  before  the  American  Society  of  Civil  Engineers,  Mr. 
Julius  Baier  stated  that  the  St.  Louis  tornado  of  1896  "gave  evidence 
that  wind  pressures  existed  at  least  equivalent  to  or  greater  than  20  Ibs. 
60  Ibs.,  and  85  to  90  Ibs.  per  square  foot  over  considerable  areas,  and  that 
the  pressures  at  higher  altitudes  were  more  severe  than  those  measured." 

After  a  thorough  study  of  the  effects  of  the  wind  pressure  during  this 
tornado  Mr.  Baier  recommended  "that  the  safety  and  interests  of  the 
community  and  of  the  owner  of  the  building  require  a  recognition  of  a 
wind  pressure  of  at  least  30  Ibs.  per  square  foot  against  the  exposed  surface 
of  a  building,  with  an  additional  local  provision  of  50  Ibs.  for  several  stories 
near  the  top ;  and  that  this  amount  should  be  safely  taken  care  of  by  some 
positive  and  definite  provision  in  the  construction  of  the  frame." 

Railway  structures  and  steel  buildings  are  commonly  designed  to  resist 
a  horizontal  wind  pressure  of  30  Ibs.  per  square  foot. 


WIND   BRACING  OF  TOWERS. 


1077 


stresses  af  and  fg,  and  draw  gh  and  ha  parallel  respectively  to 
GH  and  HA.  The  stresses  at  joints  4  and  6  are  found  in  the 
same  way  as  at  joint  2,  and  those  at  joints  5  and  7  in  the  same 
way  as  those  at  3.  At  joint  8  we  have  the  stresses  Ik  and  ke, 
and  measure  off  the  load  of  3,000  Ibs.  represented  by  em. 


PR  24,000 


P    b      P,       .c     P2      .  d      P3       e  1 


w 


Fig.  I 


Fig.  IA 


Then,  if  from  m  we  draw  a  vertical  line,  and  from  I  a  hori- 
zontal line,  the  two  intersecting  at  n,  mn  will  denote  the  an- 
chorage required  for  the  post  EK,  and  In  the  stress  in  the  girt 
or  sill,  on  the  assumption  that  the  entire  horizontal  thrust  or 
tendency  to  slide  on  the  foundation  is  resisted  by  joint  9.  In 
practice  it  is  customary  to  fasten  the  frame  to  each  of  the  piers, 
and  to  make  the  girt  or  sill  strong  enough  to  resist  one  half 
of  the  thrust. 

The  stress  denoted  by  mn  will  be  offset  to  a  considerable 
degree,  if  not  entirely  overbalanced,  by  the  weight  of  the  frame 


1078  WIND  BRACING  OF  TOWERS. 

and  its  load.  In  a  light  frame  supporting  no  load,  the  tension 
in  the  windward  columns  will  be  greater  than  the  compression, 
and  the  columns  must  be  spliced  to  resist  an  upward  pull  and 
be  anchored  to  the  foundation. 

The  uplift  at  joint  8  can  also  be  obtained  by  taking  moments 
about  joint  9.  Thus  the  total  wind  pressure  acting  against 
the  windward  side  will  be  48/X25/  4"X40  lbs.=  48,640  Ibs. 
As  each  end  resists  one  half  of  the  pressure,  the  pressure  for 
one  end  will  be  24,320  Ibs.,  or  say  24,000  Ibs.  This  pressure 
may  be  considered  as  acting  at  half  the  height  of  the  frame. 
Representing  the  pressure  by  PR,  the  moment  about  9  tending 
to  overturn  the  tower==P^X^.  To  maintain  stability  there 
must  be  a  force,  represented  by  the  arrow,  W,  acting  down. 
Considering  the  tower  as  balanced  on  the  pier  at  9,  the  force  W 
tends  to  turn  the  tower  to  the  left,  and  its  moment  =  W  X  Y. 
To  just  maintain  equilibrium  WXY  must  just  equal 


whence  W=—  ^-  —  -.     Substituting  the  values  of  PR,  X,  and  Y, 

24  000x24 

we  have  W=—  •  —  r~  -  =  48,000  Ibs.,  which  is  the  same  stress 
\2i 

as  given  by  the  stress  diagram.  To  be  perfectly  safe  against 
gusts  of  wind  or  tornadoes,  W  should  exceed  the  value  given 
by  the  above  value  by  at  least  25  per  cent. 

The  difference  between  1JTF  and  the  weight  on  the  post  must 
therefore  be  taken  care  of  by  a  rod  or  strap  extending  into 
the  foundation,  and  there  must  be  sufficient  masonry  provided 
to  balance  this  difference  between  \\W  and  the  dead  weight. 
Thus  we  will  assume  that  our  tower  weighs  80,000  Ibs.,  then 
the  load  on  each  post  will  be  one  fourth  of  this,  or  20,000  Ibs., 
W=  48,000,  and  l\W=  60,000  Ibs.  Therefore  it  will  require 
an  anchorage  of  40,000  Ibs.  to  secure  absolute  safety.  As 
the  weight  of  stone  masonry  may  be  taken  at  140  Ibs.  per 

40  000 

cubic  foot,  it  will  require  -      —  =286  cu.  ft.  to  hold  the  tower 
140 

down. 

To  the  compression  in  the  leeward  columns  due  to  wind  pressure 
must  be  added  the  compression  due  to  the  vertical  loads.  Thus 
if  the  post  7-9  has  to  support  a  dead  load  of  20,000  Ibs.,  it 
should  be  made  large  enough  to  sustain  20,000  +  48,000,  or 
68,000  Ibs.  In  computing  the  size  of  struts  or  ties  to  resist 
wind  pressure,  however,  a  greater  unit  stress  or  a  smaller 
factor  of  safety  is  generally  used  than  for  other  loads. 


WIND  BRACING  OF  TOWERS,  1079 

In  Fig.  1  only  one  diagonal  is  shown  for  each  panel,  and  if 
we  could  be  sure  that  the  wind  would  always  blow  from  the 
left,  that  is  all  that  would  be  required. 

As  the  wind  may  blow  from  any  direction,  however,  it  is 
necessary  to  insert  diagonals  in  both  directions,  and  in  each 
of  the  four  sides  of  the  tower,  and  if  it  is  necessary  to  provide 
any  anchorage  at  all,  all  of  the  posts  must  be  anchored,  and 
each  post  must  be  proportioned  for  the  maximum  net  tension 
and  maximum  compression. 

Analysis  of  Stress  Diagram. — The  stresses  given  on 
Fig.  1A  were  obtained  by  scaling  the  lines  by  the  scale  used  in 
laying  off  the  pressures  P,  Plt  etc.  Studying  the  diagram  and 
stresses,  it  will  be  seen  that  the  compression  (or  shear,  as  it 
is  commonly  called)  in  2-3  =  P+Pr  The  shear  in  4-5= 
P+Pt-|-P2,  and  so  on.  Or  the  shear  in  any  girt  equals  the  panel 
load  at  that  point  plus  all  of  the  panel  loads  above. 

Also,  the  stress  in  the  diagonals  equals  the  shear  in  strut  above 
multiplied  by  the  secant  of  the  angle  0. 

The  compression  in  the  leeward  column  from  1  to  3  equals 
af,  or  the  vertical  component  of  the  stress  in  the  diagonal. 
The  compression  from  3  to  5  equals  /£/+/«,  or  the  vertical 
component  of  the  diagonal  hg +the  compression  in  the  panel 
above,  and  this  is  true  for  every  panel. 

Now  the  line  af=P  times  tangent  0,  and  fh—fgX tangent  6. 
If  we  denote  the  vertical  component  of  the  diagonals  by  the 
term  increment,  then  the  increment  for  any  panel  is  equal  to  the 
shear  in  the  strut  at  the  top  of  -the  panel  multiplied  by  the  tan- 
gent 6,  and  the  compression  in  the  leeward  column  in  any  panel 
equals  the  increment  for  that  panel  plus  the  compression  in  the 
panel  above.  It  can  also  be  seen  that  the  tension  in  CG  equals 
the  compression  in  AF,  and  the  same  relation  is  true  for  the 
panels  below,  or  the  tension  in  the  windward  column  in  any  panel 
is  equal  to  the  compression  in  the  leeward  column  in  the  panel 
above. 

These  facts  enable  one  to  readily  compute  the  stresses  in  a 
simple  frame  like  Fig.  1,  without  drawing  the  stress  diagram, 
and  the  wind  stresses  in  the  framework  of  high  buildings  are 
usually  computed  directly  by  means  of  the  above  propositions, 
as  is  shown  on  p.  1088. 

If  the  tower  is  battering,  however,  the  above  propositions 
do  not  hold  true,  and  the  stresses  can  be  most  easily  obtained 
by  drawing  a  stress  diagram. 


1080  WIND  BRACING  OF  TOWERS. 

EXAMPLE  2. — To  show  the  application  of  the  graphic  method 
of  finding  the  wind  stresses  when  the  columns  are  inclined, 
we  will  determine  the  stresses  for  the  water-tower  shown  by 
Fig.  2.  We  will  assume  that  the  tower  is  square  in  plan  and 
open  on  the  sides.  The  tank  is  supposed  to  be  circular  and 
to  weigh,  when  two  thirds  full  of  water,  about  80,000  Ibs 
The  area  of  the  tank  exposed  to  the  wind  is  its  diameter  mul- 
tiplied by  the  average  height,  or  12x13=156  ft.  For  the 
pressure  per  square  foot  of  vertical  surface  we  will  assume 
60  Ibs.  to  provide  against  any  possible  wind.  This  would 
make  the  pressure  on  156  sq.  ft.  9,360  Ibs.  For  a  circular 
tower  or  chimney,  however,  it  is  customary  to  consider  the 
pressure  as  only  two  thirds  what  it  would  be  on  a  flat  surface, 
which  would  make  the  pressure  on  the  tank  6,240  Ibs..  or  3,120 
Ibs.  011  each  side.  For  the  pressure  on  the  tower  20  Ibs.  per 
square  foot  of  vertical  elevation  should  be  sufficient  ^consider- 
ing that  it  is  an  open  frame).  This  will  give  the  panel  loads 
to  be  resisted  by  each  side,  as  indicated  in  the  figure,  the  load 
at  the  top  of  the  frame  including  both  the  pressure  on  the  tank 
and  the  pressure  on  the  upper  half  of  the  frame. 

The  stress  diagram  (Fig.  2A)  is  drawn  in  exactly  the  same 
way  as  Fig.  1A,  commencing  by  drawing  the  line  ab,  equal 
to  the  pressure  at  joint  1,  and  from  a  and  b  lines  parallel  re- 
spectively to  AF  and  B'F.  At  joint  2  we  have  fb,  and  draw  be 
equal  to  the  pressure  at  that  joint.  Then  from  c  draw  a  line 
parallel  to  CG,  and  from  /  (the  point  of  beginning)  a  horizon- 
tal line,  the  two  lines  intersecting  at  g.  At  joint  3  the  polygon 
of  forces  is  af,  fg,  gh,  and  ha. 

The  stresses  at  joints  4  and  6  are  drawn  in  the  same  way  as 
those  at  joint  2,  and  the  stresses  at  joints  5  and  7  in  the  same 
way  as  those  at  joint  3. 

At  joint  8  we  have  Ik  and  ke,  and  draw  em  =  to  the  pressure; 
from  ra  draw  a  vertical  line,  because  the  weight  of  the  anchorage 
will  be  vertical,  and  from  I  a  horizontal  line.  Then  ran  will 
represent  the  upward  pull  on  the  windward  piers  due  to  wind 
pressure,  and  In  the  compression  on  the  bottom  girt,  assuming 
that  the  entire  stress  is  transmitted  to  joint  9. 

As  all  of  the  posts  will  be  fixed,  however,  the  girt  need  be 
proportioned  to  resist  only  one  half  of  the  stress  shown  by  In. 
The  stresses  given  in  Fig.  2A  were  obtained  by  scaling  the 
lines.  It  will  be  seen  that  all  of  the  stresses  are  considerably 
less  than  they  would  be  if  the  tower  were  of  the  same  width 


WIND  BRACING   OF  TOWERS. 


1081 


at  the  base  that  it  is  at  the  top,  or,  in  other  words,  the  resistance 
of  the  tower  is  materially  increased  by  inclining  the  posts. 
In  proportioning  the  girts  and  diagonals,  only  the  stress  due 
to  wind  pressure  need  be  taken  into  account,  as  the  vertical 
load  would  produce  no  stress  in  the  diagonals,  and  practical 
requirements  will  cause  the  girts  to  be  made  greater  than  would 


Fig.  2 


Fig.   2A 


theoretically  be  necessary.  The  posts,  however,  must  be  pro- 
portioned for  both  the  dead  load  and  wind  stress. 

Allowing  8,000  Ibs.  for  the  weight  of  the  frame,  the  dead  load 
on  each  post  will  be  22,000  Ibs.,  and  as  the  wind  stress  on  the 
leeward  posts  between  joints  7  and  9  is  12,800  Ibs.,  all  four  of 
the  posts  should  be  proportioned  to  support  34,800  Ibs.  com- 
pression. 

The  tension  in  the  windward  posts  is  only  9,100  Ibs.,  and  as 
this  is  greatly  exceeded  by  the  dead  load,  it  need  not  be  taken 
into  account.  The  uplift  on  the  windward  piers  is  12,700  Ibs., 
but  as  the  dead  load  is  22,000  Ibs  ,  no  anchorage  will  be  re- 
quired, although  it  would  be  well  to  bolt  the  posts  to  the  piers 
by  f"  or  J"  bolts  3  or  4  ft.  long. 

The  diagonals  should,  of  course,  be  run  in  both  directions, 


1082  WIND  BRACING  OF  BUILDINGS. 

in  all  four  sides  of  the  tower,  and  should  be  provided  with  turn- 
buckles,  so  that  the  rods  may  be  well  tightened  after  the  frame 
is  erected. 

In  these  two  examples  we  have  considered  towers  of  only 
moderate  height,  for  convenience  of  illustration,  but  the  analysis 
is  precisely  the  same  for  a  frame  of  any  number  of  panels  or 
stories. 

A  good  example  of  a  steel  water-tower  is  described  and  illus- 
trated in  the  Engineering  Record  of  June  20,  1903,  the  stress 
diagrams  and  details  of  construction  being  given. 

Wind  Bracing:  of  Tall  Buildings.— When  office  and 
other  buildings  of  six  to  ten  stories  were  built  with  solid  masonry 
walls  no  attention  was  paid  to  the  lateral  strains  due  to  wind 
pressure,  except,  perhaps,  to  make  the  walls  and  partitions  a  little 
heavier. 

And  as  such  buildings  were  seldom  built  of  a  less  width  than 
50  ft.,  no  other  precautions  were  really  necessary,  for  whenever 
buildings  of  ordinary  construction  with  masonry  walls  have 
been  blown  down,  it  has  generally  been  due  more  to  a  poor 
quality  of  work,  especially  in  the  walls,  or  to  lack  of  sufficient 
anchors,  rather  than  to  faulty  design,  although  occasionally 
as  in  the  St.  Louis  tornado,  a  well-built  building  has  been  blown 
down. 

The  modern  steel  buildings,  however,  are  built  to  such  great 
heights,  especially  in  proportion  to  their  width,  and  are  so  desti- 
tute of  the  ordinary  means  of  resisting  wind  pressure,  such  as 
solid  walls  and  partitions,  that  some  efficient  means  of  bracing 
the  steel  frame  would  seem  to  be  a  matter  of  necessity.  As  a 
matter  of  fact,  few  if  any  skeleton  steel  buildings  are  now 
erected  without  some  provision  for  bracing  the  steel  frame,  in- 
dependent of  the  partitions. 

In  some  buildings  these  provisions  consist  merely  in  using 
girders  built  of  angles  and  plates  of  good  depth,  in  the  use  of 
riveted  connections  at  the  columns,  and  in  breaking  joints 
of  columns  at  the  different  floor-levels,  while  in  others  heavy 
sway-bracing,  knee  or  portal  bracing,  or  both  combined  have 
been  employed. 

In  fact,  the  diversity  of  practice  as  regards  the  wind  bracing 
of  buildings  is  much  greater  than  in  any  other  feature  of  con- 
struction. 

Building's  which  Require  Bracing-. — It  is  generally 
conceded  that  buildings  of  moderate  height  with  solid  masonry 


WIND  BRACING  OF   BUILDINGS.  1083 

construction,  braced  with  permanent  partitions,  will  require 
no  special  wind  bracing;  also  that  all  steel-frame  buildings  in 
which  the  exterior  walls  are  carried  by  the  steel  frame  require 
some  provision  in  the  frame  itself  to  enable  it  to  resist  the  wind 
pressure. 

The  higher  the  building  in  proportion  to  its  width,  unless 
protected  by  adjacent  buildings,  the  greater  will  be  the  need 
of  efficient  wind  bracing. 

The  Chicago  building  ordinance  makes  the  following  require- 
ments : 

"In  the  case  of  all  buildings  the  height  of  which  is  more 
than  one  and  one  half  times  their  horizontal  dimension,  allow- 
ance shall  be  made  for  wind  pressure,  which  shall  not  be 
figured  at  less  than  thirty  pounds  for  each  square  foot  of  ex- 
posed surface.  In  buildings  of  skeleton  construction  the 
metal  frame  must  be  designed  to  withstand  this  wind  pressure." 

The  building  laws  of  Greater  New  York  require  that  "All 
structures  exposed  to  wind  shall  be  designed  to  resist  a  hori- 
zontal wind  pressure  of  thirty  pounds  for  every  square  foot 
of  surface  thus  exposed,  from  the  ground  to  the  top  of  the  same, 
including,  roof,  in  any  direction."  This  is  modified  by  the 
following  clause:  "In  buildings  under  one  hundred  feet  in 
height,  provided  the  height  does  not  exceed  four  times  the 
average  width  of  the  base,  the  wind  pressure  may  be  disre- 
garded." 

The  building  laws  of  Boston  and  Philadelphia  contain  no 
reference  to  wind  pressure.  Mr.  J.  K.  Freitag  has  a  very 
practical  chapter  on  wind  bracing  in  his  excellent  work  "Archi- 
tectural Engineering." 

Methods  of  Wind  Bracing'. — For  buildings  not  exceed- 
ing 120  ft.  in  height,  and  in  which  the  least  width  is  two  thirds 
the  height,  sufficient  rigidity  will  be  obtained  by  using  con- 
tinuous column  splices  as  in  Figs.  15  and  18  of  Chapter  XIV, 
making  the  columns  in  two-story  lengths,  alternate  columns 
breaking  joint  in  alternate  floors,  and  riveting  both  flanges  of 
girders  and  beams  to  the  columns  by  means  of  angles  or  brackets. 

Exposed  steel  buildings  in  which  the  height  exceeds  one  and 
one  half  times  the  width,  or  which  are  more  than  120  ft.  in 
height,  should  have  some  definite  form  of  metallic  bracing. 

Fig.  3  shows  in  outline  the  different  forms  of  wind  bracing 
that  have  been  employed  to  which  should  be  added  the  "portal 
bracing"  shown  by  Figs.  17  and  18.  The  form  of  bracing  to 


1084 


WIND   BRACING   OF   BUILDINGS. 


be  employed  in  any  given  building  will  be  governed  by  the 
peculiar  conditions  which  the  building  offers 

"The  height,  width,  slope,  and  exposure  of  the  structure, 
as  well  as  the  character  of  the  enclosing  walls,  will  determine 
the  amount  of  wind  pressure  to  be  cared  for,  while  the  details 
of  construction,  the  internal  appearance,  and  the  planning 
of  the  various  floors  will  largely  influence  the  manner  in  which 
the  bracing  is  to  be  treated-  The  architectural  planning  of 
the  offices,  rooms,  and  corridors  often  raises  most  serious  ob- 


XXS3 


xxxx 


Fig.  3 
Types  of  Wind  Bracing. 

stacles  to  a  proper  arrangement  of  wind  bracing,  and  the  en- 
gineer is  frequently  called  upon  to  make  most  generous  con- 
cessions for  doors,  windows,  passages,  and  even  whole  areas, 
as  is  sometimes  demanded  in  banking  or  assembly  rooms  and 
the  like."  (Freitag.) 

"The  bracing,  whatever  system  is  used,  must,  of  course,  be 
vertical,  reaching  down  to  some  solid  connection  at  the  ground 
level.  It  should  also  be  arranged  in  some  regular  symmetrical 
relation  to  the  outlines  of  the  building.  For  example,  if  the 
building  is  narrow  and  is  braced  crosswise  with  one  system  of 
bracing,  that  system  should  be  midway  between  the  ends  of 
the  building,  and  if  two  systems  are  used  they  should  be  equi- 
distant from  the  ends,  the  exact  distance  being  unimportant, 
because  the  floors  when  finished  are  extremely  rigid.  The 
symmetrical  arrangement  is  necessary  to  secure  an  equal  service 
of  the  systems  and  prevent  any  tendency  to  twist."  (C.  T. 
Purdy.) 

Intensity  of  Wind  Pressure. — The  intensity  of  wind 
pressure  which  should  be  provided  for  in  calculating  the  stresses 
in  the  braces,  columns,  and  struts  is  considered  at  considerable 
length  by  Mr.  Freitag.  The  building  laws  of  New  York  and 


WIND   BRACING   OF  BUILDINGS.  1085 

Chicago  specify  a  unit  pressure  of  30  Ibs.  Mr.  Freitag  thinks 
that  30  Ibs.  should  serve  as  a  minimum  in  high  buildings  of 
veneer  construction. 

It  is  seldom  that  the  wind  stresses  are  figured  for  a  greater 
unit  stress  than  30  Ibs. 

Many  engineers  consider  that  fully  10  Ibs.  of  wind  pressure 
will  be  resisted  by  the  connections  between  the  columns  and  the 
floor  system,  partitions,  and  dead  weight,  so  that  if  the  bracing 
is  computed  to  take  care  of  30  Ibs.  the  building  will  be  safe  to 
resist  an  actual  wind  pressure  of  40  Ibs.* 

Computation,  of  Stresses. — As  each  different  system 
of  wind  bracing  creates  stresses  unlike  those  created  by  the 
other  systems,  each  arrangement  must  be  treated  separately. 

Diagonal  Systems,  or  Sway-bracing'. — The  diagonal 
system  of  bracing  shown  by  a  and  6,  Fig.  3,  is  the  cheapest 
and  best  when  the  division  of  the  building  by  partitions  will 
admit  of  its  use. 

The  arrangement  of  diagonals  shown  at  a  is  to  be  preferred, 
but  the  location  of  doors,  etc.,  may  sometimes  be  arranged  to 
better  advantage  by  making  the  rods  pass  through  two  stories, 
as  shown  at  6.  Sway-bracing  was  used  in  the  Masonic  Temple, 
the  Venetian  Building,  and  the  Ashland  Block  in  Chicago. 

Analysis. — The  wind  stresses  in  a  diagonal  system  are 
computed  exactly  as  in  Example  1,  although  as  the  posts  are 
always  vertical  and  the  diagonals  usually  have  the  same  incli- 
nation the  stresses  can  readily  be  computed  mathematically, 
as  shown  in  the  following  example: 

EXAMPLE  3.— Let  Fig.  5  be  an  outline  elevation  of  one  set 
of  bracing  in  a  thirteen-story  building  having  the  same  plan 
and  horizontal  dimensions  as  the  Venetian  Building,  Fig.  4, 
and  being  protected  on  one  side  by  an  adjoining  building  which 
reaches  to  the  sixth  floor. 

From  an  examination  of  the  plan  it  will  be  seen  that  the 
exposed  area  contributory  to  each  set  of  bracing  for  each  story 

*  "The  weight  of  the  building  affords  some  resistance,  and  in  most  cases 
Is  worth  taking  into  account.  Most  buildings  are  filled  with  tile  or  some 
other  sort 'of  partitions,  and  when  these  are  really  constructed  and  their 
continuance  is  assured,  there  is  no  good  reason  why  we  should  not  rely 
also  on  them  to  some  extent.  There  is  also  some  resistance  to  lateral 
strains  in  the  connection  of  the  beams  to  the  columns  where  they  are  well 
riveted.  Some  of  these  considerations  will  admit  of  calculation,  but  in 
using  them  much  must  depend  on  the  experience  and  judgment  of  the 
engineer."  (C.  T.  Purdy.) 


1086 


WIND  BRACING  OF  BUILDINGS. 


is  21 TVX  height  of  story,  and  as  the  stories  are  all  12  ft.  from 
floor  to  floor,  the  area  contributory  to  each  joint  is  259  sq.  ft. 

Assuming  a  wind  pressure  of  30 
Ibs.,  the  wind  loads  at  each  floor 
will  be  7,770  Ibs.,  or  say  7,800 
Ibs.,  except  that  at  the  seventh 
floor  the  load  will  be  only  one  half 
that  at  the  floors  above. 

Note. — There  will,  of  course,  be 
a  wind  pressure  on  the  stories 
below  the  seventh,  but  it  is  safe 
to  assume  that  it  will  be  resisted 
by  the  buildings  abutting  on  the 
other  side,  particularly  as  the  ex- 
posed side  will,  in  the  business 
portion  of  a  city,  be  considerably 
sheltered  by  the  buildings  on  the 
opposite  side  of  the  street. 

In  order  to  provide  for  door 
openings  next  the  columns  it 
will  be  necessary  to  connect  the 
diagonals  with  the  struts,  18" 
in  from  centre  of  columns,  which 
will  make  the  angle  between  struts 
and  diagonals  42°  42'. 


Fig.  4 


(The  tangent  of  the  angle 


r,  or  in  this  case  .9230,  and  from 


the  table  on  natural  tangents,  p.  122,  we  find  the  angle  whose 
tangent  is  nearest  to  .9230  to  be  42°  42'.) 

We  are  not  prepared  to  compute  the  stresses  which  should 
be  entered  in  a  table  like  that  given  below.  As  shown  on 
p.  1079,  the  shear  at  each  floor  is  equal  to  the  wind  load  at  that 
floor  plus  all  of  the  loads  above,  which  enables  us  to  compute 
the  shears  directly  and  enter  them  in  the  second  column.  It 
was  also  shown  that  the  stress  in  the  diagonal  for  each  story 
is  equal  to  the  shear  in  the  strut  above  multiplied  by  the  secant 
of  the  angle  6.  From  the  table  on  p.  123a  we  find  that  the 
secant  of  42°  42'  is  1.36,  and  multiplying  the  shears  by  this 
factor,  we  have  the  values  given  in  the  third  column. 

On  p.  1079  it  was  shown  that  the  stress  in  the  leeward  column 
for  any  story  is  equal  to  the  stress  in  the  story  above  plus  the 
vertical  component  of  the  stress  in  the  diagonal  for  that  story, 


WIND  BRACING  OF  BUILDINGS. 


1087 


V, 


I\ 


\ 


13th 


10th 


and  that  the  vertical  component,  to  which  we  will  give  the 
term  increment,  is   equal  to  kthe  shear  in 
the  strut  above  multiplied  by  the  tangent     ?» 

of  the  angle  or  by  r,  which  in  this  ex- 
ample is  .923.  -^ 

Multiplying  each  shear  by  .923  we 
obtain  the  increments  given  in  the  fourth 
column  of  our  table. 

Tne  compression  in  the  leeward  column 
in  the  thirteenth  story  is  the  same  as  the 
increment.  In  the  twelfth  story  it  is 
equal  to  the  compression  in  the  thirteenth 

story  plus  the  increment  for  the  twelfth  <_ 

story  and  so  on  down  to  the  basement. 

It  will  be  seen  that  the  compression  in 
the  columns  increases  very  rapidly  in  the  — - 
lower  stories'  and  amounts  to  a  very  con- 
siderable stress  in  the  basement,  first  and 
second  stories. 

The  tension  in  the  windward  column  in 
any  story  is  equal  to  the  compression  in  3Q 
the  leeward  column  in  the  story  next 
above,  thus  the  tension  in  the  windward 
column  will  be  471,600  Ibs.  in  the  first 
story  and  525,600  Ibs.  in  the  basement. 

The  tensile  stress  exceeds  the  actual 
dead  load  on  the  columns,  including  a 
liberal  allowance  for  weight  of  furniture, 
etc.  In  this  example,  however,  the  dis- 
tance between  the  columns  is  very  short 
in  proportion  to  the  height  of  the  build- 
ing, thus  greatly  increasing  the  column 
stress. 

It  is  extremely  doubtful  if  the  wind 
blowing  against  a  building  such  as  we  are 
considering  would  actually  produce  an  up- 
lift on  the  windward  columns. 

Theoretically  both  columns    should  be 
proportioned  to  the  full  dead  load  on  the      | 
columns,  including  a  small   allowance  for 
the  weight  of  furniture,  and  also  for  the 


3rd 


Fig.  5 


1088 


WIND    BRACING  OF  BUILDINGS. 


WIND  STRESSES. 

Unit  pressure  ==30  Ibs. 
Tangent  0  =  0.923. 


EXAMPLE  3. 

Angle  6  =  42°  42'. 
Secant  5=1.36. 


Story. 

Shear  or 
Com- 
pression 
in  Strut. 

Tension  in 
Diagonal 
=  shear 
Xsec  6. 

Increment 
=  shear 
Xtan  6. 

Compression 
in  Leeward 
Col. 

Attic.                    .    . 

7,800 

Thirteenth  

15,600 

10,600 

7  200 

7  200 

Twelfth 

2$  400 

21  220 

14  400 

21  600 

Eleventh. 

31,200 

31  820 

2l'600 

43  200 

Tenth  

39,000 

42,430 

28  800 

72000 

Ninth  

46,800 

53,040 

36000 

108,000 

Eighth 

54,640 

63  640 

43  200 

151  200 

Seventh  

58,500 

74  250 

50  400 

201  600 

Sixth  

79,560 

54,000 

255,600 

Fifth  

i 

309,600 

Fourth.  .  .  . 

t 

( 

t 

363  600 

Third  

t 

( 

( 

417,600 

Second  

t 

t 

t 

471,600 

First 

i 

i 

(       • 

525  600 

Basement  

525,600 

full  wind  stresses  in  the  leeward  column  (as  the  wind  may 
blow  against  either  side  of  the  build- 
ing) ,  and  if  the  frame  stood  by  itself, 
as  in  Fig.  5,  this  method  should  be 
followed  in  practice,  and  the  columns 
should  also  be  anchored  to  the 
H  foundations  sufficient  to  resist  the 
theoretical  uplift  minus  the  dead 
load. 

In  the  building  under  considera- 
tion, however,  there  are  three  of 
these  panels  in  the  width  of  the 
building  (see  Fig.  4),  and  as  the 
floor  connections  would  assist  some- 
what in  relieving  the  braced  system 
from  the  full  theoretical  stresses, 
most  if  not  all  structural  engineers 
would  probably  cut  down  the  theo- 
retical  stresses  in  the  columns  con- 
siderably, probably  50  per  cent,  in 

the  lower  stories. 

buildings  of    even 


Partial 


FiS-  6 


on,  Venetiao 


WIND  BRACING  OF  BUILDINGS.  1089 

more  than  thirteen  stories  are  standing  with  scarcely  any  pro- 
vision for  wind  stress  *  would  indicate  that  a  considerable 
cutting  down  of  the  column  stresses  is  permissible. 

Theoretically  the  columns  should  also  be  proportioned  to 
the  eccentric  loads  due  to  the  increments  being  applied  18  ins. 
from  the  centre  of  the  columns. 

Practically  the  columns  should  be  made  wide,  in  the  direc- 
tion of  the  wind,  i.e.,  parallel  to  the  end  of  the  building,  and 
the  braces  should  be  applied  as  close  to  the  centre  of  the  columns 
as  practical  conditions  will  admit. 

All  columns  affected  by  the  wind  bracing  should  be  made 
continuous  by  means  of  splice  plates  from  the  foundation  to 
the  top. 

Where  the  rods  come  down  to  the  first-floor  level,  the  bottom 
strut  should  be  connected  to  the  columns  so  as  to  take  both 
tension  and  compression  horizontally,  so  that  both  columns 
may  assist  in  resisting  the  shear  at  that  level. 

The  clearance  spaces  between  all  of  the  first-floor  beams 
and  columns  should  be  filled  with  metal  wedges  and  the  columns 
wedged  against  the  sidewalk  walls,  so  that  the  entire  floor 
system  will  act  as  a  strut,  backed  by  the  solid  street. 

For  the  diagonal  braces,  which  should  run  in  both  directions, 
square  rods  or  flat  bars  should  be  used,  and  each  should  be 
provided  with  a  turnbuckle  for  adjustment  after  the  frame  is 
erected. 

It  is  customary  to  proportion  the  rods  to  the  theoretical 
wind  stresses,  allowing  20,000  Ibs.  to  tfye  square  inch. 

The  struts  should  be  designed  as  strut  beams  if  they  also 
assist  in  supporting  the  floor,  and  for  the  bending  moment 
produced  by  the  bracing. 

Fig.  7  shows  the  connection  between  column  and  strut  recom- 
mended by  Mr.  Purdy.  "The  strut  need  not  be  connected 
to  the  column  to  resist  horizontal  forces,  for  there  is  no  force 
tending  to  tear  the  strut  away  from  the  columns  in  this  direc- 
tion. The  force  to  be  resisted  here  is  vertical.  The  strut 
should  be  made  to  butt  the  column  squarely,  instead  of  fastening 
to  the  sides  of  the  column  by  rivets  passing  through  the  two 
members,  or  indirectly  through  connection  plates,  because 
the  forces  producing  stresses  in  the  bracing  at  this  point  must 
come  into  the  strut  by  compression  from  without  and  not 

*  See  Ajchitectijral  Engineering,  second  edition  p.  249. 


1090 


WIND  BRACING  OF    BUILDINGS. 


through  any  possible  tensile  stress.  When  the  strut  butts  the 
column  these  forces  are  introduced  into  the  strut  without  the 
aid  of  rivets,  and  the  full  value  of  all  the  rivets  can  be  used  to 


SECTION  B-B 


SECJTION  A:A 


SECTION  C-C 


Fig.  7 

Strut  and  Column  Connections. 

resist  the  vertical  component  of  the  rod  stress.  It  serves  also 
to  keep  the  arm  at  the  end  of  the  strut,  or  the  distance  from 
the  centre  of  pin  to  the  bearing  at  the  end,  as  short  as  possible, 
all  of  which  is  important.  The  top  angles  may  be  placed 


WIND  BRACING  OF  BUILDINGS. 


1091 


several  inches  above  the  strut  and  a  cast  filler  block  introduced 
between  them. 

"  Such  an  arrangement  has  several  advantages.  It  generally 
happens  that  these  angles  cannot  be  riveted  to  the  column 
directly  above  the  channels  of  the  strut,  as  shown  in  Fig.  7. 
The  consequence  is  that  whatever  intervenes  must  carry  a 
cross  strain.  The  cast  block  will  do  this  well.  It  is  also  im- 
portant that  there  should  be  absolutely  no  clearance,  other- 
wise the  whole  system  would  lack  in  stiffness  and  efficiency. 
The  block  can  be  cast  a  little  large,  and  if  necessary  it  can  be 
chipped  at  the  building  in  order  to  crowd  it  into  position. 

"  The  block  also  has  the  further  advantage  of  cheapness  and 
is  always  easily  obtained.  Every  detail  in  wind  bracing  should 
receive  the  most  careful  attention."  * 

Fig.  8  shows  a  detail  of  the  channel  struts  used  in  the  Vene- 
tian Building  up  to  and  including  the  seventh  floor.  A  lighter 
section  was  used  for  the  floors  above.  These  struts  were  in- 
dependent of  the  floor  system. 

Knee  Braces.  —  The  system  of  wind  bracing  shown  at  c, 
Fig.  3,  is  not  an  economical  method  of  bracing  a  framed  struc- 
ture, because  it  produces  heavy  bending  moments  both  in  the 
horizontal  struts  and  in  the  columns.  Nevertheless  it  is  being 


Fig.  8 
Detail  of  Strut,  Venetian  Building. 

used  more  largely  in  tall  buildings  than  any  other  type  of  wind 
bracing,  particularly  for  bracing  the  outer  columns. 

In  a  personal  letter  to  the  author,  Mr.  C.  T.  Purdy,  whose  firm 
(Purdy  &  Henderson)  has  been  identified  with  the  engineer- 
ing work  of  a  great  many  tall  buildings  built  during  the  past 
ten  years,  says:  "While  it  is  true  that  gusset-plate  and  knee- 
brace  construction  is  more  expensive  and  not  as  desirable  as 
the  diagonal  system,  yet  it  is  also  true  that  we  have  used  that 

*  C.  T.  Purdy  in  Modern  Framed  Structures,  p.  459. 


1092 


WIND   BRACING  OF   BUILDINGS. 


construction  a  good  deal,  but  almost  always  in  exterior  walh. 
In  all  of  these  cases  practical  considerations  have  counted  for 
more  than  theoretical  ones.  These  practical  considerations 
are:  (1)  On  many  buildings  the  arrangement  or  use  of  the 
building  prevents  the  direct  treatment  of  the  problem  and  the 
owner  or  architect  insists  that  the  wind  bracing  shall  be  hidden 


Wall     Bracing. 

Intermediate  Transverse  Bracing. 
Fig.  9  Fig.  10 

Wind  Bracing  in  Flat-iron  Building. 

in  the  masonry  regardless  of  cost.  (2)  When  this  construction 
is  used  we  can  make  the  heavy  girder  do  double  duty.  In 
most  cases  the  wall  or  floor  construction  also  belonging  to  these 
particular  members  would  require  considerable  metal  and  depth 
of  brace.  (3)  Experience  also  shows  that  riveted  construc- 
tion in  which  all  web  members  of  a  system  can  take  either 
tension  or  compression  makes  the  stiffest  structure  and  is  more 
satisfactory  in  every  way  than  pin-connected  work.  In  other 
words,  although  it  costs  a  little  more,  the  gusset-plate  work 


WIND   BRACING   OF  BUILDINGS. 


1093 


'Co/. 
36-^ 


in  exterior  walls  accomplishes  its  purpose  and  has  proved 
very  satisfactory." 

Gusset  plates  were  used  in  the  Fort  Dearborn  Building, 
Chicago,  by  Jennie  &  Mundie,  architects. 

Figs.  9,  10,  11,  and  12  *  show  details  of  the  wind  bracing 
in  the  Flat-iron  Building,  New  York,  of  which  D.  H.  Burnham 
&  Co.  were  archi-  ,,,— 

NS,  r&w>?&  /, 

_xV_  ?:g.^_^  £/g_y</r 


tects,  Purdy  &  Hen- 
derson consulting  en- 
gineers. This  build- 
ing is  in  plan  a 
right-angled  triangle 
with  base  and  per- 
pendicular 171  ft. 
and  86  ft.  respect- 
ively, the  angles  of  s^'^ioor 
the  building  being 
curved,  and  the 
height  is  twenty-one 
stories,  or  about  285 
ft.  above  the  curb. 

In  all  the  outer 
walls  of  the  building 
the  masonry  is  car- 
ried on  plate  girders 
in  each  floor  from  the 
first  to  the  twelfth 
stories  respectively, 
and  also  at  the 
eighteenth  floor.  All 
other  stories  above 
the  twelfth  have 


Center  Tranaverse  Bracing. 

Fig.  II 


wall  girders  made  of  a  pair  of  15-in.  channels. 

These  wall  girders  are  also  utilized  as  wind  struts  and  to 
support  the  floor  beams.  In  all  cases  they  are  connected  to 
the  columns  by  solid  web  knee  braces  above  and  below  the 
girder  as  shown  by  Figs.  9  and  14.  Besides  the  knee  bracing 
of  the  outside  walls  there  are  two  systems  of  transverse  bracing, 
shown  in  part  by  Figs.  10  and  11,  connecting  the  two  sides 
of  the  building.  The  system  shown  by  Fig.  10  connects  the 

*  These  illustrations  and  the  following  description  are  from  the  Engineer- 
ing Record  of  March  29,  1902. 


1094 


WIND  BRACING  OF  BUILDINGS. 


05 
.8 


I 
g  9 

= 1 


-  02 

o>  d 


WIND  BRACING   OF  BUILDINGS. 


1095 


third  columns  from  the  apex  of  the  triangle,  and  that  shown 
by  Fig.  11  is  51  ft.  or  3  panels  beyond.  "In  addition  to  these 
two  general  systems  of  transverse  bracing  there  is  intermediate 
between  them  a  supple- 
mental system  parallel  Iuttt*IO-°^--y— - [-.—---.[—  f- 

with  them,  extending 
from  the  second  floor  to 
the  foundation." 

Figs.  13  and  14  are 
photographic  views  of  the 
bracing,  and  Fig.  12 
shows  the  manner  in 
which  the  columns  are 
spliced.  The  lower  sec- 
tion of  column  23  has  a 
sectional  area  of  226.6 
sq.  ins. 

The  Frick  Building, 
Pittsburg,  a  twenty-story 
steel-cage  office  building, 
is  braced  by  plate  gird- 
ers and  knee  braces 
similar  to  those  in  the 
Flat-iron  Building.  A 
description  of  this  build- 
ing is  contained  in  the 
Engineering  Record  of 
Jan.  11,  1902. 

The  building  of  the 
Bank  of  the  State  of 
New  York,  New  York 
City,*  which  is  about 
85X100  ft.  in  plan  and 
twenty-five  stories,  or 
about  340  ft.  above  the 
curb,  has  all  four  outside  walls  braced  with  long  knee  braces 
and  also  two  rows  of  interior  columns.  Fig.  15  shows  the 
bracing  in  two  of  the  five  panels  in  a  section  parallel  to  the 
front. 

Details  giving  sizes  of  girders,  bracing  of  exterior  walls,  etc., 
were  published  in  the  Engineering  Record  for  Sept.  13,  1902. 

*  Clinton  &  Russell,  architects;  Purdy  &  Henderson,  consulting  engineers. 


1st  Floor 


232>< 


Fig.  15 

Partial  Transverse  Section,  Bank  of  the 
State  of  New  York. 


1096 


WIND   BRACING   OF  BUILDINGS. 


The  Battery  Place  Building,  New  York,*  has  the  two  narrow 
ends  of  the  building  braced  by  struts  formed  of  pairs  of  channels 
with  solid  web  knee  braces  above  and  below,  as  in  Fig.  9  (see 
Engineering  Record  of  July  19,  1902). 

In  the  Land  and  Title  Building,  Philadelphia,  twenty-two 
stories,  or  about  317  ft.  high  above  the  curb,  four  different 
systems  of  bracing  are  combined:  (1)  horizontal  diagonals  in 
every  floor  plane;  (2)  deep  plate  girders  at  floor  levels  in  the 
plane  of  all  wall  columns;  (3)  solid  web  knee  braces  in  the 
corners  of  all  wall  panels  excepting  in  the  two  upper  stories;  and 
(4)  extra  heavy  beam  and  girder  connections  to  interior  columns 
(construction  of  the  building  illustrated  and  described  in 
Engineering  Record  for  Oct.  3,  1903). 

The  stresses  for  a  system  such  as  is  shown  in  Fig.  16  may 
L  _n    j  be  computed  with  sufficient  ac- 

curacy  as  follows:! 
Let  P  be  the  wind  pressure  at 
top    floor,     contribu- 
h  tory  to  the  bent; 

Pl  the    wind     pressure    at 
I  next  floor  below; 

P2  the    wind     pressure    at 
second  floor  from  top, 
hl  and  so  on; 

then  max.  compression  in  strut 

s  —P" 
max.  compression  in  strut 

i  i ' 

ln  max.  compression  in  strut 


4, 

--f- 


A'2 


Fig.  16 


Tension   in    col. 

sion  in  Af=  V= 


A  =  compres- 
PXh 


Increment  for  A1  and  A/  = 


I 


*  H.  J.  Hardenbergh,  architect;  Purely  &  Henderson,  consulting  en- 
gineers. 

t  The  best  analysis  of  the  stresses  in  braced  portals  and  transverse 
bents  that  the  author  has  seen  is  in  "  Steel  Mill  Buildings,"  by  Prof.  Milo 
S.  Ketchum.C.E. 


WIND  BRACING  OF  BUILDINGS.  1097 

Tension  in  A  t  =  compression  in  A1'=V+V1. 

11  A2=  "  "  A2'=V  +  V  ,  +  V2. 

11        "  brace  B  =  compression  in  B'=V  sec  0. 


Bending  moment  at  b  =  —  j—  . 


The  struts  s,  slf  s2,  etc.,  will  be  in  tension  at  the  leeward  end; 
therefore  both  ends  of  the  strut  should  be  riveted  to  the  columns. 

In  the  Isabella  Building  in  Chicago,  Mr.  W.  L.  B.  Jenney, 
the  architect,  used  the  knee-brace  system  shown  by  Fig.  17. 
When  the  braces  meet  at  the  centre  of  the  strut,  there  is  no 
bending  moment  on  the  strut,  and  as  the  foot  of  the  brace 
naturally  comes  nearer  the  floor  below,  the  bending  moment 
on  the  column  is  materially  reduced. 

Portal  Bracing'.  —  This  system  can  be  used  in  the  place 
of  sway-rods,  where  conditions  as  to  corridors,  doors,  etc.,  prohibit 
the  crossing  of  such  spaces.  The  system  is  not  as  economical 
as  sway-bracing,  but  is  generally  considered  more  effective  and 
cheaper  than  the  knee-brace  system,  because  it  produces  prac- 
tically no  bending  moment  on  the  columns  and  struts.  The 
portal  system  with  a  curved  solid  web  was  first  used  in  the 
Old  Colony  Building,  Chicago,  completed  in  1894,  a  partial 
cross-section  of  which  is  shown  by  Fig.  18  and  a  detail  of  one 
of  the  portals  by  Fig.  19.*  "This  arrangement  of  wind  bracing 
proved  very  satisfactory  in  all  respects." 

It  has  since  been  used  in  a  few  panels  in  other  buildings, 
but  the  knee  brace  seems  generally  to  be  preferred. 

Analysis  of  Stresses.  f—  Fig.  20: 

*  From  Architectural  Engineering. 

t  The  following  analysis  by  Mr.  C.  T.  Purdy  is  taken  by  permission 
from  "  Modern  Framed  Structures." 


1098 


WIND   BRACING  OF  BUILDINGS. 


Let  A  =  accumulated  force  or  horizontal  shear  from  wind  at  the 
floor  next  above  floor  M,  applied  half  on  one  side 
and  half  on  the  other; 


B=  the  force  of  wind  or  shear  directly  tributary  to  floor  Af ; 

Z)=the  accumulated  vertical  wind  load  in  the  column  next 

above  col.  2; 
then 
Ah  +  Bh-Bc 


I 


and 


-  =  vertical  resistance  due  to  A  and  B,  or  the  incre- 
ment, as  denoted  in  the  preceding  analyses; 


— - —  =  horizontal  reactions  due  to  A  and  B. 


WIND  BRACING  OF  BUILDINGS. 


1099 


The  actual  wind  load  on  col.  2  and  the  corresponding  tension 


in  col.  1  will  = 


Ah  +  Bh-Bc 
I 


+D. 


tfOOF 


The  horizontal  shear  along  the  line  EE—A+B. 

The  horizontal  shear  in  either  leg  below  the  line  EE=  J(A  +B). 

Ah  +  Bh-Bc 
I  he  vertical  shear  on  all  vertical  planes  = , 

The  thickness  of  the  web-plates  must  be  determined  by  these 
shears.  It  should  be  noted  that  the  connection  to  the  columns 
must  be  equal  to  the 
whole  vertical  shear. 
The  direct  compression 
in  the  flange  s=  \B. 

Taking  moments 
about  the  point  of 
intersection  of  flange  r 
with  the  line  ivw,  it 
will  be  found  that  the 
sum  of  the  moments = 
zero,  that  is,  that  there 
is  no  bending  moment 
in  the  portal  on  the 
line  ww  and  that  flange 
t  is  not  strained  at 
this  point. 

For  maximum  stress 
in  flange  t  take  a 


Fig.  18 

Cross-section  showing  Portals,  Old  Colony 
Building. 


point  p  in  flange  r,  distant  x  from  the  line  ww  and  at  right 
angles  to  any  given  section  of  the  flange  t',  then  x  times  the 
vertical  shear  divided  by  ?/  =  the  stress  at  the  section  taken, 

and  this  is  maximum  when  —  has  its  greatest  value. 

The  leg  of  the  portal,  including  col.  2,  might  be  also  taken 

,.,  ..  A+B      ,  Ah+Bh-Bc 

as  a  cantilever  with  two  lorces  acting  on  it,  —  ~  —  ana  —     —  j  --  , 

with  flange  t  in  compression  and  the  column  itself  acting  as  a 
tension  cord.  Take  a  point  in  the  centre  of  the  column,  dis- 
tant x1  from  the  bottom  of  the  leg  and  at  right  angles  to  any 

A+B    x 
given  section  in  flange  t,  then  —  -  —  X  —  =  the  strain  in  flange  t, 


and  this  is  maximum  when  —  has  its  greatest  value.     There  is 


1100 


WIND  BRACING  OF  BUILDINGS. 


a  slight  error  in  this  treatment,  but  it  is  on  the  side  of  safety. 
If  flange  I  has  a  section  proportioned  to  these  maximum  stresses, 
the  requirements  will  be  fulfilled.  The  stress  and  area  re- 


Fig.  19 
Detail  of  Portal  in  Old  Colony  Building. 


quired  in  flange  r  can  be  obtained  in  a  similar  manner.  The 
connection  of  the  portal  above  this  flange  to  the  portal  and 
column  above  must  be  equal  to  \A.  at  each  leg. 

Lattice  Girders. — "In  this  type  of  bracing  the  wind 
stresses  are  transferred  to  the  ground  on  what  is  often  called 
the  'table-leg  principle;'  that  is,  each  story  is  made  rigid  in 
itself,  the  columns  being  figured  as  vertical  beams  to  resist  the 
lateral  flexure  due  to  the  wind  forces." 


WIND  BRACING  OF  BUILDINGS. 


1101 


.A 
a     2 


Fig.  20 

Analysis. —  Referring  to  Fig.  21: 
Let  A  =  accumulated 

force  or  hori-  D 

zontal  shear 
from  wind  at 
thefloor  next  _B_ 
above     floor  2 
M,     applied 
half  on   one  •— 
column    and 
half   on  the 
other; 

J3=the  force  of 
wind  or  shear 
directly  trib- 
utary to  floor 
M; 

D=the  accumu- 
lated verti- 
cal wind  load 
in  the  col- 
umn next 
above  col.  2; 


u 

1] 


Floor  M 


I 
I 
I 

i, 


A-f  B 
2 


7  -     *l 

ri 
Fig.  21 


JA-fB 


1102  WIND  BRACING  OF  BUILDINGS. 

then  1  5  may  be  considered  as  applied  in  a  line  with  each  chord 
of  the  girder.  The  horizontal  shear  due  to  the  force  B  must 
then  be  resisted  by  the  two  columns  at  any  and  all  points  be- 
tween the  lower  line  of  the  girder  and  the  top  line  of  the  girder 

D 

below.     Hence  the  foot  of  each  column  must  resist  the  shear  —  . 

2t 

4 

Also  ^-  will  equal  the  shear  at  the  foot  of  the  columns  next 

above  floor  M  ,  and  as  cols.  1  and  2  must  resist  this  shear,  as 
well  as  that  due  to  B,  the  total  shear  at  the  foot  of  each  of  the 

A  +  B 
columns  in  the  story  under  consideration=  —  —  ,  the  same  as 

L 

with  portal  bracing. 

Considering  the  external  forces  applied  as  indicated  in  Fig.  21, 
and  taking  moments  about  joint  e,  we  have  the  moment  tending 

n  D 

to  overturn  the  frame  on  e  as  a  hinge,  AX^l  +  -^-Xh2  +  -^-Xh3. 

[Neglecting  the  forces  Z>,  D,  because  they  act  through  the  centre 
of  the  columns  and  do  not  affect  the  stresses  in  the  girder  or 
the  bending  moment  in  the  column.]  This  moment  must  be 
resisted  by  the  tension  in  col.  1,  which  acts  with  an  arm  I; 
therefore 


To  this  must  be  added  the  load  or  tension  D±  from  the  column 
above. 

Taking  moments  about  /,  we  will  obtain  the  same  value  for 
V  in  col.  2  that  we  obained  above,  col.  2  being  in  compression 
and  col.  1  in  tension. 

To  find  the  compressive  stress  in  the  upper  flange  of  the 
girder  ac,  take  moments  about  b  and  denote  stress  in  ac  by  s. 
The  moments  tending  to  revolve  the  column  to  the  right  are 


These  moments  must  be  resisted  by  the  stress  in  ac  acting  with 
an  arm  a&,  =  7&2  —  /?3,  from  which  we  obtain  the  equation 


WIND  BRACING  OF  BUILDINGS.  1103 

Taking  moments  about  a  and  denoting  the  stress  in  the  bottom 
flange  of  the  girder  by  sl  we  obtain 

_KA  +  g)fr2  +  jA(fr-fr0)     B 
Sl~  h2-h3  2' 

Both  struts  are  principally  in  compression,  although  they 
must  be  connected  to  the  columns  to  resist  an  equal  amount 
of  tension.  Considering  the  columns  as  fixed  at  both  ends  the 
maximum  bending  moments  will  be  at  the  points  b  and  d  and 
will  be  equal  to* 


The  columns  must  be  designed  to  resist  this  bending  moment 
as  well  as  the  vertical  loads.  From  the  above  analysis  it  is 
readily  seen  that  the  deeper  the  girder  the  less  will  be  the  stresses. 
When  used  in  outside  walls  they  should  be  made  the  full  depth 
of  the  spandrel,  reaching  from  just  above  the  top  of  one  window 
to  immediately  below  the  sills  of  the  windows  in  the  next  story 
above. 

*  See  Architectural  Engineering,  p.  277. 


PART  ffl. 


USEFUL  INFORMATION 


ARCHITECTS,  BUILDERS,  AND  SUPERINTEND- 
ENTS 

AND   ALL    WHO   HAVE  TO    DO    WITH   THE   BUILDING  TRADES. 

NOTE. — The  Author  has  endeavored  to  arrange  the  information 
herein  contained  iii  the  following  order: 
Heating,  Ventilation,  Chimneys. 
Hydraulics  and  Plumbing. 
Illuminating-gas,  Gas-piping,  and  Lighting. 
Electrical  Definitions,  Rules,  and  Tables. 
Weights,  Quantities,  and  Data  for  Estimating  Cost. 
Dimensions  and  Data  Useful  in  the  Preparation  of  Plans. 
Miscellaneous  Information. 
Glossary  of  Technical  Terms. 
Legal  Definitions. 

1105 


HEATING  AND  VENTILATION. 

HEAT,  FUEL,  WATER,  STEAM,  AND  AIR, 

Heat  is  measured  in  two  ways:  1st,  by  the  thermometer,  as 
in  ordinary  practice,  and,  2d,  by  the  work  which  it  performs. 

The  unit  of  heat  (sometimes  called  the  British  thermal  unit)  is 
that  quantity  of  heat  which  will  raise  the  temperature  of  one 
pound  of  water  at  or  near  the  freezing-point,  1°  Fahrenheit. 

A  French  "calorie"  is  the  heat  required  to  raise  one  kilo- 
gramme of  water  1°  Centigrade,  and  is  equal  to  3.96832  British 
thermal  units. 

The  equivalent  in  force  of  the  unit  of  heat  is  the  raising  of  772 
pounds  avoirdupois  one  foot  high,  and  is  called  the  mechanical 
equivalent  of  heat. 

Various  kinds  of  fuel  contain  a  certain  number  of  thermal 
units  per  pound;  and  the  method  of  heating  which  will  convey 
the  largest  number  of  units  to  the  air  to  be  warmed  is  the  most 
economical,  so  far  as  fuel  and  heating  are  concerned.  But  no 
method  has  yet  been  devised  which  will  utilize  more  than  about 
85  per  cent,  of  the  heat-units  contained  in  the  fuel. 

Fuel.* — The  value  of  any  fuel  is  measured  by  the  number 
of  heat-units  which  its  combustion  will  generate.  The  fuels 
generally  used  in  heating  are  composed  of  carbon  and  hydrogen , 
and  ash,  with  sometimes  small  quantities  of  other  substances 
not  materially  affecting  its  value. 

"Combustible"  is  that  portion  which  will  burn,  the  ash  or 
residue  varying  from  2  to  36  per  cent,  in  different  fuels. 

The  following  table  gives,  for  the  more  common  combustibles, 
the  air  required  for  complete  combustion,  the  temperature  with 
different  proportions  of  air,  the  theoretical  value,  and  the 
highest  attainable  value  under  a  steam-boiler,  assuming  that 
the  gases  pass  off  at  320°,  the  temperature  of  steam  at  75  Ibs. 
pressure,  and  the  incoming  draught  to  be  at  60°. 

*  From  Steam,  published  by  the  Babcock  &  Wilcox  Company,  New 
York  and  Glasgow. 

1107 


1108 


FUELS. 


I 

PQ 

a 
o 

o 


PQ 


Jin 

With  Blast,  Theoreti- 
cal   Supply    of   Air 
at  60°   Gas  320°. 

O       •>&       COOSCOCO<MOO<MO» 
OS       i—  i      O  i—  '  t>-  ^  ''f    t>    O    CO 

•-5  S« 

With  Chimney  Draft. 

»O      CO       C^  T^  O  l>  OS    ^    CO    O 

GO     co     Tt^'^OGO   co  co  -*' 

1. 

*-*3  c> 

In    Pounds    of  Water 
Evaporated  from  and 
at  212°  with  1  Pound 

o  ^     o     ooo>oo  *o  o  o 

§.| 

Combustible. 

r 

In       Heat-units       per 
Pound    of   Combusti- 
ble. 

(MO       O       Ot^OtOO    O    iO    O 

With  Three  Times  the 
Theoretical  Supply  of 
Air. 

11  1        1  1  1 

11 

"S  § 

With  Twice  the  Theo- 
retical Supply  of  Air. 

IS  I  i!illa§-§ 

|| 

ti 

So 

With    \1A    limes    the 
Theoretical  Supply  of 
Air. 

OiO      iO      OOOOO    O    O    O 

COi-l         i-H         CO(MCOi-HTtH<MrHt>. 

GO»O       <M       COiOCO(Ni-(     GO     OS     CO 
COCO       CO       COCOCOCOCO    (M     <N     (N 

H 

With  Theoretical 
Supply  of  Air. 

ill  1        1  1  1 

a1 

In  Pounds  per  Pound 
of  Combustible. 

8  co     co     COCOOOGO  co  o  o 
Th       I-H       0|>OOCOCO    t^    0    GO 

Kind  of  Combustible. 

^  •  a  •  •  •~AT   "*tr 

c3    ;  g        ;    ;      %          <3 

^"o     g     J^            ^        -g 

WfS  6  6*  *  "  £     ^ 

The  effective  value  of  all  kinds  of  wood  per  pound,  when 
dry,  is  substantially  the  same.  The  following  are  the  weights 
and  comparative  value  of  different  woods  by  the  cord: 


Kind  of  Wood. 

Weight. 

Kind  of  Wood. 

Weight. 

Hickory   shellbark  

4469 

Southern  pine  

3375 

Hickory  red-heart.  . 

3705 

Virginia  pine  

2680 

White  oak  

3821 

Spruce  

2325 

Red  oak 

3254 

2137 

Beech.  .  .            

3126 

Yellow  pine  

1904 

Hard  maple 

2878 

White  pine  

1868 

The  following  table  of  American  coals  has  been  compiled  from 
various  sources: 


HEATING  VALUE  OF  COALS. 
AMERICAN  COALS. 


1109 


Coal. 
State.         Kind  of  Coal. 

Per  Cent, 
of  Ash. 

Theoretical  Value. 

In  Heat- 

uiiits. 

In  Pounds 
of  Water 
Evapo- 
rated. 

Pennsylvania, 
Kentucky, 

u 
11 

Illinois, 

u 
(( 

Indiana, 
n 

Maryland, 
Arkansas, 
Colorado, 

u 

Texas, 
Washington, 
Pennsylvania, 

Anthracite.  . 

3.49 
6.13 
2.90 
15.02 
6.50 
10.77 
5.00 
5.60 
9.50 
2.75 
2.00 
14.80 
7.00 
5.20 
5.60 
5.50 
2.50 
5.66 
6.00 
13.98 
5.00 
9.25 
4.50 
4.50 
3.40 

14,199 
13,535 
14,221 
13,143 
13,368 
13,155 
14,021 
14,265 
12,324 
14,391 
15,198 
13,360 
9,326 
13,025 
13,123 
12,659 
13,588 
14,146 
13,097 
12,226 
9,215 
13,562 
13,866 
12,962 
11,551 
20,746 

14.70 
14.01 
14.72 
13.60 
13.84 
13.62 
14.51 
14.76 
12.75 
14.89 
16.76 
13.84 
9.65 
13.48 
13.58 
13.10 
14.38 
14.64 
13.56 
12.65 
9.54 
14.04 
14.35 
13.41 
11.96 
21.47 

it 

it 

Cannel 

Connellsville.  .  .  . 
Semi-bituminous 
Stone's  gas.  .  . 

Youghiogheny.  .  . 
Brown.  . 

Caking   .  .    . 

Cannel  

u 

Lignite.  .  . 

Bureau  Co.  .  . 

Mercer  Co.  .  .  . 

Montauk  

Block 

Caking  

Cannel 

Cumberland.  .  .  . 
Lignite  

K 

u 

t( 

u 

Petroleum 

"Slack,"  or  the  screenings  from  coal,  when  properly  mixed — 
anthracite  and  bituminous — and  burned  by  means  of  a  blower 
on  a  grate  adapted  to  it,  is  nearly  equal  in  value  of  combustible 
to  coal,  but  its  percentage  of  refuse  is  greater. 

One  pound  of  pure  carbon,  when  completely  burned,  yields 
14,500  heat-units. 

Temperature  of  Fire. 

By  reference  to  the  table  of  combustibles  it  will  be  seen  that 
the  temperature  of  the  fire  is  nearly  the  same  for  all  kinds  of 
combustibles  under  similar  conditions.  If  the  temperature 


1110 


WATER. 


is  known,  the  conditions  of  combustion  may  be  inferred.  The 
following  table,  from  M.  Pouillet,  will  enable  the  temperature 
to  be  judged  by  the  appearance  of  the  fire: 


Appearance. 

Tempera 
ture  F. 

Appearance. 

Tempera- 
ture F. 

Red   just  visible 

977° 

Oranfe   deep  

2010° 

'  dull                  

1290° 

clear  

2190° 

"      cherry  dull  
"        full 

1470° 
1650° 

White  heat  
bright.  . 

2370° 
2550° 

**          **        f*lear 

1830° 

dazzling 

2730° 

To  determine  temperature  by  fusion  of  metals,  etc. 

The  following  figures  /or  the  melting-points  of  various  sub- 
stances are  given  by  Clark  (on  the  authority  of  Pouillet,  Claudel, 
and  Wilson),  except  those  marked  f,  which  are  given  by  Prof. 
Roberts-Austen  in  his  description  of  the  Le  Chatelier  pyrometer. 
These  latter  are  probably  the  most  reliable  figures.* 

Deg.  F. 

Antimony 810  to  1 150 

Aluminium 11 57t 

Magnesium 1200 

Calcium Full  red  heat 

Bronze.  .  .  . 1692 

Silver.  .  .  . '' 1733f  to  1873 

Potassium  sulphate 1859t 

Gold 1913t  to  2282 

Copper 1929t  to  1996 

Cast  iron,  white 1922  to  2075t 

"     gray    2012  to  2786  2228t 

Steel .    2372  to  2532 

"    hard 2570f;  mild,  2687f 

Wrought  iron 2732  to  2912 

Palladium 2732t 

Platinum 3227t 


Deg.  F. 

Mercury —  39 

Ice 32 

Tallow 92 

Stearine 109  to  120 

Spermaceti 120 

Wax 142  to  154 

Sodium 194  to  208 

Allov,  3  lead,  2  tin,  5  bismuth .  .    199 

Sulphur 239 

Alloy,  \1A  tin,  1  lead. 334 

Alloy,  1  tin,  1  lead 370  to  466 

Tin 442  to  446 

Cadmium 442 

Bismuth 504  to  507 

Lead 608  to  618t 

Zinc 680  to  779t 


Water. — The  several  conditions  of  water  are  usually  stated 
as  the  solid,  the  liquid,  and  the  gaseous.  Two  conditions  are 
covered  by  the  last  term,  and  water  should  be  understood  as 
capable  of  existing  in  four  different  conditions — the  solid,  the 
liquid,  the  vaporous,  and  the  gaseous. 

At  and  below  32°  F.  water  exists  in  the  solid  state,  as  ice; 
at  39°  F.,  it  reaches  its  maximum  density.  Above  39°  the 
density  diminishes. 

The  weight  per  cubic  foot  of  water  at  different  temperatures 
and  under  pressure  of  one  atmosphere  is  shown  to  two  places 
of  decimals  by  the  table  on  p.  1112  (calculated  by  Rankine's 
formula) : 

The  boiling-point  of  water  depends  upon  the  pressure.     Thus 

*  Kent,  p.  455. 


STEAM.  1111 

at  one  atmosphere  (147  lbs.}  29.22"  barometer)  the  tempera- 
ture of  ebullition  is  212°.  With  a  partial  vacuum,  or  absolute 
pressure  of  1  Ib.  (2.037"of  mercury),  the  boiling-point  is  101.40  F. 

On  the  other  hand,  if  the  pressure  be  74.7  Ibs.  absolute 
(60  Ibs.  by  the  gauge),  the  temperature  of  evaporation  becomes 
307°  F. 

When  water  is  freed  of  air,  it  may  be  elevated  in  tempera- 
ture to  270°  before  evaporation  takes  place. 

Steam. 

Dry  steam  is  steam  not  containing  any  free  moisture.  It 
may  be  either  saturated  or  superheated. 

Wet  steam  is  steam  containing  free  moisture  in  the  form  of 
spray  or  mist,  and  has  the  same  temperature  as  dry  saturated 
steam  of  the  same  pressure. 

Saturated  steam  is  steam  in  its  normal  state,  that  is,  steam 
whose  temperature  is  that  due  its  pressure;  by  which  is  meant 
steam  at  the  same  temperature  as  that  of  the  water  from  which 
it  was  generated  and  upon  which  it  rests. 

Superheated  Steam. — Steam  which  has  a  higher  tem- 
perature than  that  normal  to  its  pressure  is  termed  "  super- 
heated," or  "gaseous."  Dr.  Siemens  found  that  when  steam 
at  212°  was  heated  separate  from  water  it  increased  rapidly  in 
volume,  up  to  230°,  after  which  it  expanded  uniformly,  as  a 
permanent  gas.  The  use  in  any  steam-boiler  of  superheating 
surface  exposed  to  the  heated  gases  of  combustion  is  highly 
objectionable  and  is  of  doubtful  efficiency.  Steam  cannot 
be  superheated  when  in  contact  with  water. 

Sensible  and  Latent  Heat  of  Steam. — The  tempera- 
ture of  steam,  as  shown  by  the  thermometer,  is  called  its  sensible 
heat,  and  this  varies  with  every  different  pressure;  but  it  is 
found  that  steam  contains  more  heat  than  is  shown  by  the 
thermometer,  and  this  extra  heat  is  called  the  latent  heat  of 
steam. 

The  following  table  gives  the  number  of  British  thermal  units 
in  a  pound  of  water  at  different  temperatures  below  the  boiling- 
point.  They  are  reckoned  above  32°  F.;  for,  strictly  speaking, 
water  does  not  exist  below  32°,  and  ice  follows  another  law. 

When  a  solid  becomes  a  liquid  or  a  liquid  becomes  a  vapor 
heat  is  absorbed,  more  than  was  necessary  to  raise  it  to  the 
temperature  of  conversion;  an.cl  this  latent  heat  does  work  in 


1112 


HEAT-UNITS  IN  WATER. 


HEAT-UNITS  IN  WATER,  BETWEEN  32°  AND  212°  F., 
AND  WEIGHT  OF  WATER  PER  CUBIC  FOOT. 


Temp. 
Deg. 
Fahr. 

Heat- 
units. 

Weight, 
Lbs.  per 
Cu.  Ft. 

Temp. 
Deg. 
Fahr. 

Heat- 
units. 

Weight, 
Lbs.  per 
Cu  Ft. 

Temp. 
Deg. 
Fahr. 

Heat- 
units. 

Weight, 
Lbs.  per 
Cu.  Ft. 

32 

0 

62.42 

123 

91.16 

61.68 

168 

136.44 

60.81 

35 

3 

62.42 

124 

92.17 

61.67 

169 

137.45 

60.79 

40 

8 

62.42 

125 

93.17 

61.65 

170 

138.45 

60.77 

45 

13 

62.42 

126 

94.17 

61.63 

171 

139.46 

60.75 

50 

18 

62.41 

127 

95.18 

61.61 

172 

140.47 

60.73 

52 

20 

62.40 

128 

96.18 

61.60 

173 

141.48 

60.70 

54 

22.01 

62.40 

129 

97.19 

61.58 

174 

142.49 

60.68 

56 

24.01 

62.39 

130 

98.19 

61  .  56 

175 

143.50 

60.66 

58 

26.01 

62.38 

131 

99.20 

61.54 

176 

144.51 

60.64 

60 

28.01 

62.37 

132 

100.'20 

61.52 

177 

145.52 

60.62 

62 

30.01 

62.36 

133 

101.21 

61.51 

178 

146.52 

60.59 

64 

32.01 

62.35 

134 

102.21 

61.49 

179 

147  .  53 

60.57 

66 

34.02 

62.34 

135 

103.22 

61.47 

180 

148.54 

60.55 

68 

36.02 

62.33 

136 

104.22 

61.45 

181 

149.55 

60.53 

70 

38.02 

62.31 

137 

105.23 

61.43 

182 

150.56 

60.50 

72 

40.02 

62.30 

138 

106.23 

61.41 

183 

151.57 

60.48 

74 

42.03 

62.28 

139 

107  .  24 

61.39 

184 

152.58 

60.46 

76 

44  .  03 

62.27 

140 

108.25 

61.37 

185 

153.59 

60.44 

78 

46.03 

62.25 

141 

109.25 

61.36 

186 

154.60 

60.41 

80 

48.04 

62.23 

142 

110.26 

61.34 

187 

155.61 

60.39 

82 

50.04 

62.21 

143 

111.26 

61.32 

188 

156.62 

60.37 

84 

52.04 

62.19 

144 

112.27 

61.30 

189 

157.63 

60.34 

86 

54.05 

62.17 

145 

113.28 

61.28 

190 

158  .  64 

60.32 

88 

56.05 

62.15 

146 

114.28 

61.26 

191 

159.65 

60.29 

90 

58.06 

62.13 

147 

115.29 

61.24 

192 

160.67 

60.27 

92 

60.06 

62.11 

148 

116.29 

61.22 

193 

161.68 

60.25 

94 

62.06 

62.09 

149 

117.30 

61.20 

194 

162.69 

60.22 

96 

64.07 

62.07 

150 

118.31 

61.18 

195 

163.70 

60.20 

98 

66.07 

62.05 

151 

119.31 

61.16 

196 

164.71 

60.17 

100 

68.08 

62.02 

152 

120.32 

61.14 

197 

165.72 

60.15 

102 

70.09 

62.00 

153 

121.33 

61.12 

198 

166.73 

60.12 

104 

72.09 

61.97 

154 

122.33 

61.10 

199 

167.74 

60.10 

106 

74.10 

61.95 

155 

123.34 

61.08 

200 

168.75 

60.07 

108 

76.10 

61.92 

156 

124.35 

61.06 

201 

169.77 

60.05 

110 

78.11 

61.89 

157 

125.35 

61.04 

202 

170.78 

60.02 

112 

80.12 

61.86 

158 

126.36 

61.02 

203 

171.79 

60.00 

114 

82.13 

61.83 

159 

127.37 

61.00 

204 

172.80 

59.97 

115 

83.13 

61.82 

160 

128.37 

60.98 

205 

173.81 

59.95 

116 

84.13 

61.80 

161 

129.38 

60.96 

206 

174.83 

59.92 

117 

85.14 

61.78 

162 

130.39 

60.94 

207 

175.84 

59.89 

118 

86.14 

61.77 

163 

131.40 

60.92 

208 

176.85 

59.87 

119 

87.15 

61.75 

164 

132.41 

60.90 

209 

177.86 

59.84 

120 

88.15 

61.74 

165 

133.41 

60.87 

210 

178.87 

59.82 

121 

89.15 

61.72 

166 

134.42 

60.85 

211 

179.89 

59.79 

122 

90.16 

61.70 

167 

135.48 

60.83 

212 

180.90 

59.76 

the  destruction  of  the  force  of  cohesion  and  other  changes 
which  take  place,  and  must  be  absorbed  from  some  other  sub- 
stance. In  the  case  of  steam  in  a  boiler,  it  comes  from  the 
fuel  during  combustion.  When  steam  or  vapor  is  condensed, 
this  same  quantity  of  heat  that  was  received,  from  whatever 
source,  is  again  given  off  to  any  substance  within  its  influence — • 
air,  water,  iron  pipes,  etc. — colder  than  itself;  and  it  is  this 
property,  together  with  its  great  power  of  absorbing  and  re- 


PROPERTIES  OF  STEAM.  1113 

taining  heat,  which  makes  water  and  its  vapor  such  a  valuable 
medium  for  conveying  heat  from  the  furnace  to  the  rooms  to 
be  warmed. 

The  specific  heat  (or  heat-absorbing  capacity)  of  water  is  not 
constant,  but  rises  in  an  increasing  ratio  with  the  temperature; 
so  that  it  requires  more  heat  the  higher  the  temperature  to. 
raise  a  given  quantity  of  water  from  one  temperature  to  another. 
Thus,  the  specific  heat  at  32°  being  1,  at  212°  it  is  1.013,  and 
at  320°  (the  temperature  of  75  Ibs.  steam  pressure)  it  is  1.0294. 
The  amount  of  heat  rendered  latent  by  each  pound  of  water  in 
becoming  steam  varies  at  different  pressures,  decreasing  as  the 
pressure  increases.  This  latent  heat,  added  to  the  sensible  heat 
(or  thermometric  temperature),  constitutes  the  " total  heat." 
The  " total  heat"  being  greater  as  the  pressure  increases,  it  will 
take  more  heat,  and  consequently  more  fuel,  to  make  a  pound 
of  steam  the  higher  the  pressure. 

The  table  given  on  the  following  page  shows  the  properties  of 
steam  at  different  pressures,  from  1  Ib.  to  400  Ibs.  "  total  pres- 
sure"; i.e.,  above  vacuum. 

The  gauge  pressure  is  about  15  Ibs.  less  than  the  total  pressure; 
so  that,  in  using  this  table,  15  must  be  added  to  the  pressure 
as  given  by  the  steam-gauge. 

The  column  of  "  Temperatures "  gives  the  thermometric  tem- 
perature of  steam  and  boiling-point  at  each  pressure. 

The  " Factor  of  Equivalent  Evaporation"  shows  the  propor- 
tionate cost,  in  heat  or  fuel,  of  producing  steam  at  the  given 
pressure,  as  compared  with  atmospheric  pressure.  To  ascertain 
the  equivalent  evaporation  at  any  pressure,  multiply  the  given 
evaporation  by  the  factor  of  its  pressure  and  divide  the  quotient 
by  the  factor  of  the  desired  pressure. 

Each  degree  of  difference  in  temperature  of  feed-water  makes 
a  difference  of  0.00104  in  the  amount  of  evaporation.  Hence, 
to  ascertain  the  equivalent  evaporation  from  any  other  tem- 
perature of  feed  than  212°,  add  to  the  factor  given  as  many 
times  0.00104  as  the  temperature  of  feed-water  is  degrees  below 
212°. 

For  other  pressures  than  those  given  in  the  table,  it  will  be 
practically  correct  to  take  the  proportion  of  the  difference 
between  the  nearest  pressures  given  in  the  table. 

Air. — Air  is  a  mechanical  mixture  of  oxygen  and  nitrogen, 
the  proportion  for  pure  air  being  77  per  cent,  of  nitrogen  and 
23  per  cent,  of  oxygen  by  weight.  It  also  contains  about  ^^^ 


1114  PROPERTIES  OF  STEAM. 

TABLE  OF  PROPERTIES  OF  SATURATED  STEAM.* 


, 

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'd  3 

1 

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102 

1113.05 

1042.964 

0.0030 

330  .  36 

20620 

0.965 

2 

126.266 

1120.45 

1026.010 

0.0058 

172.08 

10720 

0.972 

3 

141.622 

1125.131 

1015.254 

0.0085 

117.52 

7326 

0.977 

4 

153.070 

1128.625 

1007  .  229 

0.0112 

89.62 

5600 

0.981 

5 

162.330 

1131.449 

1000.727 

0.0137 

72.66 

4535 

0.984 

6 

170.123 

1133.826 

995.249 

0.0163 

61.21 

3814 

0.986 

7 

176.910 

1135.896 

990.471 

0.0189 

52.94 

3300 

0.988 

8 

182.910 

1137.726 

986.245 

0.0214 

46.69 

2910 

0.990 

9 

188.316 

1139.375 

982.434 

0.0239 

41.79 

2607 

0.992 

10 

193.240 

1140.877 

978.958 

0  .  0264 

31.84 

2360 

0.994 

15 

213.025 

1146.912 

964.973 

0.0387 

25.85 

1612 

1.000 

20 

227.917 

1151.454 

954.415 

0.0511 

19.72 

1220.3 

1  .  005 

25 

240.000 

1155.139 

945  .  825 

0.0634 

15.99 

984.8 

1.008 

30 

250.245 

1158.263 

938.925 

0.0755 

13.46 

826.8 

1.012 

35 

259.176 

1160.987 

932.152 

0.0875 

11.65 

713.4 

1.015 

40 

267.120 

1163.410 

926.472 

0.0994 

10.27 

628.2 

1.017 

45 

274.296 

1165.600 

921  .  334 

0.1111 

9.18 

561.8 

1.017 

50 

280  .  854 

1167.600 

916.631 

0.1227 

8.31 

508.5 

1.021 

55 

286.897 

1169.442 

912.290 

0.1343 

7.61 

464.7 

1.023 

60 

292.520 

1171.158 

908.247 

0.1457 

7.01 

428.5 

1.025 

65 

297.777 

1172.762 

904.462 

0.1569 

6.49 

397.7 

1.027 

70 

302.718 

1174.269 

900.899 

0.1681 

6.07 

371.2 

1.028 

75 

307  .  388 

1175.692 

897  .  526 

0.1792 

5.68 

348.3 

1.030 

80 

311.812 

1177.042 

894.330 

0.1901 

5.35 

328.3 

.031 

85 

316.021 

1178.326 

891.286 

0.2010 

5.05 

310.5 

.033 

90 

320.039 

1179.551 

888.375 

0.2118 

4.79 

294.7 

.034 

95 

323  .  884 

1180.724 

885.588 

0.2224 

4.55 

280.6 

.035 

100 

327.571 

1181.849 

883.914 

0  .  2330 

4.33 

267.9 

.036 

105 

331.113 

1182.929 

880.342 

0.2434 

4.14 

265.5 

.037 

110 

334.523 

1183.970 

877  .  865 

0.2537 

3.97 

246.0 

.038 

115 

337.814 

1184.974 

875.472 

0.2640 

3.80 

236.3 

.039 

120 

340.995 

1185.944 

873.155 

0.2742 

3.65 

227.6 

.040 

125 

344.074 

1186.883 

870.911 

0.2842 

3.51 

219.7 

.041 

130 

347.059 

1187.794 

868.735 

0.2942 

3.38 

212.3 

.042 

140 

352.757 

1189.535 

864.566 

0.3138 

3.16 

199.0 

.044 

150 

358.161 

1191.180 

860.621 

0.3340 

2.96 

187.5 

.046 

160 

363.277 

1192.741 

856.874 

0.3520 

2.79 

177.3 

.047 

170 

368.158 

1194.228 

853.294 

0.3709 

2.63 

168.4 

.049 

180 

372.822 

1195.650 

849.869 

0.3889 

2.49 

160.4 

1.051 

190 

377.291 

1197.013 

846.584 

0.4072 

2.37 

153.4 

1.052 

200 

381.573 

1198.319 

843.432 

0.4249 

2.26 

147.1 

1.053 

250 

401.072 

1203.735 

831.222 

0  .  5464 

1.83 

114 

1.059 

300 

418.225 

1208.737 

819.610 

0.6486 

1.54 

96 

1.064 

350 

431.956 

1212.580 

810.690 

0.7498 

1.33 

83 

1.068 

400 

444.919 

1217.094 

800.198 

0  .  8502 

1.18 

73 

1.073 

of  its  volume  of  carbonic-acid  gas  and  some  watery  vapor,  and 
is  capable  of  absorbing  any  other  gas  or  vapor  to  a  certain 
extent,  distributing  them  through  the  whole  atmosphere  by 

*  Steam,  14th  ed.     Babcock  &  Wilcox  Company,  New  York  and  Glasgow. 


PROPERTIES  OF  AIR.  1115 

what  is  called  the  law  of  diffusion  of  gases,  a  property  which 
gases  have  of  mixing  and  diluting,  which  prevents  gases  of 
different  specific  gravities  from  stratifying  for  any  considerable 
time.  This  property  is  of  the  utmost  importance  to  air;  for, 
if  any  noxious  or  poisonous  gas  were  to  remain  separated  in 
the  atmosphere,  any  one  breathing  it  would  be  instantly  killed. 

Air  at  60°  F.,  and  with  the  barometer  at  30  ins.,  is  taken  as 
the  standard  for  the  comparison  of  the  weight  of  gases,  itself 
being  considered  as  unity. 

At  the  temperature  of  32°,  13J  cu.  ft.  of  air  weigh  a  few 
grains  over  1  Ib.  avoirdupois. 

The  ^expansion  of  air  is  nearly  uniform  at  all  temperatures, 
expanding  about  ¥Jo  °f  its  bulk  at  32°  and  for  each  increase  of 
one  degree  in  temperature. 

The  table  on  the  following  page,  giving  the  volume  and  weight 
of  dry  air,  tension  and  weight  of  vapor,  etc.,  will  be  found  use- 
ful for  reference.  In  this  table  1,000  cu.  ft.  of  dry  air  is  taken 
for  a  unit,  and  the  coefficient  of  expansion  is  taken  at  ^-j^,  the 
air  being  under  constant  pressure  of  30  ins.  of  mercury. 
Column  5  is  taken  from  Guyot's  tables,  Regnault's  data. 

Watery  Vapor  in  the  Atmosphere. — Air  is  capable 
of  holding  or  absorbing  a  certain  quantity  of  vapor  of  water,  the 
proportion  depending  on  the  temperature  of  the  air. 

The  warmer  it  is  the  larger  quantity  it  will  hold,  and  as  it 
becomes  cool  again,  it  deposits  it,  or  forms  clouds  or  fogs  which 
condense  on  anything  colder  than  the  air,  leaving  the  air,  upon 
raising  its  temperature,  capable  of  taking  up  more  moisture, 
to  be  again  deposited  in  dew  or  rain.  It  is  this  property  of  air 
which  gives  it  its  drying  qualities. 

An  absolutely  dry  atmosphere  is  almost  an  impossibility. 
Air  at  32°  contains,  when  saturated  with  moisture,  TJ7  of  its 
weight  of  water;  at  59°  it  contains  -^;  at  86°  it  contains  ^ff;  its 
capacity  for  moisture  being  doubled  by  each  increase  of  27°  F. 

Air  is  said  to  be  " saturated"  when  it  has  absorbed  all  the 
water  it  will  hold  at  that  temperature.  The  tension  of  vapors 
is  the  elastic  force  or  pressure  which  they  exert  on  the  sides  of 
vessels  in  which  they  are  contained. 

Air,  to  be  healthful,  should  contain  about  75  per  cent,  of  the 
moisture  required  for  saturation. 

It  requires  more  heat  to  raise  the  temperature  of  a  given 
quantity  of  moist  air  1°  than  for  dry  air;  but  unless  the  air  is 
saturated  this  difference  is  not  of  much  practical  importance, 


1116 


PROPERTIES  OF   AIR. 


VOLUME  AND  WEIGHT  OF  AIR  AND  WEIGHT  OF 
VAPOR  IN  SATURATED  AIR. 


Weight  of 

W'ght  of 

Tem- 
pera- 
ture. 

Volume. 

Number  of 
Cubic  Feet 
to  1  Pound 

Weight  of 
1,000 
Cubic  Feet 
Dry  Air. 

Tension  of 
Vapor. 

Vapor 
Saturated 
in  1,000 
Cubic  Feet. 

Air  Dis- 
placed 
by 
Vapor. 

1 

2 

3 

4 

5 

6 

7 

0 

0  .  9340 

1  1  .  460 

87  .  260 

0.04379 

0.07930 

0.1264 

5 

0.9449 

11.591 

86.289 

0.05747 

0.10289 

0.1646 

10 

0.9551 

11.726 

85.251 

0.07116 

0.12588 

0.2014 

15 

0.9653 

11.869 

84.317 

0.08535 

0.14932 

0.2389 

20 

0.9755 

11.992 

88.403 

0.10748 

0.18180 

0.2909 

25 

0.9857 

12.125 

82.440 

0.13367 

0.22871 

0.3661 

30 

0.9959 

12.258 

81.566 

0.16581 

0.27491 

'0.4398 

32 

1  .  0000 

12.311 

81.235 

0.17989 

0.29633 

0.4741 

36 

1  .  0082 

12.417 

80\515 

0.21066 

0.35201 

0.5632 

40 

1.0163 

12.523 

79.872 

0.24604 

0.40770 

0.6523 

44 

1.0244 

12.629 

79.176 

0.28647 

0.47070 

0.7531 

48 

1.0326 

12.735 

78.493 

0.33284 

0.54204 

0.8672 

52 

1  .  0408 

12.841 

77.825 

0.38574 

0.62282 

0.9965 

56 

1  .  0489 

12.947 

77  .  220 

0.44352 

0.71063 

1.1370 

60 

1.0571 

13.053 

76.628 

0.51683 

0.82173 

1.3147 

64 

1.0652 

13.159 

75.988 

0  .  59229 

0.93390 

1  .  4943 

68 

1.0734 

13.265 

75.357 

0.67994 

1.0631 

1.7008 

72 

1.0816 

13.371 

74.794 

0.78018 

1.21050 

1  .  9368* 

76 

1.0897 

13.477 

74.184 

0.89103 

1.31715 

2.1076 

80 

1.0979 

13.583 

73.638 

1.01669 

1  .  5540 

2.4864 

84 

1  .  1060 

13.689 

73.046 

1.15705 

1.7536 

2.8058 

88 

1.1142 

13.795 

72.464 

1.31554 

1.9772 

3.1635 

92 

1  .  1223 

13.901 

71.942 

1.49067 

2.2257 

3.5611 

96 

1  .  1305 

14.007 

71.377 

1.69214 

2.5060 

4.0096 

100 

1  .  1387 

14.113 

70.872 

1.91937 

2.8220 

4.5152 

104 

1  .  1468 

14.219 

70.323 

2.14669 

3.133 

5.0138 

108 

1  .  1550 

14.325 

69.784 

2.43323 

3.523 

5.6368 

112 

1.1631 

14.431 

69.300 

2.72984 

3.926 

6.2826 

116 

1.1713 

14.537 

68.776 

3.05954 

4.367 

6.9882 

120 

1  .  1794 

14.643 

68.306 

3.41728 

4.843 

7  .7488 

124 

1.1876 

14.749 

67.797 

3.81775 

5.371 

8.5940 

128 

1  .  1957 

14.855 

67  .  295 

4.26073 

6.088 

9.7430 

132 

1  .  2039 

14.961 

66.845 

4.72888 

6.559 

10.4950 

136 

1.2121 

15.067 

66.357 

5.25807 

7.240 

11.584 

140 

1  .  2202 

15.173 

65.919 

5.81736 

7.957 

12.731 

144 

1.2284 

15.279 

65.442 

6.48029 

8.800 

14.048 

148 

1.2365 

15.385 

64.977 

7  .  14323 

9.630 

15.408 

152 

1  .  2447 

15.491 

64.568 

7.9104 

10.595 

16.952 

156 

1  .  2528 

15.597 

64.102  - 

8.6923 

11.566 

18.506 

160 

1.2610 

15.703 

63.694- 

9  .  5948 

12.681 

20.290 

164 

1.2691 

15.809 

63.251 

10.5579 

13.828 

22.125 

168 

1.2773 

15.915 

62.814 

11.4673 

14.950 

23.920 

172 

1  .  2855 

16.021 

62.422 

12.7165 

16.47 

26.36 

176 

1.2936 

16.127 

61.996 

13.8657 

17.43 

27.89 

180 

1.3018 

16.233 

61.614 

15.2343 

19.47 

31.96 

184 

1  .  3099 

16.339 

61  .  200 

16  .  6030 

21.08 

33.73 

188 

1.3181 

16.445 

60.790 

18  .  1447 

22.89 

36.63 

192 

1  .  3262 

16.551 

60.423 

19.7441 

24.75 

39.60 

196 

1.3344 

16.657 

60.024 

21.4297 

26.69 

42.71 

200 

1.3426 

16.763 

59.666 

23  .  2962 

28.85 

46.16 

Columns  6  and  7  of  the  above  table  give  the  weight  of 
vapor  in  1,000  cu.  ft.  of  saturated  air,  and  the  weight  of  dis- 
placed air,  for  different  temperatures  from  0°  to  200°. 


PROPERTIES   OF  AIR,  1117 

The  numbers  in  column  6  are  obtained  by  multiplying  the 
corresponding  numbers  in  column  4  by  column  5  and  the 
product  by  -%%-.  Column  7  is  obtained  from  column  6  by 
multiplying  the  values  in  column  6  by  f . 

Specific  Heat  of  Air. — The  specific  heat  of  any  sub- 
stance is  the  quantity  of  heat  required  to  raise  its  temperature 
1°  compared  with  the  quantity  of  heat  required  to  raise  the 
temperature  of  1  Ib.  of  water  at  the  same  temperature  1°. 
The  specific  heat  of  air,  as  determined  by  Regnault,  is  0.2374. 
Hence  one  thermal  unit  will  raise  the  temperature  of  1  Ib.  of 
water  or  4J  Ibs.  of  dry  air  (equals  51.7  cu.  ft.  at  32°  F.)  1°  F. 
As  all  air  contains  more  or  less  moisture,  which  must  also  be 
warmed,  50  cu.  ft.  is  generally  considered  as  the  equivalent 
of  1  Ib.  of  water  in  heating. 

As  1  Ib.  of  steam  at  0  (gauge)  pressure  condensed  to  water 
gives  off  965  thermal  units,  it  is  therefore  equivalent  to  warm- 
ing about  48,000  cu.  ft.  of  air  1°. 

Drying  by  Steam.* 

There  are  three  modes  of  drying  by  steam:  1st,  by  bringing 
wet  substances  in  direct  contact  with  steam-heated  surfaces, 
as  by  passing  cloth  or  paper  over  steam-heated  cylinders,  or 
clamping  veneers  between  steam-heated  plates;  2d,  by  radiated 
heat  from  steam-pipes,  as  in  some  lumber-kilns  and  laundry 
drying-rooms;  3d,  by  causing  steam-heated  air  to  pass  over 
wet  surfaces,  as  in  glue-works,  etc. 

The  second  is  rarely  used  except  in  combination  with  the 
third. 

The  first  is  most  economical,  the  second  less  so,  and  the  third 
least.  Under  favorable  circumstances  it  may  be  estimated 
that  1  horse-power  of  steam  will  evaporate  24  Ibs.  of  water 
by  the  first  method,  20  by  the  second,  and  15  by  the  third. 

The  philosophy  of  drying  or  evaporating  moisture  by  heated 
air  rests  upon  the  fact  that  the  capacity  of  air  for  moisture  is 
rapidly  increased  by  rise  in  temperature.  If  air  at  52°  is  heated 
to  72°,  its  capacity  for  moisture  is  doubled,  and  is  four  times 
what  it  was  at  32°.  The  following  table  gives  the  weight  of  a 
saturated  mixture  of  air  and  aqueous  vapor  at  different  tem- 
peratures up  to  160°,  the  practical  limit  of  heating  air  by  steam, 
together  with  the  weight  of  vapor  in  pounds  and  percentage, 
and  total  heat,  with  the  portion  thereof  contained  in  the  vapor: 
*  From  Steam.  Babcock  &  Wilcox  Company, 


1118  PROPERTIES   OF  AIR, 

SATURATED  MIXTURES  OF  AIR  AND  AQUEOUS  VAPOR. 


*s 

£| 

1 

g 

85 

"i 

•  -J 

I'l 

•y. 

| 

sl 

_^ 

"*£J 

O.£S"2 

•1*3  *3 

^ 

rH    X 

1 

w^ 

08*0  c 

^ 

«-"  X 

1 

of  § 

'""'S    3 

^    '  ^ 

, 

.si 

o>"  § 

S  5 

. 

.si 

o  2 

*o   . 

Ife 

°jg 

*o   •  c 

~§"x 

""3 
'%•» 

ll 

|fe 

^a«c 

«g    .£H 

c  x 

.5^ 

|4 

-J  o 

c  a 

(D.!-! 

PS, 

aj.j-i 

aj  c3 

O.  0) 

be  .  w 

bd        <u 

^  . 

OJ> 

P.  ^ 

M  °  § 

Mr—,  Q) 

sa 

•Js      . 

o> 

£& 

|5! 

|2| 

«* 

PH 

S3 
w° 

li 

|1 

|g(£ 

|S3 

|3 

|.9 

35 

8.004 

0.034 

0.42 

42.8 

86.69 

100 

6.924 

0.283 

4.08 

422.0 

74.58 

40 

7.920 

0.041 

0.52 

59.8 

76.59 

105 

6.830 

0.325 

4.76 

474.7 

76.22 

45 

7.834 

0.049    0.62 

77.7 

68.98 

110 

6.741 

0.373 

5.23 

533.9 

77.88 

50 

7.752 

0.059 

0.76 

97.6 

66.29 

115 

6.650 

0.426 

6.41 

599.1 

79.52 

55 

7.688 

0.070 

0.91 

118.3 

64.58 

120 

6.551 

0.488 

7.46 

672.4 

81.14 

60 

7.589 

0.082 

1.08 

140.1 

64.31 

125 

6.454 

0.554 

8.55 

750.5 

82.62 

65 

7.507 

0.097 

1.29 

164.9 

64.76 

130 

6.347 

0.630 

9.90 

839.4 

84.13 

70 

7.425 

0.114 

1.49 

189.7 

66.21 

135 

6.238 

0.714 

11.44 

936.7 

85.57 

75 

7.342 

0.134 

1.79 

221.6 

66.74 

140 

6.131 

0.806 

13.14 

1042.7 

86.89 

80 

7.262 

0.156 

2.15 

253.6 

68.02 

145 

6.015 

0.909 

15.11 

1160.6 

88.18 

85 

7.178 

0.182 

2.54 

289.7 

69.66 

150 

5.891 

1.022 

17.33 

1288.4 

89.39 

90 

7.108 

0.212 

2.98 

330.2 

71.19 

155 

5.764 

1  .  145 

19.88  1427.4 

90.53 

95 

7.009 

0.245 

3.50 

373.4 

72.87 

160 

5.679 

1.333 

23.47 

1638.7 

91.93 

By  inspection  of  above  table,  it  will  be  seen  why  it  is  more 
economical  to  dry  at  the  higher  temperatures.  The  atmosphere 
is  seldom  saturated  with  moisture,  and  in  practice  it  will  be 
found  generally  necessary  to  heat  the  air  about  30°  above  the 
temperature  of  saturation.  Drying  on  a  large  scale  is  now 
accomplished  almost  entirely  by  the  "hot-blast"  system  of 
heating,  details  of  which  may  be  obtained  from  the  American 
Blower  Company,  Buffalo  Forge  Company,  or  the  B.  F.  Sturte- 
vant  Company. 

COMPARISON  OF  THERMOMETERS. 

To  convert  the  degrees  of  different  thermometers  from  one  into 
the  other,  use  the  following  formulas: — 
F  stands  for  degrees  of  Fahrenheit,  or  212°  ^ 
C       "        "         "        "  Celsius,*         "    100°  [•  boiling-point. 
R       "        "         "        "  Reaumur,       "     80°  ) 

9R  9(7 

F  =-r -  +32,    and    F=—  +  32  for  degrees  above  freezing-point. 

QP  Q£f 

F= 32,    and    ^  =  —  —  32  for  degrees  below  freezing-point. 


*  Often  called  Centigrade. 


DIFFERENT  COLORS  OF  IRON  CAUSED  BY  HEAT.  1119 


„     5GF-32)         ,D 
C  =  —  —  Q  -  ,  and  R= 

C/OO  _  TTTN 

C  =  —  —  <r  -  -,  and  R 


9 


,       ,  ,        .  .   . 

for  degrees  above  freezing-point. 

-  for  degrees  below  freezing-point. 


Degrees  Fahr.  below  zero  should  be  given  the  —  sign. 
Zero   of    Celsius   or    Reaumur  =+  32°    Fahrenheit.     Zero  of 
Fahrenheit  =-17.77°  C,  or  -14.22°  R. 

Ex.  1.  How  much  is  8°  Celsius  above  zero,  in  Fahrenheit? 

Qvx  Q 

F=^~  +32  =  14.4  +  32  =  46.4°  above. 
o 

Ex.  2.  How  much  is  8°  Celsius  below  zero,  in  Fahrenheit? 

9X8 


F-- 


• -32  =  14.4-32  =  17.6°  above. 


IN  CASES  WHERE  THE  PRODUCT  IS  SMALLER  THAN  32,  IT  INDI- 
CATES THAT  THE  DEGREE  IS  ABOVE  ZERO  OF  FAHRENHEIT;  SEE 
EXAMPLE  2. 

Ex.  3.  How  much  is  .19°  Celsius  below  zero,  in  Fahrenheit? 

Q  V  1Q 

F = ^p -32  =  34.2- 32  =  2.2  below  Fahrenheit. 
o 

DIFFERENT  COLORS  OF  IRON  CAUSED  BY  HEAT. 

[Pouillet.] 


C. 


Fahr. 


Color. 


210C 
221 

256 

261 
370 

500 


525 

700 

800 

900 

1000 

1100 

1200 

1300 

1400 

1500 

1600 


410° 

430 

493 

502) 
680) 

932 


977 
1292 
1472 
1657 
1832 
2012 
2192 
2372 
2552 
2732 
2912 


Pale  yellow 

Dull  yellow 

Crimson 

f  Violet,  purple,  and  dull  blue;  between  261°  and 
•j  370°  C.  it  passes  to  bright  blue,  to  sea-green, 

(     and  then  disappears 

Commences  to  be  covered  with  a  light  coating 
of  oxide,  loses  a  good  deal  of  its  hardness, 
becomes  a  good  deal  more  impressible  to  the 
hammer,  and  can  be  twisted  with  ease 

Becomes  nascent  red 

Sombre  red 

Nascent  cherry 

Cherry 

Bright  cherry 

Dull  orange 

Bright  orange 

White 

Brilliant  white,  welding  heat 

[•  Dazzling  white 


1120 


EXPANSION  BY  HEAT. 


LINEAL  EXPANSION  OF  SOLIDS    AT    ORDINARY  TEM- 
PERATURES. 

(British  Board  of  Trade ;« from  Clark.) 


For 
1°  Fahr. 

For 
1°  Cent. 

Coef. 
of 
Expan- 
sion 
from 
32°  to 
212°  F. 

Accord- 
ing to 
Other 
Author- 
ities. 

Aluminium  (cast)  

Length  =  1 
.00001234 
.00000627 
.  00000957 
.00001052 
.00000306 
.00000986 
.00000975 
.00000594 

.00000795 
.  00000887 
.00004278 
.00000451 
.00000499 
.  00000397 
.00000438 
.  00000498 
.00000786 
.  00000356 
.00000648 
.  00000556 
.00001571 

Length  =  1 
.00002221 
.00001129 
.00001722 
.00001894 
.00000550 
.00001774 
.00001755 
.00001070 

.00001430 
.00001596 
.00007700 
.,00000812 
.00000897 
.00000714 
.00000789 
.00000897 
.00001415 
.00000641 
.00001166 
-.00001001 
.00002828 

.002221 
.001129 
.001722 
.001894 
.000550 
.001774 
.001755 
.001070 

.001430 
.001596 
.007700 
.000812 
.000897 
.000714 
.000789 
.000897 
.001415 
.000641 
.001166 
.001001 
.002828 

.001083 
.001868 

.001392 
.001718 

.001235 
.001110 

.002694 

.018018 
.001279 

.  000884 

.001908 
.001079 

.001938 
.002942 

Antimony  (cryst  )  .  . 

Brass,  cast  

"   plate. 

Brick.  .   .     

Bronze  (Cu,  17;  Sn,2^;  Z,  1)  
Bismuth.  

Cement,  Portland  (mixed),  pure.  . 
Concerte:  cement,  mortar,  and 
pebbles.  . 

Copper  

Ebonite 

Glass  English  flint 

thermometer.  . 

Granite,  gray,  dry  
red,  dry  

Gold  pure 

Iron,  wrought   . 

"   cast  

Lead  .  . 

Magnesium  

n/r  i_i      •    )  from 

.00000308 
.  00000786 
.00000256 
.  00000494 
.00009984 
.00000695 
.00001129 
.00000922 
.00000479 

.00000453 
.00000200 

.00000434 

.00000788 
.00001079 
.00000577 
.00000636 
.00000689 
.00000652 
.00000417 
.00001163 
.00000489 
.  00000276 
„  0000  1407 

.00001496 

.00000554 
.00001415 
.00000460 
.00000890 
.00017971 
.00001251 
.  00002033 
.00001660 
.  00000863 

.00000815 
.00000360 

.00000781 

.00001419 
.00001943 
.00001038 
.00001144 
.00001240 
.00001174 
.  00000750 
.00002094 
.00000881 
.00000496 
.00002532 

.00002692 

.000554 
.001415 
.000460 
.000890 
.017971 
.001251 
.002033 
.001660 
.000863 

.000815 
.000360 

.000781 

.001419 
.001943 
.001038 
.001144 
.001240 
.001174 
.  000750 
.002094 
.000881 
.000496 
.002532 

.  002692 

Marbles,  various  -j  J0 

Mi  •  i  (  from. 

asonry,  brick  -j  j-c 

Mercury  (cubic  expansion)  

Nickel  

Pewter  .  .        

Plaster,  white  

Platinum   .        

Platinum,  85  per  cent.  1 

Iridium,  15  "      f  '  * 
Porcelain 

Quartz,  parallel  to  major  axis,  t  0° 
to  40°  C 

Quartz,  perpendicular  to  major 
axis,  t  0°  to  40°  C  

Silver,  pure  

Slate.  .  .        

Steel,  cast.  . 

tempered  

Stone  (canclstone),  dry  
Rauville  
Tin.              

\Vedgewood  ware.  . 

Wood,  pine  

Zinc.  .  . 

Zinc,  8  I 

Tin,  1  j  *  " 

Note. — Cubical  expansion,  or  expansion  of  volume  =  linear  expansion X 3. 


STEAM  HEATING. 


1121 


Furnace  heating  . 


Systems  of  Heating'.* 

The  various  systems  employed  for  the  warming  of  buildings, 
aside  from  the  use  of  stoves  and  fireplaces,  may  be  classified 
as  follows: 

(  Gravity  system. 
(  Fan  system. 

f  Gravity,  or  lowpressure  systems, 
a.  Direct  radiation. 
6.  Direct-indirect  radiation. 

c.  Indirect  radiation. 

d.  Paul  system. 

Non-gravity,  or  high-pressure  systems. 

a.  Gravity  circulation  with  return  trap 

or  pump. 

b.  Webster  system. 

c.  Hot-blast  systems. 
Open  system. 

Direct  or  indirect  radiation. 


Steam  heating  . 


Hot-water  heating. 


Closed  system. 

Direct  or  indirect  radiation. 


These  systems  are  briefly  described  in  the  following  pages 
and  sufficient  data  given  to  enable  an  architect  to  specify  or 
design,  in  a  general  way,  an  ordinary  heating  plant.  The  limits 
of  the  book  preclude  the  going  into  many  of  the  minor  details, 
which  are  usually  left  to  the  judgment  of  the  contractor,  or  to 
a  discussion  of  the  high-pressure  systems,  which  are  generally 
employed  only  for  very  large  buildings  or  for  power  plants,  and 
for  which  the  plant  should  be  designed  by  an  expert. 

For  further  information  on  this  subject  the  reader  is  referred 
to  "Heating  and  Ventilating  Buildings,"  by  Prof.  R.  C.  Car- 
penter, which  for  architects  and  students  is  the  best  work  on 
the  subject  that  the  author  has  seen. 

Gravity  Systems  of  Steam  Heating. 

A  steam-heating  plant  may  be  divided  into  three  distinct 
parts:  1st,  the  boiler,  or  steam  generator;  2d,  the  radiators; 
and  3d,  the  supply  and  return  pipes  connecting  the  two. 

*  In  the  preparation  of  the  article  on  Heating  the  author  has  had  the 
assistance  o  Mr.  P.  F.  Monaghan,  an  experienced  heating  engineer. 


1122  STEAM  HEATING. 

Radiators. — Radiators  are  generally  made  of  iron,  and 
may  be  of  any  shape  that  will  allow  of  a  good  circulation  of 
steam  through  them,  and  also  permit  the  air  to  circulate  freely 
about  the  outside.  It  is  also  desirable  that  the  thickness  of 
the  metal  shall  be  only  enough  to  give  sufficient  strength. 

Classes  of  Radiators. — Radiators  are  divided  into  three  classes: 
those  affording,  1st,  direct  radiation;  2d,  direct-indirect  radia- 
tion; 3d,  indirect  radiation. 

Direct  radiating  surfaces  embrace  all  heaters  placed  within 
a  room  or  hall  to  warm  the  air  already  in  the  room. 

Indirect  radiating  surfaces  embrace  heating  surfaces  placed 
outside  the  rooms  to  be  heated,  and  should  only  be  used  in  con- 
nection with  some  system  of  ventilation. 

Direct-indirect  radiation  is  a  mean  between  the  other  two 
methods.  The  radiators  are  placed  in  the  rooms  to  be  heated, 
as  in  the  first  method,  and  a  supply  of  fresh  air  brought  to  them 
through  openings  in  the  outside  wall  of  the  room  or  through  a 
space  under  the  lower  sash  of  a  window. 

Efficiency  of  Radiators. — The  condensation  of  one 
pound  of  steam  at  0,  or  pressure  of  one  atmosphere  to  water  at 
212°,  gives  out  965  thermal  units.  Hence  to  determine  the 
amount  of  heat  given  out  by  any  radiator  in  a  given  time,  it  is 
only  necessary  to  determine  the  amount  of  water  in  pounds 
which  the  radiator  condenses  in  the  same  time  and  multiply 
it  by  965. 

The  radiator  which,  under  the  same  conditions  of  steam 
pressure  and  volume  and  temperature  of  surrounding  air,  will 
condense  the  most  water  in  a  given  time  is  the  most  efficient. 

Measurement  of  Radiators. — Radiators  are  rated,  or 
measured,  not  according  to  their  size,  but  according  to  the  amount 
of  heating  surface  coming  in  contact  with  the  air.  The  size  of 
radiator  for  a  given  amount  of  heating  surface  will  depend  en- 
tirely upon  the  form  or  shape  of  the  radiator. 

Heating"  by  Direct  Radiation. — Direct  radiation  being 
much  more  economical  than  indirect  radiation,  it  will  always 
be  much  more  commonly  used  for  steam  or  hot-water  heating; 
and  in  buildings  not  requiring  a  great  amount  of  ventilation  it 
offers  a  nearly  perfect  mode  of  heating. 

Description  of  Direct  Radiators.  Pipe  Radiators. — 
The  cheapest  direct  radiator  is  one  formed  of  wrought-iron  pipes 
(1-inch  pipes  being  generally  preferred)  placed  against  a  wall  one 
above  the  other  and  connected  with  return  bends  or  branch 


RADIATORS. 


1123 


tees  and  elbows,  to  afford  a  circulation.  The  length  of  pipe  re- 
quired to  make  up  a  given 
amount  of  heating  surface  . 
can  easily  be  determined 
by  the  use  of  the  table  on 
p.  1205.  For  rooms  in 
which  it  is  desirable  that 
the  heating  apparatus 
shall  present  a  neat  ap- 
pearance and  occupy  as 
little  space  as  possible 
some  form  of  upright 
radiator  is  generally  em- 
ployed. Fig.  1  shows  a 
style  of  radiator,  known  as 
a  pipe  radiator,  which  was 
formerly  largely  used  on 
account  of  its  cheapness; 
it  is  now  seldom  seen,  how-  || 
ever.  Pipe  radiators  are 
formed  of  a  number  of 
short  upright  1-inch  tubes 
from  2  ft.  Sins,  to '2  ft.  10 
ins.  long,  screwed  into  a  hollow  cast-iron  base  or  box,  and  are 
either  connected  together  in  pairs  by  return  bends  at  their  upper 
ends  or  else  each  tube  stands  singly,  with  its  upper  end  closed, 
and  having  a  hoop-iron  partition  extending  up  inside  it  from 
the  bottom  to  nearly  the  top.  The  radiators  are  also  made 
circular  in  form,  either  in  one  piece,  or  in  halves  for  encircling 
iron  columns. 

The  table  on  next  page  shows  the  dimensions  of  1-inch  pipe 
radiators  for  differcrt  heating  surfaces. 

Ca&t-iroii  Direct  Radiators. — Direct  radiators  are 
now  made  almost  exclusively  of  cast  iron.*  Within  the  last 
decade  considerable  improvement  has  been  made  in  the  design 
and  quality  of  cast  radiators,  so  that  the  newer  patterns  have 
very  largely  superseded  those  made  previous  to  ten  or  twelve 
years  ago. 

The  principal  manufacturers  of  radiators  are  the  "  American, " 

*  Quite  recently  the  Kinnear-Hood  Steel  Co.  has  placed  on  the  market 
a  line  of  sheet-steel,  brass,  and  copper  radiators  for  direct  and  direct-indirect 
radiation.  The  manufacturers  claim  that  they  are  superior  to  cast  radiators. 


Fig.  I 

Direct  Pipe  Radiator. 


1124  STEAM  HEATING. 

TABLE  OF  VERTICAL  PIPE  RADIATORS. 


No.  of 
Rows  and 
Width  of 
Ease. 

Tubes 
in  Each 
Row. 

Surface  , 
in 
Sq.  Ft.* 

Length. 
Ft.     An. 

No,  of 
Rows  and 
Width  of 
Base. 

Tubes 
in  Each 
Row. 

Surface, 
in 
Sq.  Ft.* 

Length. 
Ft.    In. 

4 

4 

0    10M 

8 

16 

1      6M 

.. 

6 

6 

1      2M 

. 

10 

20 

1    10M 

C«    M 

8 

8 

1      6M 

.    M 

12 

24 

2     2% 

CO     * 

10 

10 

1    10/4 

[jffl    * 

14 

28 

2     6% 

c§«+*  § 

12 

12 

2      2M 

O          Q 

16 

32 

2    1014 

M-t^Q.rH 

'  16 

16 

2    10M 

P^     Q-r-l 

18 

36 

3      2K 

f|l 

20 
24 

20 
24 

3      6M 
4      2M 

f|^ 

20 
24 

40 
48 

3     6M 

4     2H 

OQfe 

28 

28 

4    10^ 

t-H-rt 

28 

56 

4    10M 

^" 

32 

32 

5      6M 

^ 

32 

64 

5     6x"C 

38 

38 

6      6M 

38 

78 

6     6M 

.  g 

8 

24 

1      6J4 

c 

4 

16 

0    10M 

12 

36 

2      2M 

<«  rt 

8 

32 

1     634 

O^  w 

16 

48 

2    10M 

c^    * 

12 

48 

2     234 

P^'Q.S 

20 

60 

3      6M 

P^14"'  ^ 

16 

64 

2    10M 

g  rtV 

24 

72 

4      2M 

f-      o 

20 

80 

3     6% 

II* 

28 

84 

4    10M 

o  "|J>~< 

24 

96 

4      234 

£l? 

32 

96 

5      6/^ 

ptj.in 

28 

112 

4    10]^ 

H£ 

38 

114 

6      6M 

^ 

32 

128 

5     63i 

*  For  radiators  35  inches  high. 

the  "National,"  the  "United  States,"  the  "Penn,"  and  the 
"  Holland"  Radiator  Companies,  the  A.  A.  Griffing  Iron  Co.,  the 
J.  L.  Mott  Iron  Works,  and  the  H.  B.  Smith  Co.,  all  of  whom 
make  several  complete  lines.  There  are  also  a  number  of 
smaller  companies  who  make  two  or  three  styles. 

The  radiators  made  by  the  American  Radiator  Co.,  however, 
are  probably  more  extensively  used  than  those  of  any  other 
make,  particularly  in  the  Western  States,  and  it  is  for  this 
reason  that  they  have  been  selected  for  illustration.  Nearly 
all  of  the  patterns  made  by  this  company,  however,  are  very 
closely  duplicated  by  the  companies  above  named,  the  varia- 
tion being  principally  in  the  ornamentation. 

There  are  some  types  of  radiators  which  are  made  for  the 
purpose  of  circulating  steam  and  hot  water  in  one  construc- 
tion, but  the  lines  of  goods  made  by  the  American  Radiator 
Co.  for  water  and  steam  circulation  are  each  made  for  its  own 
specific  purpose. 

Figs.  2,  3,  and  4  illustrate  three  of  the  most  popular  styles  of 
radiators  made  by  this  company,  although  a  large  variety  of 
radiators  in  one-,  two-,  three-,  and  four- column  and  in  extended 
single-column  and  flue  construction  are  also  made  by  them. 

The  National  and  Verona  are  "two-column  radiators";  the 
Rococo  is  a  "three-column  radiator." 


KADIATORS. 


1125 


Fig.  2 
Rococo  Radiator. 


Fig.  3 

National  Two-column  Radiator. 


Kig.  4 

Verona  Radiator. 


1126 


STEAM  HEATING. 


Fig.    5   shows  three   sections  of   the  Colonial  wall  radiator 
made  by  this  company,  which  is  very  convenient  for  use  in 


Fig.  5 

Three  Sections  of  Colonial  Wall  Radiator. 

halls  and  bathrooms,  as  it  projects  only  from  3J  to  4J  ins. 

from  the  wall. 

This  radiator  is  made 
in  three  sizes  of  sections, 
29,  23,  and  16f  ins.  long, 
by  13J  ins.  wide  and  2| 
ins.  thick,  and  contain- 
ing 9,  7,  and  5  sq.  ft. 
of  heating  surface  re- 
spectively. The  sections 
may  be  assembled 
either  horizontally  or 
vertically. 

Corner,  circular,  curved, 
and  column  radiators; 
also  dining-room,  window, 
stairway,  box-base,  and 
direct-indirect  radiators; 
also  such  auxiliaries  as 
brackets,  pedestals,  tops, 
dampers,  and  wall-boxes; 
also  special  radiator  sec- 
tions with  high,  low,  or 


Fig.  6 

Italian  Flue  Box-base  Direct-  indirect  Radi-      single       legs 
ator.     Made  by  Amer.  Rad.  Co. 


also 


made  by  the  American 
Radiator  Co.,  and  by  all  of  the  other  companies  above 
mentioned. 


RADIATORS. 


1127 


HEATING  SURFACE  IN  SQUARE  FEET  PER  SECTION 
OF  SEVERAL  STEAM-  AND  HOT-WATER  RADIA- 
TORS MADE  BY  THE  AMERICAN  RADIATOR  CO. 


Name  of  Radiator. 

Length 
per 

Section. 

Height  of  Radiator  in  Inches. 

45 

38 

32 

26 

23 

20 
2 

National  

2& 

2^ 
2^ 
2^ 
21A 
3 

5 

4 

31A 

2^ 

21A 

Ideal  
Peerless  

" 

" 

•' 

" 

Perfection  
Verona.  .  .                .... 

* 

# 

7 

5% 

4^ 

* 
* 

3M 

Italian  flue.  .  . 

Rococo  (ornamental  or  plain)  .... 
St.    Louis    standard,    or    Buffalo 
standard,  4  columns  

44 

38 

32 

26 

22 

18 

2Y* 

21A 

6 
9 

5 

8 

4^ 

&A 

m 

5K 

3 

4 

2^ 
3 

JEtna  flue  

20 

18 

16 

14 

13 

3 
3 

6 
6 

5M 

5y3 

4% 

4% 

4 

4 

3H 

Zenith  flue  

*  Not  made  in  this  height. 

The  width  of  base  of  the  National,  Ideal,  and  Peerless  radia- 
tors is  8i  ins.;  of  the  Perfection,  9}  ins.;  Rococo,  10}  ins.;  Buffalo, 
12  ins.;  St.  Louis  standard  4  col.  and  zenith  flue,  12f  ins.; 
and  of  the  ^Etna  flue,  12J  ins. 

To  find  number  of  sections  required,  divide  required  heating 
surface  in  feet  by  values  given  in  above  table. 

To  find  length  of  radiator,  multiply  the  number  of  sections. 
by  length  per  section  and  add  1  inch  for  two  bushings. 

Radiators  are  generally  put  together  at  the  factory  as  ordered. 
The  standard  height,  except  for  window  radiators,  is  38  ins.. 
Heights  less  than  38  ins.  cost  a  little  more. 


Direct-indirect  Radiation. 

The  only  difference  between  this  method  of  heating  and  th© 
direct  method  is  that  external  air  is  introduced  into  the  room  in 
such  a  way  that  it  shall  come  in  contact  with  the  radiator  and, 
becoming  heated,  circulate  through  the  room,  and  unless  other 
means  are  provided  pass  out  through  the  cracks  around  the 
doors  and  windows.  By  this  arrangement  sufficient  ventilation 
is  afforded  for  living-rooms  and  offices.  With  direct  radiation 


1128 


STEAM  HEATING. 


no  ventilation  at  all  is  afforded.  There  are  several  methods  of 
arranging  the  radiators  and  cold-air  inlets,  although  nearly  all 

require  that  the  radiator 
shall  be  located  against 
an  outside  wall. 

The  simplest  method 
of  providing  direct-in- 
direct radiation  is  by 
using  a  radiator  that 
has  the  lower  portion 
encased  so  as  to  form  a 
box,  as  shown  in  Fig.  6. 
Cold  air  can  be  con- 
ducted from  the  outside 
of  the  house*  through  a 
galvanized  iron  pipe  and 
admitted  to  the  bottom 
of  the  radiator,  as  in  Fig. 
7.  It  is  then  obliged  to 
pass  upward  between  the 
radiator  flues  their  entire 
length  and  is  brought 
into  the  room  at  an  ex- 
ceptionally high  temper- 
ature. A  small  damper 
door  is  placed  in  the 

front  of  the  box,  and  a  damper  should  also  be  put  in  the  cold-air 
supply,  so  that  the  radiator  can  be  converted  into  the  ordinary 
direct  type  by  simply  closing  the  damper  and  opening  the  doors. 
This  would  probably  be  required  in  very  cold  weather.  The 
outside  of  the  radiator,  of  course,  heats  by  direct  radiation  at 
all  times.  If  a  large  amount  of  ventilation  is  required,  some 
form  of  indirect  radiator  should  be  enclosed  in  an  incombustible 
casing  and  the  outside  air  admitted  below  the  radiator.  A 
very  good  arrangement  to  accomplish  this  purpose  is  shown 
in  Fig.  8. 

It  consists  of  a  stack  of  pin  or  other  indirect  radiators  en- 
closed in  a  box  of  either  iron,  marble,  or  wood  lined  with  tin 
and  provided  with  registers  at  the  top  for  the  escape  of  the 
heated  air.  The  cold  air  enters  through  a  hollow  iron  sill  placed 
above  the  wooden-sill  of  a  window  and  passes  down  back  of  the 


RADIATORS. 


1129 


radiator,  through  a  galvanized  iron  pipe,  to  the  space  under  the 
radiator. 

The  cold-air  inlet  is  provided  with  a  damper  so  that  it  can 
be  closed,  and  registers  are  also  placed  at  the  base  of  the  radia- 
tor casing,  so  that  in  very  cold  weather  the  cold-air  inlet  may 
be   partially  or   wholly 
closed     and      the      air 
allowed      to      circulate 
through  the  bottom  reg- 
ister,  up    through    the 
radiator,  and  out  of  the 
top  registers. 

Indirect  Radia- 
tion. 

Heating  by  indirect 
radiation  is  accom- 
plished by  two  methods, 
themore  general  method 
being  to  have  separate 
radiators  for  each  room, 
located  in  the  cellar  or 

basement,  incased  with  metal  or  wood  lined  with  tin  and  provided 
with  a  fresh -air  inlet  and  tin  pipe  to  convey  the  hot  air  to  the 
room  to  be  heated. 

The  other  method  is  to  provide  one  cold-air  inlet  for  the  whole 
building  and  place  a  large  coil  of  steam-pipes  behind  it,  so  that 
all  the  air  entering  the  building  must  pass  through  this  coil. 
Such  a  method  can  only  be  used  in  connection  with  fan  ven- 
tilation. 

Fig.  9  shows  the  usual  method  of  casing  indirect  radiators. 
The  casing  is  generally  of  galvanized  iron  or  of  wood  lined  with 
tin.  The  latter  is  best  when  the  cellar  is  to  be  kept  cool,  as 
there  is  a  greater  loss  by  radiation  and  conduction  through 
metal  cases;  otherwise  metal  is  best,  as  it  w^.11  not  crack,  and 
when  put  together  with  small  bolts  can  be  removed  to  make 
repairs  without  damage. 

,  The  boxes  should  be  fitted  with  a  door  in  the  bottom,  and 
the  cold-air  pipe  should  always  be  provided  with  a  damper. 

The  vertical  air-ducts  are  usually  tin  flues  built  into  the  wall 
when  the  building  is  going  up.  Sometimes  they  are  only  plas- 


VERTICAL  SECTION  THROUGH  RADIATOR, 
CASING  AND  WINDOW  SILL. 

Fig.  8 


1130 


STEAM   HEATING. 


tered;    but  round,  smooth  metal  linings  with  close  joints 
much  the  best  results.     The  cross-section  of  the  air-duct  should 

be  comparatively 
large,  as  a  large 
volume  of  warmed 
air  with  a  slow  ve- 


locity  gives  the  best 
results. 

There  should  be 
a  separate  vertical 
air-duct  for  every 
outlet  or*  register. 
In  branched  verti- 
cal air-ducts  one  is 
generally  a  failure. 

The  heated  air 
from  one  heater 
may  be  taken  to 
two  or  more  verti- 
cal air-ducts  when 
they  start  directly 
over  it;  the  duct 
to  the  lower  room 
being  taken  from 
the  top  and  that  to 
the  upper  room 


Fig.  9 

Section  through  Indirect  Radiator  Stack. 


from  the  side,  or  both  from  the  top.  If  both  rooms  are  on  the 
same  level,  both  ducts  should  be  taken  from  the  top  of  the  box. 

Inlet  or  cold-air  ducts  are  best  when  there  is  one  for  every 
coil  or  heater.  Sometimes  only  one  large-branched  cold-air 
duct  is  used,  but  this  system  will  give  trouble  unless  all  the 
rooms  are  ventilated  by  forced  ventilation. 

The  Radiators.  —  For  indirect  radiation  a  form  of  radia- 
tor is  employed  different  from  those  used  for  direct  heating. 
In  this  method  the  desideratum  is  to  have  as  many  feet  of 
heating  surface  in  as  little  space  as  possible,  appearance  being  of 
no  importance.  The  earliest  form  used,  and  which  is  still  used 
in  the  fan  or  hot-blast  systems,  is  the  pipe-coil  radiator,  formed 
of  a  coil  of  pipes  connected  at  the  ends  with  return  bends. 

For  ordinary  indirect  heating  cast-iron  radiators  of  one  of 
the  types  shown  by  Figs.  10,  11,  and  12*  are  now  used  almost 
*  From  the  catalogue  of  the  American  Radiator  Co. 


INDIRECT  RADIATORS. 


1131 


exclusively,  as  they  are  fully  as  cheap  if  not  cheaper  than  pipe 
radiators  and  more  satisfactory. 

The  pin  radiator  is  made  by  several  manufacturers  and  is 
one  of  the  earliest  types  of  indirect  radiators. 

The  radiator  shown  by  Fig.   10  is  made  in  two  types:    for 


Fig,  10 
Perfection  Pin,  Extra  Large,  Flange  and  Bolt. 


Fig.  II 

Excelsior  Steam  Indirect  Radiator. 

connecting  by  flange  and  bolt,  and  right  and  left  threaded, 
all  tapped  2  ins.  and  bushed.  The  sections  are  made  in  two 
sizes,  viz.,  (1)  standard  size,  11 J  ins.  wide,  36  ins.  long,  and 
occupying  2J  ins.  in  the  stack,  the  heating  surface  being  10  sq. 
ft.  per  section;  (2)  the  extra  large  size,  which  is  15J  ins.  wide, 
36  ins.  long,  occupies  2J  ins.  in  the  stack  and  has  a  heating 


1132  STEAM   HEATING. 

surface  of  15  sq.  ft.  per  section.  The  Excelsior  pattern,  shown 
by  Fig.  11,  is  36f  ins.  long,  8  ins.  wide,  occupies  3f  ins.  in  the 
stack,  has  a  heating  surface  of  12  sq.  ft.  per  section,  and  is 
tapped  1J  ins.  The  Sterling,  Fig.  12,  is  37  ins.  long,  16  ins. 
high,  occupies  3|  ins.  in  the  stack,  contains  20  sq.  ft.  per  sec- 
tion, and  is  tapped  2  ins.  and  bushed. 

Cast-iron  indirect  radiators  with  plain  surfaces  are  also  made 
by  the  "American"  and  by  some  of  the  other  radiator  com- 
panies. 

Nearly  all  indirect  radiators  may  be  used  for  either  water  or 


/ 


Fig.  12 

Sterling  Indirect  Radiator. 

steam  circulation,  although  the  American  Radiator  Company 
has  slightly  different  patterns  for  steam  than  for  water. 

Indirect  radiators  are  generally  hung  from  the  ceiling  by 
four  iron  hangers  attached  to  the  floor  joists  and  having  their 
lower  ends  shaped  so  as  to  hold  iron  pipe  or  bar  iron  on  which 
the  radiator  rests.  The  front  support  should  be  J  in.  lower 
than  the  rear,  so  that  the  upper  pipe  of  each  radiator  will  in- 
cline to  the  rear  and  the  lower  pipe  of  each  will  incline  to  the 
front.  By  this  arrangement  the  water  of  condensation  will 
follow  the  course  of  steam  throughout  each  section.  The 
outlet  side  of  each  stack  should  be  from  J  to  f  of  an  inch  lower 
than  the  inlet  side  so  as  to  allow  the  water  free  passage  through 
and  out  of  the  stack. 

Each  stack  of  radiators  should  have,  in  the  warm-air  cham- 


BOILERS. 


1133 


ber,  not  less  than  12  ins.  clear  space  above  them  and  not  less 
than  6  ins.  below  them.  The  supply  and  return  pipes  should 
always  be  of  ample  size. 

The  space  required  for  any  quantity  of  heating  surface  of 
any  one  of  the  three  radiators  described  above  may  be  readily 
determined  by  means  of  the  data  given.  The  following  table 
will  be  found  useful  in  proportioning  size  of  air-ducts: 

DATA  FOR  EXCELSIOR  INDIRECT  STEAM-RADIATORS. 


.i*1 

, 

o 

o 

0 

si, 
9 

S 

VM 
O 

j 

•§W  » 

*3o 

!** 

"*"* 

02 

02 

^,«4_j        ' 

PH 

W'y  § 

& 

i—  i      > 

bC 

L 

-S'-ip  £ 

^ 

|U.*w{2i 

"8 

Q 

•H 

o 

|l 

T-1-^1 

Ill 

"o 

t*~t    ^.^H 

$* 

|o 

|S 

•|o 

$T 

Q 

Q 

M 

CQ 

OQ 

& 

PH 

3; 

Sq.Ft. 

Sq.In. 

Inches. 

Sq.  In. 

Inches. 

Inches. 

Cu.  Ft. 

Cu.  Ft. 

Cu.  Ft. 

24 

36 

6.8 

48 

4X12 

8X   8 

720 

840 

960 

36 

54 

8.3 

72 

8X12 

9X12 

1080 

1260 

1440 

48 

72 

9.6 

96 

8X12 

10X14 

1440 

1680 

1920 

60 

90 

10.0 

120 

12X12 

12X15 

1800 

2100 

2400 

72 

108 

11.7 

144 

12X12 

12X19 

2160 

2520 

2880 

84 

126 

12.7 

168 

12X16 

14X22 

2520 

2940 

3360 

96 

144 

13.5 

192    12X16 

14X24 

2880 

3360 

3840 

108 

162 

14.4 

226    12X20 

16X20 

3240 

3780 

4320 

120 

180 

15.2 

240 

12X20 

16X24 

3600 

4200 

4800 

132 

198 

15.9 

264 

12X24 

20X20 

3960 

4620 

5280 

144 

216 

16.6 

288 

12X24 

20X24 

4320 

5040 

5760 

The  Boiler. 

Classes  of  Heating  Boilers. — There  are  a  great  many 
varieties  of  steam-boilers  in  use  for  generating  steam  for  heating 
purposes  besides  several  types  that  were  on  the  market  some 
twelve  or  fifteen  years  ago  and  are  now  practically  obsolete.  The 
larger  proportion  of  the  boilers  used  at  the  present  time  may  be 
classed  under  the  following  heads,  viz.: 

(1)  Horizontal  tubular  boilers. 

(2)  Fire-box  boilers. 

(3)  Sectional  boilers. 

a.  Boilers  with  vertical  sections. 
6.  Boilers  with  horizontal  sections. 

Horizontal  Tubular  Boilers. — This  boiler  has  been 
very  extensively  used  both  for  heating  and  power  and  is  still 


1134  STEAM  HEATING. 

preferred  by  many  engineers  for  heating  large  buildings  or 
generating  steam  for  hot-blast  heating  systems.  It  is  an 
efficient  type  of  bo.iler,  is  easily  cleaned,  and  is  usually  the  most 
economical  type  for  a  large  amount  of  radiation,  say  over  2,500 
sq.  ft.,  and  particularly  when  soft  coal  is  used  for  fuel. 

The*  chief  objection  to  its  use  is  that  should  an  explosion 
occur  from  any  cause,  it  is  liable  to  do  a  great  amount  of  damage, 
possibly  demolish  the  building.  The  chance  of  an  explosion, 
however,  is  very  small  indeed.* 

Tubular  boilers  are  manufactured  in  nearly  every  city  of 
importance  and  can  be  purchased  in  every  market  at  a  reason- 
able price. 

The  boiler  should  be  provided  with  manholes  with  strongly 
reinforced  edges,  so  that  a  person  can  enter  for  cleaning.  The 
heads  of  the  boiler  above  the  tubes  should  be  thoroughly  braced 
in  order  to  sustain  safely  any  pressure  from  the  inside  of  the 
boiler. 

Domes. — Domes  are  often  placed  above  the  horizontal 
part  of  a  boiler  for  the  purpose  of  increasing  the  capacity  for 
the  storage  of  steam  and  to  afford  a  ready  means  of  drawing 
off  dry  steam. 

The  desirability  of  domes  is  a  much  disputed  question.  The 
dome  is  always  an  element  of  weakness  in  a  boiler,  and  many 
engineers  claim  that  the  boiler  is  better  without  them.  For 
gravity  heating,  boilers  without  domes  are  probably  most  used, 
while  for  power  purposes  the  dome  is  generally  provided. 
There  seems  to  be  no  standard  proportions  for  tubular  boilers, 
as  the  practice  of  different  makers  and  engineers  varies  some- 
what. The  proportions  given  in  the  following  tables,  however, 
are  fairly  representative  of  most  of  the  boilers  made,  those  in 


*  "The  claim  for  safety  can  also  be  made  for  the  horizontal  return  tubu- 
lar boiler.  The  fact  is  that  when  boilers  of  this  type  are  properly  con- 
structed they  do  not  explode.  When  one  compares  the  few  explosions 
which  occur  with  the  great  number  of  boilers  of  this  type  which  are  manu- 
factured every  year  and  the  vastly  greater  number  which  are  in  use,  a 
large  number  of  them  carelessly  constructed  and  carrying  a  greater  pressure 
than  they  were  designed  to  carry,  it  is  a  strong  argument  in  support  of  this 
claim,  that  they  are  safety  boilers  when  proper  care  and  inspection  are 
given  to  their  construction. 

"  Moreover,  the  horizontal  return  tubular  boiler  when  well  designed  and 
carefully  constructed  is  not  only  a  safety  boiler,  but  when  compared  with 
water-tube  boilers  we  do  not  hesitate  to  say  that  it  is  more  economical." 
(Edward  Kendall  &  Sons.) 


TUBULAR  BOILERS. 


1135 


the  first  table  being  designed  for  hard  coal  and  those  in  the 
second  table  for  soft  coal. 

HORIZONTAL  TUBULAR  BOILERS. 

MANUFACTURED  BY  EDWARD  KENDALL,  &  SONS,  CAMBRIDGE,  MASS.* 


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Ins. 

Ft.Ins. 

Ins. 

Ft. 

Ins. 

Sq.  Ft. 

30 

6     0 

36 

2 

5 

4 

114 

7^ 

3,600 

5 

684 

7     0 

'4 

41 

6 

i 

137 

9-V& 

3,750 

5 

822 

8     0 

44 

44 

7 

4 

160 

10% 

3,900 

6 

990 

9     0 

" 

44 

8 

4 

182 

12 

4,050 

8 

1,092 

36 

8     0 

34 

2^2 

7 

4 

189 

4,390 

8 

1,124 

9     0 

44 

44 

8 

4 

216 

14^2 

4,600 

8 

1,296 

10     0 

44 

44 

9 

4 

243 

16 

4,810 

10 

1,458 

11     0 

44 

44 

10 

* 

270 

18 

5,090 

10 

1,620 

12     0 

44 

44 

11 

4 

297 

20 

5,300 

12 

1,782 

13     0 

28 

3 

12 

4 

321 

21 

5,510 

12 

1,926 

'  2 

10     0 

45 

2^2 

9 

1 

315 

21 

6,610 

12 

1,890 

11     0 

44 

v 

10 

4 

350 

23 

7,030 

12 

2,100 

12     0 

44 

44 

11 

4 

384 

26 

7,300 

14 

2,304 

13     0 

44 

44 

12 

4 

420 

28 

7,660 

14 

2520 

12     0 

38 

3 

11 

4 

389 

26 

7,320 

14 

2,334 

13     0 

" 

44 

12 

4 

425 

28 

7,680 

14 

2,550 

14     0 

41 

44 

13 

44 

460 

31 

7  ,950 

16 

2,760 

15     0 

" 

44 

14 

44 

495 

33 

8,220 

16 

2,970 

48 

12     2 

69 

2% 

11 

5/ie 

566 

38 

9,750 

18 

3,396 

13     2 

44 

44 

12 

44 

617 

41 

10,150 

18 

3,702 

15     2 

49 

3 

14 

44 

626 

42 

10,685 

18 

3,756 

16     2 

44 

14 

15 

44 

671 

45 

11,035 

18 

4,026 

17     2 

44 

44 

16 

44 

716 

48 

11,485 

20 

4,296 

17     2 

38 

3/^ 

16 

41 

658 

44 

12,085 

20 

3,948 

18     2 

44 

'4 

17 

** 

700 

47 

12,535 

20 

4,200 

54 

15     2 

60 

3 

14 

^Vs2 

759 

51 

14,015 

24 

4,554 

16     2 

72 

15 

" 

954 

63 

15,074 

26 

5,724 

17     2 

11 

44 

16 

44 

1,018 

68 

15,584 

28 

6,108 

18     2 

" 

44 

17 

44 

1,082 

72 

16,094 

28 

6,492 

17     2 

54 

'3]^2 

16 

44 

905 

60 

15,458 

26 

5,430 

18     2 

" 

44 

17 

44 

961 

64 

15,960 

26 

5,766 

19     2 

44 

44 

18 

44 

1,018 

68 

16,552 

28 

6,108 

60 

18     2 

92 

3 

17 

iH* 

1,364 

91 

19,000 

34 

8,284 

M 

18     2 

64 

3^ 

17 

44 

1,133 

76 

18,468 

30 

6,798 

41 

19     2 

44 

•* 

18 

44 

1,200 

80 

19,227 

32 

7,2CO 

66 

18     2 

110 

3 

17 

" 

1,615 

108 

22,430 

40 

9,690 

44 

18     2 

82 

3^y 

17 

*4 

1,426 

95 

22,190 

36 

8,556 

72 

18     2 

130 

3 

17 

Tie 

1,900 

127 

26036 

48 

11,400 

18     2 

100 

3^ 

17 

1,721 

115 

25J980 

44 

10,326 

*  Selected  from  156  sizes  listed  by  this  firm.     These  boilers  are  made 
up  to  96  ins.  diam.  and  21  ft.  long, 
t  For  hard  coal  or  coke. 
t  Proportion  6  to  1.     The  last  two  columns  added  by  the  author. 

When  soft  coal  is  used  for  fuel  the  efficiency  of  the  boiler 
may  be  increased  by  increasing  the  grate  area  about  20  per  cent. 


1136 


STEAM  HEATING. 


PROPORTIONS  OF  HORIZONTAL  TUBULAR  BOILERS. 

Made  by  the  Atlas  Engineering  Works,  Indianapolis,  Ind. 
These  are  about  the  standard  proportions  as  used  in  the  Western  States 
for  ordinary  purposes. 


Shell.t 

Mean  Thickness. 

Tubes. 

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Inches 

Feet. 

Inches. 

Inches. 

Ins. 

Feet. 

Sq.  Ft. 

Sq.  Ft. 

15 

36 

8 

1 

| 

26 

3 

8 

214 

5.8 

20 

36 

10 

| 

| 

26 

3 

10 

266 

8.3 

25 

36 

12 

4 

| 

26 

3 

12 

318 

9.5 

30 

40 

12 

| 

34 

3 

12 

404 

12 

35 

42 

12 

1 

Jie 

40 

3 

12 

464 

12.8 

40 

46 

12 

ft 

JS 

42 

3 

12 

491 

14.6 

45 

48 

12 

ft 

48 

3 

12 

551 

15.3 

50 

48 

14 

40 

3| 

14 

630 

16 

55 

52 

14 

^ie 

44 

14 

693 

16.7 

60 

54 

14 

/l6 

i 

46 

3i 

14 

721 

18 

70 

54 

16 

/ie 

1 

40 

4" 

16 

817 

20.8 

75 

60 

14 

i* 

62 

3J 

14 

940 

21.5 

85 

60 

16 

fi 

1 

52 

4 

16 

1045 

22.2 

100 

66 

16 

1 

64 

4 

16 

1265 

25 

125 

72 

16 

Cg 

I 

82 

4 

16 

1578 

29.5 

150 

72 

18 

JTe 

1 

82 

4 

18 

1775 

36.5 

*  It  will  be  noticed  that  these  boilers  are  rated  a  little  higher  than  the 
usual  standard  of  15  sq.  ft.  of  heating  surface  to  1  H.-P. 

t  In  these  boilers  the  smoke-box  is  made  of  a  separate  piece,  so  that 
the  actual  length  of  boilers  is  15  ins.  more  than  length  of  shell. 

Size  of  Tubes. — In  the  Eastern  States  where  hard  coal  is 
used,  2J-inch  tubes  are  commonly  placed  in  boilers  up  to  12  ft. 
long,  but  where  soft  coal  is  used  for  fuel,  the  tubes  should  not 
be  less  than  3  ins.  in  diameter  even  for  the  smallest  boiler, 
while  for  boilers  16  ft.  long  and  over  3}  ins.  or  4  ins.  tubes 
should  be  used. 

Setting  of  Horizontal  Tubular  Boilers. — Boilers  are 
set  with  half  fronts  and  full  fronts.  With  half-front  setting,  the 
front  end  of  the  boiler  projects  12  ins.  or  more  beyond  the 
brickwork  and  is  covered  with  a  cast-iron  frame  containing 
two  doors  for  giving  access  to  the  flues. 

With  a  full  front,  a  cast-iron  front  is  provided  the  full  width 


FIRE-BOX  BOILERS.  1137 

of  the  boiler  and  extending  from  the  floor  to  the  top  of  the 
brick  setting. 

Fig.  13  shows  the  proper  method  of  setting  a  horizontal 
tubular  boiler  with  full  front,  and  the  table  *  opposite  it  gives 
the  dimensions  indicated  by  the  letters  and  the  quantities  of 
bricks  required.  These  will  be  found  useful  in  showing  the 
boiler  setting  on  the  foundation  plan  of  the  building,  and  also 
in  estimating  the  cost  of  setting. 

Fire-box  Boilers. — A  fire-box  boiler  is  a  horizontal 
tubular  boiler  with  a  fire-box  formed  in  the  front  end,  as  in 
Fig.  14.  The  fire-box  has  double  walls,  the  space  between 
being  filled  with  water,  so  that  the  fire  is  entirely  surrounded 
with  water,  the  object  being  to  utilize  a  greater  percentage 
of  the  heat  generated  by  combustion  than  is  possible  with  the 
ordinary  tubular  boiler. 

The  American  Radiator  Co.  and  the  Kewanee  Boiler  Co. 
make  a  r  re-box  boiler  intended  especially  for  heating  purposes, 
which  would  seem  to  be  a  very  efficient  type  of  boiler  for  build- 
ings having  from  1,000  to  3,000  ft.  of  direct  steam  radiation  or 
1,500  to  6,000  ft.  of  hot- water  radiation,  and  particularly  where 
hard  coal  or  coke  is  used  for  fuel. 

These  boilers  may  be  installed  in  very  low  cellars.  The 
danger  from  explosion  with  these  boilers,  however,  when  used 
for  steam  heating  is  about  the  same  as  with  plain  tubular 
boilers. 

Fire-box  boilers  require  a  brick  setting  as  shown  by  Fig.  14. 

Sectional  Cast-iron  Boilers. — This  class  of  boiler  has 
been  used  for  a  great  many  years,  but  during  the  past  ten 
years  they  have  become  more  popular  than  ever,  and  are  now 
very  largely  taking  the  place  of  tubular  boilers  for  the  heating 
of  quite  large  private  and  public  buildings,  principally  on  ac- 
count of  their  safety  from  dangerous  explosions.  This,  in  fact, 
is  the  chief  advantage  of  the  sectional  boiler  over  a  tubular 
boiler.  In  a  sectional  boiler,  should  an  explosion  occur  from 
gross  carelessness  of  the  attendant,  it  would  probably  be  con- 
fined to  not  more  than  two  sections,  and  do  but  little  damage 
to  the  building.  Many  improvements  have  been  made  in 
these  boilers  during  the  past  decade,  so  that  some  of  the  latest 
patterns  seem  to  be  about  perfect  for  the  class  of  work  for 
which  they  are  intended. 

*  Published  by  Kellog-Mackay-CameronCo. 


1138 


STEAM  HEATING. 


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SECTIONAL   BOILERS. 


1139 


Types   of  Sectional  Boilers. — There   is   such  a  great 
variety  of  small  sectional  boilers  for  house  heating  that  it  is 


impossible  to  describe  them  in  a  work  of  this  character.  Nearly 
all  are  of  a  portable  pattern  and  are  generally  made  in  horizontal 
sections,  i.e.,  the  sections  fitting  one  on  top  of  the  other. 


1140 


STEAM  HEATING. 


SECTIONAL   BOILERS. 


1141 


For  buildings  having  more  than  400  ft.  of  direct  radiation — 
in  the  radiators — a  vertical  sectional  boiler  is  to  be  preferred 
to  one  with  horizontal  sections. 

The  vertical  sectional  boiler 
is  made  up  of  a  number  of  cast- 
iron  vertical  sections  set  one 
in  front  of  the  other  on  a  cast- 
iron  base  which  forms  the  ash- 
pit. The  sections  are  connected 
together  either  by  means  of 
push  nipples  fitting  tightly  into 
adjacent  sections  or  by  connect- 
ing each  section  to  three  drums, 
one  above  the  boiler  and  one 
on  each  side  near  the  bottom. 
The  latter  type  of  boiler  is 
designated  as  a  " screw-nipple" 
boiler  and  the  former  as  a  "  push- 
nipple  "  boiler.  The  push-nipple  boiler  is  the  later  type  and  seems 
to  be  most  in  favor  with  steam-fitters.  It  affords  a  freer  circu- 


Fig.  15 

'  Ideal  "  Sectional  Steam  Boiler. 


Fig.  16 

Gurney  Bright  Idea  Boiler,  1200  Series— Screw-nipple  Type. 

iation  of  steam  and  water  than  the  screw-nipple  type  and  is  more 
•quickly  erected. 

On  the  other  hand,  if   any   section  of  a   push-nipple    boiler 


1142  STEAM   HEATING. 

becomes  disabled,  the  entire  boiler  must  be  thrown  out  of  use 
until  a  new  section  can  be  put  in,  while  with  the  screw-nipple 
boiler,  if  an  intermediate  section  is  disabled  it  can  be  discon- 
nected from  the  drums  and  the  openings  plugged,  so  that  the 
boiler  can  be  run  temporarily,  or  even  permanently,  if  the 
boiler  is  large  enough,  without  taking  out  the  disabled  section. 

Fig.  15  shows  the  general  external  appearance  of  push- 
nipple  boilers  and  Fig.  16  of  the  screw-nipple  boilers.  Fig  17 
is  a  sectional  view  of  the  Gurney  Bright  Idea  sectional  water- 
tube  hot-water  boiler,  "1200  series,"  adapted  to  from  5,000 
to  11,000  ft  of  radiation.  Boilers  constructed  on  the  same  prin- 
ciple are  also  made  for  house  heating. 

Although  the  external  appearance  of  nearly  all  vertical  sec- 
tional boilers  is  quite  similar,  the  arrangement  of  the  flues  or 


Fig.  17 
Sectional  View  of  Gurney  Boiler. 

passages  for  the  gases  of  combustion  differs  somewhat  in  each 
different  line  of  boilers,  and  between  some  lines,  as  between 
the  Gurney  "Bright  Idea"  and  the  "Ideal"  line  of  the  American 
Radiator  Co.,  is  very  great.  In  general,  it  may  be  said  that 
those  heaters  which  have  the  greatest  amount  of  heating  surface 
in  proportion  to  the  grate  .area  are  likely  to  prove  the  most 
efficient  in  point  of  economy  of  coal  consumption. 

As  a  rule,  the  intermediate  sections  of  sectional  boilers  are 
alike,  so  that  the  capacity  of  the  boiler  may  be  varied  within 
certain  limits  by  increasing  the  number  of  sections. 


SECTIONAL   BOILERS.  1143 

The  requirements  of  an  economical  and  satisfactory  working 
boiler  for  house  heating  are  as  follows: 

First. — They  should  contain  a  quantity  of  water  sufficiently 
large  to  fill  the  pipes  and  radiators  with  steam  to  any  required 
pressure  without  lowering  the  water  in  the  boiler  to  require  an 
addition  when  steam  is  up,  for  should  the  steam  go  down  sud- 
denly, there  will  be  too  much  water  in  the  boiler  This  occurs 
in  boilers  made  with  very  small  parts  or  pipes  which  have  a 
small  capacity  at  the  water-line;  such  boilers  require  great  care 
for  should  the  boiler  have  an  automatic  water-feeder  set  for  the 
true  water-line,  it  will  fill  up,  but  cannot  discharge  again  when 
the  steam  goes  down,  while  if  it  has  no  feeder,  there  is  danger 
of  spoiling  the  boiler,  as  the  water  is  in  the  pipes  in  the  form  of 
steam. 

It  is  true  that  a  boiler  which  contains  a  small  amount  of  water 
in  proportion  to  its  heating  surface  will  get  up  steam  quicker 
than  one  containing  a  larger  quantity  of  water,  but  the  latter 
will  keep  steam  much  better  when  the  fire  is  renewed;  and 
boilers  which  contain  small  quantities  of  water  are  rapidly 
chilled  as  well  as  rapidly  heated  and  must  be  fired  often  and 
regularly. 

Second. — The  fire-box  should  be  of  iron,  with  a  water  space 
around  it,  to  prevent  clinkering  on  the  sides  and  the  necessity 
of  repaid  to  brickwork,  which  are  unavoidable  in  brick  furnaces, 

Third. — lhe  fire-box  should  be  deep  below  the  fire-door,  to 
admit  of  a  thick  fire  to  last  all  night  and  thus  keep  up  steam. 
For  large  boilers  which  require  the  services  of  an  engineer  it 
is  desirable  to  have  a  large  grate  area  and  a  thin  fire;  but  such 
a  fire  requires  to  be  renewed  too  often  to  be  suitable  for  a  house 
boiler. 

Fourth. — The  fire-box  should  be  spacious,  for  the  sake  of 
good  combustion. 

Fifth. — The  boiler  should  have  few  parts,  and  the  flues 
and  tubes  should  be  large  and  in  a  vertical  position,  so  that  they 
will  not  foul  easily,  and  that  any  deposit  may  fall  to  the  bottom. 

For  dwellings  the  writer  advises  those  forms  of  boilers  which 
are  without  tubes,  or  with  but  a  very  few,  as  the  tubes  will 
invariably  give  out  long  before  the  shell,  and  if  the  tubes  are 
not  kept  clean  they  will  transmit  but  a  small  percentage  of  heat. 

Sixth. — All  parts  should  be  readily  accessible  for  cleaning  and 
repairs.  This  is  a  point  of  the  greatest  importance  and  economy. 
When  the  heating  surfaces  become  covered  'with  soot  and  ashes, 


1144  STEAM   HEATING. 

the  economy  of  the  boiler  greatly  decreases,  as  the  soot  acts 
as  an  insulator  and  prevents  the  heat  reaching  the  boiler.  It 
is  for  this  reason  that  boilers  which  work  well  when  new  are 
found  insufficient  to  do  the  work  required  of  them  when  they 
become  dirty. 

Seventh. — The  heating  surface  should  be  arranged  as  nearly 
as  possible  at  right  angles  to  the  currents  of  heated  gases  and 
so  break  up  the  currents  as  to  extract  the  entire  available  heat 
therefrom. 

Eighth. — It  should  have,  if  possible,  no  joints  exposed  to  the 
direct  action  of  the  fire. 

Ninth. — It  should  have  a  great  excess  of  strength  over  any 
legitimate  strain,  and  should  be  so  constructed  as  not  to  be 
liable  to  be  strained  by  unequal  expansion. 

Tenth. — It  should  be  durable  in  construction  and  not  liable 
to  require  early  repairs. 

Eleventh. — The  water  space  should  be  divided  into  sections,  so 
arranged  that  should  any  section  give  out  no  general  explosion 
can  occur  and  the  destructive  effects  be  confined  to  the  simple 
escape  of  the  contents. 

Twelfth. — It  should  be  proportioned  for  the  work  to  be  done, 
and  be  capable  of  working  to  its  full  rated  capacity  with  the 
highest  economy. 

Thirteenth. — It  should  be  provided  with  the  very  best  gauges, 
safety-valves,  and  other  fixtures. 

The  boiler  should  be  set  so  that  the  water-line  in  the  boiler 
will  be  at  least  2  ft.  below  the  main  horizontal  supply-pipe. 

The  more  prominent  lines  of  sectional  boilers  for  low-pressure 
steam  or  hot-water  heating  are:  The  "Ideal"  line,  made  by 
the  American  Radiator  Co.;  the  "International"  and  "Carton," 
made  by  the  International  Heater  Co.;  the  "Bright  Idea,7' 
made  by  the  Gurney  Heater  Mfg.  Co.;  the  "Mercer"  and 
"Gold,"  made  by  the  H.  B.  Smith  Co.;  the  "Furman,"  made 
by  the  Herendeen  Mfg.  Co.;  the  "Sunray,"  made  by  the  J.  L, 
Mott  Iron  Works;  the  "Burnham,"  made  by  Lord  &  Burnham 
Co.,  and  the  "  Florence,"  made  by  the  Columbia  Heating  Co. 

The  "Ideal"  boilers  are  very  extensively  used  throughout 
the  Western  States.  Besides  being  a  very  efficient  boiler  they 
also  have  the  merit  of  being  very  low  in  stature,  thus  fitting 
them  for  installation  in  buildings  haidng  very  low  cellars 
without  the  necessity  of  constructing  special  pits.  The  American 
Radiator  Co.  makes  twenty  different  types  of  sectional  boiler^ 


RATING  OF  STEAM-BOILERS.  1145 

for  steam  and  water,  adapted  to  all  kinds  of  fuel,  and  fifteen 
different  types  of  round  boilers. 
Setting-  and  Covering-  of  Sectional  Boilers. — The 

only  brickwork  required  for  any  of  the  boilers  named  above 
is  a  suitable  foundation  with  water-tight  ash-pit  about  12  ins. 
deep. 

The  outside  of  the  boilers,  however,  should  be  plastered  with 
a  substantial  covering,  from  1  to  1|  ins.  thick,  of  plastic  as- 
bestos. 

Rating  of  Steam-boilers. — Tubular  boilers  are  often 
designated  as  so  many  "horse-power." 

Strictly  speaking,  there  is  no  such  thing  as  "horse-power" 
to  a  steam-boiler,  as  it  is  a  measure  applicable  only  to  dynamic 
effect.  But  as  boilers  are  necessary  to  drive  steam-engines, 
the  same  measure  applied  to  steam-engines  has  come  to  be 
universally  applied  to  the  boiler  and  cannot  well  be  discarded. 

The  standard  established  by  the  committee  of  judges  of  the 
Centennial  Exposition  in  1876,  and  since  adopted  by  the  A,  S. 
M.  E.,  is  "the  evaporation  of  30  Ibs.  of  water  per  hour  from 
feed-water  at  100°  Fahr.  into  steam  at  70  Ibs.  gauge  pressure." 
This  standard  is  equal  to  33,305  thermal  units  per  hour,  As 
the  amount  of  water  which  any  boiler  will  evaporate  per  hour 
depends  as  much  upon  the  management  of  the  fire  and  the 
kind  of  fuel  used  as  upon  the  size,  the  above  standard  is  a  difficult 
one  to  determine  with  accuracy,  so  that  in  practice  the  com- 
mercial horse-power  of  a  boiler  has  come  to  be  measured  by 
the  amount  of  its  heating  surface,  i.e.,  the  heating  surface 
available  in  generating  steam. 

It  is  the  general  practice  to  consider  15  sq.  ft.  of  heating  surface 
in  horizontal  tubular  boilers  and  11.5  sq.  ft.  in  water- tube  boilers 
as  equivalent  to  one  horse-power,  and  most  manufacturers  rate 
their  boilers  by  this  standard. 

The  heating  surface  of  horizontal  tubular  boilers  is  com- 
puted as  follows,  all  dimensions  being  taken  in  inches.  Mul- 
tiply two  thirds  the  circumference  of  the  shell  by  its  length, 
multiply  the  sum  of  the  circumferences  of  all  the  tubes  by 
their  common  length;  to  the  sum  of  these  products  add  two 
thirds  of  the  area  of  both  tube  sheets  less  twice  the  combined 
area  of  all  the  tubes  and  divide  the  sum  by  144  to  obtain  the 
result  in  square  feet.  Or,  the  heating  surface  is  equal  to  the 
surface  area  of  all  the  tubes  plus  two  thirds  the  surface  of  the 
shell  and  both  tube  sheets  minus  the  area  of  the  holes, 


1146  STEAM    HEATING. 

Steam-heaters,  i.e.,  boilers  intended  omy  for  the  heating 
of  buildings,  are  generally  rated  by  the  manufacturers  according 
to  the  amount  of  direct  radiating  surface  they  will  supply, 
including  all  piping.  These  ratings  are  commonly  made  pretty 
high,  so  that  it  is  a  safe  rule  to  use  a  boiler  having  a  rating 
40  per  cent,  in  excess  of  the  actual  direct  radiation  (radiators) 
when  the  mains  are  covered  and  50  per  cent,  when  they  are 
not  covered. 

Each  foot  of  indirect  radiation  should  be  figured  as  equal 
to  1}  ft.  of  direct  radiation. 

Proportioning  Radiating  Surface  to  Horizontal  Tubular 
Boilers. — To  determine  the  size  of  boiler  necessary  to  supply 
a  given  amount  of  direct  radiation,  allow  1  sq.  ft.  of  heating 
surface  in  the  boiler  to  6  to  7  sq.  ft.  of  direct  radiation  when 
all  mains  are  covered  and  1  to  5  or  6  sq.  ft.  when  the  mains  are 
not  covered.  A  large  boiler  will  usually  supply  a  greater  amount 
of  radiation  in  proportion  to  its  heating  surface  than  a  small 
one. 

In  these  rules  the  piping  is  not  to  be  included  in  the  radiating 
surface. 

It  should  be  borne  in  mind  that  no  hard  and  fast  rule  can 
be  given  for  proportioning  heating  surfaces,  hence  in  laying 
out  a  heating  plant  the  architect  will  do  well  to  be  guided  to 
some  extent  by  the  advice  of  an  experienced  steam-fitter. 

Amount  of  Coal  Burned  per  Hour. — "The  amount  of  coal 
burned  per  square  foot  of  grate  surface  per  hour  is  rarely  less 
than  15  Ibs.  with  power  boilers,  and  in  some  cases  is  very  much 
greater,  but  it  is  usually  less  than  10  Ibs.,  and  is  sometimes  as 
small  as  3  or  4  with  heating  boilers.'7  * 

Boiler  Trimmings. — Every  steam-boiler  should  be  pro- 
vided with  a  brass-cased  steam-gauge,  safety-valve,  and  water- 
column  with  gauge,  water-gauge,  and  glass.  An  automatic 
damper  regulator  with  connections  for  operating  draft  door 
and  cold-air  check  is  also  desirable  on  house  heaters.  The  best 
safety-valve  for  low-pressure  boilers  is  the  single  weighted  type; 
it  should  be  connected  at  the  top  of  the  heater. 

SYSTEMS  OF  PIPING  FOR  STEAM  HEATING. 

Distinction  Between  Gravity  and  Non-gravity 
Systems. — The  various  systems  of  steam  heating  are  divided 

*  Prof.  R.  C.  Carpenter. 


SYSTEMS  OF  STEAM  HEATING.  1147 

into  two  general  classes,  viz.,  gravity  circulating  systems  and 
non-gravity  systems.  The  former  embraces  all  systems  in  which 
the  water  of  condensation  from  the  various  radiators  returns 
to  the  boiler  by  its  own  weight,  i.e.,  by  gravity,  without  the 
aid  of  any  mechanical  device. 

Non-gravity  systems  require  some  special  machinery,  such 
as  a  pump  or  return  trap,  to  return  the  water  to  the  boiler  or 
in  some  cases  the  water  of  condensation  is  wasted. 

The  kind  of  boiler  used  or  the  character  of  the  radiation  has 
nothing  to  do  with  the  distinction  between  the  two  systems, 
although  with  the  non-gravity  systems  tubular  or  power  boilers 
are  generally  employed.  Wherever  high-pressure  steam  is 
carried  on  the  boiler,  the  non-gravity  system  must  be  used, 
hence  this  system  is  often  designated  as  the  high-pressure 
system,  but  it  is  very  seldom  that  high-pressure  steam  is  carried 
into  the  radiators.  If  high-pressure  steam  is  generated  for 
power  purposes,  that  portion  of  live  steam  which  is  used  for 
heating  is  generally  passed  through  a  reducing  valve,  so  that 
the  pressure  in  the  radiators  does  not  exceed  10  Ibs.,  and  if 
exhaust  steam  is  used  it  can  be  mixed  with  the  reduced  live 
steam;  otherwise  the  heating  system  is  exactly  the  same  as  a 
gravity  system,  except  in  returning  the  water  of  condensation 
to  the  boiler.  On  the  other  hand,  where  low-pressure  steam 
is  used  and  it  is  necessary  to  place  radiators  below  the  water- 
line  in  the  boiler,  a  non-gravity  system  must  be  used  because 
the  water  of  condensation  must  be  collected  in  a  tank  or  re- 
ceiver and  returned  to  the  boiler  by  a  return  trap  or  pump. 
For  gravity  circulation  the  lowest  radiation  must  be  at  least 
4  ft.  above  the  water-line  in  the  boiler. 

The  same  system  of  piping  may  be  used  for  both  systems, 
except  that  with  the  non-gravity  systems  the  return  pipe 
must  terminate  in  a  tank  or  receiver  placed  below  the  level 
of  the  lowest  radiator. 

Definitions  of  Terms  Used  in  Describing  Steam 
and  Hot-water  Piping'. — There  are  certain  terms  used 
in  describing  steam  or  hot-water  piping  with  which  an  architect 
or  superintendent  should  be  familiar. 

The  main  or  distributing  pipe  is  the  pipe  leaving  the  boiler 
and  which  conveys  the  steam  or  hot  water  to  the  risers  or 
branches  which  supply  radiating  surfaces.  In  steam  heating 
this  pipe  is  termed  the  main  steam-pipe,  and  in  hot- water 
heating  the  main  flow  pipe.  The  term  supply  pipe  is  some- 


1148  STEAM  HEATING. 

times  applied  to  main  steam-pipes,  but  it  is  not  technically 
correct. 

The  pipes  in  which  the  flow  takes  place  from  the  radiator 
are  called  return  pipes.  The  main  return  is  the  pipe  which 
connects  with  the  boiler  below  the  water-line,  or,  in  a  non- 
gravity  system,  connects  with  the  receiver 

Risers  are  those  pipes  which  extend  in  a  vertical  direction 
to  supply  radiators.  The  vertical  pipes  in  which  the  flow  is 
downward  are  called  return  risers. 

A  relief  or  drip  is  a  small  pipe  run  from  a  steam-main  to  a 
return.  It  must  be  used  at  all  points  where  water  is  likely  to 
gather  in  the  main. 

Pitch  is  the  inclination  given  to  any  pipe  when  running  in  a 
nearly  horizontal  direction. 

The  term  water-line  is  used  to  denote  the  height  at  which 
the  water  will  stand  in  the  return  pipes.  In  a  gravity  system 
the  water-line  is  practically  the  level  of  the  water  in  the  boiler. 

"  Water-hammer  is  a  term  applied  to  a  very  severe  concussion 
which  often  occurs  in  steam-heating  pipes  and  radiators.  It 
is  caused  by  cold  water  accumulating  to  such  an  extent  as  to 
condense  some  of  the  steam  in  the  pipe,  thus  forming  a  vacuum 
which  is  filled  by  a  very  violent  rush  of  steam  and  water.  The 
water  strikes  the  side  of  the  radiators  or  pipes  with  great  force 
and  often  so  as  to  produce  considerable  damage.  In  general, 
water-hammering  may  be  prevented  by  arranging  the  piping 
in  size  and  pitch  so  that  the  water  of  condensation  will  imme- 
diately drain  out  of  the  radiators  or  pipes."  * 

An  air-trap  is  an  upward  bend  in  a  pipe  which  accumulates 
air  to  such  an  extent  as  to  prevent  circulation  in  the  system. 
When  an  air-trap  cannot  be  avoided,  a  small  pipe  or  air-valve 
for  the  escape  of  air  should  be  connected  with  the  highest 
portion  of  the  bend  and  led  to  some  pipe  which  will  freely 
discharge  the  entrapped  air. 

Systems  of  Steam  Piping. — Three  systems  of  piping 
are  employed  in  gravity  steam  heating  which  may  be  briefly 
described  as  follows: 

First.  The  Mills,  or  Complete-circuit  System  (introduced  into 
this  country  by  J.  H.  Mills  and  sometimes  called  the  "  overhead 
single-pipe  system"). — In  this  system  the  main  pipe  is  led 
directly  to  the  highest  part  of  the  building,  usually  to  the  attic, 

*  Prof.  Carpenter. 


SYSTEMS  OF  STEAM  PIPING.  1149 

from  whence  distributing  pipes  are  run  to  the  various  return 
risers,  which  extend  to  the  basement  and  discharge  into  the 
main  return.  The  supply  for  the  radiating  surfaces  is  all 
taken  from  the  return  risers,  and  in  some  cases  the  entire  down- 
ward circulation  passes  through  the  radiating  system. 

In  this  system  the  radiators  in  the  top  story  receive  steam 
first,  and  the  steam  and  water  of  condensation  is  always  flow- 
ing in  the  same  direction  except  in  the  main  steam  riser.  But 
one  connection  is  made  to  each  radiator,  the  steam  and  water 
of  condensation  flowing  through  the  same  opening  and  riser. 
Below  the  first  floor  the  piping  carries  only  the  return  water 
and  steam. 

"This  system  is  equally  well  adapted  for  either  steam  or 
hot-water  heating,  and  on  the  score  of  positiveness  of  circula- 
tion and  ease  of  construction  is  no  doubt  to  be  commended  as 
superior  to  all  others."  *  It  is  also  the  best  system  for  com- 
pensating for  the  expansion  in  the  risers  in  tall  buildings.  The 
principal  objections  to  it  are  (1)  the  horizontal  distribution 
pipes  having  to  be  in  the  attic  or  top  story  instead  of  in  the 
basement,  which  may  or  may  not  be  of  serious  importance; 
and  (2)  the  cost  of  piping  is  a  little  greater  than  with  the  usual 
one-pipe  system,  but  as  a  rule  this  will  be  more  than  offset  by 
the  better  working  of  the  system. 

This  system  is  especially  recommended  for  high  buildings 
and  for  mills  and  factories  (see  p.  1162). 

Second.  Ordinary  One-pipe  System,  or  " One-pipe  Basement 
System.'' — In  this  system  one  large  steam-main  runs  around 
the  basement  to  a  point  where  the  last  radiator  or  riser  is  taken 
off  and  is  then  connected  into  a  return  main,  which  conveys 
the  water  of  condensation  back  to  the  boiler,  or  if  there  is  no 
occasion  for  dropping  the  return  below  the  basement  floor, 
the  steam  main  is  continued  around  the  basement  and  con- 
nected to  the  return  in  the  back  of  the  boiler. 

The  steam-main  when  it  leaves  the  boiler  is  elevated  close 
under  the  ceiling,  and  is  graded  down  from  the  boiler  about 
-|  in.  in  10  ft.,  so  that  the  water  of  condensation  will  flow  towards 
the  return.  In  this  system  as  in  the  Mills  system  there  is  only  one 
connection  made  to  each  direct  radiator,  which  is  an  advantage 
over  the  double-pipe  system,  as  there  is  only  one  valve  to  open 
or  close  in  turning  on  or  shutting  off  a  radiator.  Unlike  the 

*  Prof.  Carpenter, 


1150  STEAM  HEATING. 

Mills  system,  however,  the  steam  and  water  flow  in  opposite 
directions  in  the  risers.  With  this  system  a  good  automatic 
air- valve  should  be  placed  on  the  extreme  end  of  the  horizontal 
return  main,  above  the  water-line,  to  allow  the  escape  of  air 
that  cannot  escape  through  the  radiators. 

This  method  of  piping  is  the  one  now  used  most  extensively 
and  when  correctly  installed  gives  good  satisfaction. 
'  Third.  The  Two-pipe  System. — This  system  consists  in  hav- 
ing steam  and  return  mains  in  the  cellar  and  two  connec- 
tions to  each  radiator.  The  steam-main  is  graded  down  from 
the  boiler  about  J  in.  in  10  ft.,  and  is  reduced  in  size  as  radiator 
or  riser  connections  are  taken  off;  at  the  end  it  is  connected 
into  the  return  mam  below  the  water-line.  The  return  main 
increases  in  size  as  it  goes  towards  the  boiler,  as  connections 
are  made  to  it  from  risers  or  radiators.  Each  radiator  receives 
steam  from  a  riser  or  connection  taken  from  the  steam-main 
and  empties  into  the  return  through  a  return  riser  or  connec- 
tion, so  that  there  is  a  complete  circulation  throughout  the 
entire  system. 

This  system  was  used  almost  exclusively  twenty  or  thirty 
years  ago,  but  is  now  confined  mainly  to  large  buildings  and 
to  buildings  heated  by  indirect  radiation. 

Indirect  Radiators  must  always  have  a  flow  and  return  pipe, 
and  when  used  in  buildings  heated  by  the  one-pipe  system  the 
return  riser  must  be  entered  into  a  return  main  below  the 
water-line. 

The  two-pipe  system  is  naturally  much  more  expensive  than 
the  one-pipe  system,  because  twice  as  many  radiator  valves 
are  required  for  the  former  and  50  to  75  per  cent,  more  piping. 

The  Paul  System  of  Heating:.* — This  is  a  patented 
system  of  exhausting  all  air  from  the  radiators  and  piping,  so 
that  the  steam  circulates  below  or  a  little  above  atmospheric 
pressure.  This  is  accomplished  by  attaching  a  patented  air- 
valve  to  each  radiator,  and  at  any  points  where  air  might 
possibly  connect  on  the  returns,  and  connecting  these  valves 
by  means  of  small  air-pipes  with  an  exhausting  apparatus 
placed  in  the  boiler-room.  The  valves  are  so  constructed 
that  while  they  permit  of  the  passage  of  air  no  water  can  escape 
through  them.  The  only  difference  between  the  Paul  system 
and  the  ordinary  single-pipe  gravity  system  lies  in  exhausting 

*See  foot-note  p.  1152. 


EXHAUST  SYSTEMS  OF  STEAM  HEATING.     1151 

the  air  so  that  the  steam  will  be  sucked  through  the  pipes 
rather  than  forced. 

The  exhausting  apparatus  may  be  operated  by  steam,  elec- 
tricity, gas,  or  water,  water  being  usually  employed  with  low- 
pressure  systems. 

The  cost  of  operating  the  exhausting  apparatus  when  low- 
pressure  boilers  are  used  need  not  exceed  3  cents  per  day  for 
a  building  containing  4,500  ft.  of  radiation.  To  install  the 
system  the  steam-fitter  must  purchase  the  valves  and  exhausting 
apparatus  from  the  Paul  System  Company  and  pay  a  small 
royalty,  the  amount  depending  upon  the  amount  of  radiation 
in  the  building.  As  by  this  system  better  circulation  is  pro- 
vided than  when  the  air  discharges  into  the  rooms  through 
ordinary  automatic  air-valves  the  radiators  are  made  more 
effective,  consequently  a  little  less  radiation  and  smaller  piping 
are  required  to  do  the  same  work.  The  cost  of  installation 
under  the  Paul  system  is,  therefore,  but  little  if  any  more  than 
for  the  ordinary  single-pipe  gravity  system,  while  it  is  claimed 
that  the  system  will  effect  an  economy  of  at  least  20  per  cent, 
in  the  amount  of  coal  required  for  heating. 

The  system  is  in  successful  operation  in  a  great  many  public 
and  private  buildings,  and  the  company  has  agents  in  most 
of  the  larger  cities  from  whom  further  information  can  be 
obtained.  One  great  advantage  of  the  system  is  that  people 
in  the  rooms  cannot  tamper  with  the  air-valves  and  there  is 
no  danger  of  their  leaking. 

Return  of  Water  to  Boiler  in  ISTon-gravity  Sys- 
tems of  Steam  Heating. — As  stated  on  p.  1147,  whenever 
the  steam  pressure  in  the  radiators  is  less  than  that  in  the  boiler, 
or  when  a  radiator  is  placed  below  the  water-line,  then  the 
water  of  condensation  must  be  returned  to  a  tank,  called  a 
receiver,  placed  below  the  lowest  radiator,  and  returned  from 
the  receiver  to  the  boiler  by  means  of  some  mechanical  device. 
As  a  rule,  either  a  pump  or  a  return  trap  is  used  for  this  pur- 
pose. For  high-pressure  systems,  i.e.,  when  steam  is  used 
to  run  machinery  or  to  run  the  fan  in  a  hot-blast  system,  a  steam- 
pump  running  automatically  is  generally  considered  the  most 
satisfactory  device  for  returning  the  water  to  the  boiler. 

Where  there  is  no  engineer  in  constant  attendance,  a  return 
trap  wTill  generally  be  preferable.  The  return  trap  works  auto- 
matically and  will  return  the  water  as  well  as  a  pump,  besides 
being  less  expensive.  The  greatest  objection  to  a  return  trap 


1152  STEAM  HEATING. 

seems  to  be  that  if  it  gets  out  of  order  from  any  cause,  it  is 
not  as  easily  or  quickly  repaired  as  a  pump. 

A  return  trap  should  be  placed  upon  or  near  the  boiler  and 
the  bottom  of  the  trap  should  be  at  least  2  ft.  above  the  water- 
line  of  the  boiler.  A  pump  may  be  placed  any  distance  below 
the  water-line  of  the  boiler  and  at  a  considerable  distance  from 
the  boiler.  In  hot-blast  heating  the  pump  and  receiver  are 
generally  placed  near  the  heating-stacks  and  fan. 

The  Webster  System  *  (controlled  by  Warren  Webster 
&  Co.). — This,  like  the  Paul  system,  is  a  vacuum  system  of  steam 
heating,  but,  unlike  the  Paul  system,  it  exhausts  all  water  of 
condensation  as  well  as  air,  so  that  the  flow  pipes  are  at  all 
times  filled  with  dry  steam.  This  system  can  also  be  applied 
to  all  classes  of  non-gravity  heating  apparatus  and  where  exhaust 
steam  is  used.  A  Webster  thermostatic  water  and  air  relief 
valve  is  placed  on  the  drip  end  of  each  radiator  and  a  small 
pipe  connects  each  valve  with  the  exhausting  apparatus  near 
the  boiler.  The  water  of  condensation  is  taken  to  a  receiver, 
from  which  it  is  fed  back  to  the  boiler.  With  this  system  com- 
paratively small  supply  and  return  mains  may  be  employed, 
but  the  radiation  should,  if  anything,  be  increased. 

This  system  is  especially  adapted  to  large  heating  plants, 
hot-blast  systems,  and  dry  kilns,  and  may  be  successfully  and 
economically  applied  to  a  great  variety  of  manufacturing  processes 
by  making  slight  modifications  in  its  working  details. 

The  patentees  claim  that  the  Webster  system  will  give  a 
better  circulation  and  effect  greater  economy  in  maintenance 
than  any  other. 

It  has  been  successfully  installed  in  a  great  many  large  build- 
ings through  the  country  and  in  many  factories  and  manu- 
facturing plants. 

*  The  vacuum  system  of  heating  was  first  introduced  to  the  heating 
trade  in  this  country  some  time  in  the  past  seventies  by  N.  Y.  Williams, 
a  heating  engineer  of  Philadelphia,  Pa.  His  plan  was  to  plug  up  all 
air-vents  and  to  attach  a  pump  to  the  main  return  pipe  and  exhaust  all 
air  and  water  from  the  steam-pipes,  coils,  and  radiators  in  a  system.  The 
plan  was  an  improvement  to  the  many  poorly  constructed  plants  in  use 
at  the  time,  but  it  was  not  a  complete  success  in  itself.  It  would  "short- 
circuit,"  i.e.,  the  pump  would  act  only  on  a  portion  of  the  system. 

The  Warren  Webster  Co.  bought  the  inventor's  rights  and  some  other 
patents  and  in  time  introduced  the  Webster  thermostatic  valve,  which 
is  now  used  in  all  their  work  on  all  radiators,  and  has  had  much  to  do  in 
making  their  system  a  success.  The  Paul  and  other  vacuum  systems  have 
been  introduced  since. 


HOT-BLAST  SYSTEMS  OF  WARMING.          1153 

Further  information  concerning  this  system  may  be  obtained 
at  any  of  the  offices  of  the  company. 
Hot-blast  System  of  Warming  and  Ventilating-. 

— This  system  is  used  principally  in  buildings  where  a  large 
amount  of  ventilation  is  required.  The  principle  of  the  system 
is  the  forcing  of  large  volumes  of  air  over  or  through  a  heater 
and  thence  into  the  rooms  to  be  warmed,  and  necessitates 
a  fan  for  driving  the  air. 

It  may  be  successfully  operated  in  connection  with  hot-air 
furnaces  (see  the  author's  work  on  " Churches  and  Chapels"), 
but,  as  a  rule,  the  heat  is  furnished  by  steam-coils. 

An  ordinary  hot-blast  heating  and  ventilating  plant  consists 
of  a  steam-boiler,  one  or  more  stacks  of  steam-coils,  a  fan  or 
fans  driven  either  by  a  small  steam-engine  or  electric  motor, 
reducing- valve,  receiver,  and  pump.  The  heating  coils  are 
usually  collected  in  a  "stack,"  over  which  all  of  the  air  for 
the  building  is  passed,  and  from  the  stack  the  air  is  drawn  or 
forced  through  hot-air  pipes  to  all  parts  of  the  building.  Direct 
radiation  may  also  be  employed  in  connection  with  this  system 
for  warming  the  halls  and  corridors  or  any  rooms  which  do 
not  require  ventilation. 

This  system  is  especially  adapted  to  the  warming  and  ven- 
tilating of  schools,  churches,  hospitals,  and  public  buildings, 
and  to  many  kinds  of  manufacturing  plants.  To  insure  suc- 
cessful results,  however,  it  must  be  laid  out  with  much  care. 
Full  information  regarding  it  may  be  obtained  from  the  Ameri- 
can Blower  Co.,  the  Buffalo  Forge  Co.,  or  the  B.  F.  Sturtevant 
Co. 

Pipe,  Fittings,  and  Valves. — The  pipe  used  for  con- 
veying steam  or  hot  water  was  formerly  made  exclusively  of 
wrought  iron,  but  at  the  present  time  the  term  "  wrought-iron 
pipe"  is  used  merely  to  distinguish  wrought  from  cast  pipe. 
It  is  construed  to  mean  merchant  pipe,  which  is  generally 
made  from  soft  steel.  Persons  desiring  iron  pipe  should  specify 
"genuine  wrought-iron  pipe,"  for  which  an  extra  charge  is 
made. 

Up  to  the  present  time  the  pipe  made  of  steel  has  not  been 
as  soft  as  that  of  wrought  iron,  and  is  often  not  so  well  welded 
and  is  more  likely  to  split.  Nevertheless,  steel  pipe  is  much 
more  extensively  used  than  the  genuine  wrought-iron  pipe, 
although  the  latter  is  unquestionably  the  best. 

Steam-pipe  is  put  on  the  market  in  three  grades,  or  thick- 


1154 


STEAM  HEATING. 


nesses — standard,  extra  strong,  and  double  extra  strong  (see  tables 

of  Wrought-iron  Pipe,  pp.  1205,   1206). 

Each  length  of  pipe  as  sold  is  provided  with  a  collar  or  coupling 
(Fig.  18)  on  one  end  and  has  a  thread  cut 
on  the  other.  Connections  are  made-  by 
screwing  the  threaded  end  of  one  pipe  into 
the  coupling  on  the  other.  Pipe  is  sold  in 
random  lengths  varying  from  16  to  24  ft. 
With  the  exception  of  couplings,  the  fittings 
used  for  connecting  pipes  and  for  giving 
them  any  desired  direction  with  each  other 
are  made  of  cast  and  malleable  iron. 


Fig.  18 

Wrought-iron  Coup- 
ling. 


For  use  on  heating  pipes,  cast-iron  fittings  are  generally 
to  be  preferred  to  those  of  malleable  iron,  for  several  reasons 
(see  Carpenter,  p.  92). 

Fittings  for  Joining1  Pipes. — For  joining  pipes  in  the 
same  straight  line,  so  as  to  make  a  continuous  pipe  from  end 
to  end,  the  coupling,  Fig.  18,  with  right-hand  threads  cut  in 
both  ends  is  commonly  used.  With  right-hand  couplings  it 
is  impossible  to  disconnect  the  pipe  at  any  place  without 
commencing  at  the  farther  end  and  disconnecting  the  pipe 
section  by  section.  Reducing  couplings  are  made  for  uniting 
pipes  of  different  sizes. 

To  connect  two  lengths  of  pipe,  so  that  they  can  be  discon- 
nected at  that  point  without  interfering  with  other  joints, 
three  kinds  of  connections  are  in  use: 

(1)  Right  and  Left  Couplings. — The  most  common  fitting  for 
joining  pipes  2  ins.  diameter  and  under.     It  requires,  however, 
that  there  shall  be  room  for  end  motion 

of  one  of  the  pipes  sufficient  to  insert  it. 

(2)  Lip  Unions. — These  are  generally 
used   on   pipes   up   to    li   or   2  ins.   in 
diameter  where  it  is  desirable   to  have 
a  joint  that  may  be  readily  disconnected. 
The  union  consists  of  three  pieces;  two 
of  these  parts  screw  on  to  the  ends  of 
the  pipe  and  are  drawn  together  by  a 
revolving  collar  which  engages  with  the 
thread  on  one  of  the  pieces,  as  shown  by 
Fig.  19. 

With  this  connection  no  appreciable  play  is  required  in  the 
piping. 


Fig.  19 

Lip  Union. 


FITTINGS  AND  VALVES. 


1155 


Unions  are  now  commonly  used  in  connecting  radiators, 
the  union  being  attached  to  the  radiator  valve. 

(3)  Flange  Unions  (Fig.  20). — These  are  used  on  pipes  ex- 
ceeding 2  ins.  in  diameter.  The  two  parts  of  the  union  are 
first  screwed  to  the  pipes  and 
then  bolted  together.  A  ring  of 
packing  must  be  placed  between 
the  flanges  to  make  a  tight  joint. 

Nipples  (Fig.  21)  are  frequently 
used  in  steam  fitting  for  connect- 
ing pipes,  radiators,  and  sectional 
boilers.  They  are  made  with 
right  thread  on  both  ends  and 
right  thread  on  one  end  and  a  left 
thread  on  the  other. 

Push  nipples  are  made  with  ends  bevelled  and  ground  per- 
fectly true,  so  as  to  make  a  tight  joint  by  contact  of  the  metal. 
Their  use  is  confined  to  radiators  and  sectional  boilers. 


Fig.  22 


Fig.  20 

Flange  Union. 


Fig.  21 

Close  Nipple. 


Bushing. 


Plug. 


Bushings  are  used  for  reducing  the  size  of  opening  in  a  fitting. 
Plugs  are  used  for  closing  the  end  of  a  fitting  and  caps  for 
covering  the  end  of  a  pipe. 

A  great  variety  of  cast-iron  fittings  are  carried  in  stock, 
such  as  elbows,  tees,  crosses,  branch  tees,  Y  bends,  return 
bends,  etc.,  each  of  these  being  made  in  a  great  variety  of 
sizes  and  shapes. 

A  description  of  them  may  be  found  in  the  catalogues  of 
dealers  in  steam-fitters'  supplies. 

Valves  and  Cocks. — Three  classes  of  valves  are  used 
in  steam-fitting,  viz.,  globe  valves,  gate- valves,  and  check- 
valves. 

The  valve  shown  by  Fig.  26  is  a  globe  valve,  but  is  commonly 
designated  as  an  angle- valve,  the  term  globe  valve  being  com- 
monly restricted  to  those  valves  which  go  on  a  straight  line 
pf  pipe. 

In  tjie  gate-valye   the   disc  which   closes   the  opening  is  at 


1156 


STEAM   HEATING. 


right  angles  to  the  pipe.  The  gate-valve  when  open  offers 
less  obstruction  to  the  flow  of  steam  or  water,  and  for  this 
reason  is  largely  used  on  water-pipes.  Some  steam-fitters  con- 


Fig.  23 

Brass  Globe  Valve. 


Fig.  24 
Brass  Gate-valve  with  Union. 


tend  that  a  gate- valve  should  not  be  used  for  steam,  except 
on  the  main  return,  near  the  boiler. 

A  disc  valve  is  commonly  a  globe  or  angle  valve  with  a  com- 
position disc  or  ring  similar  to  the  washer  on  a  compression 
cock,  which  fits  against  the  seat  of  the  valve.  A  Jenkins  disc 
is  a  valve  in  which  the  disc  or  the  entire  valve  is  made  by 


Fig.  25 
Section  of  Disc  Globe  Valve. 


Fig.  26 

Angle-valve  with  Union  and  Copper  Disc. 


Jenkins   Bros.     The    common   globe    valve   has   no    removable 
disc  or  washer.      (See  Fig.  27.) 

Disc  valves  should  always  be  used  on  steam-radiators. 


STEAM-VALVES.  1 157 

A  union  valve  is  a  globe  or  angle  valve  with  a  union  on  one 
side  of  the  valve. 

Globe  valves  are  made  for  screw,  union,  or  flange  connections, 
although  the  latter  is  commonly  used  only  on  large  pipes. 

Globe  and  angle  valves  for  2-inch  pipes  and  under  are  com- 
monly made  with  brass  bodies  and  either  iron  or  wood  handles. 
The  larger  sizes  are  commonly  made  with  iron  bodies.  Radiator 
valves  should  have  brass  bodies  and  wood  wheels. 

When  it  is  desired  that  radiators  shall  not  be  under  the 
control  of  the  occupants  of  the  room,  valves  operated  by  a 
key  may  be  used.  Hot-water  radiator  valves  may  also  be 
had  with  pedal  attachments  so  that  they  may  be  opened  or 
closed  with  the  foot. 

Special  forms  of  quick-opening  valves  are  largely  used  on 
hot-water  radiators. 

Obstruction  to  Flow  Offered  by  Globe  Valves.— 
When  globe  valves  are  placed  on  horizontal  steam-mains,  the 
stem  should  always  be  placed  in  a 'horizontal  position,  for  if  set 
vertically  the  seat  of  the  valve  forms  an  obstruction  sufficient 
to  fill  the  pipe  at  least  half  full  of  water  (as  shown  by  Fig.  27). 
Bacause  of  the  obstructions  which  they  offer  to  the  flow  of 
water,  globe  valves  should  not  be  used  on  hot-water  pipes. 


Fig.  27 

Check-valves. — Where  it  is  necessary  that  the  flow  shall 
always  take  place  in  one  direction  and  there  is  danger  of  a 
reverse  flow  a  check- valve  must  be  employed.  A  check-valve 
is  always  required  on  the  water-supply  to  a  steam-boiler  and 
on  all  connections  to  high-pressure  boilers  below  water-line 
except  the  blow-off  pipes. 

Check-valves   are   of   three   kinds,   the   more   common   form 


1158  STEAM   HEATING. 

being  that  shown  by  Fig.  28,  which  has  a  valve  which  slides 
up  and  down.  The  swinging  check-valve,  Fig.  29,  is  also  com- 
monly employed.  The  third  kind  utilizes  a  ball  in  place  of 
the  sliding  valve  for  closing  the  opening.  The  ball  check-valve, 
however,  is  not  much  used  in  steam  fitting. 


Fig.  28  Fig.  29 

Common  Type  of  Check-valve.  Swing  Check-valve. 

A  cock  operates  by  means  of  a  turned  plug  which  has  one 
or  two  holes  bored  transversely  to  its  axis.  When  the  plug 
is  turned  so  that  the  hole  is  in  line  with  the  pipe  the  water 
flows  through,  and  when  the  plug  is  turned  the  water  is  shut 
off. 

Cocks  are  not  much  used  in  steam  fitting,  ^xcept  on  the 
blow-off  pipe. 

RULES  FOR  PROPORTIONING  RADIATING  SUR- 
FACE, AND  SIZE  OF  STEAM  AND  HOT- WATER 
MAINS  AND  RETURNS. 

Direct  Radiating  Surface — Steam  Heating-. — The 

common  practice  of  determining  the  direct  radiating  surface 
required  to  warm  a  given  room  is  to  allow  one  square  foot  of 
radiating  surface  to  a  certain  number  of  cubic  feet  of  space 
contained  in  the  room.  The  divisors  given  in  the  following 
table  fairly  represent  current  practice. 

To  find  square  feet  of  direct  radiation  required  divide  the 
cubic  contents  of  room  by  the  following  factors: 

For  Dwellings  Divide  by 

Living-rooms,  one  side  exposed 60  to  80 

Living-rooms,  two  sides  exposed 50  to  60 

Living-rooms,  three  sides  exposed 40  to  45 

Sleeping-rooms 50  to  70 

Halls  and  bathrooms 40  to  50 


RULES  FOR  RADIATING  SURFACE.         1159 

For  Public  Buildings  Divide  by 

Offices 50  to  75 

Schoolrooms 50  to  70 

Factories  and  stores 80  to  125 

Assembly  halls  and  churches .  100  to  150 

In  buildings  of  more  than  two  stories  the  first  and  top 
stories  require  the  same  amount  of  radiation  if  used  for  the 
same  purpose,  but  the  radiation  in  intermediate  stories  may  be 
slightly  reduced. 

City  houses  require  less  heat  than  country  houses  and  brick 
houses  less  than  wooden  houses. 

Baldwin's  Rule. — Mr.  William  J.  Baldwin,  in  his  excellent 
work  on  "Steam-heating  for  Buildings,"  *  recommends  the  fol- 
owing  rule,  which  he  has  used  for  several  years,  and  which  is  not 
wholly  empirical: 

"  Divide  the  difference  in  temperature  between  that  at  which 
the  room  is  to  be  kept  and  the  coldest  outside  atmosphere 
by  the  difference  between  the  temperature  of  the  steam-pipes 
and  that  at  which  you  wish  to  keep  the  room  and  the  quotient 
will  be  the  square  feet,  or  fraction  thereof,  of  plate  or  pipe 
surface  to  each  square  foot  of  glass  or  its  equivalent  in  wall 
surface."  f 

The  equivalent  glass  surface  is  found  by  multiplying  the 
superficial  area  of  the  walls  in  square  feet  by  the  number  oppo- 
site the  substance  in  the  following  table  and  dividing  by  1,000 
(the  value  of  glass).  The  result  is  the  equivalent  of  so  many 
square  feet  of  glass  in  cooling  power  and  should  be  added  to 

the  window  surface. 

! 

TABLE  OF  POWER  OF  TRANSMITTING  HEAT  OF  VARIOUS  BUILD- 
ING SUBSTANCES  COMPARED  WITH  EACH  OTHER. 

Window  glass 1,000 

Oak  and  walnut 66 

White  pine 80 

Pitch  pine 100 

Lath  and  plaster 75  to  100 

Common  brick  (rough) 200  to  250 

Common  brick  (whitewashed) 200 

Granite  or  slate 250 

Sheet  iron 1,030  to  1,110 

*  Published  by  John  Wiley  &  Sons,  of  New  York. 

t  It  should  be  noticed  that  this  proportion  docs  not  depend  upon  the  size 


1160  STEAM  HEATING. 

It  must  be  distinctly  understood  that  the  extent  of  heating 
surface  found  in  this  way  offsets  only  the  windows  and  other 
cooling  surfaces  it  is  figured  against,  and  does  not  provide  for 
cold  air  admitted  around  loose  windows  or  between  the  board- 
ing of  poorly  constructed  wooden  houses.  These  latter  con- 
ditions, when  they  exist,  must  be  provided  for  by  additional 
heating  surface. 

EXAMPLE  1.  What  amount  of  heating  surface  should  be  sup- 
plied to  the  sitting-room  of  a  wooden  dwelling  with  two  out- 
side walls,  one  14  ft.  by  9  ft.  high  and  the  other  15  ft.  by  9  ft., 
the  total  window  area  being  54  sq.  ft.,  the  external  temperature 
frequently  being  at  0°  F.,  and  the  steam  never  exceeding  5  Ibs. 
pressure? 

Ans. — Temperature  of  room,  70°— 0°=70°;  temperature  of 
steam-pipes  at  5  Ibs.,  228-70°=  158;  70- 158=. 443,  or  a 
little  less  than  one  half  a  square  foot  of  heating  surface  to  each 
square  foot  of  glass  or  its  equivalent. 

Area  of  outside  walls=  14X9+  15X9=  126+  135=261.  Sub- 
tracting the  glass  area,  54,  we  have  207  sq.  ft.  of  lath  and 
plaster. 

207  X     100=20,700 
54X1,000=54,000 


1,000)74,700 


Equivalent  glass  area=74.  Multiplying  this  by  .443,  we 
have  33  as  the  number  of  square  feet  of  radiating  surface  re- 
quired to  warm  the  room,  or  1  ft.  of  surface  to  58  cu.  ft.  of  air 
space. 

Rule  of  F.  Schumann* — "Divide  the  cubic  feet  of  space 
of  the  room  to  be  heated,  the  square  feet  of  wall  surface, 
and  the  square  feet  of  the  glass  surface  by  the  figures  given 
under  these  headings  in  the  following  table  and  add  the  quo- 
tients together;  the  result  will  be  the  square  feet  of  radiating 
surface  required. 

For  the  above  example  with  northwest  and  southeast  ex- 
posures and  steam  at  3  Ibs.  pressure  this  rule  would  require 
26.7  sq.  ft.  of  radiating  surface  for  a  change  of  once  per  hour 
and  45.1  sq.  ft.  for  a  change  of  twice  per  hour. 

of  the  room,  but  only  upon  the  climate,  pressure  of  the  steam,  and  desired 
temperature  of  the  room. 
*  Kent,  p.  536. 


RULES    FOR   RADIATING   SURFACE. 


1161 


SPACE,  WALL,  AND  GLASS  SURFACE  WHICH  ONE 
SQUARE  FOOT  OF  RADIATING  SURFACE  WILL 
HEAT. 


Air  Change. 

• 

Sfceam  Pressure 
in  Pounds. 

o 
IB 

3 
0 
a 

O-tJ 
02 

190 
210 
225 

Exposure  of  Rooms. 

All  Sides. 

Northwest. 

Southeast. 

Wall 
Surface. 
Sq.Ft. 

Glass 
Surface. 
Sq.  Ft. 

Wall 
Surface. 
Sq.Ft. 

Glass 
Surface. 
Sq.Ft. 

Wall 
Surface. 
Sq.Ft, 

Glass 
Surface. 
Sq.  Ft. 

Once 
per 
hour 

1 
3 
5 

13.8 
15.0 
16.5 

7 
7.7 
8.5 

15.87 
17.25 
18.97 

8.05 
8.85 
9.77 

16.56 
18.00 
19.80 

8.4 
9.24 
10.20 

Twice 
per 
hour 

1 
3 
5 

75 

82 
90 

11.1 
12.1 
13.0 

5.7 
6.2 
6.7 

12.76 
13.91 
14.52 

6.55 
7.13 
7.60 

13.22 
14.52 
15.60 

6.84 
7.44 
8.04 

Prof.  R.  C.  Carpenter  says  that  for  residences  it  is  safe  to 
assume  that  the  air  of  the  principal  living-rooms  will  change 
twice  in  an  hour,  that  of  the  halls  three  times,  and  that  of  the 
other  rooms  once  per  hour  under  ordinary  conditions. 

Prof.  Carpenter,  in  his  work  on  "Heating  and  Ventilating 
Buildings,"  gives  the  following  formula,  which  is  convenient 
and  probably  as  accurate  as  any  for  general  purposes, 


in  which  W=wall  surface,  (7=  glass  or  window  surface,  both 
in  square  feet,  C=  contents  of  room  in  cubic  feet,  N=  number 
of  times  air  will  be  changed  per  hour,  and  h=  total  heat-units 
required  per  degree  of  difference  of  temperature  between  the 
room  and  the  surrounding  space. 

Under  ordinary  conditions  of  pressure  and  temperature 
one  square  foot  of  stea/n-heating  surface  will  supply  280  heat- 
units  per  hour  and  1  sq.  ft.  of  hot-water  heating  surface  175 
heat-units  per  hour. 

To  heat  the  room  to  70°  F.  when  the  outside  temperature 
is  at  zero,  the  square  feet  of  direct  radiating  surface  required 
will  be  \h  for  steam  heating  and  -^6h  for  hot-water  heating. 
For  churches  and  auditoriums  N  should  be  taken  at  least  equal 
to  3. 

In  Example  I  we  have  C=  1,890,  TF=207,  and  £=54. 
Hence  h=  140  when  the  air  is  changed  once  per  hour  and  174 


1162  STEAM  HEATING. 

when  changed  twice  per  hour.  The  steam  radiating  surface 
required  will  be  35  and  43J  sq.  ft.  respectively. 

In  practical  work  it  is  well  to  determine  the  heating  surface 
by  two  or  more  rules  and  then  use  the  larger  quantity.  Dif- 
ferent localities  and  different  grades  of  buildings  also  affect 
the  amount  of  radiating  surface  required,  so  that  practical 
steam-fitters  are  usually  governed  to  some  extent  by  their 
experience.  There  can  never  be  any  bad  results  from  having 
an  excess  of  heating  surface  provided  all  rooms  have  their 
proportionate  amount,  while  a  deficiency  will  always  result 
in  cold  rooms  in  extremely  cold  weather. 

Overhead  Steam-pipes  (A.  R.  Wolff,  Stevens  Indicator, 
1887). — -When  the  overhead  system  of  steam  heating  is  em- 
ployed, in  which  system  direct  radiating  pipes,  usually  1J  in. 
in  diameter,  are  .placed  in  rows  overhead  suspended  upon 
horizontal  racks,  the  pipes  running  horizontally  and  side  by 
side  around  the  whole  interior  of  the  building,  from  2  to  3  ft. 
from  the*  wall  and  from  2  to  4  ft.  from  the  ceiling,  the  amount 
of  1^-inch  pipe  required,  according  to  Mr.  C.  J.  H.  Woodbury, 
for  heating  mills  (for  which  this  system  is  deservedly  much  in 
vogue)  is  about  1  ft.  in  length  for  every  90  cu.  ft.  of  space. 
Of  course  a  great  range  of  difference  exists  due  to  the  special 
character  of  the  operating  machinery  in  the  mill,  both  in  re- 
spect to  the  amount  of  air  circulated  by  the  machinery  and 
also  the  aid  to  warming  the  room  by  the  friction  of  the  journals. 
For  this  system  of  radiation  the  Mills  system  of  piping  should 
be  used. 

Direct  Radiation — Hot -water  Heating-. — Rule  of 
Thumb. — Divide  the  cubic  contents  of  room  in  cubic  feet  by 
the  following  factors;  the  result  will  be  the  square  feet  of 
radiation  required: 

For  Dwellings  Divide  by 

Living-rooms,  one  side  exposed .  .  t 40  to  50 

Living-rooms,  two  sides  exposed 30  to  40 

Living-rooms,  three  sides  exposed 20  to  25 

Sleeping-rooms 30  to  50 

Halls  and  bathrooms 20  to  30 

For  Public  Buildings  Divide  by 

Offices 30  to  40 

Schoolrooms 30  to  40 

Factories  and  stores 40  to  60 

/    Assembly  halls  and  churches 60  to  100 


RULES  FOR   INDIRECT  RADIATION.         1163 

Prof.  Carpenter's  rule  for  direct  hot-water  radiation  is  the 
same  as  for  steam  (p.  1161),  using  0.4  for  a  multiplier  instead 
ofi. 

For  Direct-indirect  Radiation  it  is  customary  to  allow 
25  per  cent,  more  surface  for  steam  and  33  J  per  cent,  for  hot- 
water  than  would  be  required  for  direct  radiation. 

Indirect  Radiating"  Surface  (Prof.  Carpenter's  Rule). 
—  The  radiating  surface  for  indirect  heating  may  be  found  by 
adding  together  the  glass  surface  in  the  room  to  be  warmed, 
one  fourth  the  exposed  wall  surface,  both  in  square  feet,  and 
multiplying  by  the  following  factors: 


First  story  

Steam 
Heating. 

0.7 

Hot  -water 
Heating. 

1.05 

Second  story  

.0.6 

0.9 

Third  storv.  . 

.  0.5 

0.8 

The  total  amount  of  incoming  air  which  this  amount  of 
radiation  will  warm  per  hour  in  cubic  feet  may  be  found  ap- 
proximately by  multiplying  the  radiating  surface  by  the  follow- 
ing factors: 

Steam  Hot-water 

Heating.,  Heating. 

First  story  ................   200  125 

Second  story  ..............   250  160 

Third  story  ...............   300  200 

If  a  greater  quantity  of  air  is  required  for  ventilating  purposes, 
an  additional  foot  of  heating  surface  should  be  allowed  for 
each  250  cu.  ft.  of  air  heated  by  steam,  or  for  each  150  cu.  ft. 
heated  by  hot  water. 

For  rooms  which  are  specially  exposed  these  results  should 
be  increased  about  10  per  cent.,  and  10  per  cent,  if  the  rooms 
are  heated  during  the  daytime  only. 

Size  of  Air-ducts  and  Registers  for  Indirect 
Radiator  Stacks  (Steam  Heating-). 

For  computing  the  area  of  duct  from  stack  to  the  room  and 
outlet  pipe  from  the  room  the  following  data  by  Prof.  Car- 
penter will  probably  give  as  good  results  as  can  be  obtained 
by  any  rule,  except  where  there  is  a  very  large  glass  area. 


1164 


STEAM  HEATING. 


Rule. — rMultiply  the  sum  of  the  glass  surface  and  one  quarter 
the  wall  area  by  the  appropriate  factor  given  in  the  following 
table: 

TABLE  OF  FACTORS  FOR  AREA  OF  AIR-FLUES. 


Story  cl  Building. 

Supply  Duct. 

Ventilating  Duct. 

o> 
3! 

.9  ^ 
S-gj 
all 

*w£ 

Velocity  in 
Feet  per 
Second. 

Factor  for 
Area. 
Sq.  Ins. 

£o 

03^- 

|i 

x  g  . 

Hi 

ftQp3 

<! 

Velocity  in 
Feet  per 
Second. 

Factor  for 
Area. 
Sq.  Ins. 

First  floor  

5 

28 
40 
50 

2.8 
6.8 
8.1 
9.0 

2.40 
0.95 
0.82 
0.71 

47 
32 
20 
10 

5.5 
4.2 
3.6 
2.6 

0.93 

1.27 
1.33 
2.17 

Second  floor.  .  .  . 

Third  floor  

Fourth  floor  

The  cold-air,  or  out-door,  supply  to  the  stack  should  have 
a  sectional  area  equal  to  about  three  fourths  of  that  of  the 
warm-air  flue. 

The  nominal  size  of  registers  should  be  about  50  per  cent, 
greater  than  the  area  of  the  warm-air  flue. 

The  following  sizes  for  air-ducts  and  registers  for  indirect 
steam  radiation  are  published  by  the  International  Heater  Co., 
and  a  similar  table  is  given  on  p.  1133.  It  is  evident  that  some 
judgment  must  be  used  with  all  three  tables. 


d 
-^  o 

Cold  -air  Duct  to 
Stack. 

Warm-air  Duct. 

Registers. 

®il 

Tapping. 

jp 

For 
First 
Floor. 

For 
Upper 
Floors. 

For 
First 
Floor. 

For 
Upper 
Floors. 

First 
Floor. 

Upper 
Floors. 

50 

Sq.  Ins. 
50 

Sq.  Ins. 
40 

Sq.  Ins. 

75 

Sq.  Ins. 
50 

Ins. 
10X12 

Ins. 
8X10 

Ins. 
1    Xf 

60 

60 

45 

90 

60 

10X14 

8X12 

HXI 

70 

70 

50 

105 

70 

12X15 

10X12 

HXI 

80 

80 

60 

120 

80 

12X15 

10X12 

HXI 

90 

90 

70 

135 

90 

12X19 

10X14 

ijxij 

100 

100 

75 

150 

100 

12X19 

12X15 

ijxii 

RULES  FOR  SIZE  OF   PIPES. 


1165 


Size  of  Steam-mains  and  Return  Pipes. 

Mr.  George  H.  Babcock  gives  the  following  rule  for  gravity 
heating  systems  with  separate  returns  (two-pipe  system) : 

"The  diameter  of  the  steam-mains  leading  from  the  boiler 
should  be  equal  in  inches  to  one  tenth  the  square  root  of  radiating 
surface,  mains  included,  in  square  feet." 

If  the  mains  are  covered  they  may  be  neglected  in  figuring 
radiating  surface. 

For  the  one-pipe  basement  system  it  will  be  safe  to  use  one 
ninth  instead  of  one.  tenth  in  the  above  rule,  unless  the  pipes 
are  very  long.  It  is  always  better  to  have  the  mains  larger  than 
is  necessary  rather  than  too  small. 

Steam-mains  should  never  be  less  than  1J  ins.  in  diameter. 

The  sizes  of  returns  that  will  prove  satisfactory  for  given  sizes 
of  steam-mains  are  given  by  Prof.  Carpenter  as  follows,  no  re- 
turn to  be  less  than  1  in.  diameter: 


Diameter 
Steam-pipe. 

Diameter 
Return  Pipe. 

Diameter 
Steam-pipe. 

Diameter 
Return  Pipe. 

Inches. 

Inches. 

Inches. 

Inches. 

U 

1 

5 

2| 

.2 

H 

6 

3 

2J 

ll 

8 

aj 

3 

If 

9 

4 

*3J 

H 

10 

4 

4 

2 

12 

5 

For  connecting  direct  radiators  with  the  single-pipe  system,  the 
following  sizes  of  pipes  should  be  used : 

For  radiators  containing  24  sq.  ft.  or  under,  1-inch  pipe;  for 
radiators  containing  24  to  60  sq.  ft.,  IJ-inch  pipe;  for  radiators 
containing  60  to  180  sq.  ft.,  IJ-inch  pipe;  for  radiators  contain- 
ing above  100  sq.  ft.,  2-inch  pipe. 

For  Two-pipe  Work. — Radiators  containing  48  sq.  ft.  and 
under,  1-inch  supply,  f-inch  return;  50  sq.  ft.  to  96  sq.  ft, 
IJ-inch  supply,  1-inch  return;  above  96  sq.  ft.,  IJ-inch  supply, 
IJ-inch  return. 

For  Indirect  Heating  it  will  usually  be  sufficiently  accurate 
to  use  a  pipe  whose  diameter  is  1.4  times  greater  than  that  for 
direct  heating.* 

*  Prof.  Carpenter. 


1166  STEAM  HEATING. 

For  Hot-water  Heating. — Prof.  Carpenter  says:  "  We  may 
take  as  a  practical  rule,  applicable  when  the  pipes  are  less  than 
200  ft.  in  length:  The  diameter  of  main  supply  or  main  return 
pipe  in  a  system  of  direct  hot-water  heating  should  be  one-pipe 
size  greater  than  the  square  root  of  the  number  of  square  feet 
of  radiating  surface  divided  by  9  for  the  first  story,  by  10  for 
the  second  story,  and  by  11  for  the  third  story  of  a  building; 
for  indirect  hot- water  heating  multiply  above  results  by  1.5." 

In  hot-water  heating  the  return  pipe  must  have  the  same  diameter 
as  the  supply  pipe,  and  the  capacity  of  both  should  be  equal 
to  total  capacity  of  risers.  For  equalizing  hot-water  pipes 
the  tables  on  p.  1203  will  be  found  very  convenient. 

The  standard  tapping  for  hot-water  radiators  is  as  follows: 
Radiators  containing  40  sq.  ft.  and  under,  1  in.;  above  40  but 
not  exceeding  72  sq.  ft.,  1^  ins.;  above  72  sq.  ft.,  1J  ins. 

Boiler. — To  find  the  size  of  boiler  necessary  to  supply  any 
given  amount  of  radiation,  see  p.  1146. 

Covering*  of  Pipes. 

Steam  and  hot-water  mains  radiate  more  heat  in  proportion 
to  their  surface  than  do  the  radiators  which  they  supply,  and 
unless  this  heat  is  needed  for  warming  the  space  through  which 
the  pipes  pass,  it  represents  a  very  material  loss  in  the  con- 
sumption of  fuel. 

To  reduce  this  loss  to  a  minimum,  it  is  customary  tov  cover 
all  pipes  in  unfinished  basements  with  some  insulating  sub- 
stance. The  saving  in  fuel  effected  by  a  good  covering  will 
more  than  pay  for  its  cost  in  a  few  seasons. 

"The  best  insulating  substance  known  is  air  confined  in 
minute  particles  or  cells,  so  that  heat  cannot  be  removed  by 
convection.  No  covering  can  equal  or  surpass  that  of  per- 
fectly still  and  stagnant  air;  and  the  value  of  most  insulating 
substances  depends  upon  the  power  of  holding  minute  quan- 
tities in  such  a  manner  that  circulation  cannot  take  place. 
The  best  known  insulating  substance  is  a  covering  of  hair-felt, 
wool,  or  eiderdown,  each  of  which,  however,  is  open  to  the 
objection  that,  if  kept  a  long  time  in  a  confined  atmosphere 
and  at  a  temperature  of  150°  or  above,  it  becomes  brittle  and 
partly  loses  its  insulating  power. 

"A  covering  made  by  wrapping  three  or  more  layers  of 
asbestos  paper,  each  about  •£%  in.  thick,  on  the  pipe,  covering 
with  a  layer  of  hair-felt  f  in.  in  thickness,  and  wrapping  the 


COVERING  OF  PIPES.  1167 

whole  with  canvas  or  paper  is  much  used.  This  covering 
has  an  effective  life  of  about  five  years  on  high-pressure  steam- 
pipes  and  ten  to  fifteen  years  on  low-temperature  pipes.  There 
are  a  large  number  of  coverings  regularly  manufactured  for 
use  in  such  a  form  that  they  can  be  easily  applied  or  removed 
if  desired.  There  is  a  very  great  difference  in  the  value  of  these 
coverings;  some  of  them  are  very  heavy  and  contain  a  large 
amount  of  mineral  matter  with  little  confined  air  and  are  very 
poor  insulators.  Some  are  composed  entirely  of  incombustible 
matter  and  are  nearly  as  good  insulators  as  hair-felt.  In  general, 
the  value  of  a  covering  is  inversely  proportional  to  its  weight, 
the  lighter  the  covering  the  better  its  insulating  properties; 
other  things  being  equal,  the  incombustible  mineral  substances 
are  to  be  preferred  to  combustible  material.  The  table  on  the 
next  page  gives  the  results  of  some  actual  tests  of  different  cover- 
ings, which  were  conducted  with  great  care  and  on  a  sufficiently 
large  scale  to  eliminate  slight  errors  of  observation.  In  general, 
the  thickness  of  the  coverings  tested  was  1  in.  Some  tests 
were  made  with  the  coverings  of  different  thicknesses,  from 
which  it  would  appear  that  the  gain  in  insulating  power  ob- 
tained by  increasing  the  thickness  is  very  slight  compared  with 
the  increase  in  cost.  If  the  material  is  a  good  conductor  its 
heat-insulating  power  is  lessened  rather  than  diminished  by 
increasing  the  thickness  beyond  a  certain  point."  * 

Sectional  Covering's. — It  may  be  seen  from  this 
table  that  magnesia,  .asbestos,  and  mineral  wool  are  the  three 
materials  most  valuable  for  the  covering  of  steam-pipes,  as 
wool  and  hair,  although  being  better  non-conductors,  are  short- 
lived on  steam-pipes.  Wool  covering  is  extensively  used, 
however,  on  hot-water  pipes.  Sectional  coverings,  moulded 
and  formed  to  fit  different  sizes  of  pipes,  are  made  by  many 
parties,  and  are  used  almost  exclusively  for  covering  steam, 
and  to  a  large  extent  for  hot-water,  pipes.  After  the  sections 
are  applied  they  are  commonly  secured  by  brass  lacquered 
bands.  The  fittings,  such  as  elbows  and  tees,  are  usually 
plastered  with  plastic  asbestos  or  magnesia  and  then  covered 
with  canvas  applied  with  flour  paste. 

The  foregoing  data,  in  connection  with  the  following  table, 
will  enable  the  reader  to  judge  which  kind  of  covering  is  likely 
to  be  the  most  effective. 

*  Prof.  Carpenter  in  "Heating  and  Ventilating  Buildings." 


1168  STEAM   HEATING. 

TESTS  OF  VARIOUS  PIPE-COVERINGS  MADE  AT  SIBLEY 
COLLEGE,  CORNELL  UNIVERSITY. 

Relative 

Kind  of  Covering.  AfmounJ 

of  Heat 
Transmitted. 

Naked  pipe 100 . 0 

Two  layers  asbestos  paper,  1  in.  hair-felt,  and  canvas 

cover 15.2 

Two  layers  asbestos  paper,  1  in.  hair-felt,  canvas 

cover,  wrapped  with  manilla  paper 15.0 

Two  layers  asbestos  paper,  1  in.  hair-felt 17.0 

Hair-felt  sectional  covering,  asbestos  lined 18.6 

One  thickness  asbestos  board 59 . 4 

Four  thicknesses  asbestos  paper 50 . 3 

Two  layers  asbestos  paper 77 .7 

Wool  felt,  asbestos  lined 23 . 1 

Wool  felt  with  air  spaces,  asbestos  lined 19.7 

Wool  felt,  plaster-of-Paris  lined 25.9 

Asbestos  moulded,  mixed  with  plaster  of  Paris 31 .8 

Asbestos  felted,  pure  long  fibre 20 . 1 

Asbestos  and  sponge 18.8 

Asbestos  and  wool  felt 20 . 8 

Magnesia,  moulded,  applied  in  plastic  condition 22 . 4 

Magnesia,  sectional 18.8 

Mineral  wool,  sectional 19.3 

Rock  wool,  fibrous 20 . 3 

Rock  wool,  felted 20.9 

Fossil  meal,  moulded,  f  inch  thick 29  7 

Pipe  painted  with  black  asphalt um 105. 5 

Pipe  painted  with  light  drab  lead  paint 108 . 7 

Glossy  white  paint 95.0 

Hot-water  Heating1. — The  system  of  heating  by  hot 
water  consists  of  circulating  hot  water  in  the  radiators  instead 
of  steam.  The  boiler,  pipes,  and  radiators  are  completely  filled 
with  water,  the  flow  or  circulation  pipes  being  attached  to 
the  top  of  the  boiler  and  the  return  pipes  to  the  bottom;  the 
water  in  the  boiler  when  heated  rises  and  circulates  through 
the  pipes  and  radiators,  parts  with  a  portion  of  its  heat,  thus 
becoming  colder  and  heavier,  and  passes  down  through  the 
return  pipes  to  the  boiler,  where  it  is  again  heated. 

There  are  two   general  systems  of  hot-water  heating,   viz., 


HOT-WATER  HEATING. 


1169 


(1)  the  open-tank  system,  and  (2)  the  closed-tank,  or  pressure, 
system. 

With  the  open-tank  system  an  open  expansion  tank  is 
connected  to  the  heating  system  in  such  a  way  as  to  receive 
the  increase  in  the  volume  of  the  water  due  to  expansion 
by  heat,  and  is  connected  with  the  outside  air  by  a  vent  pipe, 
so  that  there  is  no  pressure  on  the  tank.  Fig.  30  shows  the 
common  type  of  expansion  tank, 
although  copper-lined  wooden 
tanks  with  automatic  supply  pipe, 
similar  to  W.  C.  tanks,  are  some- 
times used. 

With  the  pressure  system 
similar  tank  is  used,  but  the 
vent  pipe  is  closed  and  a  safety- 
valve,  which  will  open  when  the 
pressure  reaches  a  certain  point, 
is  placed  on  the  overflow  pipe. 
By  increasing  the  pressure  on  the 
system,  the  water  may  be  heated 
up  to  the  temperature  of  low- 
pressure  steam,  and  hence  less 
radiatin  surface  and  smaller  pipes 
may  be  used. 

The  open  system  is  most  gen- 
erally used,  although  the  closed 
system  is  used  occasionally. 

The  closed  system  is  always 
open  to  the  danger  of  a  serious 

explosion  from  the  safety-valve  becoming  inoperative  or  from 
the  giving  away  of  any  part  of  the  apparatus.  This  system 
cannot  be  recommended  for  house  heating. 

With  the  open  expansion  tank,  about  the  only  chance  for  an 
explosion  is  by  the  stopping  of  the  expansion  pipe,  either  through 
freezing  or  by  the  closing  of  a  valve  in  the  pipe.  To  avoid 
this,  no  stop  or  valve  should  be  placed  on  the  expansion  pipe, 
and  the  expansion  pipe  should  be  well  protected  from  frost. 

The  expansion  pipe  is  usually  taken  off  from  the  supply  to 
one  of  the  radiators  in  the  upper  story  and  the  tank  should 
always  be  on  a  level  at  least  2  or  3  ft.  above  the  highest  radia- 
tor. 

The  capacity  of  the  tank  should  be  somewhat  greater  than 


Fig.  30 

Expansion  Tank. 


1170  HOT-WATER    HEATING. 

one  twentieth  of  the  total  cubical  contents  of  heater,  pipes,  and 
radiators. 

Boiler  and  Radiators. — Hot-water  radiators  have  the 
same  appearance  as  steam-radiators,  but  as  a  rule  there  is  a 
slight  difference  in  the  interior  to  improve  the  circulation. 

Almost  any  boiler  that  is  suitable  for  steam  heating  can  be 
used  for  hot-water  heating,  and  most  of  the  sectional  boilers 
mentioned  on  p.  1144  are  used  for  both  kinds  of  heating.  For 
hot  water,  the  safety-valve  and  water-gauge  are  omitted. 
For  residence  heating,  a  great  variety  of  small  boilers  especially 
designed  for  hot  water  have  been  placed  on  the  market,  notably 
the  " Ideal  Portable,"  "Spence,"  "Gurney,  400  series,"  "Palace 
King." 

Nearly  all  of  these  heaters  are  made  up  of  a  number  of  hori- 
zontal cast-iron  sections,  which  are  bolted  together  and  the 
joints  packed  or 'push-nipples  used  to  make  them  water-tight. 
The  flow  pipes  are  taken  from  the  top  of  the  upper  section, 
and  the  return  pipes  are  connected  with  the  lowest  section, 
which  generally  forms  either  the  fire-pot  or  the  ash-pit. 

The  successful  working  of  a  hot-water  heating  apparatus 
depends  very  largely  upon  the  proper  construction  of  the 
boiler.  It  is  generally  admitted  that  in  an  efficient  hot-water 
heater  the  water  must  be  cut  up  into  small  portions,  so  as  to 
heat  quickly,  and  the  whole  arrangement  of  the  heater  should 
be  such  that  the  least  possible  resistance  is  offered  to  free  cir- 
culation. 

The  boiler  in  which  the  most  powerful  circulation  is  main- 
tained with  the  least  consumption  of  fuel  is  the  most  satisfactory 
as  well  as  the  cheapest. 

The  method  employed  in  connecting  the  joints  and  the 
facilities  for  cleaning  fire  surfaces  are  also  points  that  should 
be  carefully  examined. 

For  the  capacity  of  the  various  sizes  and  styles  of  heaters  the 
architect  or  owner  must  depend  largely  upon  the  tables  given 
by  the  manufacturers. 

A  hot-water  apparatus  is  generally  filled  by  connecting  the 
house  supply  to  return  pipe  at  or  near  the  heater.  Sometimes 
a  supply  is  connected  with  the  expansion  tank  and  a  ball  cock 
placed  on  it  to  insure  that  there  shall  always  be  three  or  four 
inches  of  water  in  the  tank.  At  the  lowest  point  of  apparatus 
a  draw-off,  or  emptying-cock,  should  be  placed,  to  empty  the 
system  at  any  time. 


SYSTEMS  OF  HOT-WATER  PIPING.  1171 

The  apparatus  should  be  kept  full  of  water  during  the  summer 
months.  This  excludes  the  air  and  prevents  corrosion  or 
oxidation  of  pipes. 

System  of  Piping'. — Three  systems  of  hot- water  piping 
are  in  vogue,  corresponding  to  the  three  systems  described  for 
steam  heating: 

(1)  The  overhead  system,   in  which  the  hot  water  is  first 
conducted  to  the  highest  paft  of  the  building,  usually  to  the 
attic,  and  from  thence  distributed  to  the  radiators  by  return 
pipes,   exactly  as  in  the  Mills  system,   except  that  with  hot 
water  a  top  and  bottom  connection  is  made  with  each  radiator, 
the  water  flowing  into  the  radiator  at  the  top  and  out  at  the 
bottom. 

An  improvement  on  this  system  is  to  have  a  separate  return 
for  the  radiators  as  in  the  two-pipe  system. 

(2)  Two-pipe  System. — This  is  the   system  most  commonly 
used.     "In  this  system  the  mains  and  distributing  pipe  have 
an  inclination  upward  from  the  heater;   the  returns  are  parallel 
to   the  main   and  have  an  inclination   downward  toward  the 
heater,  connecting  at  its  lower  part.     The  flow  pipes  are  taken 
from  the  top  of  the  main  and  supply  one  or  more  radiators. 
The  return  risers  from  the  radiators  are  connected  with  the 
return  pipe  in  a  similar  manner.     In  this  system  great  care 
must  be  taken  to  produce  nearly  equal  resistance  to  flow  in 
all  branches  leading  to  the  different  radiators.     It  will  be  found 
that  invariably  the  principal  current  of  heated  water  will  take 
the  path  of  least  resistance,  and  that  a  small  obstruction,  any 
inequality  in  piping,  etc.,  is  sufficient  to  make  very  great  differ- 
ences in  the  amount  of  heat  received  in  different  parts  of  the 
same  system.     For  instance,  two    branch   pipes   connected   at 
opposite  ends  to  a  tee,  which  itself  is  connected  by  a  centre 
opening  to  a  riser,  are  almost  certain  to  have  an  irregular  and 
uncertain  circulation."  *  . 

Where  indirect  radiation  is  used  in  hot-water  heating,  the 
return  pipe  should  be  dropped  below  the  floor  and  all  return 
risers  should  be  separately  connected  with  the  main  return. 

(3)  One-pipe  System. — In  this  system  a  single   pipe  is  run 
around  the  basement  as  in  the  one-pipe  steam  system,  except 
that   the   main  hot- water  pipe  rises  from  the  boiler;    the  flow 
pipes  are  taken  from  the  top  of  the  main  and  the  water  after 

*  Prof.  Carpenter. 


1172  HOT-WATER  HEATING. 

passing  through  the  radiators  is  returned  by  a  separate  pipe 
which  is  connected  with  the  bottom  of  the  main.  With  this 
system  the  water  in  the  main  is  chilled  wherever  the  returns 
are  connected  with  it,  so  that  the  radiators  at  the  far  end  of  the 
system  cannot  be  heated  to  as  high  a  temperature  as  those 
which  receive  the  water  as  it  comes  from  the  boiler. 

A  larger  main  is  required  for  this  system  than  for  system 
No.  2.  For  small  jobs,  and  particularly  with  boilers  with 
horizontal  sections,  this  system  may  be  made  to  work  satis- 
factorily, but  the  two-pipe  system  is  always  to  be  preferred. 

For  hot-water  heating,  special  fittings  are  made  which  insure 
a  more  positive  circulation  than  the  ordinary  fittings  used  in 
steam  piping. 

Rules  for  computing  radiating  surface,  diameter  of  pipes,  etc., 
are  given  on  pp.  1162,  1163,  and  1166. 

Comparative    Advantages   and    Disadvantages  of 
Steam  and  Hot-water  Heating. 

(1)  Safety. — An   open-tank  hot-water  system  with  no  valve 
on   the   expansion    tank   cannot    possibly    explode   unless   the 
expansion  pipe  should  freeze,  which  is  quite  unlikely. 

With  steam  gross  carelessness  may  cause  an  explosion, 
although  explosions  of  gravity  heating  plants  are  quite  rare. 

(2)  Comfort. — There    is    probably    little    difference    in    this 
respect  between  steam  and  hot  water,  if  both  are  well  designed. 
Hot- water  radiators  do  not  become  as  hot  as  steam-radiators, 
and  it  is  claimed  that  for  this  reason  they  do  not  dry,  or  "scotch," 
the  air  as  much  as    steam-radiators,  and  therefore  hot-water 
heating  must  be  healthier. 

The  heat  of  a  hot-water  apparatus  can  be  perfectly  controlled 
by  either  the  fire  in  the  heater  or  the  valve  on  the  radiator, 
by  partly  closing  it;  whereas  with  steam-radiators  the  valve 
must  be  wide  open  or  tightly  closed.  Also,  with  a  hot- water 
apparatus,  some  of  the  radiators  may  be  run  at  their  full  capacity, 
while  others  may  be  partly  or  entirely  shut  off  without  causing 
noise  or  in  any  way  interfering  with  the  perfect  woi-king  of  the 
system. 

A  hot-water  apparatus  is  perfectly  noiseless  in  operation, 
there  being  none  of  the  snapping  or  gurgling  noises  common 
with  steam. 


HOT  WATER  VS.   STEAM   HEATING.          1173 

(3)  First    Cost. — On    an    average,    a    hot-water    apparatus 
costs  about  one  third  more  than  a  steam  apparatus  to  do  the 
same  work.     This  is  because  the  hot-water  apparatus  requires 
nearly  twice  as  much  radiating  surface,  larger  piping,  and  more 
expensive  fittings. 

(4)  Economy  in  Running. — With  a  steam-heating  apparatus, 
no  heat  is  given  off  unless  the  water  is  kept  boiling,  while  hot- 
water  radiators  will  give  off  heat  with  water  in  the  boiler  at  a 
temperature  of  100°,  consequently  in  moderately  warm  weather 
a  hot-water  plant  will  generally  keep   the   rooms    comfortable 
with  a  less  consumption  of  coal  than  a  steam-heating  plant. 
In  very  cold  weather,  when  the  heating  apparatus  is  worked 
to  its  full  capacity,  there  is  but  little  difference,  if  any,  in  the 
amount  of  coal  consumed  for  either  steam  or  hot-water  heating. 

In  considering  statements  as  to  the  economy  of  different 
heating  systems,  it  should  be  remembered  that  the  economy 
of  any  heating  apparatus  depends  largely  on  the  way  in  which 
it  is  run  or  upon  the  party  having  charge  of  the  plant. 

Disadvantages  of  Hot-water  Heating-. — About  the 
only  objections  that  can  be  urged  against  hot-water  heating 
are  increased  first  cost,  danger  from  freezing,  extra  space 
occupied  by  radiators,  and  the  fact  that  a  building  cannot  be 
as  quickly  warmed  by  hot  water  as  by  steam. 

It  is  also  more  difficult  to  secure  uniform  circulation  in  a 
large  hot- water  plant  than  in  a  large  steam-plant. 

While  in  large  buildings  and  those  that  are  not  kept  warm 
all  the  time  many  of  these  objections  are  of  considerable  im- 
portance, they  do  not,  as  a  rule,  hold  good  in  residences,  which 
are  kept  at  a  uniform  temperature  and  in  which  the  extra 
size  of  the  radiators  is  of  little  consequence. 

The  danger  of  freezing  is  very  much,  greater  with  hot-water 
circulation  than  with  steam,  and  on  this  account  hot- water 
indirect  radiation  must  be  used  with  much  caution. 

Summary. — For  a  residence  of  eight,  ten,  or  twelve  rooms 
probably  90  per  cent,  of  those  who  are  familiar  with  both  steam 
and  hot-water  heating  would  recommend  hot  water. 

For  larger  residences  and  small  apartment  houses,  about  as 
many  would  recommend  steam  as  hot  water,  and  for  still  larger 
buildings,  probably  90  per  cent,  of  heating  engineers  would 
recommend  a  gravity  steam  system  or  either  the  "Webster" 
or  "Paul"  system. 


1174  RESIDENCE  HEATING. 


Hot-air,    Steam,    and    Hot-water  Heating  in 
Residences. 

Much  advancement  has  been  made  of  late  years  in  the  methods 
of  heating  residences  and  in  the  apparatus  intended  for  that 
purpose.  While  it  is  impossible  in  this  book  to  treat  the  sub- 
ject in  detail,  it  is  believed  that  the  following  information  will 
be  of  value  in  deciding  upon  the  kind  of  heating  to  be  used,  and 
in  selecting  an  efficient  apparatus  and  seeing  that  it  is  properly 
put  in. 

In  deciding  upon  a  heating  apparatus  for  a  dwelling,  the 
governing  conditions  are,  generally,  (A)  the  size  of  the  building, 
and  (B)  the  limit  of  first  cost.  When  the  latter  condition  is 
not  a  controlling  one,  the  cost  of  running  the  apparatus  should 
be  given  the  first  consideration. 

For  residences  of  eight  or  ten  rooms  and  covering  not  more 
than  1,200  sq.  ft.  of  ground  the  author  would  recommend  hot- 
air  heating  by  means  of  a  good  furnace. 

For  residences  covering  1,400  sq.  ft.,  a  combination  hot-air 
and  water  system  is  recommended,  or  an  entire  hot-water 
system. 

For  still  larger  residences,  a  steam  or  hot-water  apparatus 
should  be  used. 

Furnace  Heating". — For  warming  residences  not  exceed- 
ing 1,200  sq.  ft.  of  ground  area,  the  author  believes  a  good 
furnace,  properly  set  and  with  hot-air  pipes  of  proper  size, 
suitably  located,  will  give  the  best  satisfaction,  as  it  is  economical 
in  first  cost,  easy  to  manage,  costs  little  for  repairs,  and  furnishes 
a  pleasant  and  healthy  heat  at  no  greater  expense  of  running 
than  with  steam  or  hot  water. 

The  most  common  defects  observed  in  furnace-heating  are 
overheating  of  the  air,  vitiating  of  the  air  by  the  gases  of 
combustion,  and  imperfect  distribution  of  the  heat. 

The  first  two  defects  may  be  entirely  avoided  if  sufficient  care 
is  exercised  in  the  selection  and  setting  up  of  the  furnace  and 
in  tending  the  fire,  and  the  last  defect  may  be  reduced  to  a 
minimum  by  a  wise  location  and  proper  proportion  of  the  flues 
and  registers. 

The  cause  of  the  unsatisfactory  heating  of  a  great  many 
houses  by  furnaces  is  in  the  owner  or  builder  refusing  to  pay 
the  necessary  price  for  a  first-class  furnace  and  for  the  best 


HOT-AIR  FURNACES.  1175 

workmanship  and  materials.  The  same  carelessness  and 
•''skinning"  that  is  sometimes  permitted  with  furnace  work, 
if  permitted  on  a  steam  or  hot-water  apparatus,  would  in  most 
cases  prevent  their  working  at  all. 

Furnace  heating  may  be  divided  into  two  parts,  the  produc- 
tion of  heat  and  the  distribution  of  the  heat. 

The  former  depends  entirely  upon  the  furnace,  its  setting, 
cold-air  supply,  draught,  kind  of  fuel,  and  attendance. 

The  Furnace. — In  principle,  a  hot-air  furnace  is  simply  a 
stove  or  heater  incased  with  iron  or  brick,  so  as  to  form  an  air 
chamber  between  the  heater  and  casing.  The  air  enters  at  the 
bottom  of  the  chamber,  passes  over  the  heated  surfaces  of  the 
heater,  arid  is  conducted  by  the  hot-air  pipes  to  the  various 
rooms. 

The  external  surface  of  the  fire-pot  and  all  portions  of  the 
heater  which  receive  heat  from  the  fire  or  smoke  are  called  the 
radiating  surface. 

As  a  rule,  the  furnace  which  has  the  greatest  radiating  surface 
in  proportion  to  the  size  of  the  fire-pot  will  give  off  the  most 
heat  for  a  given  amount  of  fuel  consumed. 

As  the  amount  of  radiating  surface  largely  affects  the  weight 
of  a  furnace,  and  the  latter  in  a  great  measure  the  selling  price, 
it  is  obvious  that  the  best  furnaces  must  cost  the  most.  It  is 
true  that  one  furnace  may  have  its  radiating  surfaces  better 
arranged  than  another,  so  as  to  give  off  more  heat  for  a  less 
quantity  of  metal,  but  it  is  seldom  that  a  very  light  furnace, 
particularly  if  of  cast  iron,  is  a  good  heater. 

Furnaces  should  be  so  designed  that  the  smoke,  after  leaving 
the  combustion-chamber,  mus^  travel  around  the  radiator  one 
or  more  times  before  finding  an  exit  to  the  chimney.  With 
a  chimney-flue  of  proper  size  arid  topped  out  well  above  the 
roof,  it  is  possible  to  make  the  smoke  travel  a  long  distance 
and  thus  obtain  great  economy  of  fuel.  The  best  furnaces 
are  designed  on  this  principle. 

Besides  having  a  large  radiating  surface,  the  furnace  should 
have  as  few  joints  as  possible,  and  should  be  arranged  so  as 
to  be  easily  cleaned. 

Furnaces  are  made  of  cast  iron,  wrought  iron,  and  steel,  either 
used  singly  or  combined.  The  radiating  surface  above  the  fire- 
pot  can  be  made  more  cheaply  of  wrought  iron  than  of  cast  iron, 
and  in  certain  arrangements  it  is  just  as  serviceable. 

While  there  are  excellent  furnaces  made  of  wrought  iron  and 


1176  RESIDENCE  HEATING. 

steel,  the  author  believes  that  a  heavy  cast-iron  furnace  is  the 
most  durable,  and  can  be  made  as  tight.  Some  furnaces  are 
made  chiefly  of  cast  iron,  but  with  air  or  smoke  flues  of  wrought 
iron  fitting  into  cast-iron  sockets.  This  arrangement  is  not 
generally  approved,  as  the  two  metals  expand  and  contract 
unequally,  thus  tending  to  open  the  joint. 

There  are  so  many  styles  of  furnaces  manufactured  that  it  is 
quite  impossible  to  go  further  into  details.  It  may  be  said, 
however,  that  the  furnace  shown  in  Fig.  31,  made  by  the  Richard- 


Fig.    31 

son  &  Boynton  Company,  is  representative  of  the  best  type  of 
cast-iron  furnace,  and  that  shown  in  Fig.  32,  made  by  Isaac  A. 
Sheppard  &  Co.,  of  a  modern  steel-plate  furnace.  Fig.  33,  of 
which  the  Excelsior  Steel  Furnace  Company  are  the  makers, 
shows  a  type  of  furnace  which  consists  of  a  plain  combustion- 
chamber  with  a  steel  radiator.  This  radiator  is  divided  with 
a  horizontal  partition,  so  that  smoke  must  ciculate  entirely 
around  it  before  it  enters  the  flue.  This  furnace  is  intended  for 
soft  coal.  The  more  modern  furnaces,  constructed  for  burning 


HOT-AIR   FURNACES. 


1177 


soft  coal,  have  provision  for  the  introduction  of  superheated  air 
into  the  fire-box,  thereby  preventing  the  formation  of  soot  and 
causing  thorough  combustion  and  intense  heat.  The  one 
shown  in  Fig.  31  is  a  hot-air  blast-furnace,  and  is  supplied  with 
oxygen  at  a  high  temperature  for  either  hard  or  soft  coal,  acceler- 
ating and  intensifying  combustion  to  a  very  high  degree. 

In  the  Twentieth  Century  furnace  the  fire-pot  contains  cells 
and  slots  cast  within  the  walls  of  the  pot  which  admit  air  at 
twenty  points  equally  distrib- 
uted around  the  circumfer- 
ence of  the  same.  By  reason 
of  this  admission  of  air  the 
fire  burns  from  the  top  down 
and  from  the  circumference 
toward  the  centre,  causing  an 
intense  heat  around  the  out- 
side of  the  bowl.  This  furnace  A 
can  be  operated  successfully  I  t 
with  steam  coal. 

The  Thatcher  Furnace  Com-  |l 
pany  are  makers  of  a  tubular  Hv 
furnace  that  seems  to  possess  m 
considerable  merit.  J/J 

The  casing  surrounding  the  Phi 
heater  may  be  of  brick  or  sheet 
iron.      If   of  orick,    it   should 
consist  of  two  4-inch  walls  with 
a  space  betveen,  the  inner  wall 

being  generally  built  on  a  cir-  Fig.  32 

cle  and  the  outer  one  on  a  square. 

" Brick  set"  furnaces  are  not  as  common  as  they  formerly 
were,  as  they  can  be  cased  as  well  with  iron  and  without  occupy- 
ing so  much  space  in  the  cellar.  When  cased  with  sheet  iron, 
the  furnace  is  designated  as  "portable."  Portable  furnaces 
shoula  always  have  a  double  casing  with  an  inch  space  between. 
The  jnner  casing  may  be  of  black  iron,  but  the  outer  one  should 
be  galvanized.  The  hot  air  is  thrown  into  the  pipes  better  if 
the  top  of  the  casing  is  truncated,  as  in  Fig.  32. 

Cold-air  Supply.— In  a  house  heated  by  a  furnace,  the 
temperature  of  the  rooms  is  maintained  by  a  constant  incoming 
Current  of  hot  air,  and  it  is  absolutely  necessary  for  satisfactory 
heating  that  proper  provision  be  made  for  supplying  this  air 


1178 


RESIDENCE  HEATING. 


to  the  furnace,  and  on  no  account  should  a  hot-air  furnace  be 
used  without  being  provided  with  a  direct  supply  of  air  from 
outside  the  building.  In  dwellings  this  may  be  best  accom- 
plished by  putting  an  opening  in  the  external  wall  just  beneath 
the  first-floor  joist  and  as  far  above  the  ground  as  the  elevation 
of  the  building  will  permit.  From  this  opening,  which  should 
be  covered  with  galvanized  wire  netting  of  about  three  eighths 
of  an  inch  mesh,  a  duct  or  flue  should  be  carried  to  the  air-pit 
under  the  furnace,  as  shown  in  Fig.  33. 

The  duct  may  be  either  carried  horizontally  under  the  base- 
ment ceiling  until  near  the  furnace  and  then  dropped  to  the  air- 


Fig.  33 

pit,  or  it  may  be  carried  down  against  the  cellar  wall  and  thence 
under  the  floor  to  the  furnace.  The  portion  of  the  duct  afove 
the  floor  should  be  built  of  well-seasoned  matched  boards  or 
of  galvanized  iron.  The  portion  below  the  floor  should  be  cox- 
structed  either  of  stone,  brick,  or  glazed  tile,  and  should  b» 


WARM-AIR  PIPES  AND  REGISTERS. 


1179 


tightly  cemented.  If  of  brick  or  stone,  the  duct  should  be  cov- 
ered with  stone  slabs  with  the  edges  roughly  dressed  and  the 
joints  cemented.  The  air-duct  should  not  be  carried  under  the 
floor  if  the  soil  is  at  all  damp,  nor  near  any  drain. 

Fig.  34  shows  the  formation  and  construction  of  foundation 
and  pit  of  a  portable  furnace. 

Besides  the  external  air  supply,  it  is  also  a  good  idea  to  have 
a  smaller  air-duct  leading  from  a  register  in  the  front  hall  to 
the  base  of  the  furnace.  This  duct  may  be  of  wood,  tin,  or 


Fig.  34 

Foundation  and  Pit  of  a  Portable  Furnace. 

galvanized  iron,  and  may  be  connected  either  with  the  base 
of  the  furnace  above  the  floor  or  feed  into  the  outside  duct, 
but  care  should  be  taken  to  prevent  the  air  from  blowing  from 
the  outside  duct  up  through  the  inside  one. 

An  inside  duct  will  produce  a  better  circulation  of  air  through 
the  house,  and  on  very  cold  nights  the  outside  duct  may  be 
shut  off  and  the  air  taken  entirely  from  the  front  hall,  as  the 
air  from  this  source,  having  nothing  to  contaminate  it,  will  be 
reasonably  pure. 

The  Hot-air  Pipes  and  Kegisters. — The  pipes  which 
convey  the  heated  air  from  the  furnace  to  the  various  rooms 
should  be  of  bright  IX  tin  for  sizes  less  than  14  ins.  in  diameter 
and  of  No.  26  galvanized  iron  for  larger  sizes. 

All  pipes  below  the  basement  ceiling  should  be  round,  and  for 
the  best  work  should  be  covered  with  asbestos  paper,  pasted 
to  the  pipe  with  a  specially  prepared  paste. 

The  vertical  hot-air  pipes,  to  rooms  in  second  or  third  stories, 
are  frequently  termed  "stacks."  They  usually  pass  up  be- 
tween the  studding  of  the  partitions  in  the  lower  stories,  thus 
necessitating  a  shallow  pipe. 


1180  RESIDENCE  HEATING. 

For  medium-  and  low-cost  houses  the  stacks  are  usually  made 
3 1  ins.  deep,  of  one  thickness  of  tin,  and  wrapped  with  asbestos 
paper  pasted  to  the  tin.  For  a  better  class  of  buildings  double 
pipes  are,  or  should  be,  used  for  the  stacks.  These  stacks  have 
an  air  space  between  the  outside  and  inside  pipes,  affording 
a  circulation  of  air,  which  makes  the  stacks  absolutely  safe, 
thus  obviating  the  necessity  of  iron  lath  in  front  of  the  stack. 

The  table  on  p.  1197  gives  the  sizes  and  dimensions  of  safety 
double  hot-air  stacks  made  by  the  Excelsior  Steel  Furnace 
Company. 

In  providing  for  hot-air  stacks,  it  should  be  remembered  that 
the  friction  against  the  sides  of  the  pipe  largely  affects  the 
volume  of  air  conveyed,  and  that  consequently  a  round  pipe 
is  always  to  be  preferred  to  a  square  one,  and  a  square  pipe  to 
a  shallow  pipe.  In  large  residences,  5-  or  6-inch  studding 
should  be  used  for  partitions,  so  that  thicker  pipes  may  be  used. 

Brick  flues  should  not  be  used  for  conveying  hot  air,  as  the 
loss  of  heat  by  absorption  is  very  great,  and  economical  results 
cannot  be  obtained. 

The  hot-air  registers  should  be  set  in  double  register  boxes 
made  of  tin,  and  the  bottom  of  the  stacks  should  terminate  in 
a  "boot"  or  "footing,"  arranged  in  such  a  way  as  will  insure 
the  quick  and  easy  flow  of  hot  air  from  the  feed-pipe  into  the 
stacks. 

Warm-air  Radiators. — In  the  use  of  warm-air  furnaces 
it  is  oftentimes  extremely  difficult  to  heat  rooms  located  at  a 
distance  from  the  furnace,  rooms  that  are  without  any  means 
of  ventilation,  or  rooms  which  are  greatly  exposed  to  outside 
winds.  This  difficulty  may  sometimes  be  overcome  by  using 
a  warm-air  radiator  placed  over  the  outlet  of  the  furnace  pipe, 
which  must  be  in  the  floor.  These  radiators  are  made  of  sheet 
steel  and  are  so  constructed  that  they  set  up  a  circulation  of 
air  in  the  room  which  tends  to  draw  the  air  from  the  furnace. 
They  somewhat  resemble  a  direct-indirect  steam-radiator.* 

Ventilation. — A  hot-air  furnace  plant,  properly  put  in, 
will  furnish  a  good  supply  of  fresh  air,  and  therefore  afford  fairly 
good  ventilation,  if  means  are  provided  for  carrying  off  the  foul 
air  in  the  rooms.  The  warm  air  entering  a  room  must  of  neces- 
sity force  out  an  equal  quantity  of  the  air  already  in  the  room; 

*  A  very  good  pattern  of  warm-air  radiator  is  made  by  the  International 
Heater  Co. 


LOCATING   THE  FURNACE.  1181 

exits  are  often  found  in  the  spaces  around  the  doors  and  windows, 
but  these  are  rarely  sufficient  to  carry  away  the  air  as  fast  as  it 
would  enter  if  unimpeded.  Fireplaces,  especially  if  kept  in 
use,  afford  excellent  ventilation.  A  good  arrangement  for  ob- 
taining ventilation  is  by  building  a  large  flue  in  a  central  chim- 
ney and  using  a  galvanized-iron  smoke-stack,  placed  in  the 
centre  of  it,  for  the  furnace.  The  space  surrounding  the  smoke- 
pipe  may  then  be  used  for  ventilation  and  ducts  from  different 
rooms  connected  with  it. 

Location  of  Furnace, — Upon  the  location  of  the  fur- 
nace the  successful  heating  of  the  house  often  depends,  and  it 
is  a  matter  that  requires  careful  consideration. 

As  a  general  rule,  the  furnace  should  be  located  in  the  base- 
ment, near  the  centre  of  the  space  occupied  by  the  registers, 
and  a  little  nearer  the  side  from  which  the  prevailing  winds 
come  in  winter-time.  The  tendency,  in  hot-air  heating,  when 
the  wind  is  blowing  strong  in  severe  cold  weather,  is  for 
the  rooms  on  the  further  side  of  the  house  from  the  wind  to  be 
overheated,  while  those  against  the  wind  are  poorly  heated, 
the  registers  on  the  windward  side  delivering  almost  no  hot  air. 
Therefore,  to  counteract  this  tendency,  the  furnace  should  be 
placed  some  few  feet  toward  the  windward  side  of  the  building, 
provided  this  does  not  make  the  pipes  to  the  general,  or  family, 
living-rooms  longer  than  the  others. 

The  height  of  the  basement  should  be  such  that  the  "  leaders," 
or  horizontal  hot-air  pipes  below  basement  ceiling,  may  have 
a  pitch  of  1J  ins.  per  running  foot  upward  from  the  furnace. 
If  there  is  no  inclination  to  these  pipes,  the  first-story  rooms 
will  be  heated  with  difficulty.  For  a  residence  of  ten  rooms 
the  furnace-room  should  have  a  clear  height  of  at  least  7  ft. 
6  ins. 

Cold-air  Opening. — If  only  one  external  cold-air  supply 
is  used,  it  should  be  taken  from  the  direction  from  which  the 
prevailing  winds  come.  For  buildings  in  exposed  situations 
it  is  desirable  to  have  a  cold-air  supply  from  the  opposite  side 
of  the  building  also,  the  ducts  connecting,  and  each  being  fur- 
nished with  a  damper,  so  that  either  duct  may  be  used,  accord- 
ing to  the  direction  of  the  wind.  Cases  have  been  known  where 
the  wind  blowing  from  the  opposite  direction  of  the  cold-air 
supply  has  sucked  the  air  from  the  house  through  the  furnace 
and  cold-air  duct,  thus  actually  reversing  the  natural  operation 
of  the  furnace.  Two  supplies  will  obviate  this  possibility. 


1182  RESIDENCE  HEATING. 

Location  of  Stacks  and  Kegisters. — To  insure  the 
best  results,  the  location  of  furnace,  stacks,  and  registers  should 
be  planned  out  before  the  work  of  construction  begins,  for  while 
the  building  need  not  be  planned  to  suit  the  heating  apparatus, 
it  almost  always  happens  that  the  setting  of  the  partitions, 
swinging  of  doors,  and  placing  of  studs  and  joists  can  be 
arranged  so  as  to  favor  the  placing  of  stacks  and  registers, 
without  seriously  affecting  any  desired  arrangement  of  the  plan, 
and  this  can  be  done  much  better  on  the  plans  than  after  the 
house  is  started. 

It  is  generally  conceded  that  the  hot-air  stacks  should  be 
placed  in  the  partitions  and  as  near  to  the  furnace  as  practicable, 
and  that  all  horizontal  branches  should  be  as  short  as  possible, 
as  the  air  travels  much  slower  in  the  horizontal  branches  and 
more  heat  is  lost  from  radiation.  The  registers  should  be 
placed  as  near  the  stack  as  possible;  they  should  not  be  placed 
near  the  windows,  nor  where  the  doors  will  swing  over  or 
against  them,  nor  in  the  floor  near  an  open  fireplace. 

Whether  the  register  shall  be  placed  in  the  floor  or  partition 
is  a  matter  that  should  be  decided  by  the  owner.  It  is  claimed 
that  the  circulation  from  a  wall  register  is  not  as  good  as  from 
one  placed  in  the  floor,  and  the  wall  above  the  register  generally 
becomes  discolored  after  a  time  by  the  dust  that  is  occasionally 
blown  up  through  the  pipes.  On  the  other  hand,  floor  registers 
catch  much  more  dirt  from  sweeping  the  rooms,  and  many 
ladies  object  to  having  their  carpets  cut.  The  author  believes 
that  it  is  healthier  to  have  the  registers  placed  in  the  wall. 
Convex  registers  are  to  be  preferred  for  walls,  as  they  deliver 
more  air  than  do  the  ordinary  flat  registers.  It  sometimes 
happens  that  the  stacks  must  be  put  in  an  outside  wall.  When 
such  is  the  case,  the  stack  should  be  double  and  wrapped  with 
asbestos  paper  as  well.  Stacks  should  not  be  placed  in  out- 
side wa}ls,  however,  when  it  is  possible  to  avoid  it. 

Calculations  for  Size  of  Furnace,  Pipes,  and 
Registers. 

There  appears  to  be  no  rule  by  which  the  architect  can  deter- 
mine the  size  of  the  furnace  that  should  be  used  to  heat  a  given 
building  other  than  by  using  the  tables  given  by  the  various 
manufacturers.  Rules  have  been  given  for  determining  the 
necessary  grate  area  of  a  furnace,  but  it  is  utterly  impossible 
to  make  such  a  rule  that  will  apply  to  all  furnaces,  as  the  heating 


CAPACITY  OF  AIR  PIPES  AND  REGISTERS.    1183 


capacity  depends  almost  as  much  upon  the  amount  and  char- 
acter of  the  radiating  surface,  and  these  vary  with  the  make 
of  the  furnace.  Some  manufacturers  give  rules  which  take 
into  account  not  only  the  cubic  space  to  be  heated,  but  also  the 
outside  wall  and  the  glass  area,  both  of  which  should  be  con- 
sidered in  deciding  on  the  size  of  the  heater.  Most  furnace- 
makers,  however,  merely  give  the  amount  of  cubic  space  that 
the  different  sizes  of  their  particular  furnaces  will  heat,  and 
as  there  is  no  way  of  telling  how  reliable  these  figures  are,  except 
by  experience,  it  is  wise  to  have  the  contractor  give  a  guarantee 
that  the  furnace  shall  heat  the  building  to  70°  in  zero  weather 
without  forcing  the  furnace. 

Pipes  and  Registers. — The  tables  given  in  various  books 
and  catalogues  for  the  size  of  pipes  and  registers  vary  a  great 
deal  and  must  be  used  with  considerable  judgment.  The  follow- 
ing table  appears  to  the  author  to  be  as  reliable  as  any: 

TABLE  OF  CAPACITY  OF  HOT-AIR   PIPES  AND 
REGISTERS. 


Size  of 
Register. 

Equivalent 
in  Round  or 
LeaderPipe. 

Equivalent 
in  Square  or 
Riser  Pipe. 

Cubic  Feet 
of  Space  on 
First  Floor 
Same  Will 
Heat. 

Cubic  Feet 
on  Second 
Floor. 

Cubic  Feet 
on  Third 
Floor. 

6X   8 

6  in. 

4X   8 

400 

450 

500 

*8X   8 

7 

4X10 

450 

500 

560 

*8X10 

8 

4X10 

500 

850 

880 

*8X12 

8 

4X11 

800 

1000 

1050 

*9X12 

9 

4X12 

1050 

1250 

1320 

*9X14 

9 

4X14 

1050 

1350 

1450 

*  10X12 

10 

4X14 

1500 

1650 

1800 

*  10X14 

10 

6X10 

1800 

2000 

2200 

10X16 

10 

6X10 

1800 

2000 

2200 

12X14 

12 

6X12 

2200 

2300 

2500 

*12X15 

12 

6X12 

2250 

2300 

2500 

*12X17 

12 

6X14 

2300 

2600 

2800 

12X19 

12 

6X14 

2300 

2600 

2800 

*  14X18 

14 

6X16 

2800 

3000 

3200 

*  14X20 

14 

6X16 

2900 

3000 

3200 

*  14X22 

14 

8X16 

3000 

3200 

3400 

*  16X20 

16 

8X18 

3600 

4000 

4250 

*  16X24 

16 

8X18 

3700 

4000 

4250 

*  20X24 

18 

10X20 

4SOO 

5400 

5750 

*  20X26 

20 

10X24 

6000 

7000 

7450 

1184  RESIDENCE  HEATING. 

This  table  gives  different  sizes  of  hot-air  registers  used  in 
furnace  practice,  together  with  the  equivalents  of  the  capacity 
of  the  same  in  round  leader  pipes  from  furnace,  with  eleva- 
tion of  at  least  one  inch  to  the  foot;  also  equivalent  in 
riser  pipes  (or  stacks),  and  also  the  cubic  feet  of  space  on 
first,  second,  and  third  floors  which  said  registers  with  their 
proper  round  and  square  pipes  will  heat.  The  table  is  based 
on  normal  conditions,  with  runs  of  pipe  of  usual  length,  and 
is  intended  to  show  the  size  of  registers  and  pipes  neces- 
sary to  raise  the  temperature  of  air  from  zero  outside  to  70° 
on  the  inside,  within  reasonable  time,  without  forcing.  The 
sizes  that  are  marked  with  an  asterisk  are  those  recom- 
mended for  general  use.  The  larger  the  register  the  less  resist- 
ance to  the  flow  of  the  heated  air,  but  sizes  mentioned  will 
produce  good  results,  and,  being  stock  sizes,  will  always  be 
found  in  stock.  In  planning  work  arrange  to  use  the  sizes 
referred  to. 

It  should  always  be  borne  in  mind,  however,  that  uniform 
heating  does  not  depend  so  much  upon  the  actual  size  of  the 
pipes  as  upon  the  relative  sizes.  For  example,  in  a  two-story 
house  of  eight  rooms  of  exactly  the  same  size  and  the  same  amount 
of  wall  and  glass  area  the  best  heating  results  will  be  obtained 
not  by  using  the  same  size  of  pipes  for  all  the  rooms,  even  if  the 
pipes  are  of  ample  capacity,  but  by  carefully  proportioning 
the  sizes  of  the  pipes  according  to  the  exposure,  length  of  the 
leaders,  and  whether  the  room  is  in  the  first  or  second  story. 
The  registers  in  the  rooms  with  north  and  west  exposures  should 
be  a  little  nearer  the  furnace,  if  possible,  than  the  others,  and 
the  pipes  to  the  first  story  should  be  larger  than  those  leading 
to  the  second  story. 

The  International  Heater  Company  states  that  1  sq.  in.  of 
capacity  of  hot-air  pipe  will  heat  50  cu.  ft.  in  stores  and  90 
cu.  ft.  in  churches  when  there  is  but  one  pipe  directly  over 
the  furnace. 

Cold-air  Box. — The  sectional  area  of  the  cold-air  box 
should  be  equal  to  three-fourths  of  the  aggregate  sectional  area 
of  the  leaders.  The  box,  or  duct,  should  be  10  or  12  ins.  deep 
(for  dwellings)  and  wide  enough  to  give  the  required  sectional 
area.  It  should  also  always  be  provided  with  a  damper,  so 
that  the  supply  may  be  regulated  to  the  heavy  winds  and  ex- 
treme cold  weather. 


SPECIFICATIONS  FOR  FURNACE  WORK.      1185 

Specifications. 

The  following  form  is  given  as  a  guide  to  architects  in  pre- 
paring the  specifications  for  furnace  work: 

SPECIFICATIONS  FOR  FURNACE  WORK  IN  RESIDENCE  FOR  MR. 

„ TO    BE    BUILT    AT 

Architect. 

Furnace. — Furnish  and  set  up  complete,  where  shown  on  base- 
ment plan,  one  No.  —  —  furnace,  portable  pattern,  with 
double  casings.  Connect  the  furnace  with  the  chimney  with 
No.  24  galvanized-iron  smoke-pipe  of  the  same  size  as  the  collar 
on  the  furnace ;  all  bends  or  turns  to  be  made  with  three-piece 
elbows;  the  pipe  to  be  strongly  supported  by  wire,  and  to  be 
kept  12  ins.  below  the  ceiling. 

Air-pit. — Excavate  for  and  build  a  cold-air  chamber  under 
the  furnace  not  less  than  18  ins.  deep,  with  8-inch  brick  walls, 
laid  and  plastered  with  cement;  also  cement  the  bottom 
of  the  chamber.  Build  the  cold-air  duct  under  cellar,  floor, 
where  shown  on  plan,  to  be  —  ft.  long,  14  ins.  deep  in  the  clear, 
and  —  ins.  wide,  with  sides  of  hard  brick  in  cement,  and  the  sides 
and  bottom  smoothly  plastered  with  cement.  Cover  the  duct 
with  3-inch  flag-stones  with  tight  joints,  leaving  opening  of 
proper  size  for  the  wooden  box  to  be  built  by  the  carpenter 
(wooden  box  should  be  included  in  carpenter's  specifications). 

Hot-air  Pipes. — Furnish  and  properly  connect  with  funiace 
and  register  boxes,  leaders  and  stacks  of  the  following  sizes, 
all  to  be  made  of  bright  IX  tin,  and  the  stacks  to  be  double 
with  air  space  between.  All  turns  in  leaders  to  be  made  by 
three-  or  four-piece  elbows,  and  the  stacks  to  have  boots  or 
starters  of  approved  pattern. 

SIZES    OF    PIPES    AND    REGISTERS. 

Hall 12"  leader  No  stack  12"  X 15"  register 

Parlor 10"  "  4"X14"  stack  10"X12" 

Dining-room....  12"  "  6"X12"  "  12"X15"        " 

Library 10"  "  4"X14"  "  10"X12"       " 

Chamber  No.  1...     9"  "  4"X14"  "  9"X14" 

2. .  .     9  4   X12  9    X 12' 

"    3...     8"  "  4"X10"  "  8''X10"       " 

Registers. — All  registers  are  to  be  of  sizes  given  in  the  fore- 
going list,  of  the  Tuttle  and  Bailey  manufacture,  japanned, 


1186  RESIDENCE  HEATING. 

except  those  in  the  first  story,  which  are  to  be  electro-bronze- 
plated.  All  floor  registers  are  to  be  set  in  iron  borders  corre- 
sponding with  the  registers. 

Register  Boxes. — All  register  boxes  to  be  made  double;  for 
first-floor  boxes  the  joists  are  to  be  lined  with  tin  and  provided 
with  ceiling  plates  full  size  of  register,  with  plaster  collar  attached, 
so  that  pipes  and  boxes  can  be  removed  without  disturbing 
the  plastering  or  defacing  the  ceiling. 

Miscellaneous. — All  horizontal  pipes  in  the  basement  to"  be 
round,  and  where  they  pass  through  partitions  they  are  to  be 
provided  with  collars,  so  that  the  pipes  can  be  removed  without 
disturbing  the  plastering.  All  leaders  to  be  provided  with 
dampers  and  tin  tags  designating  the  different  rooms  they 
supply;  and  whenever  pipes  run  near  woodwork  the  same  is 
to  be  properly  covered  with  tin  and  protected  from  any  danger 
from  fire.  The  contractor  is  to  remove  all  rubbish  made  by 
him,  clean  up  all  ironwork,  and  leave  the  whole  apparatus  in 
complete  working  order,  and  furnish  a  poker  of  proper  size. 

Guarantee. — The  contractor  is  to  guarantee  that  the  furnace 
shall,  under  proper  management,  heat  all  rooms  with  registers 
connected  with  the  furnace  to  70°  Fahr.  when  temperature 
outside  indicates  10°  below  zero.  In  event  of  the  failure  of  the 
furnace  to  do  this,  the  contractor  is  either  to  make  the  furnace 
heat  said  rooms  or  substitute  another  furnace  that  will  heat 
the  rooms  at  his  own  expense  and  without  unnecessary  delay. 


Hot  Air  and  Water  Combination. 

It  is  quite  difficult,  if  not  impossible,  to  heat  throughout 
dwellings  covering  more  than  1,400  sq.  ft.  with  warm  air  alone. 
On  account  of  the  much  larger  exposure  and  the  increased 
length  of  leaders,  it  becomes  necessary  to  supplement  the  warm 
air  with  an  auxiliary  heat  which  can  be  carried  to  remote  and 
exposed  parts  of  the  house,  and  which  will  not  be  affected  by 
pressure  of  wind  or  long  and  crooked  pipes.  For  supplying 
this  auxiliary  heat,  hot  water  has  been  found  best  adapted  as 
a  rule,  and  a  great  variety  of  "  combination "  furnaces  are  now 
made  which  contain  provisions  for  heating  water  which  may 
be  carried  by  pipes  to  radiators  located  in  the  portions  of  the 
house  most  difficult  to  heat  by  warm  air.  Such  combination 
systems  have  been  used  with  great  success,  and  for  heating 


COMBINATION  SYSTEMS.  1187 

dwellings  of  ten  average-size  rooms  the  author  believes  it  to 
be  the  most  successful  system,  as  it  guarantees  the  comfortable 
warming  of  the  house,  and,  if  properly  put  in,  thorough  venti- 
lation, which  cannot  be  obtained  by  any  system  of  direct  hot- 
water  or  steam  radiation.  It  is  claimed  that  nearly  200  sq.  ft. 
of  hot-water  radiation  can  be  obtained  by  absorbing  the  surplus 
heat  which  would  usually  be  wasted  in  a  warm-air  furnace. 

The  construction  of  the  parts  for  heating  the  water  varies 
greatly  with  different  makes  of  furnaces.  Some  furnaces  have 
a  portion  of  the  fire-pot  hollow,  and  the  water  is  heated  there; 
others  have  a  separate  heater  suspended  over  the  fire-pot.  It 
is  impossible  here  to  consider  the  relative  merits  of  the  various 
heaters;  the  architect  should  examine  the  heaters  for  himself 
and  look  up  their  record  before  specifying  any  particular  make. 

As  a  rule,  the  portions  of  the  house  which  should  be  heated 
by  the  hot  water  are  the  halls,  bathroom,  and  perhaps  the  rooms 
on  the  north  or  west  side  of  the  house. 

The  same  rules  govern  the  size  of  the  radiators  and  piping 
and  the  manner  of  installing  as  in  an  entire  hot-water  plant. 

Hot  Air  and  Steam  Combination. — There  are  also 
several  furnaces  which  have  a  small  steam-boiler  placed  above 
the  fire  by  means  of  which  a  few  rooms  may  be  heated  by  direct 
steam  radiation.  Safety-valves  are  provided  so  that  the  steam 
pressure  cannot  exceed  5  Ibs.,  and  if  the  directions  for  running 
the  apparatus  are  followed,  the  apparatus  is  perfectly  safe. 
The  steam  combination  possesses  some  advantages  over  the 
hot-water  combination,  and  for  a  large  residence  the  author 
believes  that  it  will  give  more  satisfactory  results  with  intelli- 
gent management. 

Hot-water  Heating  in  Residences. — As  stated  on 
p.  1173,  there  is  no  better  system  of  warming  residences  of  ten 
or  twelve  rooms  than  the  hot-water  system,  and  it  is  being 
used  to  a  greater  extent  every  year. 

The  general  principles  of  hot-water  heating,  as  explained 
on  pp.  1168  to  1172,  apply  to  residences  as  to  all  other  buildings. 
The  open-tank  system  should  always  be  used  for  this  class  of  work. 
The  following  Advice  to  Fitters,  published  by  the  Gurney  Heater 
Manufacturing  Company,  contains  many  practical  suggestions 
that  should  be  of  almost  equal  interest  to  the  architect  and 
owner: 

"When  estimating  upon  a  job,  take  well  into  consideration  the 
extent  of  all  flow,  return  pipes,  and  risers,  also  their  situation, 


1188  RESIDENCE  HEATING. 

and  calculate  them  as  radiating  surface  in  addition  to  what 
is  placed  in  rooms,  and  allow  heater  power  accordingly. 

"Due  care  must  be  exercised  to  provide  for  any  special  con- 
ditions, such  as  exposure  of  building,  material  of  construction, 
location,  length  and  size  of  mains  governing  plant  under  con- 
sideration. 

"Allowances  should  be  made  for  loose  construction  of  doors 
and  windows,  which  admit  large  volumes  of  cold  air,  and  if 
there  are  outside  doors  which  are  used  frequently  and  open 
directly  into  the  room,  a  radiator  should  be  placed  near  them. 

"In  estimating  the  radiating  surface,  it  should  be  borne  in 
mind  that  a  large  surface  at  a  comparatively  low  temperature 
gives  a  much  pleasanter  atmosphere  than  a  small  surface  at  a 
high  temperature. 

"Excess  of  surface  is  no  discomfort,  as  is  the  case  with  steam, 
since  the  temperature  can  easily  be  controlled  by  varying  the 
fire  or  by  valve  on  radiator. 

"All  flow  and  return  pipes  in  cellar  should  be  properly  covered 
with  hair-felt  or  some  other  good  non-conducting  material,  to 
obtain  the  best  and  most  economical  results.  Doing  this  will 
save  one  sixth  of  the  heat.  If  no  covering  is  used,  paint  all  ex- 
posed pipes  in  basement  a  black  or  maroon  japan.  The  heater 
should  be  neatly  plastered  with  plastic  asbestos." 

Indirect  Radiation. — Every  large  residence  heated, 
either  by  hot-water  or  steam  radiation,  should  have  at  least 
two  indirect  radiators,  to  provide  for  some  ventilation.  These 
should  be  placed  in  the  cellar  and  connected  with  registers  in 
the  front  hall  and  principal  living-room.  The  common  method  of 
providing  for  indirect  radiation  is  explained  on  pp.  1129  and  1130. 

Direct  radiation,  as  has  been  explained  elsewhere,  simply 
heats  the  air  in  the  room  over  and  over,  and  not  only  does  not 
afford  any  ventilation,  but  tends  to  decrease  the  vitalizing 
qualities  of  the  air. 

Specification. 

The  following  may  serve  as  a  guide  in  specifying  hot-water 
heating  for  residences: 

SPECIFICATION  FOR  HOT-WATER  HEATING  APPARATUS  IN  RESI- 
DENCE FOR  JOHN  JONES,  ESQ.,  BROOKLINE,  MASS. 

This  specification  contemplates  a  complete  two-pipe  circu- 
lating S3^stem,  guaranteed  perfect  in  every  respect. 


SPECIFICATIONS  FOR  HOT-WATER  APPARATUS.    1189 

Heater. — Furnish  and  set  up  in  cellar  where  shown  on  plan 
one  No.  (55  Ideal  portable)  water-boiler,  guaranteed  free  from 
all  flaws  and  defects. 

The  heater  to  set  on  a  substantial  foundation  of  hard  brick 
laid  in  cement  mortar  and  put  in  by  the  heating  contractor. 

Furnish  and  deliver  one  set  of  fire  tools,  consisting  of  one 
poker,  one  slice-bar,  and  one  fine  brush  and  handle. 

Smoke-pipe. — Connect  the  boiler  to  the  chimney  by  means 
of  smoke-pipe  made  of  No.  20  galvanized  iron,  the  diameter  of 
the  pipe  to  be  equal  to  the  outlet  on  the  heater. 

Trimmings. — The  boiler  to  be  provided  with  one  expansion 
thermometer  registering  from  80°  F.  to  250°  F.  Attach  to 
main  flow  pipe,  near  the  boiler,  one  Standard  altitude  gauge.* 

Water  Connections  and  Blow-off. — Feed-water  with  its  supply 
pipe  will  be  brought  within  6  ft.  of  the  boiler  by  the  plumber 
and  left  with  one  f-inch  cast-iron  fitting  for  boiler  con- 
nection, which  is  to  be  made  by  this  contractor,  with  suitable 
cock. 

Draw-off  cock  to  be  placed  on  lowest  point  of  system  and 
to  be  fitted  for  hose-nipple  attachment. 

Pipes. — Furnish  and  run  all  necessary  flow  and  return  pipes 
of  ample  size,  connecting  them  to  radiators  with  pipes  of  ample 
size'to  insure  the  free  and  rapid  flow  of  hot  water  to  the  radiators 
and  easy  flow  of  the  cooler  water  back  to  the  heater. 

All  connections  from  risers  to  radiators  to  be  made  below 
floors. 

Quality  of  Materials. — All  materials  used  in  the  construction 
of  this  apparatus  are  to  be  the  best  of  their  respective  kinds, 
all  fittings  to  be  heavily  beaded  and  made  of  the  best  gray  iron 
with  clean-cut  threads,  and,  when  practicable,  Y's  and  45°  L's 
are  to  be  used. 

Reaming. — The  ends  of  all  pipes  used  in  the  construction 
of  this  apparatus  are  to  be  reamed  out  and  all  obstructions 
removed  before  pipes  are  placed  in  position. 

All  flow  and  return  pipes  in  basement  to  be  supported  by 
neat,  strong,  adjustable  hangers,  arranged  to  suit  expansion 
and  contraction,  and  properly  secured  to  timbers  overhead. 

At  all  points  where  pipes  pass  through  ceilings,  floors,  or 
partitions,  the  pipes  shall  be  encased  in  iron  or  tin  tubes  and 
the  holes  protected  with  floor  or  ceiling  plates. 

Expansion  Tank. — The  expansion  tank  to  be  made  of  No.  22 
galvanized  iron,  30  ins.  high  and  14  ins.  in  diameter,  and  is  to 
be  furnished  with  a  proper  gauge-glass  with  brass  mountings 
complete.  It  is  to  be  placed  above  all  the  radiators  in  some 
suitable  place  and  supported  on  a  proper  shelf.  From  this 
tank  an  overflow  pipe  will  be  run  to  basement  or  other  suitable 
place  with  a  vent  pipe  through  the  roof. 

*  An  altitude  gauge  indicates  the  amount  of  water  in  the  system  and 
is  a  convenient  attachment  which  avoids  the  necessity  of  consulting  the 
gauge-glass  in  the  tank.  It  can  be  dispensed  with  if  desired. 


1190  RESIDENCE   HEATING. 

Radiators. — Furnish  and  set  up  the  following  radiators,  viz.: 


No.  of  Radiators. 

Square  Feet  of 
Radiating 
Surface. 

Main  hall.  .  .    . 

1  indirect  radiator 
1       " 
1  direct  radiator 
1 
1 
1 
1 
1 
1 

108  s( 
120 
40 
60 
40 
44 
36 
32 
32 

v\ 

t. 

Sitting-room  

Library.  .  . 

Dining-room   . 

Sitting-room  chamber  
Library  chamber  

Dining-room  chamber  
Kitchen  chamber  

Bathroom  

9  radiators 

512  sq.  ft. 

In  all  284  sq.  ft.  of  direct  surface  and  22S  sq.  ft.  of  indirect; 
total  surface,  512  sq.  ft. 

The  direct  radiators  to  be  (American  Radiator  Co.'s  Rococo 
hot-water  pattern)  38  ins.  high. 

Air-valves. — Each  radiator  will  have  properly  connected  to 
it  a  nickel-plated  air- valve  to  be  opened  and  closed  with  a  key. 

Radiator  Valves. — All  direct  radiators  will  be  promptly  con- 
nected to  the  system  of  piping  with  a  (Gurney)  quick-opening 
nickel-plated  radiator  valve  and  union  elbow. 

Indirect  Radiation. — The  indirect  radiators  shall  consist  of 
two  stacks  of  the  (American  Radiator  Co.'s  Excelsior  hot-water 
radiator)  connected  together  with  tight  joints  and  firmly  sus- 
pended from  the  basement  ceiling  by  suitable  wrought-iron 
hangers. 

The  stacks  shall  be  so  piped  and  hung  as  to  permit  a  quick, 
noiseless,  and  constant  flow  throughout  of  the  heated  water. 

Each  stack  to  be  enclosed  in  galvanized  iron  chamber  with 
proper  inlet  for  fresh  air  and  a  corresponding  outlet  for  warm 
air,  connected  by  a  galvanized  pipe  to  the  register  in  the  room 
which  the  stack  is  intended  to  heat. 

The  registers  to  be  of  the  Tuttle  &  Bailey  pattern,  electro 
bronzed  plated,  and  of  the  following  sizes:  hall,  12X19;  sitting- 
room,  14X22. 

To  have  floor  borders  and  to  be  set  in  a  register  box.  The 
pipe  connecting  the  stack  and  register  is  to  be  so  arranged  that 
all  fresh  air  coming  in  will  be  properly  heated  and  conveyed 
without  loss  to  its  destination.  In  arranging  indirect  boxes, 
care  is  to  be  exercised  in  getting  ample  space  for  cold  air  under 
the  stack,  and  a  corresponding  space  for  warm  air  over  the 
stack;  unless  otherwise  specified,  this  space  is  not  to  be  less 
than  12  ins.  above  and  10  ins.  below  the  stack. 

Covering  of  Pipe. — All  flow  and  return  pipe  and  fittings  in 
cellar  above  the  floor  to  be  properly  covered  with  1-inch  hair- 


STEAM  HEATING  FOR  RESIDENCES.         1191 

felt  neatly  sewed  up  in  canvas  and  painted  one  coat  of  good 
white  lead,  or  to  be  covered  with  asbestos  or  magnesia  sec- 
tional covering  with  canvas  cover  and  secured  by  brass  lac- 
quered bands. 

Boiler  Covering. — Cover  all  exposed  parts  of  boiler,  except 
the  front,  with  plastic  asbestos  (H)  inches  thick,  neatly  applied 
and  trowelled  smooth. 

Workmanship. — All  work  to  be  done  in  a  neat,  substantial, 
and  workmanlike  manner,  and  the  apparatus,  when  completed, 
to  be  thoroughly  tested  and  left  in  good  working  order. 

Guarantee. — The  contractor  is  to  guarantee  that  the  apparatus, 
when  completed  in  accordance  with  this  specification,  will  be 
of  ample  capacity  to  evenly  maintain  a  temperature  of  70°  F. 
in  the  rooms  in  which  radiators  are  located  when  the  outside 
temperature  is  at  zero,  and  that  the  apparatus  throughout 
will  have  a  free  and  rapid  circulation  when  in  operation. 

Steam  Heating1  for  Residences. 

Although  hot  water  is  perhaps  more  popular  just  now  for  resi- 
dence heating,  there  can  be  no  question  that  a  building  can  be  as 
thoroughly  warmed  and  ventilated  by  steam  as  by  any  other 
system,  and  generally  at  a  smaller  first  cost.  In  very  cold  weather, 
it  is  doubtful  if  hot-water  heating  is  as  satisfactory  as  steam. 

For  indirect  radiation,  steam  heat  is  generally  considered 
cheaper  than  hot- water  heat,  and  in  every  way  as  satisfactory. 

For  very  large  residences,  the  author  would  recommend  steam 
heat,  all  of  the  principal  rooms  to  be  heated  by  indirect  radia- 
tion, and  only  the  bathroom,  halls,  and  perhaps  the  attic  and 
one  or  two  rooms  on  the  north  side,  which  generally  includes 
the  dining-room,  by  direct  radiation.  For  dining-rooms  a 
special  direct  radiator,  containing  a  warming  closet,  is  made. 

The  air-supply  to  the  indirect  stacks  should  be  very  large 
arid  provided  with  a  damper,  so  that  the  supply  may  be  regu- 
lated according  to  the  weather. 

The  same  principles  apply  in  heating  a  residence  by  steam 
as  in  heating  any  other  building,  and  there  is  no  difference  in 
the  piping  and  radiators.  The  boilers  used  in  residence  heating, 
however,  are  generally  of  the  cast-iron  sectional  type  described 
on  pp.  1141  to  1144. 

The  single-pipe  system  is  commonly  used  in  dwellings,  all 
indirect  radiators,  however,  being  connected  with  a  return 
pipe  dropped  below  the  water-line.  Two  specifications  are 
appended  for  steam  heating,  one  for  all  direct  radiation  and 
one  for  all  indirect  radiation;  the  latter  can  be  easily  amended 
to  provide  for  some  direct  radiation. 


1192  RESIDENCE  HEATING. 


Typical  Specification. 

FOR  A  FIRST-CLASS  LOW-PRESSURE  STEAM-HEATING  APPARATUS 
FOR  HEATING  BY  ALL  DIRECT  RADIATION. 

Intention. — This  specification  is  intended  to  cover  everything 
necessary  to  fully  finish  and  install  in  the  above-mentioned 
building  a  complete  steam-heating  system  in  strict  accordance 
with  the  plans  and  this  specification,  as  prepared  by  T.  Square, 
architect. 

Plans. — The  plans  herewith  are  intended  to  show  only  the 
location  of  the  boiler,  piping,  and  radiators;  the  arrangement 
of  the  piping  will  be  left  largely  to  the  contractor,  subject  to 
the  approval  of  the  architect. 

General  Requirement. — This  contractor  is  to  provide  all 
necessary  tools  and  appliances  for  the  erection  and  completion 
of  the  work,  and  when  completed  must  remove  all  apparatus, 
refuse,  and  debris  from  the  building  and  grounds,  leaving  the 
work  in  a  clean,  uninjured,  and  perfect  condition.  No  cutting 
of  any  description  tending  to  weaken  the  building  structurally 
ihall  be  undertaken  without  consulting  the  architects. 

This  contractor  shall  be  fully  responsible  for  the  safety  and 
good  condition  of  the  work  and  material  embraced  in  this  con- 
tract until  the  completion  and  acceptance  of  the  same. 

All  work  must  be  of  the  best  quality,  and  should  at  any 
time  improper,  imperfect,  or  unsound  material  or  faulty  work- 
manship be  observed,  whether  before  or  after  same  has  been 
built  into  the  structure,  this  contractor  shall,  upon  notice  from 
the  architect,  remove  same  and  good  and  proper  material  and 
workmanship  be  substituted  without  delay  in  place  thereof, 
in  default  of  which  the  architect  will  effect  same  by  other  means 
as  may  be  deemed  best,  and  shall  deduct  the  cost  of  such  altera- 
tions from  the  sum  due  the  contractor  under  this  contract. 

System. — The  heating  to  be  effected  by  direct  radiation  dis- 
tributed throughout  as  shown  on  plans,  and  the  circulation 
of  the  steam  shall  be  by  the  one-pipe  basement  system. 

Boiler. — This  contractor  is  to  build  foundation  for  boiler, 
where  shown,  12"  deep,  of  common  hard  brick  laid  in  cement 
mortar.  Leave  ash-pit  for  boiler  of  proper  size,  12"  deep, 
cemented,  and  made  water-tight.  Furnish  and  set  up  one 
( —  Ideal  C.  I.  sectional)  boiler,  provided  with  6"  low-pressure 
brass-cased  steam-gauge,  water-gauge,  and  glass,  gauge-cocks, 
ombination  column,  safety-  and  blow-off  valves,  and  all  other 
usual  and  necessary  trimmings  to  complete  the  boiler,*  and 
full  set  of  fire  tools,  consisting  of  one  slicirig-bar,  one  hoe,  one 
poker,  and  a  cleaning  brush.  Cover  boiler  with  1J"  of  asbestos 
cement,  neatly  trowelled  to  a  smooth  finish. 

Water  Feed. — -The   plumber  will  bring   the  water-supply   to 

*  For  house-heating  plants  it  is  well  to  specify  also  "  one  automatic 
damper  regulator  of  approved  pattern,  with  connection  for  operating 
draught  door  and  cold-air  check." 


SPECIFICATIONS:  STEAM-HEATING  APPARATUS.   1193 

within  6  ft.  of  boiler,  and  this  contractor  is  to  make  connection 
with  boiler  with  f "  iron  pipe,  stop-cock,  and  check- valve. 

Catch-basin. — Furnish  and  set  one  cast-iron  catch-basin, 
2S"X36",  where  shown  on  plans.  Connect  the  boiler  blow-off 
pipe  to  catch-basin,  connect  same  to  sewer,  and  vent  with  1 J" 
pipe  to  roof.  (Note.  Catch-basins  are  usually  omitted  in 
house  heating,  a  hose  being  attached  to  the  blow-off  valve  for 
blowing  off.) 

Smoke-pipe. — Connect  the  boiler  with  the  chimney  with  a 
round  smoke-pipe  made  of  No.  16  black  iron  with  suitable 
balance  damper.  This  connection  to  be  of  same  size  as  left 
for  this  purpose  by  maker  of  boiler. 

Main  Pipes  and  Risers. — The  main  steam-pipe  is  to  be  of 
ample  size  to  carry  all  the  risers  and  radiators  attached  to 
the  system,  and  is  to  be  so  graded  that  all  water  of  condensa- 
tion will  flow  freely  back  to  the  boiler  without  noise.  From 
the  top  of  this  main  the  various  branches  are  to  be  taken  to 
radiators  and  risers,  the  connections  for  which  are  to  be  so  made 
that  no  traps  are  formed,  and  when  horizontal  runs  occur 
they  are  to  have  a  relief  pipe  to  carry  off  all  water  of  conden- 
sation. 

Eccentric  fittings  only  to  be  used  on  heating  mains  where 
reduced  in  size. 

Sizes  of  supplies  to  radiators  to  be  V  to  24  sq.  ft.,  \\"  to 
60  sq.  ft.,  and  1J"  to  all  above.  Radiators  on  first  floor  to 
be  connected  direct  to  steam  main. 

All  horizontal  pipes  to  be  one  size  larger  than  the  vertical 
pipes. 

All  steam  connections  from  heating  main  to  radiators  and 
risers  to  run  on  a  45°  angle  from  heating  main  and  to  be  one 
size  larger  than  risers  and  radiator  feeds. 

Pipe  and  Fittings. — All  pipe  used  throughout  shall  be  of 
the  best  quality  wrought-iroii  pipe  of  standard  weight  and 
thickness,  smooth  inside,  free  from  imperfections,  and  true 
to  shape.  All  threads  to  be  clean-cut,  straight,  and  true. 
All  fittings  to  be  of 'the  best  heavy  gray  iron,  with  taper  threads 
and  heavy  beaded.  No  inferior  pipe  or  fittings  will  be  allowed. 

All  couplings  used  must  be  of  the  best  make,  with  recessed 
ends,  except  reducers,  which  are  to  be  offset. 

Supports. — All  piping  to  be  supported  by  approved  expan- 
sion hangers  or  rollers  not  to  exceed  10  ft.  apart.  Use  neat 
cast-iron  floor  and  ceiling  plates  where  pipes  pass  through 
floors,  ceilings,  and  partitions. 

Radiators. — Furnish  direct  radiation  to  the  amount  as  enu- 
merated on  plans  of  the  American  Radiator  Co.'s  make  or  equal, 
all  38"  radiators  to  be  the  (Perfection)  pattern.  All  radiators 
14"  high  to  be  "^Etna  flue." 

Radiator  Valves. — The  radiators  are  to  be  furnished  with 
Jenkins  disc  union  valves  of  the  best  metal  nickel-plated  and 
have  hard- wood  handles. 

Valves. — All  valves  2"  and  under  to  have  brass  bodies  and 
iron  wheels,  over  2"  to  be  heavy  cast  iron  with  brass  stem  and 


1194  RESIDENCE  HEATING. 

trimmings  and  iron  wheels;  all  valves  4"  and  over  to  have 
heavy  yokes.  All  gate-valves  to  be  of  (Crane  Co.'s)  make 
or  equal. 

Air-valves.— Each  radiator  throughout  the  entire  building 
shall  be  furnished  with  a  Marsh  automatic  air-valve. 

Painting  and  Bronzing. — All  radiators  and  exposed  pipes 
in  rooms  or  halls  are  to  be  neatly  painted  two  coats  best 
radiator  enamel  or  bronzed  in  desired  colors. 

Finally. — When  completed,  test  the  apparatus  to  20  Ibs. 
pressure  and  make  tight  at  that  pressure,  said  test  to  be  con- 
ducted under  the  supervision  of  the  architect.  Fuel  for  the 
test  to  be  furnished  by  the  owner,  and  when  accepted  the 
apparatus  is  to  be  turned  over  to  the  owner  in  complete  working 
order. 

All  valves  and  stuffing-boxes  to  be  properly  packed  and  the 
plant  to  be  completed  in  all  its  parts,  it  being  understood 
that  this  contractor  is  to  furnish  all  miscellaneous  material, 
tools,  labor,  etc.,  necessary  to  complete  the  work  in  a  first- 
class  and  workmanlike  manner. 

Guarantee. — This  contractor  shall  guarantee  that  when  the 
apparatus  is  completed  in  accordance  with  these  specifications 
and  drawings  it  will  be  free  from  all  mechanical  defects  and 
of  ample  capacity  to  heat  all  rooms  where  radiation  is  placed 
to  a  temperature  of  70°  when  the  outside  temperature  is  10° 
below  zero. 


Typical  Specincatione 

FOR  A  SUPERIOR  LOW-PRESSURE  STEAM-HEATING  APPARATUS 
FOR  HEATING  BY  THE  INDIRECT  SYSTEM,  WITH  A  STEAM 
PRESSURE  OF  FROM  ONE  TO  FIVE  POUNDS  PER  SQUARE  INCH. 

[NOTE.  —  This  specification  should  be  accompanied  by  a  heating  plan 
showing  the  position  of  all  indirect  radiation  stacks  in  the  basement,  the 
cold-air  inlets  to  the  same,  and  the  size  and  general  position  of  the  main 
steam  and  return  pipes  and  the  connections  to  the  radiators. 

The  return  main  should  be  placed  at  or  below  the  floor  and  the  steam 
main  close  under  the  ceiling. 

The  size  and  location  of  warm-air  registers  should  be  shown  on  the  gen- 
eral floor  plans.] 

General  Requirements. — Boiler,  trimmings,  and  smoke  and 
feed  connection  same  as  in  preceding  specification. 

System  of  Piping. — The  system  of  piping  throughout  will  be 
constructed  on  the  double-pipe  "gravity  return"  plan,  and 
all  pipes  erected  will  be  of  ample  size  to  insure  the  active  delivery 
of  dry  steam  to  the  radiators  and  easy  flow  of  the  water  of 
condensation  back  to  the  boiler. 

Furnish  and  erect  all  «upply  and  steam  mains  and  branch 
connecting  pipes  of  the  sizes  and  located  in  the  relative  posi- 
tions shown  on  the  plans.  All  piping  to  be  graded  and  properly 
dripped  and  the  steam  mains  to  be  hung  in  position  by  means 
of  expansion  pipe-hangers. 


SPECIFICATIONS:  INDIRECT  STEAM  HEATING.     1195 

The  main  return  to  be  run  at  or  under  basement  floor  and 
protected  from  moisture.* 

Pipe  Covering. — All  pipes  in  the  cellar  above  the  floor  to  be 
covered  with  asbestos  (or  magnesia)  sectional  covering  with 
canvas  cover  and  secured  by  brass  lacquered  bands. 

Stack  Boxes  and  Flws. — The  heating  of  the  several  apart- 
ments will  be  accomplished  by  means  of  indirect  radiators 
set  in  clusters  of  "stacks/'  each  hung  from  the  ceiling  of  the 
cellar,  and  the  heat  from  these  "stacks"  will  be  conveyed  to 
the  room  to  be  heated  by  means  of  tin  hot-air  pipes  set  in  the 
walls  and  leading  from  stack  to  the  room  to  be  heated;  each 
room  heated  to  have  an  independent  "stack"  and  to  be  con- 
nected therewith  by  an  independent  tin  hot-air  pipe.  Each 
of  the  "stacks"  of  indirect  radiators  to  be  enclosed  in  a  well- 
made  box  or  galvanizd  iron  chamber  and  from  each  "stack" 
a  galvanized-iron  duct  of  proper  size  is  to  lead  to  the  opening 
in  outside  wall  provided  for  the  same.  Place  a  damper  in  the 
cold-air  duct  and  a  tight  door  in  the  stack  casing  below  the 
radiator. 

The  radiators  shall  be  hung  and  the  chambers  made  so  that 
there  shall  be  a  space  of  not  less  than  (12)  ins.  above  and  (10) 
ins.  below  the  stack,  and  the  cold-air  duct  shall  connect  with 
the  bottom  of  the  chamber,  at  a  point  farthest  from  the  warm- 
air  outlet. 

Radiators. — Furnish  and  erect  in  cellar,  in  the  positions  as 
shown  on  plans,  ten  "stacks"  of  approved  pattern  indirect 
radiators  that  in  the  aggregate  will  contain  not  less  than  (732) 
sq.  ft.  of  radiating  surface,  and  divided  up  for  the  several  rooms 
to  be  heated  as  follows,  viz.: 

First  Story: 

Hall 1  "stack"  to  contain  108  sq.  ft. 

Parlor 1         "        "        "          96    "" 

Dining-room 1         "         "         "        108    "" 

Library 1         "         "         "          96    "    " 

Rear  hall 1         "         "        "          48    "    " 

Second  Story: 

Chamber  over  parlor 1  "stack"  to  contain    72  sq.  st, 

Chamber  over  dining-room   .1         "         "         "          72    "     " 

Chamber  over  library 1         "         "         "          72    "     " 

Hall  bedroom 1         "         "        "         36    "" 

Bathroom 1         "  24    "    " 

No  valves  are  to  be  placed  in  either  the  supply  or  return  to 
radiating  stack,  but  an  improved  automatic  air- valve  must 
be  placed  on  each  stack. 

Pipe  Covering. — All  cellar  pipes  to  be  neatly  covered  with 
asbestos  sheathing,  then  1-inch  thick  hair-felt  and  canvas 
casing  sewed  on. 

*  In  damp  situations  the  return  pipes,  when  necessary  to  drop  below 
floor,  should  be  run  in  brick  ducts  laid  in  cement  mortar  and  the  pipe 
packed  with  mineral  wool  or  asbestos. 


1196  RESIDENCE  HEATING. 

Registers. — Furnish  and  set  in  position  in  each  room  heated 
a  vertical  wheel  register  of  the  size  shown  on  plans.  All  registers 
for  first  story  to  be  bronze  finish,  and  all  others  to  be  black  or 
white  japanned  finish,  as  shall  be  selected. 

Tin  and  Galvanized-iron  Work. — Furnish  to  builder  (and 
by  him  to  be  set  in  position  as  shown  on  plans)  all  tin  wall  pipes 
and  register  boxes  for  hot  air  to  the  rooms  to  be  heated,  all 
to  b*e  made  of  IX  tin  and  of  the  sizes  shown  on  plan. 

Furnish  and  erect  the  galvanized-iron  casings  for  the  ten 
stacks  as  above  specified,  with  galvanized-iron  ducts  to  the 
outside  openings,  to  be  constructed  in  a  substantial  and  work- 
manlike manner. 

Guarantee. — The  contractor  is  to  guarantee  that  the  apparatus 
when  completed  will  be  of  ample  capacity  to  maintain  an  even 
temperature  of  70°  F.  in  the  rooms  heated  when  the  outside 
temperature  is  zero,  and  that  the  apparatus  will  afford  free 
circulation  throughout  and  be  noiseless  in  operation. 

Books  on  Residence  Heating. — Much  valuable  infor- 
mation on  residence  heating  may  be  obtained  from  pamphlets 
published  by  different  manufacturers,  among  whom  are  the 
American  Radiator  Co.,  the  International  Heater  Co.,  the 
Gurney  Heater  Manufacturing  Co.,  Gorton  &  Lidgerwood  Co., 
Isaac  A.  Sheppard  &  Co.,  and  the  Excelsior  Steel  Furnace  Co., 
of  Chicago.  The  latter  company  publish  a  very  complete  book 
on  furnace  heating  and  furnace  fittings  which  every  architect 
should  have. 


DATA  FOR  HOT-AIR  STACKS. 


1197 


TABLES. 

The  following  tables  will  be  found  useful  in  estimating  the 
size  of  registers,  piping,  and  heating  surface  ci  p'pes  and  boiler 

tubes: 


TABLE  OF  SIZES  AND  DIMENSIONS  OF  SAFETY  DOUBLE 
HOT-AIR  STACKS 

Made  by  the  Excelsior  Steel  Furnace  Company. 


wg 


35 
43 

48 
53 
63 
71 
87 
102 
119 
186 
264 
330 


o 

*OjD 
02 


6X  8 
8X10 
8X12 
9X12 
10X12 
10X14 
12X15 
12X17 
14X20 
16X24 
20X24 
21X29 


500 
850 
1000 
1250 
1650 
2000 
2300 
2600 
3000 
4000 
5400 
7000 


'I® 
W 


6X  8 
8X10 
9X11 
10X12* 
12X14 
12X17 
14X17 
15X18 
15X20 
20X20 
20X27 
20X35 


35 

45 

55 

60 

70 

80 

115 

120 

156 

210 

270 

34Q 


1198 


DIMENSIONS  OF  REGISTERS. 


DIMENSIONS  OF  REGISTERS  AND  BORDERS.* 

Made  by  the  Tuttle  &  Bailey  Manufacturing  Co. 


Size  of 
Body. 

Register. 

Border. 

Extreme 
Dimensions. 

Depth 
Open. 

With  Ribs. 
Floor  Opening. 

Tin-box  Size. 

4X    6 

5f   X   7| 

If 

4X   8 

5i   X   9i 

2i 

4X10 

6i    X1H 

2i 

4X13 

5i    X14J 

2J 

4X15 

5i   X16% 

2J 

4X18 

5i   Xl9i 

2i 

5X   8 

6|    X   9| 

2 

8J   X  Ill- 

5%X   8¥6 

5X11 

fX12| 

2 

Si   Xl4i 

5JKx*ijZ 

5X13 

X14| 

2 

8}   X16J 

5^X13% 

5X16 

X17I 

2 

8J   X19J 

5%X16% 

6X   6 

7%X   7% 

2f 

9%X  9% 

6%X   6% 

6X   8 

7%X   9% 

2a 

9%XH% 

6%X   8% 

6X  9 

7%X10% 

2§ 

9%X12% 

6%X   9% 

6X10 

7%X11% 

2| 

9%X13% 

6%X10% 

6X14 

7%X15% 

2| 

9%X17% 

6%X14% 

6X16 

7%X17% 

2| 

9%X19% 

6%  XI  6% 

6X18 

7%X19% 

21 

9%X21% 

6%X18% 

6X24 

7%X25% 

2f 

9^X27% 

6%X24% 

7X   7 

8%X   8% 

2| 

10^X10% 

7%X   7% 

7X10 

8%X11% 

2| 

10^X13% 

7%X10% 

8X   8f 

9f   X  9| 

3 

11}   Xll} 

8f   X   8f 

8X10 

9J   Xllf 

3 

11}   X13} 

8f   XlOf 

8Xl2f 

9f   X13J 

3 

11}   X15} 

8f   X12| 

8X15 

9f   X16% 

3 

11}   X18} 

8f   Xl5f 

8X18 

9f   X19| 

3 

11}   X21} 

8f   Xl8f 

8X21 

9f    X22f 

3 

11}   X24} 

8f   X21f 

8X24 

9f    X25f 

3 

11}   X27} 

8f   X24f 

9X   9 

10}   X10} 

3t 

13^X13^ 

9%X   9% 

9xl2f 

10}   X13} 

3i 

13Y6X16X6 

9^X12% 

9X13 

11      X15 

3i 

13^X17^6 

9%X13% 

9Xl4f 

10}   X15} 

3i 

13^X18^ 

9%X14% 

9X16 

101-   X17% 

31 

13^X20^6 

9%X16% 

9X18 

10}   X19J 

Bi 

13;%  X  22  Ye 

9%X18% 

9X20 

10}   X21} 

3i 

13^X24^6 

9%X20% 

10X10 

n%xn% 

3| 

14^6  X  14% 

io%xio% 

10X12 

n%xi3% 

3f 

14^X16^ 

10%X12% 

10X14 

12     XI  5% 

3f 

14^X18% 

10%X14% 

10X16 

11%X17J 

3| 

14^X20% 

10%X16% 

10X1S 

11%X19} 

3f 

14^X22% 

10%X18% 

10X20 

H%X2l| 

3| 

14^X24% 

10%X20% 

12X12 

14^X14^ 

4 

16Y6X16Y6 

12%X12% 

12X14 

14Y6X16^6 

4 

16^X18% 

12%X14% 

12X15 

13%X16% 

4 

16.%  X  19^6 

12%X15% 

*  For  special  side- wall  registers,  see  p.  1201. 

t  These  sizes  are  those  most  likely  to  be  found  in  stock  of  local  dealers. 


DIMENSIONS  OF  REGISTERS.  1199 

DIMENSIONS  OF  REGISTERS  AND  BORDERS.— Cont. 


Register. 


Extreme 
Dimensions. 


Depth 
Open. 


Border. 


With  Ribs. 
Floor  Opening. 


Tin-box  Size. 


14^6  X 18 

14)6X19 

14^X20^6 

14Y6  X  21)6 

143/6X22 

14^X26 

14)6X32 

14)6X38 


16f    X24J 


18%X20% 
18^6  X  22% 
18%X24% 


18%X34% 
20%X20% 
20%X23% 
20%X26% 


20^6  X32i 


22f    X22| 
22f    X26f 


23f   X31f 
26^X26% 
26)6 X 29 J 


26)6  X34f 

26)6  X38f 


29%X29% 
29)6X401 
32f   X32| 
32f   X38| 
32f   X44§ 


4i 
4f 


4f 
4f 


51 
51 


5! 

6 

a 

7f 


16^X20% 


16^X22% 
16^X23^ 
16)6X24)6 
16^X28% 


.18^X20% 
18^X26% 


20 J  X20J 

20 J  X22J 

20 J  X24J 

20 J  X26J 

20 J  X28J 

20 J-  X32J 

20 J  X36| 


22%  X  2*% 


22%X40% 
25|   X25J 
25i   X29J 
25^   X31J 
26J 


14J-  X18J 

14|  X22| 

16} 
16f 

16}  X20| 

16f  X22| 

16f  X28J 

16}  X32| 

18}  X18| 

18}  X21J 


18  J 


24^X30% 


*  These  sizes  are  those  most  likely  to  be  found  in  stock  of  local  dealers. 


1200      CAPACll/  OP  PIPES  AND  REGISTERS. 


ESTIMATED  CAPACITY  OF  PIPES  AND  REGISTERS. 

ROUND    PIPES. 


Diameter 
of  Pipe. 

Area  in 
Sq.  Inches. 

Diameter 
of  Pipe. 

Area  in 
Sq.  Inches. 

Diameter 
of  Pipe. 

Area  in 
Sq.  Inches. 

7  inches 
8      " 
9      " 

10      ** 
11       " 

38 
50 
63 

78 
95 

12  inches 
14       " 
16       " 
18       " 
20 

113 
154 
201 
254 
314 

22  inches 

24       " 
26       " 
28       " 
30 

380 
452 
531 
616 

707 

RECTANGULAR    PIPES. 

Size 

Area  in 

Size 

Area  in 

Size 

Area  in 

of  Pipe. 

Sq.  Inches. 

of  Pipe. 

Sq.  Inches. 

of  Pipe. 

Sq.  Inches. 

4X8 

32 

8X20 

160 

12X18 

216 

4X10 

40 

8X24 

192 

12X20 

240 

4X12 

48 

10X12 

120 

12X24 

288 

4X16 

64 

10X15 

150 

14X14 

196 

6X10 

60 

10X16 

160 

14X16 

224 

6X12 

72 

10X18 

180 

14X20 

280 

6-X16 

96 

10X20 

200 

16X16 

256 

8*X10 

80 

12X12 

144 

16X18 

288 

8X12 

96 

12X15 

180 

16X20 

320 

8X16 

128 

12X16 

192 

16X24 

384 

REGISTERS. 


Size  a  of 
Opening. 

Capacity  in 
Sq.  Inches. 

Size  of 
Opening. 

Capacity  in 
Sq.  Inches. 

Size  of 
Opening. 

Capacity  in 
Sq.  Inches. 

6X10 
8X10 
8X12 
8X15 
9X12 
9X14 
10X12 

40 
53 
64 

80 

72 
84 
80 

10X14 
10X16 
12X15 
12X19 
14X22 
15X25 
16X24 

93 

107 
120 
152 
205 
250 
256 

20  X  20 
20X24 
20X26 
21X29 
27X27 
27X38 
30X30 

267 
320 
347 
406 
486 
684 
600 

ROUND    REGISTERS. 


Size  of 
Opening. 

Capacity  in 
Sq.  Inches. 

Size  of 
Opening. 

Capacity  in 
.Sq.  Inches. 

Size  of 
Opening. 

Capacity  in 
Sq.  Inches. 

7  inches 
8      " 
9      " 
10 

26 
33 

42 
52 

12  inches 
14       " 
16       " 
18       " 

75 
103 
134 
169 

20  inches 
24       " 
30       " 
36       " 

209 
301 
471 
679 

SIZES  FOR  HOT-WATER  FLOW  PIPES.        1201 


T.  &  B.  SPECIAL  SIDE-WALL  REGISTERS  FOR  SHALLOW 
FLUES  AND  THIN  PARTITIONS  FOR  USE  IN  BASE- 
BOARDS. 

This  register  has  a  single  valve,  and  the  front  projects  2  inches  into  the 
room;  with  it  a  6"X13"  flue  can  be  used  with  3"  studding,  i.e.,  in  the 
first-story  rooms. 

SIZES    AND    CAPACITY. 


Register 

Tin  Flue. 

Round  Pipe. 

Net  Air 

List 
Size. 

Opening  in 
Register 
Face. 

Size. 

Capacity. 

Size. 

Capacity. 

Inches. 

Sq.  inches. 

Inches. 

Sq.  inches. 

Inches. 

Sq.  inches. 

7X10 

47 

4   X10 

40 

7 

38 

7X12 

56 

4   X12 

48 

8 

48 

8X13 

70 

5   X13 

65 

9 

63 

8X15 

80 

5   X15 

75 

10 

78 

10X13 

86 

6   X13 

78 

10 

78     >. 

8X17 

95 

5JX17 

93 

11 

95 

DIAMETER  OF  MAIN  AND  BRANCH  PIPES  AND  SQUARE 
FEET  OF  COIL  SURFACE  THEY  WILL  SUPPLY  IN 
AN  OPEN  HOT-WATER  APPARATUS  WHEN  COILS 
ARE  AT  DIFFERENT  ALTITUDES  FOR  DIRECT 
RADIATION  OR  IN  THE  LOWER  STORY  FOR  IN- 
DIRECT RADIATION.* 


« 

d 

.2* 

o 

^ 

"Sis 

Direct  Radiation. 

p 

ti 

Height  of  Coil  above  Bottom  of  Boiler,  in  Feet. 

S  " 

0 

10 

20 

30 

40 

50 

60 

70 

80 

100 

Sq.ft. 

Sq.ft. 

Sq.ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft 

Sq.  ft. 

M 

49 

50 

52 

53, 

55 

57 

59 

61 

63 

68 

1 

87 

89 

92 

95 

98 

101 

103 

108 

112 

121 

1M 

136 

140 

144 

149 

153 

158 

161 

169 

175 

189 

1M 

196 

202 

209 

214 

222 

228 

235 

243 

252 

271 

2 

349 

359 

370 

380 

393 

405 

413 

433 

449 

483 

2}^ 

546 

561 

577 

595 

613 

633 

643 

678 

701 

755 

3 

785 

807 

835 

856 

888 

912 

941 

974 

1,009 

1,086 

3^ 

1,069 

1,099 

1,132 

1,166 

1,202 

1,241 

1,283 

1,327 

1,374 

1,480 

4 

1  ,395 

1,436 

1,478 

1,520 

1,571 

1,621 

1,654 

1,733 

1,795 

1,933 

4V£ 

1,767 

1,817 

1,871 

1,927 

1,988 

2,052 

2,120 

2,193 

2,272 

2,445 

5 

2,185 

2,244 

2,309 

2,379 

2,454 

2,531 

2,574 

2,713 

2,805 

3,019 

6 

3,140 

3,228 

3,341 

3,424 

3,552 

3,648 

3,763 

3,897 

4,036 

4,344 

7 

4,276 

4,396 

4,528 

4.664 

4,808 

4,964 

5,132 

5,308 

5,496 

5,920 

8 

5,580 

5,744 

5,912 

6,080 

6,284 

6,484 

6,616 

6,932 

7,180 

7,735 

9 

7,068 

7,268 

7,484 

7,708 

7,952 

8,208 

8,482 

8,774 

9,088 

9,780 

10 

8,740 

8,976 

9,236 

9,516 

9,816 

10,124 

10;296 

10,852 

11,220 

12,076 

*  F.  Schumann,  C.E. 


1202 


SIZES  FOR  STEAM  MAINS. 


DIAMETER  OF  STEAM-SUPPLY  PIPES  AND  SQUARE 
FEET  OF  DIRECT  RADIATION  THEY  WILL  SUPPLY 
WITH  3  POUNDS  STEAM  PRESSURE.* 


Diam- 
eter of 
Pipe, 

Distance  of  Radiator  from  Boiler,  in  Feet. 

in 

Inches 

9 

64 

100 

225 

324 

400 

484 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

K 

240 

90 

72 

48 

40 

36 

32 

i 

491 

185 

148 

98 

82 

74 

68 

114 

863 

324 

259 

172 

144 

129 

118 

1% 

1,361 

510 

408 

272 

226 

204 

185 

2    • 

2,796 

1,049 

839 

559 

466 

419 

381 

2y2 

4,884 

1,831 

1,465 

977 

814 

732 

666 

3 

7,700 

2,887 

2,310 

1,540 

1,283 

1,155 

1,050 

3^ 

11,323 

4,246 

3,097 

2.264 

1,887 

1,698 

1  ,544 

4 

15,819 

5,932 

4,745 

3,164 

2,636 

2,372 

2,157 

4H 

21,226 

7,959 

6,368 

4,245 

3,537 

3,184 

2,894 

5 

27,997 

10,361 

8,289 

5,599 

4,666 

4,144 

3,768 

6 

44,230 

16,586 

13,269 

8,846 

7,372 

6,634 

6,031 

7 

64,013 

24,005 

19,204 

12,802 

10,668 

9,602 

8,729 

8 

89,615 

33,605 

26,884 

17,923 

14,936 

13,442 

12,220 

9 

120,275 

45,103 

36,082 

24,055 

20,046 

18,041 

16,401 

10 

156,277 

58,604 

46,883 

31,255 

26,046 

23,441 

21,310 

*  F.  Schumann,  C.E. 

USEFUL  MEMORANDA:    HOT-WATER  HEATING. 

MEASUREMENT    OF    FLOW   AND    RETURN    PIPES. 

For  the  purpose  of  ascertaining  the  amount  of  heating  surface 
in  flow,  return  pipes,  and  risers,  the  following  table  is  used. 


1 

Surface  of  Pipe  Cover- 
ing 24  Inch  Hair-felt 
and  Canvas. 

Table  of  Quantity  of 
Water  contained  in  100 
Lineal  Feet  of  Pipe  of 
Different  Diameters. 

Size  of 
Pipe. 

Square  Feet 
in  One  Lin- 
eal Foot. 

Size  of 
Pipe. 

Multiply 
Length  by 

Diameter 
of  Pipe. 

Contents  in 
100  Feet  in 
Length. 

Inches. 

Inches. 

Inches. 

Gallons. 

i 

.27 

1 

.79 

1 

4.50 

.34 

11 

.96 

H 

7.75 

H 

.43 

U 

1.04 

li 

10.59 

11 

.50 

2 

1.09 

2 

17.43 

2 

.62 

21 

1.20 

2} 

24.80 

2J 

.75 

3 

1.37 

3 

38.38 

3 

92 

3£ 

1.49 

3i 

51.36 

3J 

1.05 

4 

1.64 

4 

66.13 

4 

1.17 

EQUALIZATION   OF  PIPE  AREAS. 


1203 


To  obtain  the  surface,  multiply  length  of  pipe  by  figures  given 
in  the  table,  always  pointing  off  two  places. 

Example:   500  lineal  feet  1-inch  pipe  multiplied  by  .34  equals 
170  sq.  ft. 

EQUALIZATION  OF  PIPE  AREAS. 

(R.  C.  Carpenter.) 


Diam. 
of 
Pipes, 
Inches. 

Number  of  Small  Pipes  Required  to  Make  Area  Equivalent  to 
One  Larger  Pipe  with  Allowance  for  Friction. 

£ 

*A 
In. 

1 
In. 

\K 

In. 

1H 
In. 

2 
In. 

2H 

In. 

3 
In. 

&A 
In. 

4 
In. 

fA 
In. 

5 
In. 

,» 

¥ 
i" 

&A 
4 

VA 

5 

1 

2.0 
1 

3.7 
1.8 
1 

7.6 
3.7 
2.0 
1 

11.3 
5.4 
3.1 
1.5 
1 

19 
9.2 
5.1 
2.6 
1.7 
1 

37 
16.7 
9.3 
4.5 
3.1 
1.83 
1 

55 
25.5 
14.7 
7.3 
4.7 
2.9 
1.7 
1 

80 
39 
27 
10.6 
7.1 
4.1 
2.5 
1.5 
1 

108 
53 
30 
14.7 
9.8 
5.8 
3.5 
2.4 
1.4 
1 

146 
70 
39 
19.5 
13.4 
7.8 
4.7 
2.7 
1.8 
1.3 
1 

188 
90 
53 
25 
16.8 
9.9 
5.9 
3.5 
2.5 
1.7 
1.25 
1 

EQUALIZATION  OF  PIPE  AREAS. 

(Babcock  and  Wilcox.) 


Number  of  Smaller  Pipes  Equivalent  to  One  Larger  Pipe. 


g  B 

c3  o> 

S£ 

X 

In. 

1 
In. 

1H 

In. 

o 
In. 

3 
In. 

4 
In. 

5 
In. 

6 
In. 

7 
In. 

8 
In. 

9 
In. 

10 
In. 

? 
V 

VA 
3 
4 
5 
6 
7 
8 

2.27 
1 

4.88 
2.05 
1 

15.8 
6.9 
3.5 
1 

31.7 
14 
6.8 
1.3 
1 

96.9 
42.5 
20.9 
6.1 
3.1 
1.8 
1 

205 
90.4 
44.1 
13 
6.5 
3.87 
2.12 
1 

377 
166 
81.1 
23.8 
11.9 
7.1 
3.9 
1.8 
1 

620 
273 
133 
39.2 
19.6 
11.7 
6.4 
3 
1.6 
1 

918 
405 
198 
58.1 
29.0 
17.4 
9.5 
4.5 
2.4 
1.5 
1 

569 

278 
81.7 
40.8 
24.4 
13.3 
6.3 
3.4 
2.1 
1.4 
1 

779 
380 
112 
55.8 
33.4 
20.9 
8.6 
4.7 
2.8 
1.9 
1.3 

536 
157 
78.5 
47.0 
23.7 
12.1 
6.6 
4.0 
2.7 
1.9 

*  Nominal  diameters  standard  steam-  and  gas-pipes. 

EXAMPLE.- — To  find  number  of  2-inch  pipes  to  deliver  as  much  fluid  as 
one  5-inch  pipe:  In  column  headed  5,  and  opposite  2,  read  9.9  upper  table 
and  11.9  lower  table,  the  equivalent  number  of  2-inch  pipes. 


1204     DIMENSIONS,  ETC.,  OF  BOILER  TUBES. 


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DIMENSIONS,   ETC.,  OF  STEAM  PIPES.         1205 


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1206       DIMENSIONS,  ETC.,  OF   STEAM  PIPES. 


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SMOKE  PREVENTION. 


1207 


DIMENSIONS  OF  STANDARD  DOUBLE  EXTRA 
STRONG  PIPE. 


Nominal. 

Actual 
External 
Diameter. 

Actual 
Internal 
Diameter. 

Thickness. 

Metal 
Area. 

Nominal 
Weight 
per  Foot, 
Pounds. 

i 

.840 

.244 

.298 

.507 

1.7 

i 

1.050 

.422 

.314 

.726 

2.44 

1.315 

.587 

.364 

1.087 

3.65 

a 

1.660 

.885 

.388 

1.549 

5.2 

H 

1.900 

1.088 

.406 

1.905 

6.4 

2 

2.375 

1.491 

.442 

2.686 

9.02 

2* 

2.875 

1.755 

.560 

4.073 

13.68 

3 

3.500 

2.284 

.608 

5.524 

18.56 

3} 

4.000 

2.716 

.642 

6.772 

22.75 

4 

4.500 

3.136 

.682 

8.180 

27.48 

4J 

5.000 

3.564 

.718 

9.659 

32.53 

5 

5  563 

4.063 

.750 

11.341 

38.12 

6 

6.625 

4.875 

.875 

15.807 

53.11 

7 

7.625 

5.875 

.875 

18.555 

62.35 

8 

8.625 

6.875 

.875 

21.304 

71.62 

LAP-WELDED    CASING. 


8J 

8.625 

8.265 

.1?0 

4.775 

16.07 

81 

8.625 

8.167 

.229 

6.040 

20.10 

8i 

8.625 

8.082 

.271 

7.125 

24.38 

8f 

9 

8.640 

.180 

4.987 

17.60 

9f 

10 

9.577 

.211 

6.504 

21.90 

IQf 

11 

10  .  594 

.203 

6.886 

26.72 

III 

12 

11.594 

.203 

7.526 

30.35 

m 

13 

12.457 

.271 

10.852 

33.78 

13J 

14 

13.432 

.2S4 

12.24 

42.02 

14* 

15 

14.416 

.292 

13.49 

47.66 

16} 

16 

15.416 

.292 

14.41 

51.47 

Smoke  Prevention. 

Prof.  O.  H.  Landreth,  in  a  report  to  the  State  Board  of  Health 
of  Tennessee  (published  in  Engineering  News,  June  8,  1893, 
and  quoted  by  Kent,  p.  712)  classifies  the  great  number  of 
smoke-prevention  devices  which  had  been  invented  up  to  that 
date  as  follows. 

(a)  Mechanical  Stokers. — They  effect  a  material  saving 
in  the  labor  of  firing  and  are  efficient  smoke  preventers  when  not 
pushed  above  their  capacity  and  when  the  coal  do^s  not  cake 


1208  SMOKE  PREVENTION. 

badly.     They  are  rarely  susceptible  to  the  sudden  changes  in 
the  rate  of  firing  frequently  demanded  in  service. 

(b)  Air-flues    in    side    walls,    bridge-wall,   and    grate-bars 
through  which  air  when  passing  is  heated.     The   results  are 
always  beneficial,  but  the  flues  are  difficult  to  keep  clean  and  in 
order. 

(c)  Coking  Arches,  or  spaces  in  front  of  the  furnace  arched 
over  in  which  the  fresh  coal  is  coked,  both  to   prevent   cooling 
of  the  distilled  gases  and  to  force  them  to  pass  through  the 
hottest  part  of  the  furnace  just  beyond  the  arch      The  results 
are  good  for  normal  conditions,  but  ineffective  when  the  fires 
are  forced.     The  arches  also   are   burned  out   and    injured   by 
working  the  fire. 

(d)  Dead-plates,  or  a  portion  of  the  grate  next  the  furnace 
doors  reserved  for  warming  and  coking  the  coal  before  it  is 
spread  over  the  grate.     These  give  good  results  when  the  fur- 
nace is  not  forced  above  its  normal  capacity.     This   embodies 
the  method  of  " coke-firing"  mentioned  before. 

(e)  Down-draught  Furnaces,  or  furnaces  in  which  the 
air  is  supplied  to  the  coal  above  the  grate  and  the  products  of 
combustion  are  taken  away  from  beneath  the  grate,  thus  caus- 
ing a  downward  draught  through  the  coal,  carrying  the   dis- 
tilled gases  down  to  the  highly  heated  incandescent  coal  at  the 
bottom  of  the  layer  of  coal  on  the  grate.     This  is  the  most 
perfect    manner    of    producing  combustion  and    is    absolutely 
smokeless. 

(/)  Steam-jets  to  draw  air  in  or  inject  air  into  the  furnace 
above  the  grate,  and  also  to  mix  the  air  and  the  combustible 
gases  together.  A  very  efficient  smoke  preventer,  but  one 
liable  to  be  wasteful  of  fuel  by  inducing  too  rapid  a  draught. 

(g)  Baffle-plates  placed  in  the  furnace  above  the  fire  to 
aid  in  mixing  the  combustible  gases  with  the  air. 

(h)  Double  Furnaces,  of  which  there  are  two  different 
styles,  neither  of  which  have  proved  practical. 

Among  the  devices  which  seem  to  have  proven  both  prac- 
tical and  effective  are  those  of  the  Smoke  Prevention  Company 
of  America  and  of  the  American  Stoker  Company. 

Ventilation. 

Ventilation  as  applied  to  a  room  or  building  consists  in  supply- 
ing pure  air  to  dilute  and  drive  out  that  which  has  become 
vitiated. 


VENTILATION.  1209 

Perfect  ventilation  consists  in  supplying  an  adequate  amount 
of  fresh  air  warmed  or  cooled  to  a  comfortable  temperature 
in  such  a  manner  that  the  circulation  shall  be  constant  and 
thorough  in  all  parts  of  the  room  or  building  and  at  the  same 
time  without  the  creation  of  draughts. 

Ventilation  may  be  broadly  classified  as  Systematic  and  Non- 
systematic. 

Noil-systematic  Ventilation  may  be  considered  as  in- 
cluding all  ventilation  produced  without  systematic  provision 
for  the  admission  and  escape  of  the  fresh  air  and  power  for 
moving  the  air. 

All  rooms  in  a  building  of  ordinary  construction  receive 
some  ventilation  whenever  the  temperature  of  the  room  is 
above  or  below  that  of  the  surrounding  air. 

Pettenkofer  found  that  by  diffusion  through  the  walls  the 
air  of  a  room  in  his  house  containing  2,650  cu.  ft.  was  changed 
once  every  hour  when  the  difference  of  exterior  temperatures 
was  34°.  With  the  same  difference  of  temperature,  but  with 
the  addition  of  a  good  fire  in  a  stove,  the  change  rose  to  3,320 
cu.  ft.  per  hour.  With  all  the  crevices  and  openings  about 
doors  and  windows  pasted  up  air-tight  the  change  amounted 
to  1,600  cu.  ft.  per  hour.* 

Prof.  Carpenter  says:  "Even  in  the  case  of  direct  heating, 
where  no  air  is  purposely  supplied  for  ventilation,  there  will 
be  a  change  of  air  by  diffusion  of  the  air  in  the  room  which  the 
writer  has  found  practically  met  by  an  allowance  equal  to 
one  to  three  changes  in  the  cubic  contents  per  hour." 

Whenever  air  is  introduced  into  a  room  as  by  ordinary  in- 
direct or  hot-air  heating,  an  equal  amount  of  air  must  be  driven 
from  the  room,  or  if  air  is  drawn  from  a  room,  as  by  the  draught 
in  a  fireplace,  an  equal  amount  of  air  must  enter  the  room. 

Heating  by  hot-air  furnaces  and  by  indirect  steam  or  hot- 
water  radiation  will  generally  provide  sufficient  ventilation  for 
private  residences,  especially  if  the  principal  rooms  are  pro- 
vided with  fireplaces  or  ventilation  flues. 

For  Systematic  Ventilation  provision  must  be  made 
for  the  admission  and  expulsion  of  the  air  through  flues  or 
definite  openings  and  for  power  for  moving  the  air. 

The  power  for  moving  air  for  ventilating  purposes  is  obtained 
in  two  ways:  (1)  by  expansion  due  to  heating,  and  (2)  by  a 
fan  operated  by  an  electric  motor  or  by  a  steam-  or  gas-engine. 

*  Heating  and  Ventilating  Buildings,  p.  35. 


1210  VENTILATION. 

Systematic  ventilation  also  presupposes  an  attempt  to  admit 
a  definite  amount  of  air,  and  the  first  step  in  any  system  of 
ventilation  would  naturally  be  to  decide  upon  the  amount  of 
air  required. 

Amount  of  Air  Required  for  Ventilation. — 
Authorities  differ  greatly  on  this  point,  except  that  for  school 
buildings  it  is  generally  agreed  that  30  cu.  ft.  of  air  per  minute 
for  each  occupant  or  1,800  cu.  ft.  per  hour  should  be  the 
standard.* 

For  churches  the  same  amount  will  give  very  fair  ventila- 
tion, but  for  theatres  and  auditoriums  which  are  usually  more 
closely  packed  and  occupied  for  a  longer  period,  the  air-supply 
should  be  from  2,000  to  2,500  cu.  ft.  per  sitting  per  hour. 

Hospitals  require  the  greatest  air  dilution,  and  for  such 
buildings  an  air-supply  of  from  4,000  to  6,000  cu.  ft.  per  hour 
for  each  bed  should  be  provided,  depending  upon  the  character 
of  the  cases  treated,  contagious  diseases  naturally  requiring 
the  greater  amount. 

The  quantity  of  air  required  is  sometimes  measured  by  the 
number  of  times  the  air  in  a  room  will  need  to  be  changed, 
but  to  determine  this  accurately  it  is  necessary  to  fall  back 
to  the  supply  per  person. 

Thus,  if  a  schoolroom  27'X32'  and  13"  high  contains  fifty 
pupils  and  a  teacher  and  1,800  cu.  ft.  per  hour  is  required  per 
person,  the  total  air-supply  required  per  hour  will  be  1,800X51, 
or  91,800  cu.  ft.  As  the  capacity  of  the  room  is  11,232  cu.  ft., 
the  air  in  the  room  must  be  changed  8.26  times  per  hour  to 
supply  30  cu.  ft.  of  air  per  minute  to  each  person. 

It  is  seldom  that  the  air  in  a  room  is  changed  oftener  than 
four  times  per  hour  by  natural  ventilation. 

Velocity  of  Entering1  Air. — The  velocity  of  the  air 
through  the  inlet  registers  or  grilles  should  not  exceed  4  to  6  ft. 
per  second,  the  general  allowance  being  5  ft.  per  second  when 
the  inlet  is  7  ft.  or  more  from  the  floor. 

Estimating'  Quantity  of  Air. — The  quantity  of  air 
passing  through  a  flue  or  opening  is  measured  by  multiplying 
the  sectional  area  of  the  flue,  or  the  net  area  of  opening,  in 
square  feet  by  the  velocity. 

Thus  with  a  velocity  of  5  ft.  per  second  the  quantity  of  air 
passing  through  an  unobstructed  opening  1  ft.  square  will 

*  This  amount  is  required  by  law  in  Massachusetts. 


VENTILATION,  1211 

equal  5  cm,  ft.  per  second,  300  cu.  ft.  per  minute,  or  1,800  cu,  ft, 
per  hour. 

Velocities  of  air  are  measured  by  an  instrument  called  an 
anemometer. 

Location  of  Inlet  and  Outlet. — Mr.  W.  R.  Briggs,  of 
Bridgeport,  Conn.,  some  years  ago  demonstrated  quite  -  conclu- 
sively that  in  a  rectangular  room  of  moderate  size  the  best 
results  are  obtained  when  the  inlet  is  in  an  inner  wall  near  the 
ceiling  arid  the  outlet  is  nearly  under  the  inlet  and  close  to 
the  floor. 

This  is  now  the  general  practice  in  well-designed  schoolhouses, 
and  for  churches  and  hospitals  when  warmed  by  indirect  radia- 
tion. 

For  cubical  rooms  not  exceeding  50  ft.  square  the  author 
considers  that  one  inlet  is  better  thaia  several. 

In  the  ventilation  of  theatres  the  air  is  sometimes  admitted 
through  the  ceiling,  but  more  often  through  the  risers  of  the 
floor  or  through  specially  designed  seat  ends, 

Size  of  Flues. — The  size  of  the  flues  both  for  inlet  and  out- 
let is  determined  by  the  quantity  of  air  to  be  moved  and  the 
velocity,  or 
Sectional  area  of )   _  j  Quantity  of  air  in  cubic  feet  per  minute 

flue  in  sq.  ft.    f  ~~   (  ~~         Velocity  in  feet  per  minute. 

The  actual  velocity  will  depend  upon  the  motive  power, 
the  length,  size,  shape,  and  surface  of  the  flue,  the  number  of 
turns  or  offsets,  and  whether  the  flue  is  vertical  or  horizontal 
so  that  after  the  theoretical  size  of  the  flue,  has  been  deter- 
mined, the  actual  size  will  oftentimes  need  to  be  increased  by 
an  amount  which  must  be  determined  largely  by  the  judgment 
of  the  designer.  For  this  reason  considerable  practical  experi- 
ence with  forced  hot-air  heating  and  ventilating  is  required  to 
lay  out  the  system  of  flues  to  the  best  advantage,  and  the 
architect  when  designing  such  a  plant  will  do  well  to  secure  the 
assistance  of  an  expert. 

With  fan  systems  of  ventilation  the  inlet  openings  should 
be  of  such  size  that  the  required  amount  of  air  may  be  in- 
troduced with  a  velocity  not  exceeding  500  ft.  per  minute 
when  the  inlet  is  5  ft.  from  the  floor  or  288  ft.  per  minute  when 
the  inlet  is  in  the  floor  or  in  the  walls  near  the  floor. 

In  figuring  the  size  of  ordinary  registers  the  requifed  area 
should  be  increased  about  50  per  cent,  to  allow  for  the  grilles 


1212  VENTILATION. 


or  pattern.  With  light  grilles  of  T/'XiV  iron  an  allowance 
of  10  per  cent,  will  ordinarily  be  sufficient. 

The  velocity  in  vertical  flues  supplying  the  inlets  should  not 
exceed  that  through  the  opening  by  more  than  50  per  cent., 
which  gives  a  velocity  in  the  vertical  flues  of  from  500  to  800  ft. 
per  minute.  The  rate  of  flow  through  the  connections  to  the 
base  of  the  flues  should  in  turn  be  higher  than  that  through 
the  flues,  while  the  velocity  in  the  main  horizontal  distributing 
ducts  should  be  still  higher.  "In  fact,  in  schools  and  churches 
the  plan  should  be  to  gradually  reduce  velocities  from  the 
point  of  leaving  the  fan  to  the  point  of  discharge  to  the  rooms. 
Careful  investigat:on  has  shown  that,  everything  considered, 
the  velocity  in  the  main  horizontal  ducts  from  the  fan  should 
not  fall  below  1,500  ft.  per  minute  and  preferably  2,000  ft.  per 
minute."  * 

The  size  of  vent  or  eduction  flues  when  air  is  forced  into  the 
rooms  by  a  fan  should  be  two  thirds  to  three  fourths  the  sec- 
tional area  of  the  induction  flues. 

Velocity  of  Air  in  Vertical  Flues  Due  to  Expan- 
sion by  Heat.  —  The  velocity  of  air  in  heated  flues  is  depend- 
ent upon  the  excess  of  temperature  of  the  air  in  the  flue  above 
that  of  the  room  or  space  into  which  the  flue  empties,  the 
height  of  the  flue,  the  loss  by  friction,  and  the  pressure  which 
must  be  resisted  by  the  entering  air.  Thus  in  a  room  heated 
by  indirect  radiation  or  a  warm-air  furnace  if  no  provision 
is  made  for  ventilation  the  heated  air  must  force  its  way  into 
the  room,  pushing  out  an  equal  volume  of  air  around  doors  or 
windows,  while  if  there  is  a  good  ventilating  flue  the  movement 
of  air  into  the  warm-air  flue  is  assisted.  The  table  on  opposite 
page,  quoted  by  various  writers,  shows  the  velocities  f  of  air  that 
may  be  expected  in  vent  flues  under  the  conditions  noted. 

To  obtain  the  cubic  feet  of  air  discharged  per  hour  per  square 
foot  of  cross-section  of  the  flue,  multiply  the  figures  in  the 
tab'e  by  60. 

While  this  table  does  not  strictly  apply  to  flues  conveying 
warm  air  into  a  room  it  is  sufficiently  accurate  for  practical 
purposes. 

Prof.  Carpenter  says  that  in  residence  heating  the  velocity 
in  flues  is  likely  to  be  as  follows,  in  feet  per  minute:  First  story, 

*  Ventilation  and  Heating.     B.  F.  Sturtevant  Co. 

t  The  velocity  in  a  flue  1  foot  square  being  the  same  as  the  quantity  of 
air  discharged. 


VENTILATION. 


1213 


TABLE  SHOWING  THE  QUANTITY  OF  AIR,  IN  CUBIC 
FEET,  DISCHARGED  PER  MINUTE  THROUGH  A 
FLUE  OF  WHICH  THE  CROSS-SECTIONAL  AREA  IS 
ONE  SQUARE  FOOT. 

(EXTERNAL  TEMPERATURE  OF  THE  AIR,  32°  FAHR.  ;  ALLOWANCE 
FOR  FRICTION,  50  PER  CENT.) 


Height 
of 
Flue,  in 
Feet. 

Excess  of  Temperature  of  Air  in  Flue  above  that  of  External  Air. 

10° 

15° 

20° 

25° 

cO° 

50° 

100° 

1£0° 

1 

34 

42 

48 

54 

59 

76 

108 

133 

5 

76 

94 

109 

121 

134 

167 

242 

298 

10 

10S 

133 

153 

171 

188 

242 

342 

419 

15 

133 

162 

188 

210 

230 

297 

419 

514 

20 

153 

188, 

217 

242 

265 

342 

484 

593 

25 

171 

210 

242 

271 

297 

383 

541 

663 

30 

188 

230 

265 

297 

325 

419 

593 

726 

35 

203 

248 

286 

320 

351 

453 

640 

784 

40 

217 

265 

306 

342 

375 

484 

684 

838 

45 

230 

282 

325 

363 

398 

514 

724 

889 

50 

242 

297 

342 

383 

419 

541 

765 

937 

60 

264 

325 

373 

420 

461 

594 

835 

1006 

70 

2°6 

351 

405 

465 

497 

643 

900 

1115 

80 

306 

375 

453 

485 

530  « 

688 

965 

1185 

90 

324 

398 

460 

516 

564 

727 

1027 

1225 

100 

342 

420 

485 

534 

594 

768 

1080 

1325 

125 

383 

468 

542 

604 

662 

855 

1210 

1480 

150 

420 

515 

596 

665 

730 

942 

1330 

1630 

150  to  240;  second  story,  300;  third  story,  360;  fourth  story, 
420.  Also  that  in  usual  conditions  of  residence  heating  the 
temperature  of  the  air  in  the  supply  flues  averages  about  30° 
above  the  temperature  of  the  air  in  the  room. 

Shape  and  Material  of  Air-ducts. — The  smoother 
the  surface  of  a  flue  the  less  will  be  the  friction  of  the  air  against 
it  and  the  greater  the  velocity.  Hot-  or  warm-air  flues  should 
always  be  made  of  metal,  preferably  galvanized  iron  for  flues 
exceeding  12  ins.  in  diameter.  Brick  flues  should  be  lined 
with  tin  or  galvanized  iron  when  they  convey  warm  air,  not 
only  to  reduce  the  friction  but  also  to  lessen  the  cooling  of  the 
air.  When  brick  flues  are  used  for  ventilation  lining  is  not 
so  necessary,  although  it  will  materially  increase  the  draught. 

Regarding  the  shape  of  the  flue  or  duct,  round  pipes  are 
the  best,  square  pipes  next  best,  and  rectangular  pipes  should 
always  be  made  as  nearly  square?  as  possible. 


1214  VENTILATION. 

With  indirect  or  natural  systems  of  ventilation  each  inlet 
register  should  be  supplied  by  a  separate  pipe  from  the  heater, 
and  but  one  pipe  should  be  taken  from  a  steam  or  hot-water 
stack. 

With  forced  systems  of  warming  and  ventilation  all  of  the 
air  from  the  heater  often  enters  one  large  main,  from  which 
distributing  pipes  are.  taken  off  to  supply  the  risers  to  the 
registers.  With  this  system  no  branches  should  leave  the 
mains  at  right  angles,  but  should  branch  off  at  an  angle  of  45° 
with  easy  radius  curves  in  all  cases.  No  90°  elbow  should  be 
made  with  less  than  seven  pieces  or  less  inside  radius  than  the 
diameter  of  the  pipe.  No  45°  elbow  should  be  made  of  less 
than  four  pieces.  Each  and  every  branch  air-duct  to  flues 
should  have  a  damper  near  base  of  flue,  and  at  every  "Y"  in 
the  system  there  should  be  placed  a  regulating  damper.  All 
of  these  dampers  and  fenders  should  be  adjustable.  Upon 
completion  of  the  system,  these  dampers  should  be  adjusted 
by  trial  so  that  each  register  will  receive  its  proportionate 
supply  of  air  and  then  "set." 

All  warm-air  pipes  should  be  covered  with  one  or  more  thick- 
nesses of  asbestos  paper  to  reduce  loss  of  heat. 

Natural  Systems  of  Heating1  and  Ventilating.— 
All  systems  in  which  the  air  moves  upwards,  due  to  the  ex- 
pansion produced  by  its  own  heat,  are  commonly  classified  as 
natural  systems. 

With  such  systems  the  ventilation  is  sometimes  produced 
by  aspirating  shafts  or  large  flues  containing  a  heater  of  some 
sort  at  its  base  to  increase  the  temperature  of  the  air  in  the 
flue  and  thus  increase  the  velocity.  Except  where  they  can 
be  heated  without  additional  cost,  aspirating  shafts  are  not 
as  economical,  as  a  rule,  as  fans. 

Buildings  containing  but  one  large  room  can  generally  be 
fairly  well  ventilated  by  using  a  heavy  galvanized-iron  smoke- 
flue  for  the  furnace  or  boiler  and  locating  the  flue  in  the  centre 
of  a  large  brick  chimney,  utilizing  the  space  around  the  flue 
for  ventilation.  The  heat  which  escapes  from  the  flue  will 
cause  a  good  draught  and  without  additional  cost. 

A  draught  may  also  be  produced  in  a  vent  flue  by  means  of 
coils  of  steam-pipes  placed  in  the  flue  just  above  the  air-inlet, 
or  a  gas  heater  may  be  employed  for  heating  the  flue. 

The  draught  produced  by  aspiration  is  not  usually  sufficient 
to  draw  air  any  distance  through  horizontal  ducts. 


VENTILATION.  1215 

Natural  systems  of  ventilation  are  only  effective  when  used 
in  connection  with  warming  and  afford  no  ventilation  in  warm 
weather. 

One  of  the  most  effective  ways  of  warming  and  ventilating 
without  a  fan  system  is  by  means  of  indirect  steam  radiation, 
which  may  be  supplemented,  if  the  room  is  very  large,  by  suffi- 
cient direct  radiation  to  offset  the  heat  lost  througli  the  walls 
and  windows  or  a  total  direct  radiating  surface  equal  to  one 
fourth  the  sum  of  the  glass  area  plus  one  fourth  the  exposed 
wall  surface.  The  indirect  radiation  surface  required  can  be 
estimated  by  the  data  given  on  p.  1163.  A  good  arrangement 
for  the  indirect  radiation  and  flues  in  a  church  or  schoolhouse 
is  illustrated  in  " Churches  and  Chapels,"  p.  133. 

The  author  has  obtained  good  results  in  warming  and  venti- 
lating schoolrooms  by  hot-air  furnaces,  -  using  a  furnace  for 
every  two  rooms  and  vertical  vent  flues  for  each  room  extend- 
ing straight  up  through  the  roof.  There  are  but  few  furnaces 
made,  however,  that  will  give  satisfaction  for  this  class  of  work; 
they  should  be  of  the  horizontal  tubular  pattern  with  large 
radiating  surface  in  proportion  to  the  grate  area  and  set  in 
brick  with  a  large  air-chamber.  An  excellent  furnace  of  this 
type  is  made  by  Lewis  &  Kitchen,  of  Kansas  City  and  Chicago. 

Fan  Systems  of  Ventilation. — Ventilation  by  means 
of  a  fan  may  be  effected  by  either  of  two  systems,  (a)  The  Plenum 
System,  in  which  the  air  is  forced  into  the  room  to  be  warmed 
and  ventilated,  and  (b)  The  Exhaust  System,  in  which  the  air 
is  exhausted  from  the  room. 

The  Exhaust  System. — There  are  many  objections  to 
the  adoption  of  this  system,  and  as  a  rule  it  should  be  avoided 
when  the  plenum  method  can  possibly  be  used.  With  the 
exhaust  system  a  partial  vacuum  is  created  within  the  room  and 
all  currents  and  leaks  are  inward,  so  that  air  rushes  around  doors 
and  windows,  forming  unpleasant  and  sometimes  dangerous 
currents  of  air.  The  circulation  of  the  air  in  the  room  is 
also  less  thorough  when  exhausted  than  when  forced  in.  The 
exhaust  system  as  a  rule  is  used  principally  for  affording  venti- 
lation in  hot  weather  or  for  removing  disagreeable  odors,  dust, 
etc.,  for  which  purpose  it  is  both  economical  and  effective 
when  properly  installed. 

An  exhaust  fan  can  also  be  used  to  advantage  for  ventilating 
churches  in  connection  with  hot-air  furnaces  or  indirect  steam 
radiation,  as  it  can  be  used  both  in.  winter  and  summer  and 


1216  VENTILATION. 

for  as  short  a  time  as  may  be  needed.  The  ventilation  re- 
quired in  a  church  varies  greatly  at  different  times;  a  church 
seating  500  persons  cannot  be  sufficiently  ventilated  when 
every  seat  is  occupied  without  a  fan,  while  when  there  are  only 
one  or  two  hundred  people  present,  a  fan  may  not  be  required. 
By  this  system  the  fan  should  be  placed  in  the  top  of  the  main 
ventilation  shaft  or  in  a  tower  or  ventilating  chamber  under 
the  roof,  with  ducts  leading  to  the  outlet  registers,  and  should 
be  operated  by  electricity. 

The  Plenum,  or  Hot-blast  system,  on  the  other  hand, 
maintains  a  slight  pressure  in  the  room  or  rooms  ventilated 
and  the  leakage  is  outward  instead  of  inward.  By  this  system 
the  temperatur^  of  the  air  and  point  of  admission  are  com- 
pletely under  control.  The  denser  the  air  also  up  to  a  certain 
limit  the  better  it  is  fpr  comfort  and  good  acoustics. 

For  heating  and  ventilating  theatres,  hospitals,  and  large 
schools  and  churches  this  is  undoubtedly  the  best  system  that 
can  be  employed,  and,  with  the  possible  exception  of  churches, 
is  as  economical  of  fuel  and  maintenance  as  an  indirect  steam- 
heating  plant,  while  affording  superior  ventilation  and  greater 
comfort.  This  system  has  also  been  applied  to  office  buildings, 
factories,  and  buildings  used  for  various  purposes.  The  system 
may  be  used  in  summer  as  well  as  in  winter,  and  by  providing 
a  cooling  chamber,  the  air  may  be  cooled  to  any  desired  tem- 
perature. 

As  ordinarily  installed  a  forced-blast  system  consists  of  a 
heater  and  fan  with  flues  and  ducts  for  conveying  the  air  to 
the  various  apartments  as  explained  on  p.  1153,  and  the  entire 
apparatus  with  the  exception  of  the  vertical  flues  is  usually 
located  in  the  basement. 

Two  cy stems  of  ducts  are  commonly  employed,  viz.,  the 
single-duct  and  double-duct  system.  A  typical  arrangement 
of  the  single-duct  system  is  shown  by  Fig.  35.  The  fan  is 
located  at  one  side  of  the  fresh-air  chamber,  so  that  air  is  drawn 
into  it  at  A  and  is  forced  through  the  heater  into  a  warm-air 
chamber  from  which  one  large  duct  with  distributing  branches 
is  taken  off.  A  by-pass  is  provided  so  that  a  portion  of  the 
air  passes  under  the  heater  without  being  warmed,  and  by 
means  of  a  damper  at  the  mouth  of  the  duct  more  or  less  of 
the  cool  air  may  be  mixed  with  the  heated  air  as  desired. 

With  this  system  all  of  the  air  conveyed  through  the  ducts 
is  of  the  same  temperature. 


VENTILATION. 


1217 


With  the  double-duct  system  the  upper  duct  conveys  only 
warm  air  and  the  under  duct  cool  air,  and  the  mixing  damper 
is  placed  at  the  bottom  of  the  riser  to  each  outlet.  By  this 
system  the  temperature  of  the  air  to  each  room  may  be  regu- 
lated independently  of  the  others. 

A  modification  of  the  single-duct  system  is  commonly  used 
in  heating  schools  in  which  a  large  double  chamber  is  located 
near  the  heating  stack,  one  portion  being  at  all  times  filled 
with  warm  air  and  the  other  portion  with  cool  air.  From  this 
double  chamber  a  single  duct  is  led  to  each  room,  and  the 
connection  is  made  with  the  chamber  in  such  a  way  that  either 


Chamber 


Heater 

Coil 


o|?o|?o|?ol8ol? 


Passage 


£:       a 


* 


Fig.  35 

all  warm  or  all  cool  air,  or  any  proportion  of  both,  may  be  ad- 
mitted into  the  duct,  the  mixing  being  controlled  by  a  damper 
operated  by  a  thermostat  placed  in  the  room  with  which  the 
duct  connects.  This  arrangement  saves  the  cost  of  running 
two  pipes,  and  when  a  thermostat  regulating  apparatus  is 
used  to  control  the  dampers  is  the  most  practical  system. 

When  there  are  several  rooms  to  be  warmed  and  a  thermo- 
static  regulating  apparatus  is  not  employed,  so  that  the  mixing 
dampers  must  be  operated  by  hand,  the  double-duct  system 
should  be  employed. 

The  system  shown  by  Fig.  35  answers  very  well  for  warming 
churches  and  auditoriums 

The  various  systems  of  piping  are  fully  described  in  the 
catalogues  of  the  companies  named  on  p.  1153. 

When  the  fan  is  to  be  run  in  warm  weather  provision  should 


1218  VENTILATION. 

be  made  so  that  the  entire  capacity  of  the  air  may  pass  around 
the  heater. 

By  the  arrangement  illustrated  in  Fig  35  the  fan  is  placed 
between  the  heater  and  the  cold-air  chamber  and  forces  the 
air  through  the  heater.  The  fan  may,  however,  be  placed  on 
the  other  side  of  the  heater  so  as  to  pull  the  air  through  it  by 
exhaustion,  at  the  same  time  forcing  the  heated  air  into  the 
ducts.  Both  arrangements  are  used,  but  the  former  is  the 
one  more  commonly  employed. 

With  the  forced-blast  systems  of  warming  and  ventilating 
a  fresh-air  chamber  of  ample  size  must  be  provided  adjacent 
to  the  fan  or  heater  and  communicating  with  the  outside  air 
by  a  large  duct,  the  opening  to  which  should  be  located  as  high 
above  the  ground  as  practical  conditions  will  admit. 

Forced  Blast  in  Connection  with  Warm-air  Fnr- 
11  aces. — Several  schools  and  churches  have  been  successfully 
warmed  and  ventilated  by  utilizing  warm-air  furnaces  of  the  long 
tubular  pattern  to  supply  the  heat  and  an  electric  motor  for 
power.  For  churches  of  moderate  size  this  system  would 
appear  to  have  some  advantages,  especially  in  economy,  over 
the  steam  systems.  A  description  of  such  a  system  with 
illustrations  may  be  found  in  l(  Churches  and  Chapels,"  p.  148. 

Fans. — Three  types  of  fans  are  used  in  connection  with  the 
heating  and  ventilating  of  buildings,  viz.,  the  disc  fan,  the 
blower,  or  paddle-wheel  fan,  and  the  cone  fan. 

The  disc  fan  receives  the  air  at  one  side  and  delivers  it  at 
the  opposite  side,  the  principal  motion  of  the  air  being  parallel 
with  the  axis.  This  type  is  only  used  for  exhausting  air,  and 
is  commonly  used  for  ventilating  single  rooms  in  warm  weather. 
Most  of  the  electric  fans  used  for  ventilating  kitchens,  restau- 
rants, etc.,  are  of  this  type. 

The  paddle-wheel  fan  is  the  type  commonly  used  with  the 
forced-blast  systems  of  heating.  The  fan  in  steel-plate  blowers 
is  of  the  paddle-wheel  type.* 

The  cone  fan  is  a  special  type  of  the  paddle-wheel  fan  which 
has  been  used  for  maintaining  a  plenum  in  a  large  chamber 
under  an  audience  room.  It  is  not  adapted  to  high  pressures. 

Fans  may  be  driven  from  a  running  countershaft,  from  an 
engine  directly  connected,  or  from  an  electric  or  water  motor. 

Disc  fans  are  commonly  driven  by  an  electric  motor,  and 
this  will  be  found  the  most  convenient  power  for  driving  steel- 

*  The  three  types  of  fans  are  illustrated  in  "  Churches  and  Chapels." 


VENTILATION.  1219 

plate  blowers  in  churches  and  theatres,  as  in  the  summer-time 
no  heat  is  required.  In  schools,  which  are  not  used  much  in 
warm  weather,  and  in  buildings  where  steam  is  kept  up  all  the 
year  round,  a  small  steam-engine  will  generally  be  most  eco- 
nomical. 

All  fans  make  some  noise,  hence  they  should  be  located 
where  they  will  be  heard  the  least. 

Capacity  of  Fans. — The  catalogued  capacities  of  all 
makes  of  fans  are  their  capacities  when  running  light  in  the 
open  air,  not  being  attached  to  any  ducts  or  heating  coils. 
These  capacities  will  be  reduced  from  25  to  50  per  cent,  when 
so  attached,  depending  on  the  length  of  the  ducts  and  the 
method  of  distribution. 

In  figuring  capacity  of  fans  for  forcing  air  through  heating 
coils  and  ducts  it  is  customary  to  call  the  peripheral  velocity 
of  the  fan  blades  equal  to  the  linear  velocity  of  the  air,  and 
to  take  one  half  of  the  theoretical  delivery  as  the  actual  effi- 
ciency. 

The  peripheral  velocity  is  obtained  by  multiplying  the  revo- 
lutions per  minute  by  the  circumference  of  the  wheel. 

Thus  a  fan  6  ft.  in  diameter  running  200  revolutions  per 
minute  has  a  peripheral  velocity  =  200X18.84=  3,768  ft.  per 
minute.  Deducting  50  per  cent,  for  loss,  the  actual  velocity 
of  the  air  would  be  1,884  ft.  per  minute.  The  discharge  opening 
in  a  fan  6  ft.  in  diameter  will  have  an  area  of  at  least  11.5  sq.  ft 
Multiplying  this  area  by  the  working  velocity  we  have  21,666 
cu.  ft.  per  minute  as  the  probable  actual  discharge  of  the  fan. 

Mr.  F.  R.  Still,  of  Detroit,  who  has  had  extensive  engineering 
experience  with  forced-blast  systems,  says  that  the  maximum 
limit  of  speed  of  a  blower  without  making  a  serious  noise  is 
250  revolutions  per  minute,  and  that  except  in  rare  cases  the 
blower  should  run  at  from  180  to  200  revolutions  per  minute. 

With  a  disc  fan,  used  for  ventilation  only,  the  velocity  should 
never  exceed  900  ft.  per  minute. 

As  explained  above,  the  actual  capacity  when  connected 
with  a  heating  and  ventilating  system  will  be  reduced  from 
25  to  50  per  cent,  from  the  values  in  the  table  on  the  next  page, 
while  the  horse-powers,  on  the  other  hand,  are  probably  some- 
what in  excess  of  those  actually  required. 

For  further  information  on  this  subject  the  reader  is  referred 
to  the  catalogues  of  the  various  manufacturers  of  blowers 
&nd  to  " Heating  and  Ventilating  Buildings," 


1220 


CHIMNEYS. 


TABLE   OF  CAPACITY  AND   POWER   REQUIRED   FOR 

STEEL-PLATE  BLOWERS  OF  VARIOUS  SIZES. 

WITH  FREE  INLET  AND  OUTLET. 


M-ounce  Pressure. 

H-ounce  Pressure. 

Diam- 

Size, 

eter  of 

Inches. 

Wheel, 
Inches. 

Revo- 
lutions. 

Cubic 
Feet  per 
Minute. 

H.P. 

Revo- 
lutions. 

Cubic 
Feet  per 
Minute. 

H.P. 

70 

42 

214 

10,336 

.3 

312 

14,628 

1.3 

£0 

48 

188 

12,584 

.5 

265 

17,809 

1.6 

90 

54 

167 

16,150 

.7 

236 

22,856 

2.0 

100 

60 

150 

20723 

.9 

212 

29,329 

2.6 

110 

66 

137 

24,548 

1.1 

193 

34,741 

3.1 

120 

72 

125 

30,165 

1.3 

177 

42,678 

3.8 

140 

84 

107 

40,465 

1.8 

152 

57,26S 

5.1 

160 

96 

94 

51,344 

2.3 

133 

72,264 

6.4 

M-ounce  Pressure. 

1-ounce  Pressure. 

Diam- 

Size, 

eter  of 

Inches. 

Wheel, 
Inches. 

Revo- 
lutions. 

Cubic 
Feet  per 
Minute. 

H.P. 

Revo- 
lutions. 

Cubic 
Feet  per 
Minute. 

H.P. 

70 

42 

377 

17,928 

1.6 

428 

20,700 

3.7 

80 

48 

325 

21,827 

2.4 

367 

25202 

4.5 

90 

54 

289 

28,012 

3.7 

333 

32  343 

5.7 

100 

60 

260 

35,945 

4.8 

300 

41,503 

7.4 

110 

•    66 

236 

42,579 

5.7 

273 

49,162 

8.8 

120 

72 

217 

52,304 

7.0 

250 

60,392 

10.7 

140 

84 

186 

70,188 

9.4 

214 

81,040 

14.4 

160 

96 

163 

89,057 

11.5 

152 

102,807 

18.3 

Chimneys. 

Object. — A  chimney  is  required  for  two  purposes,  (1)  to 
produce  the  draught  necessary  for  the  proper  combustion  of 
the  fuel,  and  (2)  to  furnish  a  means  of  discharging  the  noxious 
products  of  ^ombustL  .1  into  the  atmosphere  at  such  a  height 
from  the  ground  th:,';  ey  may  not  prove  a  nuisance  to  people 
living  in  the  vicinity  of  the  chimney. 

A  good  draught  is  absolutely  essential  to  the  satisfactory 
and  economical  working  of  either  a  heating  or  power  plant.  It 
is  claimed  by  Kent  that  chimneys  over  150  ft.  in  height  are  not 
justified  from  the  standpoint  of  economy,  but  where  the  gases 
of  combustion  are  poisonous,  as  in  the  case  of  smelters,  or 


CHIMNEYS.  1221 

specially  noxious,  tall  chimneys  enhance  the  value  of  sur- 
rounding property,  if  in  a  town,  far  more  than  the  cost  of  the 
chimney,  and  should  be  required  by  law. 

Theory  of  Chimneys.* — To  produce  an  effective  draught 
in  the  furnace  a  chimney  requires  size  and  height. 

Each  pound  of  coal  burned  yields  from  13  to  30  Ibs.  of  gas 
the  volume  of  which  varies  with  the  temperature. 
»  The  Weight  of  Gas  carried  off  by  a  chimney  in  a  given  time 
depends  upon  three  things — size  of  chimney,  velocity  of  flow, 
and  density  of  gas.  But  as  the  density  decreases  directly  as 
the  absolute  temperature,  while  the  velocity  increases,  with  a 
given  height,  nearly  as  the  square  root  of  the  temperature,  it 
follows  that  there  is  :,,  temperature  at  which  the  weight  of  gas 
delivered  is  a  rnaximum.  This  is  about  550°  above  the  sur- 
rounding air.  Temperature,  however,  makes  so  little  differ- 
ence that  at  550°  above,  the  quantity  is  only  four  per  cent. 
greater  than  at  300°.  Therefore  height  and  area  are  the  only 
elements  necessary  to  consider  in  an  ordinary  chimney. 

The  Intensity  of  Draught  is,  however,  independent  of  the  size, 
and  depends  upon  the  difference  in  weight  of  the  outside  and 
inside  columns  of  air,  which  varies  directly  with  the  product 
of  the  height  into  the  difference  of  temperature.  This  is  usually 
stated  in  an  equivalent  column  of  water  and  may  vary  from 
0  to  possibly  2  ins. 

To  Fin  (I  the  Maximum  Draught  for  any  given  chimney, 
the  heated  column  being  612°  F.  and  the  external  air  62°: 
Multiply  the  height  above  grate  in  feet  by  .GO 7 5  and  the  product 
is  the  draught  power  in  inches  of  water. 

The  intensity  of  draught  required  varies  with  the  kind 
and  condition  of  the  fuel  and  the  thickness  of  the  fires.  Wood 
requires  the  least  and  fine  ooal  jr  slack  the  most.  To  burn 
anthracite  slack  to  advantage,  a  draught  of  1}  ins.  of  water  is 
necessary,  which  can  be  attained  by  a  well-proportioned  chim- 
ney 175  ft.  high. 

A  round  chimney  is  better  than  square  and  a  straight 
flue  better  than  tapering,  though  it  may  be  either  larger  or 
smaller  at  top  without  detriment. 

*  Babcock  &  Wilcox  Co. 


1222  CHIMNEYS  FOR  POWER  PLANTS. 


Size  of  Chimneys  for  Power  Plants.* 

The  effective  area  of  a  chimney  for  a  given  power  varies 
inversely  as  the  square  root  of  the  height.  The  actual  area,  in 
practice,  should  be  greater,  because  of  retardation  of  velocity 
due  to  friction  against  the  walls.  On  the  basis  that  this  is  equal 
to  a  layer  of  air  2  ins.  thick  over  the  whole  interior  surface,  and 
that  a  commercial  horse-power  requires  the  consumption  of  an 
average  of  5  Ibs.  of  coal  per  hour,  we  have  the  following  for- 
mulas: 


.  (1) 

#=3.33#\/F;     ........  (2) 

S  =  12VE+4;    ........  (3) 

D  =  13.54\/^+4;    .....     .     .  (4) 

0.3#\2 


In  which  H=  horse-power;  h=  height  of  chimney  in  feet; 
.#=  effective  area,  and  A  =  actual  area  in  square  feet;  $  =  side 
of  square  chimney  and  £)=dia.  of  round  chimney  in  inches. 
The  first  table  on  the  next  page  was  calculated  by  means  of 
these  formulae, 

High  Chimneys  Not  Necessary.  f  —  "Chimneys  above 
150  ft.  in  height  are  very  costly  and  their  increased  cost  is 
rarely  justified  by  increased  efficiency.  In  recent  practice  it 
has  become  somewhat  common  to  build  two  or  more  smaller 
chimneys  instead  of  one  large  one.  A  notable  example  is  the 
Spreckles  sugar  refinery  in  Philadelphia,  where  three  separate 
chimneys  are  used  for  one  boiler  plant  of  7,500  H.P.  The  three 
chimneys  are  said  to  have  cost  several  thousand  dollars  less  than 
a  single  chimney  of  their  combined  capacity  would  have  cost." 

Size  of  Chimneys  for  House  Heaters.  —  Chimney- 
flues  for  heating  apparatus  should  be  ample  in  size  and  carried 
as  nearly  straight  as  possible  from  a  point  near  the  cellar  floor 
to  above  the  highest  projection  of  the  roof.  They  should  be 
independent,  having  no  connection  with  other  flues  or  openings, 
and  always  of  the  same  area  from  top  to  bottom.  A  well- 

*  These  formulae  are  those  given  by  Kent,  and  are  generally  accepted 
as  reliable. 
t  Kent. 


CHIMNEYS  FOR  HOUSE  HEATERS. 


1223 


MZES   OF    CHIMNEYS  WITH    APPROPRIATE    HORSE- 
POWER OF  BOILERS. 


Diameter  in 
Inches. 

Effective  Area, 
Square  Feet. 

Actual  Area, 
Square  Feet. 

Height  of  Chimneys. 

y 

3-S 

cr  o 

CQ»-H 

"s 

^5 

02 

16 
19 
22 
24 
27 
30 
32 
35 
38 
43 
48 
54 
59 
64 
70 
75 
80 
86 

50 
Ft. 

60 
Ft. 

70 
Ft. 

80 
Ft. 

90 
Ft. 

100 
Ft. 

110 
Ft. 

125 
Ft. 

150 
Ft. 

175 
Ft. 

200 
Ft. 

Commercial  H.P.  of  Boiler. 

18 
21 
24 
27 
30 
33 
36 
39 
42 
48 
54 
60 
66 
72 
78 
84 
90 
96 

0.97 
1.47 
2.08 
2.78 
3.58 
4.48 
5.47 
6.57 
7.76 
10.44 
13.51 
16.98 
20.83 
25.08 
29.73 
34.76 
40.19 
46.01 

1.77 
2.41 
3.14 
3.98 
4.91 
5.94 
7.07 
8.30 
9.62 
12.57 
15.90 
19.64 
23.76 
28.27 
33.18 
38.48 
44.18 
50.27 

23 
35 
49 
65 

84 

25 

38 
54 
72 
92 
115 
141 

27 
41 
58 
78 
100 
125 
152 
183 
216 

62 
83 
107 
133 
163 
196 
231 
311 

113 
141 
173 

208 
245 
330 
427 
536 

182 
219 
258 
348 
449 
565 
694 
835 

271 
365 
472 
593 
728 
876 
1038 
1214 

389 
503 
632 
776 
934 
1107 
1294 
1496 

551 
692 
849 
1023 
1212 
1418 
1639 
1876 

748 
918 
1105 
1310 
1531 
1770 
2027 

981 
1181 
1400 
1637 
1893 
2167 

jointed  tile  flue,  preferably  round,  is  better  than  a  square  brick 
flue  of  larger  area.  The  chimney  flue  should  be  carried  3  or 
4  ft.  below  the  smoke-pipe  entrance  and  provided  with  a  clean- 
out  door  at  the  base,  tightly  fitted,  to  facilitate  the  removal 
of  accumulated  dust  and  soot. 

The  size  of  flues  may  be  calculated  from  the  following  table: 


Tile  Flues, 

Tile 

Standard 

Flues, 

Brick 

Total  Contents  of 
Building,  Cubic  Feet 
of  Space. 

Average  of 
Direct  Radiation 
Steam,  Square 
Feet. 

Sizes, 
Square  or 
Rectangu- 
lar, Out- 

Standard 
Sizes, 
Round, 
Inside 

Flues, 
Inside 
Dimen- 

side  Di- 

Dimen- 

• 

mensions. 

sions. 

Inches. 

Inches. 

Inches. 

10,000  to    20,000 

200  to     400 

8JX8i 

8 

8X   8 

25,000  to    50,000 

450  to     900 

8^X13 

10 

8X12 

60,000  to  100,000 

1,000  to  1,600 

13X13 

12 

12X12 

100,000  to  150,000 

1,600  to  3,000 

18X18 

16 

16X16 

Indirect  radiation  should  be  counted  as  50  per  cent,  more 
than  direct  and  corresponding  areas  of  flue  be  provided  for. 


1224      CONSTRUCTION  OF  BRICK  CHIMNEYS. 

The  amount  of  radiation  determines  the  requisite  size  of  boiler, 
and  therefore  the  area  of  the  flue. 

No  chimney-flue  should  be  less  than  8  ins.  in  depth,  nor  of 
a  smaller  size  than  the  smoke-pipe  from  the  heater. 

For  a  kitchen  range  an  8X8  tile  flue  will  generally  answer, 
but  an  8X12  flue  is  better. 

For  fireplaces  the  sectional  area  of  the  flue  for  burning  wood 
or  bituminous  coal  should  be  one  tenth  to  one  eighth  that  of 
the  fireplace  opening  for  a  rectangular  flue  and  one  twelfth  for 
a  circular  flue.  For  burning  anthracite  coal  the  above  pro- 
portions may  be  reduced  to  one  twelfth  and  one  sixteenth  re- 
spectively. 

When  practicable,  chimneys  should  extend  above  the  highest 
surrounding  roof,  to  prevent  down-draught  caused  by  eddies. 
When  this  is  impracticable  a  revolving  chimney-top  will  often 
prevent  down-draughts.  They  may  also  often  be  avoided  by 
covering  the  top  of  the  chimney  with  a  stone  flag  and  leaving 
openings  in  two  parallel  sides  of  the  chimney,  the  sides  parallel 
to  the  ridge  of  the  adjoining  roof  or  building  being  closed. 

The  watts  of  the  flue  should  be  as  smooth  as  possible.  Tile- 
flue  lining  is  preferable.  Brick  flues  should  be  either  smoothly 
plastered  on  the  inside  with  rich  lime  mortar  or  the  joints 
should  be  filled  full  and  struck  with  the  point  of  the  trowel. 
If  the  bricks  are  laid  in  cement  mortar,  the  author  recom- 
mends striking  the  joints  instead  of  plastering. 

The  walls  of  attached  chimneys  with  flues  not  exceeding 
8"X12"  may  be  4"  thick  for  heights  of  50  ft.  Flues  12"X12" 
and  larger  should  have  walls  8"  thick  to  within  10  ft.  of  the 
top.  Aside  from  strength  or  stability,  thick  walls  are  preferable 
to  thin  walls, 

Stability  of  Chimneys. — A  general  rule  for  diameter  of 
base  of  brick  chimneys  standing  free,  approved  by  many  years 
of  practice  in  England  and  the  United  States,  is  to  make  the  di- 
ameter of  the  base,  or  side  of  a  square  chimney,  one  tenth  of  the 
height. 

Construction  of  Brick  Chimneys. — "For  chimneys 
of  4  ft.  in  diameter  and  100  ft.  high  and  upwards,  the  best 
form  is  circular  with  a  straight  batter  on  the  outside.  A  cir- 
cular chimney  of  this  size,  in  addition  to  being  cheaper  than 
any  other  form,  is  lighter,  stronger,  and  looks  much  better  and 
more  shapely. 

"  Chimneys  of  any  considerable  height  are  not  built  up  of  uni- 


CONSTRUCTION  OF  BRICK  CHIMNEYS.      1225 

form  thickness  from  top  to  bottom  nor  with  a  uniformly  varying 
thickness  of  wall,  but  the  wall,  heaviest  of  course  at  the  base, 
is  reduced  by  a  series  of  steps. 

"All  boiler  chimneys  of  any  considerable  size  should  consist 
of  an  outer  stack  of  sufficient  strength  to  give  stability  to  the 
structure  and  an  inner  stack  or  core  independent  of  the  outer 
one.  This  core  is  by  many  engineers  extended  up  to  a  height 
of  but  50  or  60  ft.  from  the  base  of  the  chimney,  but  the  better 
practice  is  to  run  it  up  the  whole  height  of  the  chimney;  it 
may  be  stopped  off,  say,  a  couple  feet  below  the  top  and  the 
outer  shell  contracted  to  the  area  of  the  core,  but  the  better 
way  is  to  run  it  up  to  about  8  or  12  ins.  of  the  top  and  not 
contract  the  outer  shell.  But  under  no  circumstances  should 
the  core  at  its  upper  end  be  built  into  or  connected  with  the 
outer  stack.  This  has  been  done  in  several  instances  by  brick- 
layers, and  the  result  has  been  the  expansion  of  the  inner  core, 
which  lifted  the  top  of  the  outer  stack  squarely  up  and  cracked 
the  brickwork."  * 

Notwithstanding  the  above,  a  number  of  tall  brick  chimneys 
liave  been  built  without  an  interior  wall,  an  instance  of  which 
Is  given  on  the  next  page. 

Thickness  of  Walls. — The  following  is  considered  as  a 
Tsafe  rule  for  the  thickness  of  the  outer  wall  of  tall  chimneys: 
.For  the  first  25  ft.  from  the  top,  one  brick  (8  or  9  ins);  for  the 
second  25  ft.,  1J  bricks,  and  so  on,  increasing  one  half  brick 
:for  each  25  ft.  from  the  top  downwards.  If  the  inside  diam- 
eter exceeds  5  ft.  the  top  length  should  be  1 J  bricks,  the  next  two 
bricks,  etc. ;  if  under  3  ft.,  the  top  may  be  one  half  brick  for  10  ft. 

The  batter  should  be  not  less  than  1  in  36  to  give  stability. 

The  inside  core  may  be  4  ins.  thick  for  25  ft.  from  the  top, 
$hen  8  or  9  ins.  for  50  ft. 

Two  chimneys  of  the  Edison  station,  Brooklyn,  each  150  ft. 
;high,  have  inner  cores  80  ft.  high  and  one  brick  thick  for  the 
full  height,  the  first  50  ft.  being  of  fire-brick. 

Fire-brick  Lining-. — If  a  chimney  has  but  one  wall  it  should 
foe  lined  with  fire-brick  for  at  least  30  ft.,  and  if  it  has  an  inner 
core,  the  latter  is  usually  built  of  firebrick  for  30  or  50  ft.  from 
the  bottom. 

The  top  of  tall  brick  chimneys  should  be  protected  by  a  cast- 
iron  cap. 

*  From  The  Locomotive,  1884  and  1886. 


1226      CONSTRUCTION   OF   BRICK  CHIMNEYS. 

Examples  of  Tall  Brick  Chimneys. — Several  tall 
brick  chimneys  are  described  in  the  thirteenth  edition  of  this 
book,  also  in  Kent,  p.  737. 

Chimney-stack  at  the  West  Cumberland  Hema- 
tite Iron  Works. — Designed  by  Professor  J.  Macquorn 
Rankine,  and  considered  as  a  model  chimney. 

Duty. — The  duty  of  this  chimney  is  to  carry  off  the  gaseous 
products  of  combustion  from  four  blast-furnaces  and  from 
various  stoves  and  boilers.  The  total  amount  of  fuel  consumed 
is  estimated  at  about  10 J  tons  per  hour  when  all  the  furnaces 
are  at  work. 

The  actual  temperature  inside  the  chimney  when  doing  about 
three  fourths  of  its  full  duty  is  490°  F.,  and  the  pressure  of  the 
draught  is  1J  ins.  of  water. 

Figure  and  Dimensions. — Above  ground  the  chimney  is  a  frus- 
tum of  a  cone,  with  a  straight  batter.  Underground  there  is  a 
plinth  or  basement,  octagonal  outside  at  the  ground  line  and 
square  at  the  bottom;  cylindrical  inside  and  pierced  with  four 
circular  openings  for  flues. 

Height  of  chimney  above  the  ground,  250  ft. 

Depth  of  foundation  below  the  ground,  17  ft. 

Total  height  from  foundation  to  top,  267  ft. 

Inside  diameter  at  top  of  cone,  13  ft. 

Inside  diameter  2  ft.  above  bottom  of  cone,  21  ft.  10  ins. 

Inside  diameter  in  basement,  18  ft.  10  ins. 

Inside  diameter  of  archway  for  flues,  7  ft.  6  ins. 

Outside  diameter  at  top  of  cone,  15  ft.  3  ins. 

Outside  diameter  2  ft.  above  bottom  of  cone,  25  ft.  7  ins. 

Outside  dimensions  of  square  basement,  30  ft.X30  ft. 

Size  of  foundation  course,  31  ft.  6  ins.  X31  ft.  6  ins. 

Size  of  concrete  foundations,  34  ft.  6  ins.  X 34  ft.  6  ins.  and 
3  ft.  thick. 

Thickness  of  Brickwork. — First  2  ft.  above  foundation  stepping 
from  four  bricks  to  2J  bricks;  next  88  ft.,  2J  bricks;  next 
80  ft.,  2  bricks;  remaining  80  ft.,  \\  bricks. 

The  pressure  on  the  ground  below  the  concrete  is  1.6  tons 
on  the  square  foot. 

Fire-brick  Lining. — The  thickness  of  brickwork  given  above 
included  the  fire-brick  lining,  which  was  one  brick  in  thickness 
in  the  first  90  ft.  and  one  half  brick  the  remaining  height,  the 
fire-brick  being  bonded  in  with  the  common  brick,  but  being 


LIST  OF  TALL  CHIMNEYS.  1227 

laid  in  fire-clay.  This  method  of  construction  was  considered 
better  than  that  of  the  inner  cone. 

Strips  of  No.  15  hoop  iron,  tarred  and  sanded,  were  laid  in  the 
bed-  joints  of  the  cone  at  intervals  of  4  ft.  in  height,  with  their 
ends  turned  down  in  the  side-joints.  The  length  of  the  iron 
was  twice  the  circumference  of  the  chimney. 

Cap  and  Lightning  Conductor.  —  On  the  top  of  the  chimney 
is  a  pitch-coated,  cast-iron  curb  1  in.  thick,  coming  down 
3  ins.  on  the  outside  and  inside.  The  lightning  conductor  is  a 
copper-  wire  rope  f  in.  in  diameter.  It  terminates  in  a  covered 
drain,  in  which  there  is  always  a  sufficient  run  of  water. 

SOME  OF  THE  TALLEST  CHIMNEYS  ON  EARTH.* 

Height 
in  Feet. 

t  Freiberg,  Saxony,  Germany,  Halsbrucke  Foundry  ......  460 

Glasgow,  Port  Dundas,  Scotland,  F.  Townsend.  ...  .......  454 

Glasgow,  St.  Rollox,  Scotland,  Tenant  &  Co  .............  436J 

Creusot,  France,  Messrs.  Musprath  Chemical  Works  ......  406 

Halifax,  Dean  Clough  Mill,  Scotland,  Messrs.  Crossley's.  .  .  381 

Lancashire,  Bolton,  England,  Dobson  &  Barlow  .........  367 

Boston,  Mass.,  United  States,  Fall  River  Iron  Co  ........  350 

Chicago,  Illinois,  United  States  ........................  350 

East  Newark,  N.  J.,  United  States,  Clark  Thread  Co  ......  335 

Barmen,  Prussia,  Germany,  Wessenfield  &  Co  ...........  331 

Edinburgh,  Scotland,  Gas  Works  .......................  329 

Huddersfield,  England,  Brook  &  Son,  Fire-clay  Works.  .  .  315 

Smethwick,  England,  Adams  Soap  Works  .....  ..........  312 

Carlisle,  England,  P.  Dickon  &  Son  ....................  300 

Bradford,  England,  Mitchell  Brothers  ..................  300 

Greenhithe,  Kent,  England,  J.  C.  Johnson  ...............  297 

Lowell,  Mass.,  United  States,  Merrimack  Mfg.  Co  ........  283 

Dundee,  Scotland,  Camperdown,  Linen  Works,  Cox  Bros.  ,  282 

Creusot,  France,  Schneider  &  Co  .......................  280 

Darwin,  North  Lancashire,  Darwin  &  Mostyn  Iron  Co.  ...  275 

Pittsburg,  Pennsylvania,  United  States  .................  275 

Lancashire,  Eng.,  Barrow-in-Furness,  Hematite  Iron  Co..  .  259 

Bradford,  England,  Manningham  Mills,  Lester  &  Co  ......  256^ 

Manchester,  N.  H.,  United  States,  Amoskeag  Mfg.  Co  .....  255 

West  Cumberland,  England,  Hematite  Iron  Works  .......  250 

Lancaster,  England,  Story  Brothers  ....................  250 

Lawrence,  Mass.,  Washington  Mills  .....................  250 

Cheshire,  England,  Connah's  Quay,  Chemical  Co  .........  245 


pu 
bee 
chimneys. 

t  Built  by  H.  R.  Heinicke,  of  perforated  radial  bricks,  and  claimed  to  be 
the  tallest  chimney  in  the  world, 


1228  LIST  OF  TALL  CHIMNEYS. 

Height 
in  Feet. 

Bradford,  England,  Newland's  Mill 240 

Boston  Navy  Yard,  Mass.,  United  States 239 

Providence,  R.  I.,  Narragansett  E.  L.  Co 238 

Lawrence,  Mass.,  United  States,  Pacific  Mills 233 

Harwich,  Dovercourt,  England,  Pattrie  &  Sons 230 

Lowell,  Mass.,  United  States,  Fremont  &  Suffolk  Co 225 

Woolwich  Arsenal,  England,  Shell  Foundry 224 

New  York  City,  N.  Y.,  U.  S.,  New  York  Steam  Heating  Co.  221 

Northfleet,  England,  F.  C.  Gostling  &  Co 220 

*  Elizabethport,  N.  J.,  Plymouth  Cordage  Co 220 

Ivorydale,  Ohio,  United  States,  Procter  &  Gamble 218 

Lawrence,  Mass.,  United  States,  The  Tower  Pacific  Mills.  . .  215 

Philadelphia,  Pa.,  The  Fidelity  Insurance  Co 212 

Dewsbury,  England,  Olroyd  &  Sons •.  .  210 

Lanarkshire,  England,  Coltness  Iron  Works 210 

Wilmington,  Delaware,  United  States,  City  Water  Works.  204 

Philadelphia,  Penn.,  United  States,  Finley  &  Schlecter.  .  .  .  202 

Camden,  N.  J.,  U.  S.,  Highland  Mill,  S.  B.  Still  &  Co 202 

Ironton,  Ohio,  United  States,  Etna  Iron  Works 200 

Lamokin,  Penn.,  United  States,  John  M.  Sharpless  &  Co. .  .  200 

Duluth,  Minn.,  United  States,  Hartman  Gen.  Electric  Co..  200 

Passaic,  N.  J.,  Passaic  Print  Works 200 

Creusot,  France,  Schneider  &  Co 197 

East  Newark,  N.  J.,  United  States,  Clark's  Thread  Mill.  .  .  192 

Cleveland,  Ohio,  United  States,  Ohio  Rolling  Mill  Co 190 

Nottingham,  England,  Stanton  Iron  Co 190 

Deepear,  Sheffield,  England,  Fox  &  Co 186 

Philadelphia,  Penn.,  United  States,  John  Lang  Paper  Mills.  181 

Bayonne,  N.  J.,  U.  S.,  Lombard,  Ayres  &  Co.  Oil  Refinery.  180 

A  few  of  the  tall  chimneys  built  by  the  Alphonse  Custodis 
Chimney  Construction  Co.: 

Location.  *!&*% 

Constable  Hook,  N.  J.,  Oxford  Copper  Co 365  10 

Providence,  R.  L,  Rhode  Island  Suburban  R'y  Co 308  16 

New  York  City,  Manhattan  R'y  Co 278  17 

Philadelphia,  Pa.,  Southern  Elec.  L'.t  and  Power  Co.  .  .   275  18 

Kansas  City,  Mo.,  Metropolitan  St.  R'y  Co 265  16 

Kansas  City,  Mo.,  Armour  Packing  Co 250  14 

Boston,  Mass.,  Edison  Elec.  111.  Co. 250  16 

New  York  City,  Jacob  Ruppert  Ice  Plant 250  10 

Kansas  Git  y,  Mo.,  Cons' I'd  Elec.  Light  and  Power  Co.  .   243  10 

Cleveland,  Ohio,  Cleveland  City  R'y  Co 240  13 

Milttnocke*-,  Me.,  Great  Northern  Paper  Co 235  12 

Weehawken,  N.  J.,  N.  Y.  Cen.  and  H.  R.  R.  Co 233  11 

Edgewater,  N.  J.   N.  Y.  Glucose  Co 225  12 

Washington,  D.  C.,  St.  Elizabeth's  Insane  Hospital. .  .    225  10 

*  Reinforced  concrete. 


CHIMNEYS  OF  REINFORCED  CONCRETE.     1229 

Radial  Block  Chimneys. — Radial  blocks  for  chimney 
construction  have  been  used  extensively  in  England,  Germany, 
France,  and  Russia  for  many  years,  but  their  use  in  this  country 
has  been  quite  limited. 

Some  thirty  years  ago,  Alphonse  Custodis,  of  Germany,  origi- 
nated a  method  of  building  tall  chimneys  of  perforated  radial 
blocks,  made  from  selected  clays  and  burned  at  a  very  high 
temperature,  and  a  company  *  was  formed  for  the  purpose  of 
erecting  chimneys  by  this  method  of  construction.  Since  that 
time  the  company  through  its  various  agencies  has  built  over 
4,000  chimneys  in  all  parts  of  the  world. 

The  blocks  are  formed  to  suit  the  circular  and  radial  lines 
of  each  section  of  the  chimney,  so  that  they  can  be  laid  with 
thin  even-  joints  and  regular  smooth  surfaces.  The  blocks 
being  much  larger  than  common  bricks  there  are  only  about 
half  as  many  joints.  These  chimneys  are  always  circular  in 
plan  above  the  base,  and  except  for  chemical  works,  metal 
refineries,  furnaces,  etc.,  with  a  single-shell  construction.  They 
are  undoubtedly  stronger  and  superior  in  every  way  to  common 
brick  chimneys, 

H.  R.  Heinicke,  of  Chemnitz,  Germany,  builder  of  the  460-ft. 
stack  at  Halsbriicke  and  many  tall  chimneys  in  Europe  and 
America,  also  employs  radial  blocks  made  especially  for  each 
chimney  and  very  much  resembling  those  described  above.  A 
branch  office  is  maintained  at  160  Fifth  Ave.,  New  York. 

The  Steinl  Improved  Chimney  Construction  Company  of 
Birmingham,  Ala.,  designs  and  erects  an  improved  radial  block 
chimney  in  which  every  block  is  moulded  for  the  position  it  is 
to  occupy  and  is  tongued  and  grooved  on  the  sides,  so  that 
the  blocks  interlock,  thereby  forming  a  ring  which  it  would 
seem  to  be  impossible  to  separate.  The  blocks  are  also  per- 
forated vertically  so  as  to  receive  the  cement  when  in  place. 

Chimneys  of  Reinforced  Concrete. — Within  the  past 
ten  years  a  number  of  tall  chimneys  have  been  built  of  rein- 
forced concrete,  and  it  seems  more  than  probable  that  this 
material  will  largely  supersede  brick  for  this  purpose  in  the 
future.  A  well-built  steel-concrete  chimney  should  be  more 
durable  than  either  brick  or  steel,  and  in  every  respect  as  good, 
while  the  cost  of  erection  is  less  than  for  a  brick  chimney. 

In  July  and  August,  1902,  a  concrete-steel  chimney  180  ft. 

*  Alphonse  Custodis  Chimney  Construction  Company,  517  Bennett  Build- 
ing, New  York. 


1230        SELF-SUSTAINING  STEEL   CHIMNEYS. 

high  from  bottom  of  footing  and  165  ft.  above  floor  of  boiler- 
room  was  built  by  Mr.  Carl  Leonardt  for  the  Pacific  Electric 
Railway  Company  at  Los  Angeles,  CaL,  the  Ransome  system 
of  construction  being  employed.  The  inner  diameter  is  11  ft. 
for  the  entire  height.  A  detailed  description  of  this  chimney 
was  published  in  the  Engineering  Record  of  April  11,  1903. 

A  chimney  built  in  1903  for  the  Laclede  Fire-brick  Mfg.  Com- 
pany at  St.  Louis,  Mo.,  has  an  inside  diameter  of  5  ft.  and  a 
height  of  130  ft.  above  foundation.  The  materials  used  in  the 
construction  are  river  sand  and  T  bars. 

Up  to  the  height  of  65  ft.  the  chimney  consists  of  two  in- 
dependent shells,  the  outer  being  6  ins.  thick  and  the  inner  4 
ins.,  separated  by  a  3-iiich  air  space. 

At  the  height  of  65  ft.  both  shells  join,  the  inner  shell  con- 
tinuing and  tapering  in  proper  intervals  from  5  ins.  to  4  ins., 
and  finally  3  ins.  at  the  top.  The  air  space  is  connected  directly 
above  the  grade,  by  means  of  four  openings  4"X6",  with  the 
outside  air,  which  at  the  65-foot  height  is  allowed  to  enter  from 
the  air  space  to  the  chimney  proper  through  round  holes.  This 
provision  is  to  allow  the  inner  shell  which  receives  the  direct 
heat  to  expand  and  contract  while  being  protected  by  the 
outer  shell  against  sudden  cooling  from,  the  atmosphere.* 

In  1900  a  chimney  was  built  on  the  Ransome  system  for  the 
Pacific  Coast  Borax  Company  at  Bayonne,  N.  J.,  6  ft.  diameter 
by  150  ft.  high.  It  consists  of  one  outer  and  one  inner  shell 
from  grade  to  top,  both  shells  being  reinforced  by  means  of 
twisted  square  rods,  vertically  and  horizontally. 

A  large  number  of  these  chimneys  have  been  constructed 
on  the  Ransome  system,  among  which  are  two  at  South  Bend, 
Ind.,  and  one  for  the  Plymouth  Cordage  Company  at  Eliza- 
bethport,  N.  J.  The  latter  is  220  ft.  high,  witn  an  interior 
diameter  of  8  ft.  8  ins.  It  is  built  in  two  shells  each  having 
vertical  ribs  running  contiguously  in  the  air  space. 

Self-sustaining'  Steel  Chimneys  are  largely  coming 
into  use,  especially  for  tall  chimneys  of  iron-works  and  power- 
houses from  150  to  300  ft.  in  height.  "The  advantages  claimed 
are:  Greater  strength  and  safety;  smaller  space  required; 
smaller  cost  by  30  to  50  per  cent,  as  compared  with  brick  chim- 
neys; avoidance  of  infiltration  of  air  and  consequent  checking 
of  the  draught,  common  in  brick  chimneys.  They  are  usually 

*  A  more  complete  description  of  this  chimney,  with  illustrations,  may 
be  found  in  Cement  and  Engineering  News  for  February,  1904, 


HYDRAULICS. 


1231 


made  cylindrical  in  shape,  with  a  wide  curved  flare  for  10  to 
25  ft.  at  the  bottom.  A  heavy  cast-iron  base  plate  is  provided, 
to  which  the  chimney  is  riveted,  and  the  plate  is  secured  to 
a  massive  foundation  by  holding-down  bolts.  No  guys  are 
used."  * 

The  Philadelphia  Engineering  Works,  which  built  a  large 
number  of  steel-plate  chimneys,  published,  in  1894,  a  pamphlet 
discussing  the  strength  and  stability  of  such  chimneys  and  con- 
taining tables  of  dimensions  for  stacks  of  varying  diameter  and 
height.  This  company  has  been  succeeded  by  the  Niles-Bemeiit- 
Pond  Co.,  who  confine  themselves  exclusively  to  the  con- 
struction of  electric  traveling  cranes.  The  following  table  is 
compiled  from  the  pamphlet  above  mentioned: 

SIZES  OF  FOUNDATIONS  FOR  SELF-SUSTAINING  STEEL 
CHIMNEYS,  HALF  LINED. 


Diameter,  clear,  ft... 

3 

4 

5 

6 

7 

9 

11 

Height  in  feet  
Least  diam.  of  foun- 
dation   
Least  depth  of  foun- 
dation   

100 
15'  9" 
6'  6" 

100 
15'  3" 

150 
20'  4" 
9' 

150 
21'  10" 

8' 

150 
22'  7" 
9' 

175 
25'  9" 

10' 

225 
29'  11" 
13' 

Height  in  feet.  .  . 

125 

200 

200 

250 

275 

300 

Least  diam.  of  foun- 
dation. .  .  . 

17'  6" 

23'  8" 

25'    0" 

29'  8" 

33'  6" 

36'  0" 

Least  depth  of  foun- 
dation    

7'  6" 

10' 

10' 

12' 

12' 

14' 

The  details  of  a  self -sustained  steel-plate  stack  5  ft.  inside 
diameter  and  120  ft.  high  above  the  base  ring  are  published 
in  Engineering  Record  for  February  15,  1902. 

Hydraulics. 

Water  is  practically  an  incompressible  liquid,  weighing,  at 
the  average  temperature  of  62°  F.,  62.355  Ibs.  to  the  cubic  foot 
and  8.335  Ibs.  to  the  gallon.  These  figures  change  slightly  with 
changes  in  temperature  and  atmospheric  pressure,  and  a  slight 
variation  for  the  same  temperature  will  be  found  in  different 
works. 

Pressure    of    Water.— The   pressure   of  still  water  in 

pounds  per  square  inch  against  the  sides  of  any  pipe  or  vessel 

of  any  shape  whatever  is  due  alone  to  the  head,  or  height  of 

the  surface  of  the  water  above  the  point  considered  pressed 

*  Kent,  p.  740. 


1232 


FLOW  OF  WATER  IN  PIPES. 


upon,  and  is  equal  to  0.433  Ib.  per  square  inch  for  every  foot 
of  head  at  62°  F.  The  fluid  pressure  per  square  inch  is  equal 
in  all  directions. 

To  find  the  total  pressure  of  quiet  water  against  and  per- 
pendicular to  any  surface,  whether  vertical,  horizontal,  or  in- 
clined at  any  angle,  whether  it  be  flat  or  curved,  multiply 
together  the  area  in  square  feet  of  the  surface  pressed,  the 
vertical  depth  of  its  centre  of  gravity  below  the  surface  of  the 
water,  and  the  constant  62.4.  The  product  will  be  the  required 
pressure  in  pounds.  This  may  be  expressed  by  formula  as 
follows: 

P  =  62.4AZ), 

in  which  P=the  pressure  in  pounds  of  quiescent  water  on  the 

surface  considered; 

A  =the  area  pressed  upon  in  square  feet;  and 
D=the  vertical  depth  in  feet  of  centre  of  gravity  of 
surface  considered. 

TABLE  A.— PRESSURE  IN  POUNDS  PER  SQUARE  INCH 
FOR  DIFFERENT  HEADS  OF  WATER. 


Head, 
Feet. 

0 
10 
20 
30 
40 
50 
60 
70 
80 
90 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.433 
4.763 
9.093 

13.423 
17.753 
22.083 
26.413 
30.743 
35.073 
39.403 

0.866 
5.196 
9.526 
13.856 
18.180 
22.516 
2G.846 
31.176 
35.506 
39.836 

1.299 
5.629 
9.959 
14.289 
18.619 
22.949 
27.279 
31.609 
35.939 
40.269 

1.732 
6.062 
10.392 
14.722 
19.052 
23.382 
27.712 
32.042 
36.372 
40.702 

2.165  2.598  3.031 
6.495  6.928  7.361 
10.82511.258  11.691 
15.155  15.588  16.021 
19.485  19.918  20.351 
23.815  24.248  24.681 
28.145J28.578  29.011 
32.475  32.908  33.341 
36.805  37.238  37.671 
41.135J41.568  42.001 

3.464 
7.794 
12.124 
16.454 
20.784 
25.114 
29.444 
33.774 
38.104 
42.436 

3.897 
8.227 
12.557 
16.887 
21.217 
25.547 
29.877 
34.207 
38.537 
42.867 

4.330 
8.660 
12.990 
17.320 
21.650 
25.980 
30.310 
34.640 
38.970 

The  pressure  for  greater  heads  can  be  readily  found  by  mul- 
tiplication or  addition,  thus:  the  pressure  for  a  head  of  110  ft. 
is  ten  times  that  for  11.  The  pressure  for  118  ft.  is  equal  to 
the  pressure  for  110  ft.  plus  that  for  8  ft. 


Flow  of  Water  in  Pipes. 

[NoTE. — Owing  to  the  many  practical  and  variable  conditions 
which  affect  the  flow  of  water  in  pipes,  such  as  the  smoothness 
of  the  pipe,  number  and  character  of  the  joints,  bends  and 


FLOW  OF  WATER  IN  PIPES. 


valves  in  the  pipe,  to  say  nothing  of  the  size  and  length  of  the 
pipe,  all  formulas  for  the  velocity  and  discharge  of  water  in  and 
through  pipes  can  only  be  considered  as  approximate.  The 
following  formulas  and  data  are  taken  largely  from  the  National 
Tube  Company's  "Book  of  Standards,"  1902  edition.  They 
agree  fairly  well  with  similar  tables  in  "Kent"  and  "Trautwine," 
both  of  whom  devote  much  space  to  this  subject.] 

The  quantity  of  water  passing  through  a  given  pipe  is  governed 
by  the  sectional  area  of  the  pipe  or  outlet  and  the  mean  velocity. 
The  velocity  depends  primarily  upon  the  pressure  or  head,  and 
is  greatly  affected  by  friction,  which  again  varies  with  the 
smoothness  of  the  bore,  the  diameter  and  length  of  the  pipe, 
and  whatever  obstructions  there  may  be  in  the  pipe. 

Head  is  the  vertical  distance  from  the  surface  of  the  water 
in  the  reservoir  to  the  centre  of  gravity  of  the  lower  end  of  the 
pipe  when  the  discharge  is  into  the  air,  or  to  the  level  surface 
of  the  lower  reservoir  when  the  discharge  is  under  water. 

When  the  pressure  is  produced  by  mechanical  means,  the 
head  in  feet  of  water  may  be  readily  determined  by  the  follow- 
ing table: 

TABLE     B.*  —  FOR     CONVERTING      PRESSURE     PER 
SQUARE  INCH  INTO  FEET  HEAD  OF  WATER. 


££ 
£g 

0 

1 

o 

3 

4 

5 

6 

7 

8 

9 

0 

2.309 

4.619 

6.928 

9.238 

11.547 

13.857 

16.166 

18.476 

20.785 

10 

23.0947 

25.404 

27.714 

30.023 

32.333 

34.642 

36.952 

39.261 

41.570 

43.880 

20 
30 

46.1894 
69.2841 

48.499 
71.594 

50.808 
73.903 

53.118 
76.213 

55.427 

78.522 

57.737 

80.831 

60.046  62.356  64.665 
83.14185.45087.760 

66.975 
90.069 

40 

92.3788 

94.688 

96.998 

99.307 

101.62  103.93 

106.24  108.55 

110.85 

113.16 

50 

115.4735 

117.78 

120.09 

122.40 

124.71il26.02 

129.33 

131.64 

133.95 

136.26 

60 

138.5682  140.88 

143.19 

145.50 

147.81  150.12 

152.42  1M.73 

157.04 

159.35 

70 

80 

161.66291163.97 

184.7576  187.07 

166.28 
189.38 

168.59 
191.69 

170.90 
194.00 

173.21 
196.31 

175.52  177.83|180.14 
198.61  200.92  203.23 

182.45 
205.54 

90 

207.8523 

210.16 

212.47 

214.78 

217.09 

219.40 

221.71 

224.02 

226.33 

228.64 

*  Tables  A  and  B  are  exact  for  water  at  62°  F.  and  atmospheric  pres- 
sure =14.7  Ibs. 

To  find  the  velocity  of  water  discharged  from  a 
pipe  line  longer  than  four  times  its  diameter,  knowing  the 
head,  length,  and  inside  diameter,  use  the  following  formula, 


1234  FLOW  OF   WATER  IN  PIPES. 

in  which      v=approximate  mean  velocity  in  feet  per  second; 
m  =  coefficient  from  the  table  below; 
d= diameter  of  pipe  in  feet; 
h = total  head  in  feet; 
L=  total  length  of  line  in  feet. 

VALUES  OF  COEFFICIENT  m. 


Diameter  of  Pipe  in  Feet. 

4/    M 

V  L+54d 

0.05 

0.10 

0.50 

1 

1.5 

2 

3 

4 

m 

m 

m 

m 

m 

m 

m         m 

0.005 

29 

31 

33 

35 

37 

40 

44 

47 

0.01 

34 

35 

37 

39 

42 

45 

49 

53 

0.02 

39 

40 

42 

45 

49 

52 

56 

59 

0.03 

41 

43 

47 

50 

54 

57 

60 

63 

0.05 

44 

47 

52 

54 

56 

60 

64 

67 

0.10 

47 

50 

54 

56 

58 

62 

66 

70 

0.20 

4S 

51 

55 

58 

60 

64 

67 

70 

The  above  coefficients  are  averages  deduced  from  a  large 
number  of  experiments.  In  most  cases  of  pipes  carefully  laid 
and  in  fair  condition,  they  should  give  results  from  5  to  10  per 
cent,  ot  the  truth. 

EXAMPLE.— Given  the  head,  ft  =  50  ft.:  the  length,  L=  5,280  ft, 
and  the  diameter,  d  =  2  ft.;  to  find  the  velocity  and  quantity 
of  discharge. 

Substituting  these  values  in  above  formula,  we  get 


dXh 


2X50 


5280+ 108 ~ 


"  =0.130. 


In  column  headed 


find  0.10,  which  is  the  value 


hd 

/L+54d 

nearest  to  O.136,  and  look  along  this  line  until  column  headed 
"2"  is  reaches,  then  read  62  as  the  value  of  coefficient  m. 

Then  v=  62X0.136  =  8.432  ft.  per  sec.,  the  required  velocity. 

To  find  the  discharge  in  cubic  feet  per  second,  multiply 
this  velocity  by  area  of  cross-section  of  pipe  in  square  feet. 

Thus,  3. 1416X (1)'X8.432  =26.49  cu.  ft.  per  second. 

Since  there  are  7.48  gal.  in  a  cubic  foot,  the    discharge    in 
gallons  per  second  =  26.49X7.48  =  198.2. 

The  above  formula  is  only  an  approximation,  since  the  flow 
is  modified  by  bends,  joints,  incrustations,  etc.     Wrought-irou 


FLOW  Ofr   WATER  IN  PIPES.  1235 

and  steel  pipes  are  smoother  than  cast-iron  ones,  thereby 
presenting  less  friction  and  less  encouragement  for  deposits; 
and,  being  in  longer  lengths,  the  number  of  joints  is  reduced, 
thus  lessening  the  undesirable  effects  of  eddy  currents. 

To  find  the  head  in  feet  necessary  to  give    a  stated 
discharge  in  cubic  feet,  use  the  formula  * 

,     0.000704  Q2(L+  54  d) 

*-  —55—         -• 

in  which  h=* total  head  in  feet; 

L=  total  length  of  line  in  feet; 
d  =  diameter  of  pipe  in  feet; 
Q=  quantity  of  water  in  cu.  ft.  per  second. 
EXAMPLE. — Given  the  diameter  of  pipe,  d=0.5  ft.;  the  length 
of  pipe,  Z/  =  20  ft.;   and  the  quantity  of  water  to  be  discharged, 
g=3.07  cu.  ft.  per  second;   to  find  the  necessary  head. 
Substituting  these  values  in  the  above  formula,*  we  get 

,      0.000704  X  9.4  X  (20+ 27) 

(0.5)5 
0.000704X9.4X47 


0.03125 


9.95  ft.,  the  required  head. 


The  following  formula  *  is  simpler  and  can  be  used  when 
4d  in  relation  to  L  is  so  small  as  to  be  negligible: 

,     0.000704  Q2XL 


If  the  pipe  instead  of  being  straight  has  easy  curves  (say 
with  radius  not  less  than  five  diameters  of  the  pipe)  either 
horizontal  or  vertical,  the  discharge  will  not  be  materially 
diminished  so  long  as  the  total  heads  and  total  actual  lengths 
of  pipe  remain  the  same,  but  it  is  advisable  to  make  the  radius  as 
much  more  than  five  diameters  as  can  conveniently  be  done. 

To  find  the  diameter  of  a  pipe  of  given  length  to  deliver  a 
given  quantity  of  water  under  a  given  head  use  the  following, 


0.234 


*  The  small  5  in  these  formulas  denotes  the  fifth  power  or  root,  as  the 
case  may  be. 


1236  FLOW  OF  WATER  IN   PIPES. 

in  which  d  =  diameter  of  pipe  in  feet; 

Q=  cubic  feet  per  second  delivered; 
L  =  length  of  line  in  feet; 
h  =  head  in  feet. 

EXAMPLE.  —  Given  the  head,  ft  =  700  ft.;  the  length  of  pipe, 
L  =3,000  ft.;  the  quantity  to  be  delivered,  Q=  4  cu.  ft.  per  sec.; 
required  the  diameter  of  pipe  necessary. 

Substituting  these  values  in  the  above  formula,*  we  get 


4  5  1 


d  =  0.234  5   -—         =0.234     68^7  =  0.545  ft.  =6.54  ins. 


To  find  the  diameter  of  pipe  required  to  deliver  a  given  quantity 
of  water  with  a  given  head. 

RULE:  1st,  Reduce  the  head  to  feet  per  100  ft.; 
then,  2d,  From  Table  C,  find  the  discharge  for  the  head  thus 
obtained  through  a  pipe  1  ft.  in  diameter; 

then,  3d;  Divide  the  required  discharge  by  that  obtained  from 
Table  C;  then  look  for  the  quotient  in  the  column  of  Table 
D  headed  "  Ratio  of  Discharge"  and  opposite  it,  in  columns 
1  and  2,  will  be  found  the  required  diameter. 

NOTE.  —  The  use  of  Tables  C  and  D  is  not  sufficiently  correct 
for  pipes  less  than  700  diameters  long. 

EXAMPLE.  —  Given  the  head  from  a  reservoir  to  point  of 
delivery  as  20  it.  in  3,  distance  of  1,860  ft.,  what  is  the  diameter 
oi  a  pipe  to  deliver  6  cu.  ft.  of  water  per  second? 

20 

20  ft.  head  in  1,860  ft.  =  ^-^  ft.  in  100  ft.,  or  1.075  ft.  in  100. 
lo.uU 

From  Table  C  we  find  the  discharge  per  second  with  a  head 
of  1.136  is  3.9S9;  lor  a  head  of  1.075  it  would  be  about  3.8  cu.  ft. 
Dividing  required  discharge  (6)  by  3.8,  we  have  1.58.  From 
Table  D  the  diameter  ol  pipe  having  ratio  of  discharge  =  1.5S 
is  found  to  be  about  14  J,  therefore  we  must  use  a  15-inch  pipe 
to  obtain  the  required  discharge.  If  the  required  discharge 
is  in  gallons  divide  by  7.5.  to  reduce  to  cubic  feet.  If  in  cubic 
feet  per  minute,  divide  by  60  to  reduce  to  feet  per,  second. 

*  The  small  5  in  these  formulas  denotes  the  fifth  power  or  root,  as  the 
case  may  be. 


FLOW   OF  WATER  IN  PIPES. 


1237 


TABLE  C.  —  THE  VELOCITIES  AND  DISCHARGES 
THROUGH  A  STRAIGHT,  SMOOTH  PIPE  ONE 
FOOT  IN  DIAMETER  AND  ONE  MILE,  OR  5,280 
DIAMETERS,  IN  LENGTH. 


Head  in 
Feet  per 
100  Feet. 

Head  in 
Feet  per 
Mile. 

Velocity  in 
Feet  per 
Second. 

Discharge  in 
Cubic  Feet 
per  Second. 

Discharge  in 
Cubic  Feet 
per  24  Hours. 

.0568 

3 

1.13 

.8914 

76,982 

.0758 

4 

1.31 

1.028 

88,862 

.0947 

5 

1.47 

1.150 

99,403 

.1136 

6 

1.61 

1.264 

109,209 

.1325 

7 

1.74 

1.366 

118,022 

.1514 

8 

1.86 

1.455 

.    125,740 

.1703 

9 

1.96 

1.539 

132,969 

.1894 

10 

2.08 

1.633 

141,145 

.2273 

12 

2.27 

1.782 

153,964 

.2652 

14 

2.45 

1.924 

166,233 

.3030 

16 

2.62 

2.057 

177,724 

.3409 

18 

2.78 

2.183 

188,611 

.3788 

20 

2.93 

2.301 

198,806 

.4735 

25 

3.28 

2.572 

222,156 

.5682 

30 

3.59 

2.819 

243,604 

.6629 

35 

3.88 

3.047 

263,260 

.7576 

40 

4.15 

3.267 

282,288 

.8523 

45 

4.40 

3.451 

298,209 

.9470 

50 

4.64 

3.638 

314,352 

1.136 

60 

5.08 

3.9S9 

344,649 

1.326 

70 

5.49 

4.311 

372,470 

1.515 

80 

5.85 

4.602 

397,613 

1.704 

90 

6.23 

4.900 

423,435 

1.894 

100 

6.56 

5.144 

444,312 

2.083 

110 

6.87 

5.395 

466,128 

2.272 

120 

7.18 

5.639 

487,209 

2.462 

130 

7.47 

5.866 

506,822 

2.652 

140 

7.76 

6.094 

526,521 

2.841 

150 

8.05 

6.322 

546,048 

3.030 

160 

8.30 

6.534 

564,576 

3.219 

170 

8.55 

6.715 

580,176 

3.408 

180 

8.80 

6.903 

596,418 

3.596 

190 

9.04 

7.100 

613,440 

3.788 

200 

9.28 

7.276 

628,704 

4.261 

225 

9.84 

7.696 

664,848 

4.735 

250 

10.4 

8.168 

705,728 

5.208 

275 

10.8 

8.482 

732,844 

5.682 

300 

11.3 

8.914 

769,824 

6.629 

350 

12.3 

9.621 

831,168 

7.576 

400 

13.1 

10.28 

888,624 

8.532 

450 

13.9 

10.91 

943,056 

1238 


FLOW  OF  WATER  IN  PIPES. 


TABLE  C.  —  THE  VELOCITIES  AND  DISCHARGES 
THROUGH  A  STRAIGHT,  SMOOTH  PIPE  ONE 
FOOT  IN  DIAMETER  AND  ONE  MILE,  OR  5,280 
DIAMETERS,  IN  LENGTH— (Continued} . 


Head  in 
Feet  per 
100  Feet. 

Head  in 
Feet  per 
Mile. 

Velocity  in 
Feet  per 
Second. 

Discharge  in 
Cubic  Feet 
per  Second. 

Discharge  in 
Cubic  Feet 
per  24  Hours. 

9.47 

500 

14.7 

11.50 

994,032 

10.41 

550 

15.4 

12.09 

1,044,576 

11.36 

600 

16.1 

12.64 

1,092,096 

12.30 

650 

16.7 

13.11 

1,132,704 

13.25 

700 

17  .4 

13.66 

1,180,224 

14.20 

750 

18.0 

14.13 

1,220,832 

15.15 

800 

18.6 

14.55 

1,257,408 

16.09 

850 

19.1 

15.00 

1,296,000 

17.04 

900 

19.6 

15.39 

1,329,696 

17.99 

950 

20.3 

15.94 

1,377,216 

18.94 

1000 

20.8 

16.33 

1,411,456 

22.73 

1200 

22.7 

17.82 

1,539,648 

26.52 

1400 

24.5 

19.24 

1,662,336 

30.30 

1600 

26.2 

20.57 

1,777,248 

34.03 

1800 

27.8 

21.83 

1,886,112 

37.87 

2000 

29.3 

23.01 

1,988,064 

47.35 

2500 

32.8 

25.72 

2,221,560 

56.81 

3000 

35.9 

28.19 

2,436,040 

FLOW   OF   WATER  IN   PIPES. 
TABLE  D. 


1239 


Ratio  of 

Ratio  of 

Diam- 
eter of 

Diameter 

Discharge  to 
that  through 

Diam- 
eter of 

Diameter 

Discharge  to 
that  through 

Pipe  in 
Inches. 

of  Pipe  in 
Feet. 

a  1-foot  Pipe 
with  the 

Pipe  in 
Inches. 

of  Pipe  in 
Feet. 

a  1-foot  Pipe 
with  the 

Same  Head 

Same  Head 

per  Mile. 

per  Mile. 

1 

.0833 

.0020 

12} 

1.042 

1.106 

1J 

.1250 

.0055 

13 

1.083 

1.221 

2 

.1667 

.0113 

14 

1.167 

1.470 

2} 

.20*3 

.0198 

15 

1.250 

1.746 

3 

.2500 

.0310 

16 

1.333 

2.053 

3} 

.2917 

.0453 

17 

1.417 

2.388 

4 

.3333 

.0643 

18 

1.5 

2.754 

4J 

.3750 

.0857 

19 

1.5^3 

3.153 

5 

.4167 

.1119 

20 

1.667 

3.585 

*>} 

.4583 

.1422 

21 

1.75 

4.051 

6 

.5 

.1767 

22 

1.833 

4.551 

6J 

.5417 

.2159 

23 

1.917 

5.084 

7 

.5^33 

.2600 

24 

2 

5.649 

7} 

.6250 

.3090 

24f 

2.052 

6.000 

8 

.6667 

.3631 

26 

2.167 

6.912 

8} 

.7083 

.4220 

28 

2.333 

8.319 

9 

.75 

.4871 

30 

2.5 

9.822 

9J 

.7917 

.5575 

3Q1 

2.521 

10 

10 

.8333 

.6337 

32 

2.667 

11.6 

10} 

.8750 

.7157 

34 

2.  £33 

13.5 

11 

.9167 

.8044 

36 

3 

15.5 

11} 

.9583 

.8987 

38 

3.167 

17.8 

12 

1 

1 

40 

3.333 

20.2 

This  table  also  shows  the  relative  discharging  capacities  of 
long  pipes.  Thus,  one  12-inch  pipe=two  9-inch  pipes,  nearly 
six  6-inch  pipes,  or  thirty-three  3-inch  pipes. 


1240 


FLOW   OF  WATER  IN   PIPES. 


TABLE    E.— FLOW  OF  WATER  IN  HOUSE-SERVICE 
PIPES. 

(Thomson  Meter  Co.) 
To  find  discharge  in  gallons  multiply  by  7.47. 


Condition 
of  Dis- 
charge. 

Pressure  in  Main, 
Lbs.  per  Sq.  Inch. 

Discharge  in  Cubic  Feet  per  Minute  from  the  Pipe. 

Nominal  Diameters  of  Iron  or  Lead  Service  Pipe 
in  Inches. 

X 

5/8 

H 

1 

6.13 

7.08 
7.92 

8.67 
9.70 
11.20 

12.77 

1H 

16.58 
19.14 
21.40 
23.44 
26.21 
30.27 
34.51 

2 

33.34 

38.50 
43.04 
47.15 
52.71 
60.87 
69.40 

3 

4 

6 

Through  35 
feet  of 
service 
Eipe,  no 
ack 
pressure. 

30 
40 
50 
60 
75 
100 
130 

1.10 
1.27 
1.42 
1.56 
1.74 
2.01 
2.29 

1.92  3.01 
2.22  3.48 
2.48  3.89 
2.71  4.26 
3.034.77 
3.505.50 
3.996.28 

88.16 
101.80 
113.82 
124.68 
139.39 
160.96 
183.52 

58.19 
67.19 
75.13 
82.30 
92.01 
106.24 
121.14 

173.85 
200.75 
224.44 
245.87 
274.89 
317.41 
361.91 

444  .  63 
513.42 
574  .  02 
628.81 
703.03 
811.79 
925  .  58 

Through 
100  feet 
of  service 
Eipe,  no 
ack 
pressure. 

30 
40 
50 
60 
75 
100 
130 

0.66 
0.77 
0.86 
0.94 
1.05 
1.22 
1.39 

l.ie'l.84 
1.342.12 
1.502.37 
1.652.60 
1.84  2.91 
2.133.36 
2.42  3.83 

3.78 
4.36 
4.88 
5.34 
5.97 
6.90 
7.86 

10.40 
12.01 
13.43 
14.71 
16.45 
18.99 
21.66 

21.30 
24.59 
27.50 
30.12 
33.68 
38.89 
44.34 

118.13 
136.41 
152.51 
167.06 
186.78 
215.68 
245.91 

317.23 
366  .  30 
409.54 
448  .  63 
501.58 
579.18 
660  .  36 

Through 
100  feet 
of  service 
pipe  and 
15  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.55 
0.66 
0.75 
0.83 
0.94 
1.10 
1.26 

0.96 
1.15 
1.31 
1.45 
1.64 
1.92 
2.20 

1.52 
1.81 
2.06 
2.29 
2.59 
3.02 
3.48 

3.11 
3.72 
4.24 

4.70 
5.32 
6.21 
7.14 

8.57 
10.24 
11.67 
12.94 
14.64 
17.10 
19.66 

17.55 
20.95 
23.87 
26.48 
29.96 
35.00 
40.23 

47.90 
57.20 
65.18 
72.28 
81.79 
95.55 
109.82 

97.17 
116.01 
132.20 
146.61 
165.90 
193.82 
222  .  75 

260.56 
311.09 
354.49 
393.13 
444.85 
519.72 
597.31 

Through 
100  feet 
of  service 
pipe    and 
30  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.44 
0.55 
0.65 
0.73 
0.84 
1.00 
1:15 

0.77 
0.97 
1.14 
1.28 
1.47 
1.74 
2.02 

1.22 
1.53 
1.79 
2.02 
2.32 
2.75 
3.19 

2.50 
3.15 
3.69 
4.15 
4.77 
5.65 
6.55 

6.80 
8.68 
10.16 
11.45 
13.15 
15.58 
18.07 

14.11 
17.79 
20.82 
23.47 
26.95 
31.93 
37.02 

38.63 
48.68 
56.98 
64.22 
73.76 
87.38 
101.33 

78.54 
98.98 
115.87 
130.59 
149.99 
177.67 
206.04 

211.54 
266.59 
312.08 
351.73 
403.98 
478.55 
554.96 

Table  E  may  also  be  used  when  pressure  is  in  feet  head  of 
water  by  reducing  the  head  in  feet  to  pounds  per  square  inch 
by  Table  A.  Thus,  if  we  wish  the  discharge  per  minute  through 
a  f-inch  pipe  100  ft.  long  with  a  head  of  70  ft,,  we  find  from 
Table  A  that  a  head  of  70  ft.  corresponds  to  a  pressure  of  30  Ibs. 
per  square  inch,  and  from  Table  E  we  find  the  discharge  through 
a  f-inch  pipe  100  ft.  long  with  a  pressure  of  30  Ibs.  to  be  1.84 
cu.  ft.  per  minute. 


FLOW  OF   WATER  IN  PIPES. 


1241 


TABLE  F.— FRICTION  OF  WATER  IN  PIPES  BASED  ON 
ELLIS  AND  ROWLAND'S  EXPERIMENTS. 

The  following  table  gives  the  friction  loss  in  pounds  pressure 
per  square  inch  for  each  100  ft.  of  length  in  different  size  clean 
iron  pipes  discharging  given  quantities  of  water  per  minute. 
This  friction  loss  is  greatly  increased  by  bends  or  irregularities; 
in  the  pipe. 

To  find  "friction  head"  in  feet  multiply  figures  by  2.3. 


Gallons 
per 
Min- 
ute. 

Sizes  of  Pipes,  Inside  Diameter. 

f-Inch. 

1-Inch. 

li  inch. 

l^-inch. 

2-inch. 

2^-inch. 

3-inch. 

4-inch. 

5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
75 
100 
125 
150 
175 
200 
250 
300 
350 
400 
450 
500 
600 
700 

3.3 
13.0 

23.7 
50.4 

78.8 

0.84 
3.16 
6.98 
12.3 
19.0 
27.5 
37.0 
48.0 

0.31 
1.05 
2.38 
4.07 
6.40 
9.15 
12.4 
16.1 
20.2 
24.9 
56.1 

0.12 
0.47 
0.97 
1.66 
2.62 
3.75 
5.05 
6.52 
8.15 
10.0 
22.4 
39.0 

0.12 

0.26 
0.42 
0.64 
0.91 
1.22 
1.60 
2.02 
2.44 
5.32 
9.46 
14.9 
21.2 
28.1 
37.5 

0.21 

0.10 

0.20 

0.35 
0.74 
1.31 
1.99 
2.85 
3.85 
5.02 
7.76 
11.2 
15.2 
19.5 
25.0 
30.8 

0.27 

0.09 
0.23 
0.33 
0.49 
0.69 
0.94 
1.22 
1.89 
2.66 
3.65 
4.73 
6.01 
7.43 
9.54 
14.32 

0.81 
1.80 
3.20 
4.89 
7.00 
9.46 
12.47 
19.66 
28.06 

"Water-pipe  is  usually  tested  to  300  Ibs.  pressure  per  square 
inch  before  delivery,  and  a  hammer  test  should  be  made  while 
the  pipe  is  under  pressure. 

The  usual  length  for  each  section  of  cast-iron  water-pipe  is 
12  ft.  4  ins.  to  12  ft.  6  ins.,  depending  upon  the  depth  of  the 
socket,  each  length  making  approximately  12  ft.  of  pipe  when 
laid.  Pipes  2  to  4  ins.  diameter  are  sometimes  made  in  8  or 
9  ft.  lengths. 


1242    SAFE  PRESSURES  FOR  CAST-IRON   PIPES. 


SAFE  PRESSURES  AND  EQUIVALENT  HEADS  OF  WATER 
FOR  CAST-IRON  PIPE  OF  DIFFERENT  SIZES  AND 
THICKNESSES. 

(Calculated  by  F.  H.  Lewis  from  Farming's  Formula.) 


1 

§ 

H-l 

d 

.2 
H 

f6 

I 

1 

Size  of  Pipe,  Inches. 

4 

6 

8 

10 

12 

14 

15 

112 
224 
336 

.9 

258 
516 

774 

8 

a 

|a 

|| 

II 

.9 

II 

-g-g 

£'rt 

11 

97 
170 
244 
316 
392 
465 
538 
612 

49 
124 
199 

274 

112 
2SO 

45S 
631 

18 
74 
130 
186 

42 
171 
300 
429 

44 
89 
132 
177 

224 

101 
205 
304 
408 
516 

24 
621 
99 
137 
174 
212 
249 

55 
143 

228 
316 
401 
488 
574 

42 
74 
106 
138 
170 
202 
234 
266 

H 

H 
i« 
li 
if 
if 

16 

18 

20 

24 

30 

36 

32 
44 
57 

82 
107 
132 
157 

182 
207 

74 

101 
131 
189 
247 
304 
362 
419 
477 

56 

84 
112 
140 
168 
196 
224 

129 
194 

253 
323 
387 
452 
516 

41 
66 
91 
116 
141 
166 
191 
216 

95 
152 
210 
267 
325 
382 
440 
497 

51 
74 
96 
119 
141 
164 
209 
256 

118 
170 
221 

274 
325 

378 
481 
589 

30 
49 
68 
86 
105 
124 
161 
199 
237 

69 
113 
157 

198 
242 

286 
371 

458 
546 

24 
39 
54 
69 
84 
114 
144 
174 
204 
234 

55 
90 
124 
159 
194 
263 
332 
401 
470 
538 

WEIGHTS  OF  LEAD  AND  GASKET  FOR  PIPE  JOINTS. 

(Dennis  Long  &  Co.) 


Diameter 
of  Pipe. 

Lead. 

Gasket. 

Diameter 
of  Pipe. 

Lead. 

Gasket. 

Inches. 

Lbs. 

Lbs. 

Inches. 

Lbs. 

Lbs. 

2 

2.5 

0.125 

12 

15 

0.250 

3 

3.5 

0.170 

14 

18 

0.375 

4 

4.5 

0.170 

16 

22 

0.500 

6 

6.5 

0.200 

18 

26 

0.500 

8 

9.0 

0.200 

20 

33 

0.625 

10 

13.0 

0.250 

WEIGHT  OF  CAST-IRON  WATER-PIPES.     1243 


WEIGHTS,  PER  FOOT,  OF  CAST-IRON  PIPES  IN  GEN- 
ERAL USE  INCLUDING  SOCKET  AND  SPIGOT 
ENDS. 

(Dennis  Long  &  Co.,  Inc.,  Louisville,  Ky.) 


Diam- 
eter. 

Thick- 
ness. 

Weight 
per 

Foot. 

Diam- 
eter. 

Thick- 
ness. 

Weight 
per 
Foot. 

Diam- 
eter. 

Thick- 
ness. 

Weight 
per 
Foot. 

Ins. 

In. 

Lbs. 

Ins. 

Ins. 

Lbs. 

Ins. 

Ins. 

Lbs. 

3 

i 

12* 

16 

f 

129 

30 

2 

662 

^6 

15 

I 

152 

36 

1 

334 

i 

18 

1 

175 

382 

% 

20i 

18 

| 

120 

li 

432 

23 

146 

li 

482 

4 

| 

17 

J. 

171 

If 

532 

X 

20 

1 

197 

il 

587 

4 

23f 

li 

223 

If 

632 

% 

26f 

li 

249 

IJ 

683 

! 

30 

20 

% 

148 

If 

734 

6 

%,+ 

30 

f 

161 

2 

786 

1 

34 

f 

190 

42 

1 

445 

% 

38i 

1 

216 

li 

471 

42£ 

it 

247 

li 

560 

f 

52 

ii 

276 

If 

629 

8 

% 

40 

if 

305 

ll 

675 

i 

43J 

if 

334 

If 

734 

% 

49J 

24 

i 

191 

If 

794 

56 

1 

225 

l| 

853 

| 

68 

258 

2 

912 

10 

% 

50 

ii 

293 

48 

li 

572 

i 

54 

li 

327 

li 

637 

% 

60 

if 

361 

If 

701 

f 

68 

if 

395 

H 

768 

1 

82 

if 

430 

If 

835 

12 

i 

70 

If 

465 

1| 

901 

% 

76 

30 

?1/6 

258 

1| 

967 

f 

82  ' 

278 

2 

1034 

1 

99 

1 

319 

60 

li 

797 

1 

117 

li 

360 

If 

880 

14 

% 

85 

li 

405 

li 

964 

f 

94 

if 

448 

If 

1049 

1 

113 

if 

489 

If 

1133 

I 

137 

if 

532 

if 

1216 

16 

% 

100 

if 

575 

2 

1300 

f 

108 

ll 

619 

2i 

1470 

There  is  no  standard  weight  of  pipe  for  any  given  pressure. 


1244 


THE  HYDRAULIC  RAM, 


Private  Water-supply:— Pumps. 

The  architect  is  frequently  required  to  furnish  a  water-supply 
for  isolated  buildings,  and  even  in  cities  it  is  becoming  quite 
common  for  manufacturing  establishments  and  large  buildings 
to  have  their  own  water-supply,  so  that  some  knowledge  of 
the  various  methods  of  supplying  water  is  requisite. 

Power  pumps  are  of  so  many  kinds  and  so  intricate  in  con- 
struction that  no  attempt  will  be  made  to  describe  them. 

The  Hydraulic  Ram. — Where  a  small  stream  of  water 
having  a  fall  of  5  ft.  or  more  flows  near  the  premises,  an  hydraulic 
ram  may  be  used  to  great  advantage  to  furnish  water  for  domestic 
purposes,  or  even  for  irrigation.  The  ram  is  operated  by  the 
pressure  of  the  stream,  and  delivers  water  into  an  open  tank. 
Water  can  be  conveyed  by  a  ram  3,000  ft.  and  elevated  200  ft., 
provided  there  is  sufficient  fall.  The  drive  pipe  supplying  the 
ram  should  be  30  or  40  ft.  long  to  give  the  necessary  pressure. 
This  is  the  most  economical  method  of  obtaining  a  water- 
supply,  as  there  is  no  expense  for  maintenance  except  for 
repairs,  and  the  cost  of  installation  is  also  small. 

TABLE  OF  ACTUAL  TESTS  WITH  GOULD'S  HYDRAULIC 
RAMS.* 


Size 
of 
Ram. 

Length 
of  Drive 
Pipe. 

Head  or 
Fall  of 
Drive 
Pipe. 

Length 
of  Dis- 
charge 
Pipe. 

Height 
or  Lift 
of  Dis- 
charge 
Pipe 

Water 
Supplied 
Ram  per 
Minute. 

Water 
Discharge 
at  Point  of 
Delivery 
per 

List 
Price. 

Minute. 

Feet. 

Feet. 

Feet. 

Feet. 

Gallons. 

Gallons. 

2 

70 

12 

100 

50 

2.1 

.3 

$9 

3 

70 

10 

200 

100 

2.4    , 

.2 

11 

4 

70 

12 

200 

100 

5.6 

.5 

14 

5 

70 

13 

200 

100 

7-    ' 

.8 

22 

5 

126 

20 

400 

200 

14 

1.5 

6 

70 

10 

100 

50 

12.4 

2.4 

40 

6 

125 

25 

400 

200 

18 

2 

7 

70 

11 

100 

40 

33 

7.6 

75 

7 

184 

23 

767 

118 

27 

4.5 

8 

100 

12 

300 

100 

44 

4 

125 

*  Made  by  N.  O.  Nelson  Mfg.  Co. 

Deep  Wells  and  Plunder  pumps. — The  most  common 
method  of  obtaining  a  private  water-supply  is  to  drive  a  deep 
well  until  a  sufficient  supply  of  water  is  obtained.  The  depth 
to  which  a  well  must  be  driven  will  of  course  depend  upon  the 


BEEP  WELLS  AND  PUMPS. 


1245 


locality,  and  can  only  be  determined  by  drillings.  As  the  well 
is  driven,  a  large  wrought-iron  pipe  is  sunk  to  form  the  casing. 
Casings  are  seldom  less  than  6"  inside  diameter  or  more  than 
10",  8"  being  the  most  common  size. 

When  the  water-pocket  has  been  reached,  the  water  will  usually 
rise  and  stand  in  the  pipe  several  hundred  feet  above  its  bottom, 
and  the  amount  of  water  that  can  usually  be  pumped  from  such 
wells,  without  lowering  the  water,  is  practically  unlimited. 

The  cost  of  drilling  deep  wells,  per  foot  olf  depth,  including 
the  casing,  is  approximately  as  follows: 

Well  with  6f"  casing $3.25  per  ft. 

"        "     7J"     "       3.75    "     " 

"        "     gi"      "      4.50    "     " 

"        "     10"      "      5.25    "     " 

For  raising  the  water  into  an  open  tank  a  single-acting  pump 
consisting  of  a  working-head,  which  operates  a 
cylinder  placed  in  a  smaller  pipe  lowered  into  the 
well  through  which  the  water  is  raised,  is  most 
commonly  employed. 

The  cylinder  should  preferably  be  placed  below 
the  water-line  in  the  well,  and  is  usually  con- 
nected with  the  working-head  by  wooden  sucker- 
rods. 

The  working-head  may  be  operated  by  hand, 
or  by  a  crank-rod  attached  to  a  pumping- jack, 
windmill,  or  engine. 

With  a  single-acting  pump  the  plunger  is 
raised  and  lowered  once  with  every  revolution 
of  the  driving-wheel,  the  principle  of  operation 
being  the  same  as  in  an  ordinary  hand  suction- 
pump. 

The  illustration  on  next  page  shows  the 
simplest  arrangement  for  operating  a  working- 
head  by  belt  power  (the  trade  term  for  the  ap- 
paratus being  "pumping- jack"). 

The  "jack"  is  usually  elevated  some  10  or  12 
ft.  above  the  top  of  the  well,  so  that  a  crank- 
rod  8  or  9  ft.  long  may  be  used  to  connect  with 
the  working-head  which  is   set  over  the  top  of          Working- 
the  well. 

A  more  substantial  arrangement  is  an  iron  frame,  containing 


1246 


DEElj  WELLS  AND  PUMPS. 


the  entire  operating  gear,  but  such  a  pump  costs  three  or  four 
times  as  much  as  a  jack  and  working-head. 

The  jack  shown  will  give,  variations  in  stroke,  viz.,  8,  10, 
12,  16,  18,  or  20  ins.,  by  changing  the  connection  of  the  crank- 
rod.  The  longer  the  stroke  the  greater  will  be  the  amount  of 
water  pumped,  but  it  will  also  require  more  power  to  operate. 

The  amount  of  water  pumped  in  a  minute  by  any  single- 
acting  pump  is  determined  by  the  diameter  of  the  suction 


Pumping-jack. 

cylinder,  the  length  of  stroke,  and  the  number  of  strokes  per 
minute. 

The  table  on  opposite  page  gives  the  capacity  per  stroke  for 
cylinders  of  different  diameters,  and  for  strokes  of  different 
length. 

To  find  the  capacity  per  minute,  multiply  the  figures  given 
in  the  table  by  the  revolutions  per  minute.  The  usual  speed 
of  single-acting  working-heads  and  pumping- jacks  is  25  to  30 
revolutions  per  minute. 

Cylinders  over  2f  ins.  in  diameter  should  have  a  substantial 
iron  working-head. 

Hot-air  Engines. — These  are  very  extensively  used  for 
pumping  water  for  country  houses,  as  they  are  absolutely  safe, 
require  little  attention,  and  have  no  valves,  springs,  or  gauges 
to  get  out  of  order.  They  are  also  adapted  to  almost  any 


HOT-AIR  ENGINES. 


1247 


TABLE  SHOWING  CAPACITY  OF  SINGLE-ACTING 
PUMPS  OF  GIVEN  DIAMETER  AND  LENGTH  OF 
STROKE. 


Diam. 
of 
Cylin- 
der in 
Inches. 

Length  of  Stroke  in  Inches. 

6 

8 

10 

12 

14 

16 

18 

20 

24 

Capac 

ity  per 

Stroke 

in  Gal 

Ions. 

\\£ 

.0319 

.0425 

.0531 

.0637 

.0743 

.0848 

.0955 

.1062 

.1274 

1% 

.0385 

.0513 

.0642 

.077 

.089 

.1027 

.1156 

.1280 

.1541 

11A 

.0459 

.0612 

.0765 

.0918 

.1071 

.1224 

.  1377 

.1530 

.1836 

1% 

.0625 

.0833 

.1041 

.1249 

.1457 

.1666 

.1874 

.2082 

.2499 

2 

.0816 

.1088 

.136 

.1632 

.1904 

.2176 

.2448 

.2720 

.3264 

2*4 

.1033 

.1377 

.1721 

.2063 

.241 

.2754 

.3096 

.3442 

.4128 

2y2 

.1275 

.17 

.2125 

.255 

.2975 

.34 

.  3825 

.425 

.51 

2M 

.1543 

.2057 

.2571 

.3085 

.3598 

.4114 

.4626 

.5142 

.617 

3 

.1836 

.2448 

.306 

.3672 

.4284 

.4896 

.5508 

.612 

.7344 

3K 

.2154 

.2872 

.3594 

.4312 

.503 

.5748 

.6466 

.7182 

.8624 

&A 

.2499 

3332 

.4165 

.4998 

.5831 

.6664 

.7497 

.833 

.9996 

3M 

.2868 

.3824 

.478 

.5736 

.6692 

.7648 

.8605 

.9561 

1.147 

4 

.3264 

.4352 

.544 

.6528 

.7616 

.8704 

.9792 

1.088 

1.3056 

±y± 

.3684 

.4912 

.6141 

.7368 

.8596 

.9824 

1.105  1.228  il.473 

±1A 

.4131 

.5508 

.6885 

.8262 

.9639 

1.1016 

1.2393!  1.377 

1  .  6524 

±y± 

.4602 

.6136 

.7671 

.9204 

1.073 

1.227 

1.S80 

1.534 

1.84 

kind  of  fuel,  such  as  coal,  coke,  wood,  gas,  or  kerosene  oil.  They 
will  pump  from  either  a 'shallow  or  a  deep  well,  but  are  best 
adapted  to  wells  in  which  the  surface  of  the  water  is  within 
20  ft.  of  the  top  of  the  well. 

The  best  known  hot-air  engines  are  the  Rider  and  Ericsson, 
which  have  been  in  successful  operation  for  over  twenty-six 
years. 

These  engines  have  capacities  ranging  from  150  to  3,500 
gallons  per  hour  and  will  deliver  water  from  50  to  350  ft.  above 
the  surface  of  water  in  the  well,  although  the  higher  the  water 
is  raised  the  less  will  be  the  quantity  delivered. 

The  cost  of  these  engines  with  pump  attached  varies  from 
$120  for  the  smallest  size,  having  a  capacity  of  150  gals,  per 
hour  raised  50  ft.,  to  $540  for  the  largest  size,  having  a  capacity 
of  3,500  gals,  per  hour  raised  50  ft.  The  smaller  size  requires 
about  1  quart  of  kerosene  or  3  Ibs.  of  anthracite  coal  per  hour. 

Hot-air  engines  should  be  placed  close  to  source  of  supply, 
and  when  the  latter  is  a  deep  well  the  engine  must  be  placed 
so  that  the  pump-rod  will  be  in  a  vertical  line  above  the  cylinder 
in  the  well,  the  operation  of  pumping  being  the  same  as  that 
of  the  ordinary  single-acting  deep-well  pump. 


1248 


WINDMILLS. 


It  is  not  practical  to  draw  water  more  than  20  to  25  ft.  (in 
height)  with  any  form  of  suction  pump,  because  of  the  difficulty 
of  keeping  the  pipe,  valve,  and  fittings  absolutely  air  tight. 

For  further  information,  see  catalogue  of  the  Rider-Ericsson 
Engine  Co. 

Windmills. — In  the  country  and  on  large  suburban 
estates,  windmills  are  extensively  used  for  pumping  water. 
Aside  from  the  noise  of  operation,  the  only  objection  to  the 
windmill  (where  it  can  be  used)  is  the  irregularity  of  its  supply, 
but  with  a  large  storage  tank  this  is  not  a  serious  objection 
when  used  for  domestic  purposes  only.  Prof.  Thurston  says, 
regarding  wind  mills:  "In  estimating  the  capacity,  a  working- 
day  of  eight  hours  is  assumed,  but  the  machine,  when  used 
for  pumping,  may  actually  do  its  work  twenty-four  hours  a  day 
for  days,  weeks,  and  even  months  together,  whenever  the  wind 
is  stiff  enough  to  turn  it.  It  costs  for  work  done  only  one  half 
or  one  third  as  much  as  steam,  hot-air,  or  gas  engines  of 
similar  power. 

The  wind  mill  operates  the  plunger  in  the  well,  the  process 
of  pumping  being  the  same  as  that  of  the  single-acting  pumps 
described  above. 

The  following  table  of  capacity  was  prepared  by  Alfred  11. 
Wolff,  and  is  sufficiently  accurate  for  all  practical  purposes: 

CAPACITY  OF  THE  WINDMILL. 


*o 

I 

Is 

Ipi 

Velocity  of  Wind 
in  Miles  per  Hr. 

Revolutions  of 
Wheel  per 
Minute. 

Gallons  of  Water  Raised  per  Minute  to 
an  Elevation  of 

Equivalent  Actual 
Useful  H.P. 
Developed. 

25 
Feet. 

50 
Feet. 

75 
Feet. 

100 
Feet. 

150 
Feet. 

200 
Feet. 

wheel 
Feet. 
8H 
10 
12 
14 
16 
18 
20 
25 

16 
16 
16 
16 
16 
16 
16 
16 

70  to  75 
60       65 
55       60 
50       55 
45       50 
40       45 
35       40 
30       35 

6.192 
19.179 
33.941 
45.139 
64  .  600 
97.682 
124.950 
212.381 

3.016 
9.563 
17.952 
22  .  569 
31  .  654 
52.165 
63.750 
106.964 

0.04 
0.12 
0.21 
0.28 
0.41 
0.61 
0.78 
1.34 

6.638    4.750 
11.851    8.435 
15.304i  11.  246 
19.542  16.150 
32.51324.421 
40.80031.248 
7-1.60449.725 
1 

5.680 
7.807 
9.771 
17.485 
19.284 
37  .  349 

'4i998 
8.075 
12.211 
1  5  .  938 
26.741 

The  horse-power  of  windmills  of  the  best  construction  is 
proportional  to  the  squares  of  their  diameters  and  inversely 
as  their  velocities;  for  example,  a  10-ft.  mill  in  a  16-mile  breeze 


AIR-LIFT  PROCESS.  1249 

will  develop  0.15  horse-power  at   65  revolutions  per  minute; 
and  with  the  same  breeze: 

A  20-ft.  mill  40  revolutions,  1   horse-power. 

A  25-ft.     "  35  "  If      " 

A  30-ft.     "  28  "  3J      "          " 

A40-ft.     "  22  "  7i      " 

A  50-ft.     "  18  "  12      " 

The  increase  in  power  from  increased  velocity  of  the  wind  is 
equal  to  the  square  of  its  proportional  velocity;  as,  for  example, 
the  25-ft.  mill  rated  above  for  a  16-mile  wind  will,  with  a  32-mile 
wind,  have  its  horse-power  increased  to, 4 X If  =7  horse-power.* 

A  windmill  "will  run  and  produce  work  in  a  4-mile  breeze." 

Windmills  have  also  been  used  successfully  for  the  generating 
and  storage  of  electricity  for  small  lighting  plant s.f 

Air-lift  Process. —  Compressed  air  is  now  being  used 
to  an  increasing  extent  for  raising  water  from  artesian  wells. 
The  process  in  general  consists  of  submerging  a  discharge 
pipe  in  a  closed  well,  with  a  smaller  pipe  inside  delivering 
compressed  air  into  it  at  the  bottom.  The  compressed  air 
by  its  inherent  expansive  force  lifts  a  column  of  mingled  air 
and  water  which  is  conveyed  to  an  open  tank,  to  permit 
of  the  escape  of  the  air.  If  desired  the  water  may  then  be 
conveyed  by  gravity  into  a  series  of  closed  tanks,  and  forced 
by  air  pressure  to  different  parts  of  a  building,  the  only  ma- 
chinery required  being  an  air-compressor  and  power  for  driving 
it. 

The  method  of  piping  a  well  differs  according  to  its  general 
conditions  and  the  quantity  of  water  to  be  pumped.  "No 
two  wells  are  alike,  and  consequently  the  method  of  piping 
which  might  be  applied  to  one  would  be  unsuited  to  another." 

Information  as  to  the  best  method  of  piping  any  particular 
well  may  be  obtained  from  the  Ingersoll-Sergeaiit  Drill  Co. 

Advantages  of  the  Air-lift  Process. — Froni  two  to  six  times 
as  much  water  may  be  obtained  from  a  given  diameter  of  well 
as  with  any  other  known  system,  because  there  are  no  valves r 
cylinders,  or  rods  to  hinder  the  rapid  discharge  of  water. 

One  air-compressor  operates  any  number  of  wells,  which, 
may  be  any  distance  apart  so  as  not  to  affect  one  another. 

*  Kent,  p.  497,  quoted  from  the  Iron  Age. 
t  See  Kent,  p.  498. 


1250    HORSE-POWER  REQUIRED  TO  RAISE  WATER. 

There  is  nothing  outside  the  engine-room  to  look  after  or 
wear  out.  Nothing  but  common  pipe  in  the  wells. 

Water  is  cooled  and  purified  by  the  thorough  admixture  and 
expansion  of  air;  iron,  sulphur,  and  gases  are  thrown  off. 

Sand  or  gravel  does  no  harm. 

The  cost  of  raising  1,000  gallons  of  water  by  this  method, 
including  fuel,  labor,  oil,  interest  on  cost  of  well,  boiler,  com- 
pressor, foundations,  pipes,  real  estate,  and  erection,  taxes, 
and  fifteen  per  cent,  for  depreciation,  runs  from  two  and  one- 
half  cents  down  to  one  fifth  of  one  cent,  according  to  the  size 
of  the  plant,  height  of  lift,  and  other  local  conditions.  With 
the  average  outfit  of  medium  or  small  size,  it  is  usually  under 
one  and  one  half  cents.* 

The  air-lift  process  is  now  extensively  used  in  iceworks, 
breweries,  cold-storage  houses,  textile  mills,  dyeworks,  etc., 
and  a  great  variety  of  industrial  plants,  and  for  the  water- 
supply  of  quite  a  number  of  the  smaller  cities. 

In  Newark,  N.  J.,  pumps  of  this  type  are  at  work  having  a 
total  capacity  of  1,000,000  gallons  daily,  lifting  water  from 
three  8-in.  artesian  wells.  (Kent.) 

Horse-power  Required  to  Raise  Water  to 
Different  Heights. 

The  power  required  to  raise  a  certain  quantity  of  water  to 
a  certain  height  varies  directly  with  the  quantity  to  be  raised, 
and  also  the  height. 

For  instance,  it  requires  twice  as  much  power  to  raise  200 
gallons  per  minute  10  ft.  high  as  it  does  to  raise  100  gallons 
to  the  same  height  and  in  the  same  time;  and  to  raise  100 
gallons  20  ft.  high  requires  twice  as  much  power  as  it  does  to 
raise  100  gallons  10  ft.  high. 

To  find  the  theoretical  horse-power  necessary  to  elevate 
water  to  a  given  height,  multiply  the  number  of  gallons  per 
minute  by  8.35,  weight  of  one  gallon,  and  this  result  by  the 
total  number  of  feet  the  water  is  raised  (that  is,  from  the  sur- 
face of  the  water  to  the  highest  point  to  which  the  water  is 
raised),  and  the  result  gives  the  power  in  foot-pounds;  divide 
by  33,000,  and  the  quotient  is  the  horse-power.  To  the  theo- 
retical power  a  liberal  allowance  must  be  made  for  the  in- 
efficiency of  the  pump. 

*  Ingersoll-Sergeant  Drill  Co. 


FIRE  STREAMS.  1251 

For  a  cylinder  pump  add  75  to  100  per  cent. 

To  the  actual  height  to  which  the  water  is  to  be  raised  add 
the  friction  loss  in  feet,  as  given  in  Table  F,  when  the  discharge 
is  to  be  piped  any  distance. 

EXAMPLE. — Find  the  theoretical  horse-power  required  to 
raise  100  gallons  per  minute  120  ft.  high,  through  a  3-in.  pipe, 
200  ft.  long. 

Ans.  From  Table  F,  the  friction  head  for  100  gallons  per 
minute  in  3-in.  pipe,  100  ft.  long,  is  1.31X2.3  or  3  ft.  For 
200  ft.  it  will  be  6  ft.,  which  added  to  120  gives  126  ft.  for  the 

100X8.35X126 
height.      Then      theoretical      horse -power  =        —  — 

OO  jUUvJ 

=3.2  H.P.  The  actual  horse-power  required  will  probably 
vary  from  5  to  6,  according  to  the  efficiency  of  the  pump. 

The  mistake  of  using  too  small  a  discharge  pipe  can  easily 
be  seen  from  Table  F. 

For  instance,  if  one  attempted  to  force  100  gallons  per  minute 
through  100  ft.  of  2-in.  pipe,  the  back  pressure  would  be  equiva- 
lent to  raising  the  water  22  ft.  high.  The  fuel  used  would 
ba  correspondingly  increased.  Right-angle  turns  are  to  be 
avoided,  as  the  friction  is  very  materially  increased,  being 
practically  equal  to  the  friction  of  25  ft.  of  straight  pipe. 


Fire   Streams. 

The  following  is  an  extract  from  a  paper  read  by  Mr.  John  R. 
Freeman  at  a  meeting  of  the  New  England  Waterworks  Asso- 
ciation, entitled  "Some  Experiments  and  Practical  Tables 
Relating  to  Fire  Streams." 

"When  unlined  linen  hose  is  used  the  friction  or  pressure 
loss  is  from  8  to  60  per  cent.,  increasing  with  the  pressure. 
This  kind  of  hose  is  best  for  inside  use  in  short  lengths.  Mill 
hose  is  better  than  unlined  linen  hose  for  long  lengths,  but 
ordinarily  the  best  quality  of  smooth  rubber-lined  hose  is  supe- 
rior to  the  mill  hose,  having  less  frictional  resistance. 

"The  ring  nozzle  is  inferior  to  the  smooth  nozzle  and  actually 
delivers  less  water  than  the  smooth  nozzle.  For  instance, 
the  I"  ring  nozzle  discharges  the  same  quantity  of  water  as 
a  f "  smooth,  and  a  1"  ring  nozzle  the  same  as  a  J"  smooth. 

"Two  hundred  and  fifty  gallons  per  minute  is  a  good  standard 
fire  stream  at  80  Ibs.  pressure  at  the  hydrant.  100  Ibs.  pressure 


1252 


CYLINDRICAL   WOODEN  TANKS. 


should  not  be  exceeded  except  for  very  high  buildings  or  lengths 
of  hose  exceeding  300  ft." 

TABLE  OF  EFFECTIVE  FIRE  STREAMS, 

Using   100  ft.  of   2J"  ordinary   best  quality   rubber-lined   hose 
between  nozzle  and  hydrant  or  pump. 


Smooth  Nozzle,  Size.  .  .  . 

24-inch. 

Js-mch. 

Pressure  at  hydrant,  Ibs.  . 

32 

54 

65 

75 

86 

34 

5. 

69 

80 

91 

Pressure  at  nozzle,  Ibs.  .  . 

30 

50 

60 

70 

80 

30 

5 

60 

70      80 

Vertical  height,  feet  48 

67 

72 

76 

79 

49 

71 

77 

81 

85 

Horizontal  distance,  feet 

37 

50 

54 

68 

62 

42 

55 

61 

66 

70 

Gals,  discharged  per  min. 

90 

116 

127 

137 

147 

123 

159 

74 

188 

201 

Smooth  Nozzle,  Size.  .  .  . 

1-inch. 

lK-inch. 

Pressure  at  hvdrant,  Ibs  . 

37    62 

75 

87 

100 

42 

70 

84 

98 

112 

Pressure  at  nozzle,  Ibs.    .  . 

30    50;     60 

70 

80 

30 

50 

60 

70 

80 

Vertical  height,  feet  

51     73 

79 

85 

8^ 

52 

75 

83 

88 

92 

Horizontal  distance,  feet 

47    61 

67 

72 

76 

50 

66 

72 

77 

81 

Gals,  discharged  per  min  . 

161  208 

228 

246 

263 

206 

266 

291 

314 

336 

Notes  oil  the  Construction  of  Cylindrical  Wooden 
Tanks.* 

Material  should  be  either  cedar,  cypress,  or  white  pine,  free 
from  imperfections  and  thoroughly  air-dry.  Where  exposed  to 
freezing,  Michigan  pine  free  from  sapwood  is  generally  con- 
sidered the  most  durable. 

Staves  and  bottom  to  be  made  of  24-inch  (dressed  to  about 
2J-inch)  stock  for  tanks  12  ft.  and  not  exceeding  16  ft.  diam- 
eter or  16  ft.  deep.  For  larger  tanks  3-in.  (dressed  to  about 
2f-in.)  stock  to  be  used. 

Staves  to  be  connected  about  one  third  tke  distance  from 
the  top  by  a  f-inch  dowel  to  hold  in  position  during  erection. 

The  bottom  planks  to  be  dressed  four  sides,  and  the  edges 
of  each  plank  to  be  bored  with  holes  not  over  3  feet  apart  for 
f-inch  dowels. 

Taper. — The  batter  to  each  side  should  not  be  less  than  -J  in. 
nor  more  than  J  in.  per  foot. 


*  These  notes  have  been  condensed  from  specifications  published  by  the 
Inspection  Department  of  the  Factory  Mutual  Fire  Insurance  Co.,  31 
Milk  Street,  Boston;  a  most  excellent  pamphlet. 


CYLINDRICAL  WOODEN  TANKS. 


1253 


Hoops.  —  All  to  be  of  round  wrought  iron  or  mild  steel  of  good 
quality.  Wrought  iron  is  preferable  because  it  does  not  rust  so 
easily  as  steel. 

There  are  to  be  no  welds  in  any  of  the  hoops.  Where  more 
than  one  length  of  iron  is  necessary,  lugs  are  to  be  used  to  make 
the  joints;  and  when  more  than  one  piece  is  necessary  the  several 
pieces  constituting  one  hoop  should  be  tied  together  in  pre- 
paring for  shipment. 

Hoops  to  be  chosen  of  such  a  size  and  spacing  that  the  stress 
in  no  hoop  will   exceed  12,500   Ibs.  per  square 
inch  when  computed  from  the  area  at  root  of 
thread. 

On  account  of  the  swelling  of  the  bottom 
planks,  the  hoops  near  the  bottom  may  be  sub- 
jected to  a  strain  greater  than  that  due  to  the 
water  pressure  alone;  therefore  additional  hoops 
should  be  provided.  For  tanks  up  to  20  ft.  in 
diameter,  one  hoop  of  the  size  used  next  above 
it  should  be  placed  around  the  bottom  opposite 
the  croze  and  not  counted  upon  as  withstand- 
ing any  water  pressure.  For  tanks  20  ft.  or  more 
in  diameter,  two  hoops,  as  above,  should  be 
used. 

Hoops  with  "  upset"  ends  must  not  be  used. 
The  top  hoop  to  be  placed  within  2  ins.  of  the 
top  of  staves,  so  that  overflow  pipe  may  be  in- 
serted as  high  as  possible.  Hoops  to  be  so  placed 
that  the  lugs  will  not  come  in  a  vertical  line.  No 
hoop  to  be  less  tlmn  J  in.  diameter.  All  to  be 
cleaned  of  mill-scale  and  rust  and  painted  one 
coat  red  lead,  lampblack,  and  boiled  oil  before 
erecting. 

[NOTE.—  The  strength  of  a  tank  depends  chiefly 
on  its  hoops.  Round  hoops  are  specified 
because  they  do  not  rust  as  quickly;  a  slight 
amount  of  rust  does  not  have  the  same  weaken- 
ing effect  as  on  a  flat  hoop,  and  round  hoops 
are  not  likely  to  burst  when  the  tank  swells, 
as  they  will  sink  into  the  wood.] 

Spacing  of  Hoops.~The  hoops  to  be  spaced  so  that  each  hoop 
will  have  the  same  stress  per  square  inch,  and  no  space  to  be 
greater  than  21  ins. 


Fig.  I 


1254 


CYLINDRICAL  WOODEN  TANKS. 


To  meet  this  requirement  the  hoops  must  be  spaced  quite 
close  together  at  the  bottom,  the  space  between  hoops  gradually 
increasing  towards  the  top.  Fig.  1  shows  the  proper  spacing 
of  hoops  for  a  tank  18  ft.  diameter  with  18-ft.  staves.  The 
spacing  for  seven  other  sizes  of  tanks  is  given  in  the  pamphlet 
referred  to.  It  may  be  computed  by  the  following  formula: 

Strength 
Spacing  of  hoop  in  inches  =  — 

2.6Xdiameter  in  feet XH 

For  strength  of  a  f-inch  rod  use  3,750;    of   a  J-in.  rod,  5,250; 
of  a  1-in.  rod,  6,875;   and  of  a  IJ-m-  rod,  8,625. 

H  is  the  distance  from  top  of  water  to  centre  of  hoop  in  feet. 
EXAMPLE. — How  far  apart  should  1-in.  hoops  be  placed,  at 
15  ft.  2  ins.  from  top  of  tank,  on  a  tank  20  ft.  diameter? 

6,875  . 

S'  2.6X20X15" 

Lugs  are   to  be  as   strong  as   the   hoops.     A  lug  similar  to 

Fig.  2  is  simple  and  fulfils 
the  requirement  for  strength. 
Malleable  lugs  are  preferable. 
Support. — The  weight  of 
the  tank  should  be  supported 
entirely  from  its  bottom;  and 
in  no  event  should  any  weight 
come  on  the  bottom  of  the 
staves.  The  planks  upon  which  the  tank  bottom  rests  should 
cover  at  least  one  fifth  the  area  of  the  bottom  and  be  not  over 
18  ins.  apart,  and  of  such  thickness  that  the  bottom  of  the  staves 
will  be  at  least  an  inch  from  the  floor  (see  Fig.  3). 


Not  over  18  inches 
in  the  clear. 


Fig.  2 

Lug  for  Hoops. 


Fig.   3 
Support  for  Bottom  of  Tank. 

Discharge  Pipe  will  preferably  leave  the  bottom  of  the 
tank  at  its  centre  and  extend  up  inside  of  the  tank  4  ins.,  to 
allow  for  sediment  collecting  in  the  bottom  of  the  tank. 

The  Overflow  Pipe  should  be  placed  as  near  the  top  of  the 


CYLINDRICAL  WOODEN  TANKS. 


1255 


tank  as  possible,  discharging  either  through  side  or  bottom,  as 
may  be  desired.  An  overflow  is  much  to  be  preferred  to  a 
telltale,  as  the  latter  is  liable  to  get  out  of  order. 

Heating. — Tanks  of  moderate  size  need  to  be  provided  with 
some  means  to  prevent  freezing. 

When  a  tank  is  in  an  enclosed  room,  as  in  a  mill  tower,  the 
best  method  is  to  keep  the  room  wa  m  by  a  coil  of  steam-pipe 
with  a  return  to  the  boiler-room.  A  covered  tank  out  of  doors 
may  often  be  similarly  heated  by  placing  the  steam-pipe  in  the 
bottom  of  the  tank. 

With  a  tank  located  on  a  high  trestle,  or  at  a  distance  from 
the  steam-supply,  it  is  often  impracticable  to  arrange  a  return 
pipe.  In  this  case  steam  may  be  blown  directly  into  the  water 
in  the  tank.  A  1-inch  pipe  is  generally  sufficient  for  this  pur- 
pose. It  should  be  carried  to  the  top  of  the  tank  and  there 
bend  over  and  dip  downwards,  so  that  its  outlet  is  about  1  foot 
below  the  high- water  line.  A  check-valve  is  to  be  placed  in  this 
steam-pipe,  near  its  point  of  discharge,  to  prevent  water  being 
drawn  back  by  siphon  action  when  the  steam  is  shut  off. 

Frost  -  proofing  for  Pipes  —  The  discharge  pipe  from  a 
tank  on  a  trestle,  or  one  elevated  above  the  roof,  must  be  pro- 
tected from  freezing.  The  most  common  practice  is  to  enclose 

2  in.  horizontal  nailing  strips 
spaced  about  3  ft.  apart./ ; 


/2in.  air  s 


//2  in.  air  space\\ 


If    2  in.  air  space\\\ 


2  Thicknesses  of  tarred  paper,     %  in.  Tongued  and 
around  each  box  except  outside,   grooved  sheathing. 

Fig.  4 
Method  of  Frost-proofing  Pipes. 

the  pipe  in  a  double,  triple,  or  quadruple  box  made  of  boards 
and  tarred  paper  as  shown  by  Fig.  4.  If  steam  is  supplied 
to  the  tank,  the  steam-pipe  is  carried  inside  the  box. 


1256 


CYLINDRICAL  WOODEN   TANKS. 


In  New  England,  New  York,  and  Canada  the  quadruple 
boxing  is  generally  used,  whereas  in  the  milder  regions  to 
the  south  triple  or  double  boxing  is  used. 

The  boxing  should  always  be  carried  down  into  the  ground 
below  the  frost-line,  and  a  good  tight  joint  made  at  the  under- 
side of  the  tank. 

Covers. — For  economy  in  heating  and  to  prevent  birds, 
leaves,  etc.,  from  getting  into  the  water,  all  out-of-door  tanks 
should  be  covered.  A  double  cover  is  recommended  consist- 
ing of  a  tight  flat  cover  made  of  matched  boards  'supported 
by  joists  which  span  the  top  of  the  tank,  and  above  this  a 
shingled,  conical  roof.  To  prevent  the  covering  from  being 
blown  off,  it  should  be  firmly  fastened  to  the  top  of  the  tank 
by  straps  of  iron. 

In  order  to  keep  out  the  wind  particular  attention  should 
be  given  to  making  a  tight  joint  where  the  roof  rests  on  the 
top  of  the  staves. 


DIMENSIONS  OF  TANKS  OF  STANDARD  SIZES. 


Size 

Thickness  of 

B   N 

Approx- 
imate 

(Outside 
Dimensions). 

Lumber  after 
being  Machined. 

5~      \    I     c 

Hoops. 

Net 

j    j 

Capac- 

1 pM 

ity. 

Average 
Diam- 
eter. 

Length 
of 
Stave. 

Staves. 

Bot- 
tom. 

Num- 
ber 
of 

Size. 

A 

B 

c 

Gallons. 

Ft.  Ins. 

Ft. 

Ins. 

Ins. 

Ins. 

In.      Ins. 

Ins. 

10,000 

13  4 

12 

21 

21 

31 

I 

2i 

11 

J 

15,000 

14  6 

14 

21 

21 

31 

f 

2J 

14 

1 

i 

20,000 

15  6 

16 

21 

21 

31 

I 

2* 

]  11 

f 

25,000 

17  6 

16 

2f 

2f 

3i 

! 

2| 

j    4 

1 

1 

30,000 

18  0 

18 

2f 

2— 

31 

3. 
4 

2| 

J    4 
1  16 

f 

I 

50,000 

22  0 

20 

2J 

2i 

31 

J 

2f 

4 
U9 

I 

4 

1 

75,000 

24  6 

24 

21 

O3 

3i 

1 

2f 

1    6 

1 

(21 

Jl 

100,000 

28  6 

24 

2a 

2f 

3$ 

3. 

4 

2f 

(    5 
]29 

1 
It 

NOTES  ON  STEEL  TANKS.  1257 

Scuttles  should  be  arranged  in  both  the  conical  and  flat 
covers  to  give  access  to  the  inside  of  the  tank  and  a  substantial, 
permanent  ladder  erected  to  give  easy  access  to  the  top  of  the 
tank. 

Notes  on  Steel  Tanks.* 

Steel  tanks  of  sizes  commonly  used  for  fire  protection  cost 
from  40  to  100  per  cent,  more  than  do  wooden  tanks.  The 
additional  cost  for  large  tanks  is  relatively  less  than  for  small 
tanks.  A  steel  tank  of  about  40,000  gallons  capacity  or  over 
can  be  erected  on  a  steel  trestle  at  about  the  same  cost  as  a 
wooden  tank,  since  a  saving  can  be  made  in  the  cost  of  sup- 
ports by  making  a  hemispherical  or  conical  bottom  to  the 
steel  tank  and  supporting  the  tank  directly  on  the  legs  of  the 
trestle,  thus  saving  the  expense  of  horizontal  supporting  beams. 

A  steel  tank  is  superior  to  a  wooden  tank  in  (1)  that  it  will 
last  for  an  indefinite  time  if  kept  thoroughly  painted  inside 
and  out,  whereas  a  wooden  tank  will  have  to  be  replaced  in 
from  twelve  to  thirty  years  (usually  about  fifteen  years);  (2) 
that  it  will  be  absolutely  tight  when  once  well  erected  and 
properly  cared  for,  whereas  a  wooden  tank  will  shrink  and  leak 
if  the  water  gets  low;  (3)  that  it  will  not  be  at  all  likely  to 
burst  suddenly  (if  originally  correctly  designed)  even  if  paint- 
ing is  neglected,  for  experience  shows  that  a  few  spots  will  first 
rust  through  and  thus  show  the  weak  condition  by  small  leaks, 
whereas  a  wooden  tank,  if  neglected,  may  burst  its  hoops 
suddenly  and  cause  serious  damage. 

The  objections  to  steel  tanks  are:  (1)  They  require  skilled 
boiler-makers  to  erect  them,  thus  adding  considerable  to  the 
cost  when  erected  at  a  distance  from  a  boiler-shop;  (2)  they 
are  more  difficult  to  protect  against  freezing;  (3)  they  give 
more  trouble  by  "sweating"  when  placed  in  a  mill  tower;  (4) 
they  deteriorate  rapidly  if  painting  is  neglected. 

*  Inspection  Department  of  the  Factory  Mutual  Insurance  Co.,  Boston. 


1258      CAPACITY  OF  PIPES  AND   CYLINDERS. 


CONTENTS  IN  CUBIC  FEET  AND  U.  S.  GALLONS  OF 
PIPES  AND  CYLINDERS  OF  VARIOUS  DIAMETERS 
AND  ONE  FOOT  IN  LENGTH. 

1  gallon  =  231  cubic  inches.     1  cubic  foot  =  7.4805  gallons. 


For  1  Foot  in 

For  1  Foot  in 

For  1  Foot  in 

ti 
..# 

Length. 

|3 

Length. 

a 

Length. 

fej 

aj^3 

Cu.Ft,, 

U.S. 

ii 

"oJ-d 

Cu.  Ft., 

U.S. 

ii 

Cu.  Ft., 

U.S. 

1 

also  Area 

Gals., 

2  rt 

also  Area 

Gals., 

&  ,* 

also  Area 

Gals., 

CJhH 

in  Sq.  Ft. 

231 

.SM 

inSq.  Ft. 

231 

§£ 

in  Sq.  Ft. 

231 

p 

Cu.In. 

P 

Cu.  In. 

'S 

Cu.  In. 

~x 

.0003 

.0025 

6M 

.2485 

1.859 

19 

1.969 

14.73 

B/16 

.0005 

.004 

.2673 

1.999 

19K 

2.074 

15.51 

H 

.0008 

.0057 

7M 

.2867 

2.145 

20 

2.182 

16  32 

%i 

.001 

.0078 

7^ 

.3068 

2.295 

20^ 

2.292 

17.15 

K 

.0014 

.0102 

7M 

.3276 

2.45 

21 

2.405 

17.99 

9/i6 

.0017 

.0129 

8 

.3491 

2.  Gil 

21^ 

2.521 

18.86 

H 

.0021 

.0159 

8^ 

.3712 

2.777 

22 

2.640 

19.75 

!%e 

.0026 

.0193 

8^ 

.3941 

2.948 

22^ 

2.761 

20.66 

M 

.0031 

.0230 

8M 

.4176 

3.125 

23 

2.885 

21.58 

13/16 

.0036 

.0269 

9 

.4418 

3.305 

23^ 

3.012 

22  .  53 

% 

.0042 

.0312 

9*4 

.4667 

3.491 

24 

3  .  142 

23  .  50 

15/16 

.0048 

.0359 

9^2 

.4022 

3.682 

25 

3.409 

25.50 

1 

.0055 

.0408 

&i 

.5185 

3.879 

26 

3.687 

27.58 

1# 

.0085 

.0638 

10  ~ 

.5454 

4.08 

27 

3.976 

29.74 

m 

.0123 

.0918 

IOM 

.5730 

4.286 

28 

4.276 

31.99 

1M 

.0167 

.1249 

IOH 

.6013 

4.498 

29 

4.587 

34.31 

2 

.0218 

.  1632 

10M 

.6303 

4.715 

30 

4.909 

36.72 

2# 

.0276 

.2066 

11 

.66 

4.937 

31 

5.241 

39.21 

2^ 

.0341 

.2550 

11M 

.6903 

5.  104 

32 

5.585 

41.78 

2% 

.0412 

.3085 

HH 

.7213 

5.396 

33 

5.940 

44.43 

3 

.0491 

.3672 

HM 

.7530 

5.633 

34 

6.305 

47.16 

3M 

.0576 

.4309 

12 

.7354 

5.875 

35 

6.681 

49.98 

3^ 

.0668 

.4998 

12^ 

.8522 

3.375 

36 

7.069 

52.88 

3M 

.0767 

.5738 

13 

.9218 

6.895 

37 

7.467 

55.86 

4 

.0873 

.6528 

13^ 

.994 

7.436 

38 

7.876 

58.92 

4/€ 

.0985 

.7369 

14 

1.0G9 

7.997 

39 

8.296 

62.06 

43^ 

.1134 

.8263 

14^ 

1.147 

8.578 

40 

8.727 

65.28 

4M 

.1231 

.9206 

15 

.227 

0.180 

41 

9.168 

68.58 

5 

.1364 

1.020 

153^ 

.310 

9.801 

42 

9.621 

71.97 

5« 

.1503 

1.125 

16 

.396 

10.44 

43 

10.085 

75.44 

5^ 

.1650 

1  .  234 

16^ 

.485 

11.11 

44 

10  .  559 

78.99 

5M 

.  1803 

1.349 

17 

.576 

11.79 

45 

11.045 

82.62 

6 

.1963 

1.469 

17H 

.070 

12.49 

46 

11.541 

86.33 

6tf 

.2131 

1  .  594 

18 

.768 

13.22 

47 

1  2  .  048 

90.13 

6j^ 

.2304 

1.724 

18H 

.867 

13.96 

48 

12.566 

94.00 

*  Actual. 

To  find  the  capacity  of  pipes  greater  than  those  given,  look  in 
the  table  for  a  pipe  of  one  half  the  given  size  and  multiply  its 
capacity  by  4,  or  one  of  one  third  its  size  and  multiply  ita 
capacity  by  9,  etc. 

The  find  the  weight  of  water  in  any  of  the  given  sizes  multiply 
the  capacity  in  cubic  feet  by  the  weight  of  a  cubic  foot  of  water 
at  the  temperature  of  the  water  in  the  pipe  (see  page  1112). 

To  find  the  capacity  of  a  cylinder  in  U.  S.  gallons  multiply  the 
length  by  the  square  of  the  diameter  and  by  0.0034. 


CAPACITY  OF  CYLINDRICAL  TANKS. 


1259 


CYLINDRICAL  VESSELS,  TANKS,  CISTERNS,  ETC. 

Diameter  in  feet  and  inches,  area  in  square  feet,  and  U.  S. 

gallons  capacity  for  one  foot  in  depth. 

1  gallon  =  231  cubic  inches  =  0.1337  cubic  foot. 


Diam.      Area. 

Gals. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Ft.  In. 

Sq.  Ft. 

1-Foot 

Ft.  In. 

Sq.  Ft. 

1-Foot 

Ft.  In. 

Sq.  Ft. 

1-Foot 

* 

Depth. 

* 

Depth. 

* 

Depth. 

1 

.785 

5.87 

5  8 

25.22 

188.66 

19 

283  .  53 

2120.9 

1       1 

.922 

6.89 

5  9 

25.97 

194.25 

19  3 

291.04 

2177.1 

1       2 

1.069 

8.00 

5  10 

26  .  73 

199.92 

19  6 

298  .  65 

2234  .  0 

1       3 

1.227 

9.18 

5  11 

27.49 

205.67 

19  9 

306  .  35 

2291.7 

1       4 

1.396 

10.44   1 

6 

28.27 

211.51 

20 

314.16 

2350.1 

1       5 

1.576 

11.79 

6  3 

30.68 

229  .  50 

20  3 

322  .  06 

2409.2 

1       6 

1.767 

13.22 

6  6 

33.18 

248.23 

20  6 

330  .  06 

2469.1 

1       7 

1,969 

14.73 

6  9 

35.78 

267.69 

20  9 

338.16 

2529  .  6 

1       8 

2.182 

16.32 

7 

38.48 

287.88 

21 

346.36    2591.0 

1       9 

2.405 

17.99 

7  3 

41.28 

308.81 

21  3 

354.66    2653.0 

1     10 

2.640 

19.75 

7  6 

44.18 

330.48 

21  6 

363.05!   2715.8 

1     11 

2.885 

21.58 

7  9 

47.17 

352.88 

21  9 

371.54    2779.3 

2 

3.142 

23.50 

8 

50.27 

376.01 

22 

380.13    2843.6 

2       1 

3.409 

25.50 

8  3 

53.46 

399.88 

22  3 

388.  82  !   2908.6 

2       2 

3.687 

27.58 

8  6 

56.75 

424  .  48 

22  6 

397.611   2974.3 

2       3 

3.976 

29.74 

8  9 

60.13 

449.82 

22  9 

406.49!   3040.8 

2       4 

4.276 

31.99 

9 

63.62 

475.89 

23 

415.48:   3108.0 

2       5 
2       6 

2       7 

4.587 
4.909 
5.241 

34.31 
36.72 
39.21 

9  3 
9  6 
9  9 

67.20 
70.88 
74.06 

502.70 
530.24 
558.51 

23  3 
23  6 
23  9 

424  .  56 
433  .  74 
443.01 

3175.9 
3244  .  6 
3314.0 

2       8 

5  .  585 

41.78 

10 

78.54 

587  .  52 

24 

452  .  39 

3384  .  1 

2       9 

5.940 

44.43 

10  3 

8°  52 

617.26 

24  3 

461.86 

3455.0 

2     10 

6.305 

47.16 

10  6 

86!  59 

647.74 

24  6 

471.44 

3526.6 

2     11 

6.681 

49.98 

10  9 

90.76 

678.  95 

24  9 

481.11 

3598.9 

3 

7.069 

52.88 

11 

95.03 

710.90 

25 

490  .  87 

3672.0 

3       1 

7.467 

55.86 

11  3 

99.40 

743  .  58 

25  3 

500  .  74 

37^5.8 

3       2 

7.876 

58.92 

11  6 

103.87 

776.99 

25  6 

510.71 

3820  .  3 

3       3 

8.296 

62.06 

11  9 

108.43 

811.14 

25  9 

520  .  77 

3895  .  6 

3       4 
3       5 
3       6 
3       7 
3       8 
3       9 
3     10 
3     11 
4 
4       1 
4       2 
4       3 
4       4 
4       5 
4       6 
4       7 
4       8 
4       9 
4     10 
4     11 
5 
5       1 
5       2 
5       3 
5       4 
5       5 
5       6 
5       7 

8.727 
9.168 
9.621 
10.085 
10.559 
11.045 
11.541 
12.048 
12.566 
13.095 
13.635 
14.186 
14.748 
15.321 
15.90 
16.50 
17.10 
17.72 
18.35 
18.99 
19.63 
20.29 
20.97 
21.65 
22.34 
23.04 
23.76 
24.48 

65.28 
68.58 
71.97 
75.44 
78.99 
82.62 
86.33 
90.13 
94.00 
97.96 
102.00 
106.12 
110.32 
114.61 
118.97 
123.42 
127.95 
132.56 
137.25 
142.02 
146.88 
151.82 
156.83 
161.93 
167.12 
172.38 
177.72 
183.15 

12 
12  3 
12  6 
12  9 
13 
13  3 
13  6 
13  9 
14 
14  3 
14  6 
14  9 
15 
15  3 
15  6 
15  9 
16 
16  3 
16  6 
16  9 
17 
17  3 
17  6 
17  9 
18 
18  3 
18  6 
18  9 

113.10 
117.86 
122.72 
127.68 
132.73 
137.89 
143.14 
148.49 
153.94 
159.48 
165.13 
170.87 
176.71 
182.65 
188.69 
194.83 
201.06 
207.39 
213.82 
220.35 
226.98 
233.71 
240.53 
247.45 
254.47 
261.59 
268.80 
276.12 

846.03 
881.65 
918.00 
955.09 
992.01 
1031.5 
1070.8 
1110.8 
1151.5 
1193.0 
1235.3 
1278.2 
1321.9 
1366.4 
1411.5 
1457.4 
1504.1 
1551.4 
1599.5 
1648.4 
1697.9 
1748.2 
1799.3 
1851.1 
1903.6 
1956.8 
2010.8 
2065.5 

26 
26  3 
23  6 
26  9 
27 
27  3 
27  6 
27  9 
28 
2S  3 
28  6 
28  9 
29 
29  3 
29  6 
29  9 
30 
30  3 
30  6 
30  9 
31 
31  3 
31  6 
31  9 
32 
32  3 
32  6 
32  9 

530  .  93 
541  .  19 
551.55 
562  .  00 
572  .  56 
588.21 
593  .  96 
604.81 
615.75 
626  .  80 
637  .  94 
649.18 
660  .  52 
671.96 
683  .  49 
695.13 
706  .  86 
718.69 
730  .  62 
742  .  64 
754  .  77 
766.99 
779.31 
791.73 
804.25 
816.86 
829.58 
842  .  39 

3971.6 
4048.4 
4125.9 
4204.1 
4283.0 
4362  .  7 
4443  .  1 
4524.3 
4606.2 
4688  .  8 
4772  .  1 
4856  .  2 
4941.0 
5026.6 
5112.9 
5199.9 
5287  .  7 
5376.2 
5465.4 
5555.4 
5646.1 
5737.5 
5829.7 
5922.6 
6016.2 
6110.6 
6205.7 
6301.5 

*  Also  cubic  feet  for  1  foot  iu  depth. 


1260        CAPACITY  OF  CYLINDRICAL  TANKS. 


CAPACITY  OF  CISTERNS  AND  TANKS. 
NUMBER  OF  BARRELS  (31J  GALS.)  IN  CISTERNS  AND  TANKS. 


Diameter,  in  Feet. 

Depth, 

in  Feet. 

7 

9 

5 

6 

8 

10 

11 

12 

13 

5 

23.3 

33.6 

45.7 

59.7 

75 

5 

93.2 

112.8 

134.3 

157.6 

6 

28.0 

40.3 

54.8 

71.7 

90 

.0 

111.9 

135.4 

161.1 

189.1 

7 

32.7 

47.0 

64.0 

8 

3.G 

105 

.7 

130.6 

158.0 

188.0 

220.6 

8 

37.3 

53.7 

73.1 

95.5 

120 

.9 

149.2 

180.5 

214.8 

252.1 

9 

42.0 

60.4 

82.2 

107  4 

136 

.1) 

167.9 

203.1 

241.7 

283.7 

10 

46.7 

67.1 

91.4 

11 

9.4 

151 

.1 

186.5 

225.7 

268.6 

315.2 

11 

51.3 

73.9 

100.5 

131.3 

166.2 

205.1 

248.2 

295.4 

346.7 

12 

56.0 

80.6 

109.7 

143.2 

181 

.3 

223.8 

270.8 

322.3 

378.2 

13 

60.7 

87.3 

1 

18.8 

15 

5.2 

196 

.4 

242.4 

293.4 

349.1 

409.7 

14 

65.3 

94.0 

127.9 

167.1 

211 

.5 

261.1 

315.9 

376.0 

441.3 

15 

70.0 

100.7 

1 

37.1 

17 

9.0 

226 

.6 

289.8 

338.5 

402.8 

472.8 

16 

74.7 

107.4 

146.2 

191.0 

241 

.7 

298.4 

361.1 

429.7 

504.3 

17 

79.3 

114.1 

155.4 

202.9 

256 

.8 

317.0 

383.6 

456.6 

535.8 

18 

84.0 

120.9 

1 

64.5 

21 

1.8 

272 

.0 

335.7 

406.2 

483.4 

567.3 

19 

88.7 

127.6 

1 

73.6 

22 

6.8 

287 

.0 

354.3 

428.8 

510.3 

598.0 

20 

93.3 

134.3 

182.8 

238.7 

302 

.1 

373.0 

451.3 

537.1 

630.4 

Diameter,  in  Feet. 

Depth, 

in  Feet. 

16 

18 

14 

15 

17 

19 

20 

21 

22 

5 

182.8 

209.8 

238.7 

269.5 

302 

.1 

336.6 

373.0 

411.2 

451.3 

6 

219.3 

251.8 

2 

86.5 

32 

M 

362 

.6 

404.0 

447.6 

493.5 

541.6 

7 

255.9 

293.7 

334.2 

377.3 

423 

.0 

471.3 

522.2 

575.7 

631.9 

8 

292.4 

335.7 

382.0 

431.2 

483 

.4 

538.6 

596.8 

658.0 

722.1 

9 

329.0 

377.7 

4 

29.7 

48 

5.1 

543 

.8 

605.9 

671.4 

740.2 

812.4 

10 

365.5 

419.6 

477.4 

539.0 

604 

.3 

673.3 

746.0 

822.51  902.7 

11 

402.1 

461.6 

5 

25.2 

59 

2.9 

667 

.7 

740.6 

820.6 

904.7 

992.9 

12 

438.6 

503.5 

572.9 

646.8 

725 

.1 

807.9 

895.2 

987.0 

1083.2 

13 

475.2 

545.5 

6 

20.7 

70 

0.7 

785 

.6 

875.2 

969.8 

1069.2 

1173.5 

14 

511.8 

587.5 

668.2 

754.6 

846.0 

942.6 

1044.4 

1151.5 

1263.7 

15 

548.3 

629.4 

716.2 

808.5 

906.4 

1009.9 

1119.0 

1233.7 

1354.0 

16 

584.9 

671.4 

7 

73.9 

86 

2.4 

966 

.8 

1077.2 

1193.6 

1315.9 

1444.3 

17 

621.4 

713.4 

811.6 

916.3 

1027 

.2 

1044.6 

1268.2 

1398.2 

1534.5 

18 

658.0 

755.3 

8 

59.4 

97 

0.2 

1087 

.7  1211.9 

1342.8 

1480.4 

1624.8 

19 

694.5 

797.3 

907.1 

1024.1 

1148 

.1)1279.2 

1417.4 

1562.7 

1715.1 

20 

731  .  1 

839.3  954.91078.0 

1208 

.5  1346.5 

1492.0 

1644.9 

1805.3 

Depth, 

Diameter, 

in  Feet. 

in  Feet. 

23 

24 

25 

26 

27 

28 

29 

30 

5 

493.3 

537.1 

582.8 

630.4 

679.8 

731  .  1 

784.2 

839.3 

6 

592.0 

644.5 

699.4 

756.5 

815.8 

877.3 

941.1 

1007.1 

7 

690.6 

752.0 

815.9 

882.5 

951.7 

1023.5 

1097.9 

1175.0 

8 

789.3 

859.4 

932.5 

1008.6 

1087.7 

1169.7 

1254.8 

1342.8 

9 

887.9 

966.8 

1049.1 

1134.7 

1223.6 

1316.0 

1411.6 

1510.7 

10 

986.6 

1074.2 

1165.6 

1260.8 

1359.6 

1462.2 

1568.2 

1678.5 

11 

1085.2 

1181.7 

1282.2 

1386.8 

1495.6 

1608.7 

1723.0 

1846.4 

12 

1183.9 

1289.1 

1398.7 

1512.9 

1631.5 

1754.6 

1882.2 

2014.2 

13 

1282.6 

1396.5 

1515.3 

1639.0 

1767.5 

1900.8 

2039.0 

2182.0 

14 

1381.2 

1503.9 

1631.9 

1765.1 

1903.4 

2047.1 

2195.9 

2343.9 

15 

1479.9 

1611.4 

1748.4 

1891.1 

2039.4 

2193.3 

2352.7 

2517.8 

16 

1578.5 

1718.8 

1865.0 

2017.2 

2175.4 

2339.5 

2509.6 

2685.6 

17 

1677.2 

1826.2 

1981.6 

2143.3 

2311.3 

2485.7 

2666.4 

2853.5 

18 

1775.9 

1933.6 

2098.1 

2269.4 

2447.3 

2631.9 

2823.3 

3021.3 

19 

1874.5,  2041.1 

2214.7 

2395.4 

2583  .  2 

2778.1 

2980.1 

3189.2 

20 

1973.21  2148.5 

2321.2 

2521.5 

2719.2 

2924.4  3137.0 

3357.0 

For  tanks  that  are  tapering,  measure  the  diameter  four  tenths  from  large  end, 


CAPACITY  OF  RECTANGULAR   TANKS.       1261 


NUMBER  OF  U.  S.  GALLONS  IN  RECTANGULAR  TANKS 
FOR  ONE  FOOT  IN  DEPTH. 

1  cu.  ft.  =  7.4805  gallons. 


Width,  in 
Feet. 

Length  of  Tank,  in  Feet. 

2 

2.5 

3 

3.5 

4 

4.5 

5 

5.5 

82.29 
102.8 
123.43 
144.00 
164.57 
185.14 
205.71 
226.28 

6 

6.5 

7 

104.73 
130.91 
157.09 
183.27 
209.45 
235.63 
261.82 
288.00 
314.18 
340.36 
366.54 

2 
2.5 
3 
3.5 
4 
4.5 
5 
5.5 
6 
6.5 
7 

29.92 

37.40 
46.75 

44.88 
56.10 
67.32 

52.36 
65.45 
78.54 
91.64 

59.84 
74.80 
89.77 
104.73 
119.69 

67.32 
84.16 
100.99 
117.82 
134.65 
151.48 

74.81 
93.51 
112.21 
130.91 
149.61 
168.31 
187.01 

89.77 
112.21 
134.65 
157.09 
179,53 
201.97 
224.41 
246.86 
269.30 

97.25 
121.56 
145.87 
170.18 
194.49 
218.80 
243.11 
267.43 
291.74 
316.05 

-1 

Length  of  Tank,  in  Feet. 

'$* 

7.5 

8 

8.5 

9 

9.5 

10 

10.5 

11 

11.5 

12 

2 

112.21 

119.69 

127.17 

134.65 

142.13 

149.61 

157.09 

164.57 

172.05 

179.53 

2.5 

140.26 

149.61 

158.96 

168.31 

177.66 

187.01 

196.36 

205.71 

215.06 

22441 

3 

168.31 

179.53 

190.75 

202.97 

213.19 

224.41 

235.63 

246.86 

258.07 

269.30 

3.5 

196.36 

209.45 

222.54 

235.63 

248.73 

261.82 

274.90 

288.00 

301.09 

314.18 

4 

221.41 

239.37 

254.34 

269.30 

284.26 

299.22 

314.18 

329.14 

344.10 

359.06 

4.5 

252.47 

269.30 

286.13 

302.96 

319.79 

336.62 

353.45 

370.28 

387.11 

403.94 

5 

280.52 

299.22 

317.92 

336.62 

355.32 

374.03 

392.72 

411.43 

430.13 

448.83 

5.5 

308.57 

329.14 

349.71 

370.28 

390.85 

411.43 

432.00 

452.57 

473.14 

493.71 

6 

336.62 

359.06 

381.50 

403.94 

426.39 

448.83 

471.27 

493.71 

516.15 

538.59 

6.5 

36467 

388.98 

41330 

437.60 

461.92 

486.23 

510.54 

534.85 

550.16 

583.47 

7 

392.72 

418.91 

445.09 

471.27 

497.4^ 

523.64 

549.81 

575.00 

602.18 

628.36 

7.5 

420.78 

448.83 

476.88 

504.93 

532.98 

561.04 

589.08 

617.14 

645.19 

673.24 

8 



478.75 

508.67 

538.59 

568.51 

598.44 

628.36 

658.28 

688.20 

718.12 

8.5 

540  46 

572  25 

604  05 

635  84 

667  63 

690  42 

731.21 

703.00 

9 

605.92 

639'.58 

673*25 

706.90 

740.'  5  6 

774.*23 

807^89 

9.5 

675.  1  1 

710^65 

746!  17 

781.71 

817^24 

852.77 

10 

748  !  05 

785.'  45 

822.86 

860.26 

897.66 

10.5 

824!  73 

864  00 

903  26 

942.56 

11 

905.14 

946.27 

987.43 

11.5 

989.29 

1032.3 

12 

1077.2 

To  find  weight  of  water  in  pounds  at  62°  F.  multiply  number 
of  gallons  by  8}. 

EXAMPLE. — To  find  number  of  gallons  in  a  rectangular  tank 
that  is -7. 5  ft.  by  10  ft.,  the  water  being  4  ft.  deep:  Look  in 
extreme  left-hand  column  for  7.5  and  opposite  to  this  in  column 
headed  "10"  read  561.04,  which  being  multiplied  by  4,  the 
depth  of  water  in  the  tank,  gives  2244.2,  the  number  of  gallons 
required. 


1262  PLUMBING   DEFINITIONS. 

Plumbing-. 

The  water-supply  of  buildings,  including  the  apparatus  for 
heating  water,  the  system  of  drainage  and  sewage,  and  the 
various  fixtures  connected  therewith,  are  installed  by  the 
plumber,  usually  in  accordance  with  specifications  prepared 
by  the  architect  and  subject  to  municipal  regulations.  An 
efficient  and  safe  system  of  plumbing  is  a  matter  of  vital  im- 
portance. The  following 

EXTRACTS  FROM  THE  RULES  AND  REGULATIONS  OF  THE  DEPART- 
MENT OF  BUILDINGS  OF  THE  CITY  OF  NEW  YORK 
may  be  used  as  a  reliable  guide  in  any  locality. 

Definition  of  Terms. 

12.*  The  term  "  private  sewer"  is  applied  to  main  sewers  that 
are  not  constructed  by  and  under  the  supervision  of  the  Depart- 
ment of  Sewers. 

13.  The  term  "house  sewer"  is  applied  to  that  part  of  the 
main  drain  or  sewer  extending  from  a  point  2  ft.  outside  of  the 
outer  wall  of  building  vault  or  area  to  its  connection  with  public 
sewer,  private  sewer,  or  cesspool. 

14.  The  term  "house  drain"  is  applied  to  that  part  of  the 
main  horizontal  drain  and  its  branches  inside  the  walls  of  the 
building  vault  or  area  and  extending  to  and  connecting  with 
the  house  sewer. 

15.  The  term  "soil-pipe  "  is  applied  to  any  vertical  line  of 
pipe  extending  through  roof,  receiving  the  discharge  of  one  or 
more  water-closets  with  or  without  other  fixtures. 

16.  The  term  "waste-pipe"  is  applied  to  any  pipe,  extending 
through  roof,  receiving  the  discharge  from  any  fixtures  except 
water-closets. 

17.  The   term   "vent-pipe"   is   applied   to   any   special   pipe 
provided  to  ventilate  the  system  of  piping  and  to  prevent  trap 
siphonage  and  back  pressure. 

Materials  and  Workmanship. 

Soil-  and  Vent-pipe. — 19.  All  cast-iron  pipes  and  fittings 
must  be  uncoated,  sound,  cylindrical,  and  smooth,  free  from 
cracks,  sand  holes,  and  other  defects,  and  of  uniform  thickness 
and  of  the  grade  known  in  commerce  as  "extra  heavy." 

*  Paragraph  numbers  are  the  same  as  those  in  the  Official  Regulations, 
Missing  numbers  show  where  paragraphs  have  been  omitted, 


PLUMBING   REQUIREMENTS. 


1263 


20.*  Pipe,  including  the  hub,  shall  weigh  not  less  than  the 
following  average  weights  per  lineal  foot: 


Diameters. 

Weights  per 
Lineal  Foot. 

2  inc 
3 
4 
5 

6 
7 
8 
10 
12 

hes                               

5|  pou 
9* 
13 
17 
20 
27 
33i 
45 
54 

nds 

22.  All  joints  must  be  made  with  picked  oakum  and  molten 
lead  and  be  made  gas-tight.  Twelve  (12)  oz.  of  fine,  soft  pig 
lead  must  be  used  at  each  joint  for  each  inch  in  the  diameter  of 
the  pipe. 

24.  Wrought-iron  and  steel  pipes  must  be  galvanized,  and 
each  length  must  have  the  weight  and  maker's  name  stamped 
on  it. 

30.  All  brass  pipe  for  soil-,  waste-,  and  vent-pipes  and  solder 
nipples  must  be  thoroughly  annealed,  seamless,  drawn,  brass 
tubing  of  standard  iron-pipe  gauge. 

Lead  Waste-pipes. — 38.  The  use  of  lead  pipes  is  restricted  to 
the  short  branches  of  the  soil-  and  waste-pipes,  bends  and  traps, 
and  roof  connections  of  inside  leaders.  "Short  branches "  of 
lead  pipe  shall  be  construed  to  mean  not  more  than 

5  feet  of  1 J  inch  pipe 

A         U          It      O  II  (( 

OH  ((      O  ((  <t 

2    "     "4       "        " 

39.  All  connections  between  lead  pipes  and  between  lead  and 
brass  or  copper  pipes  must  be  made  by  means  of   "wiped" 
solder  joint. 

40.  All  lead  waste,  soil,  vent,  and  flush  pipes  must  be  of  the 
best  quality,  known  in  commerce  as  "D,"  and  of  not  less  than 
the  following  weights  per  lineal  foot: 

*  See  foot-note  on  page  1262. 


1264  PLUMBING  REQUIREMENTS. 


Diameters. 

Weights  per 
Lineal  Foot. 

1|  inches  (for  flush-pipes  only)  

2J  pounds 

2 

4          " 

3         "     

6          " 

4  and  4^  inches  

8          " 

41.  All  lead  traps  and  bends  must  be  of  the  same  weights  and 
thicknesses   as   their   corresponding   pipe  branches.     Sheet  lead 
for  roof  flashings  must  be  6-lb.  lead  and  must  extend  not  less 
than  6  ins.  from  the  pipe,  and  the  joint  made  water-tight. 

42.  Copper  tubing  when  used  for  inside  leader  roof  connec- 
tions must  be  seamless-drawn   tubing  not  less  than  22  gauge, 
and  when  used  for  roof  flashings  must  be  not  less  than  18  gauge. 

Yard,  Area,  and  Other  Drains. 

57.  All  yards,  areas,  and  courts  must  be  drained. 

58.  Tenement-houses    and    lodging-houses    must    have    their 
yards,  areas,  and  courts  drained  into  the  sewer. 

59.  These    drains,    when    sewer  connected,  must   have    con- 
nections not  less  than  3  ins.  in  diameter.     They  should  be  con- 
trolled by  one  trap — the  leader  trap  if  possible. 

Leaders. 

63.  All  buildings  shall  be  kept  provided  with  proper  metallic 
leaders  for  conducting  water  from  the  roofs  in  such  manner 
as  shall  protect  the  walls  and  foundations  of  said  buildings  from 
injury.     In  no  case  shall  the  water  from  said  leaders  be  allowed 
to  flow  upon  the  sidewalk,  but  the  same  shall  be  conducted  by 
pipe  or  pipes  to  the  sewer.     If  there  be  no  sewer  in  the  street 
upon   which  such  buildings  front,   then   the  water  from   said 
leaders  shall  be  conducted  by  proper  pipe  or  pipes  below  the 
surface  of  the  sidewalk  to  the  street  gutter. 

64.  Inside  leaders  must  be  made  of  cast  iron,  wrought  iron, 
or  steel,  with  roof  connections  made  gas-  and  water-tight  by 
means  of  a  heavy  lead  or  copper-drawn  tubing  wiped  or  soldered 
to  a  brass  ferrule  or  nipple  calked  or  screwed  into  the  pipe. 

65.  Outside  leaders  may  be  of  sheet  metal,  but  they  must 
connect  with  the  house  drain  by  means  of  a  cast-iron  pipe  ex- 
tending vertically  5  ft.  above  the  grade  level. 


PLUMBING  REQUIREMENTS. 


1265 


66.  Leaders  must  be  trapped  with  cast-iron  running  traps 
so  placed  as  to  prevent  freezing. 

67.  Rain-water  leaders  must  not  be  used  as  soil-,  waste-,  or 
vent-pipes,  nor  shall  any  such  pipe  be  used  as  a  leader. 

The  House  Sewer,  House  Drain,  House  Trap,  and 
Fresh-air  Inlet. 

72.  The  house  drain  must  properly  connect  writh  the  house 
sewer  at  a  point  2  ft.  outside  of  the  outer  front  vault  or  area 
wall  of  the  building.     An  arched  or  other  proper  opening  in  the 
wall  must  be  provided  for  the  drain  to    prevent  damage    by 
settlement. 

73.  If  possible,  the  house  drain  must  be  above  the  cellar  floor. 
The  house  drain  must  be  supported  at  intervals  of  10  ft.  by 
8-inch  brick  piers  or  suspended  from  the  floor-beams,   or  be 
otherwise  properly  supported  by  heavy  iron-pipe   hangers  at 
intervals  of  not  more  than  10  ft.     The  use  of  pipe-hooks  for 
supporting  drains  is  prohibited. 

74.  No  steam-exhaust,  boiler  blow-off,  or  drip-pipe  shall  be 
connected  with  the  house  drain  or  sewer.     Such  pipes  must  first 
discharge  into  a  proper  condensing  tank,  and  from  this  a  proper 
outlet  to  the  house  sewer  outside  of  the  building  must  be  pro- 
vided.    In   low-pressure   steam   systems   the   condensing   tank 
may  be  omitted,  but  the  waste  connection  must  be  otherwise 
as  above  required. 

75.  The  house  and  drain  sewer  must  be  run  as  direct  as  possi- 
ble, with  a  fall  of  at  least  J  in.  per  foot,  all  changes  in  direction 
made  with  proper  fittings,  and   all  connections  made  with  Y  • 
branches  and  one  eighth  and  one  sixteenth  bends. 

Size  of  House  Sewer. — 76.  The  house  sewer  and  house  drain 
must  be  at  least  4  ins.  in  diameter  where  water-closets  discharge 
into  them.  Where  rain-water  discharges  into  them,  the  house 
sewer  and  house  drain  up  to  the  leader  connections  must  be  in 
accordance  with  the  following  table : 


Diameter. 

Fall  X  Inch 
per  Foot. 

Fall  Y2 

Inch  per  Foot. 

6  ins    .  .    . 

5,000  sq.  ft. 

7,500  sq   ft 

of  drainage  of  area 

7   "  
8  "  

6,900      " 
9,100      " 

10,300      " 
13,600      " 

«                 ((                It,          U 

f(           (t           11       (t 

9   "  

11,600      " 

17,400      " 

It           (t           ft       (t 

1266  PLUMBING  REQUIREMENTS. 

77.  Full  size  Y  and  T  branch  fittings   for  hand-hole    clean- 
outs  must  be  provided  where  required  on  house  drain  and  its 
branches. 

78.  An  iron  running  trap  must  be  placed  on  the  house  drain 
near  the  wall  of  the  house,  and  on  the  sewer  side  of  all  connec- 
tions, except  a  drip-pipe  where  one  is  used.     If  placed  outside 
the  house  or  below  the  cellar  floor,  it  must  be  made  accessible 
in  a  brick  manhole,  the  walls  of  which  must  be  8  ins.  thick, 
with  an  iron  or  flagstone  cover.     When  outside  the  house  it 
must  never  be  less  than  3  ft.  below  the  surface  of  the  ground. 

79.  A  fresh-air  inlet  must  be  connected  with  the  house  drain 
just  inside  of  the  house  trap;  where  under  ground  it  will  be 
of  extra  heavy  cast  iron.     Where   possible   it  will   extend   to 
the  external  air,  and  finish  with  an  automatic  device  approved 
by  the  Department   of   Buildings,  at  a  point  just  outside  the 
front   wall   of   building.     The   fresh-air  inlet   must   be   of   the 
same  size  as  the  drain  up  to  4  ins.     For  5-  and  6-in.  drains  it 
must  be  not  less  than  4  ins.  in  diameter.     For  7-  and  8-in.  drains 
not  less  than  6  ins.  in  diameter  or  its  equivalent,  and  for  large 
drains  not  less  than  8  ins.  in  diameter  or  its  equivalent. 

[Note. — The  fresh-air  inlet  and  running  trap  prescribed  by 
Sections  78  and  79  are  not  required  in  many  cities,  and  it  is  a 
disputed  question  whether  or  not  they  are  desirable.] 

Soil-,  Waste-,  and  Vent-pipes. 

80.  All  main,  soil,  waste,  or  vent  pipes  must  be  of  iron,  steel, 
or  brass. 

89.  The  diameters  of  soil-  and  waste-pipes  must  not  be  less 
than  those  given  in  the  following  table: 

Main  soil-pipes 4  inches 

Main  soil-pipes  for  water-closets  on  five  or  more  floors.  5  " 

Branch  soil-pipes 4  " 

Main  waste-pipes 2  " 

Main  waste-pipes  for  kitchen  sinks  on  five  or  more  floors  3  " 

Branch  waste-pipes  for  laundry  tubs 1 J  " 

When  set  in  ranges  of  three  or  more 2  " 

Branch  waste  for  kitchen  sinks 2  " 

Branch  waste  for  urinals 2  " 

Branch  waste  for  other  fixtures 1 J  " 

96.  The  sizes  of  vent-pipes  throughout  must  not  be  less  thai\ 
the  following: 


PLUMBING  REQUIREMENTS.  1267 

For  main  vents  and  long  branches,  2  ins.  in  diameter;  for 
water-closets  on  three  or  more  floors,  3  ins.  in  diameter;  for 
other  fixtures  on  less  than  seven  floors,  2  ins.  in  diameter;  3-in. 
vent-pipe  will  be  permitted  for  less  than  nine  stories;  for  more 
than  eight  and  less  than  sixteen  stories,  4  ins.  in  diameter; 
for  more  than  fifteen  and  less  than  twenty-two  stories,  5  ins.  in 
diameter.;  for  more  than  twenty-one  stories  6  ins.  in  diameter; 
branch  vents  for  traps  larger  than  2  ins.,  2  ins.  in  diameter; 
branch  vents  for  traps  2  ins.  or  less,  1J  ins.  in  diameter. 

For  fixtures  other  than  water-closets  and  slop-sinks  and  for 
more  than  eight  stories,  vent-pipes  may  be  1  in.  smaller  than 
above  stated. 

Traps. 

98.  Every  fixture  must  be  separately  trapped  by  a  water- 
sealing  trap  placed  as  close  to  the  fixture  outlet  as  possible. 

99.  A  set  of  wash-trays  may  connect  with  a  single  trap,  or 
into  the  trap  of  an  adjoining  sink,  provided  both  sink  and  tub 
waste  outlets  are  on  the  same  side  of  the  waste  line  and  the 
sink  is  nearest  the  line.     When  so  connected  the  waste-pipe 
from  the  wash-trays  must  be  branched  in  below  the  water  seal. 

100.  The  discharge  from  any  fixture  must  not  pass  through 
more  than  one  trap  before  reaching  the  house  drain. 

106.  All  earthenware  traps  must  have  heavy  brass  floor  plates 
soldered  to  the  lead  bends   and  bolted  to  the  trap  flange  and 
the  joint  made  gas-tight  with  red  or  white  lead.     The  use  of 
rubber  washers  for  floor  connections  is  prohibited. 

107.  No  trap  shall  be  placed  at  the  foot  of  main  soil-  and 
waste-pipe  lines. 

108.  The  sizes  for  traps  must  not  be  less  than  those  given  in 
the  following  table: 

Traps  for  water-closets 4  inches  in  diameter 

Traps  for  slop-sinks " 2        "     "         " 

Traps  for  kitchen  sinks 2        "      "         " 

Traps  for  wash-trays 2        "     "         " 

Traps  for  urinals 2        "      "          " 

Traps  for  other  fixtures .*.  .  .    li      "     "         " 

Traps  for  leaders,  areas,  floor  and  other  drains  must  be  at 
least  3  ins.  in  diameter. 


1268  PLUMBING  REQUIREMENTS. 

Water-closets. 

118.  In  tenement-houses,  lodging-houses,  factories,  workshops, 
and  all  public  buildings  the  entire  water-closet  apartment  and 
side  walls  to  a  height  of  16  ins.  from  the  floor,  except  at  the 
door,  must  be  made  waterproof  with  asphalt,  cement,  tile, 
metal,  or  other  water-proof  material  as  approved  by  the  Board 
of  Buildings. 

121.  The  general  water-closet  accommodations  for  a  tene- 
ment- or  lodging-house  cannot  be  placed  in  the  cellar. 

130.  In  all  sewer-connected   occupied  buildings  there  must 
be   at   least   one   water-closet,    and   there   must   be   additional 
closets  so  that  there  wrill  never  be  more  than  fifteen  persons 
per  closet. 

131.  In  tenement-houses  and  lodging-houses  there  must  be 
one  water-closet  on  each  floor,  and  when  there  is  more  than 
one  family  on  a  floor,  there  will  be  one  additional  water-closet 
for  every  two  additional  families. 

132.  In   lodging-houses   where   there   are   more   than   fifteen 
persons  on  any  floor,  there  must  be  an  additional  water-closet 
on   that  floor  for  every   fifteen  additional  persons   or  fraction 
thereof. 

133.  Water-closets    and    urinals    must    never    be    connected 
directly  with  or  flushed  from  the  water-supply  pipes. 

136.  Iron   water-closets   and   urinal   cisterns   and   automatic 
water-closets  and  urinal  cisterns  are  prohibited. 

137.  The  copper  lining  of  water-closets  and  urinal   cisterns 
must  not  be  lighter  than  10  oz.  copper. 

138.  Water-closet   flush-pipes   must  not  be  less  than  1J  ins. 
and  urinal  flush-pipes  1  in.  in  diameter,  and  if  of  lead  must  not 
weigh  less  than  2  J  Ibs.  and  2  Ibs.  per  lineal  foot.    Flush-couplings 
must  be  of  full  size  of  the  pipe. 

Sinks  and  Wasli-tuus. 

143.  In  tenement-houses  and  lodging-houses  sinks  must  be 
entirely  open,  on  iron  legs  or  brackets,  without  any  enclosing 
woodwork. 

144.  Wooden    wash-tubs    are    prohibited.     Cement    or    arti- 
ficial stone  tubs  will  not  be  permitted  unless  approved  by  the 
Board  of  Buildings. 


PLUMBING  REQUIREMENTS.  1269 

Testiug  the  Plumbing  System. 

155.  The  entire  plumbing  and  draining  system  within   the 
building  must  be  tested  by  the  plumber,  in  the  presence  of  a 
plumbing  inspector,   under  a  water   or  air   test,   as   directed. 
All  pipes  must  remain  uncovered  in  every  part  until  they  have 
successfully    passed    the    test.     The    plumber    must    securely 
close  all  openings  as  directed  by  the  Inspector  of  Plumbing. 
The  use  of  wooden  plugs  for  this  purpose  is  prohibited. 

156.  The  water   test  will  be   applied   by   closing   the   lower 
end  of  the  main  house  drain  and  filling  the  pipes  to  the  highest 
opening  above  the  roof  with  water.     The  water  test  shall  in- 
clude at  one  time  the  house  drain  and  branches,  all  vertical 
and  horizontal  soil,  waste  and  vent  and  leader  lines  and  all 
branches  therefrom  to  point  above  the  surface  of  the  finished 
floor  and   beyond   the   finished   face   of  walls   and   partitions. 
Deviation  from  the  above  rule  will  not  be  permitted,  unless 
upon  written  application  to  and  approval  by  the  Commissioner 
of  Buildings.     If  the  drain  or  any  part  of  the  system  is  to  be 
tested  separately,  there  must  be  a  head  of  water  at  least  6  ft. 
above  all  parts  of  the  work  so  tested,  and  special  provision 
must  be  made  for  including  all  joints  and  connections  in  at 
least  one  test. 

157.  The   air  test  will  be   applied  with  a  force-pump   and 
mercury  columns  under  ten  pounds  pressure,  equal  to  20  ins. 
of  mercury.     The  use  of  spring  gauges  is  prohibited. 

158.  After  the  completion  of  the  work,  when  the  water  has 
been  turned  on  and  the  traps  filled,  the  plumber  must  make 
a  peppermint  or  smoke  test  in  the  presence  of  a  plumbing  in- 
spector and  as  directed  by  him. 

159.  The  material  and  labor  for  the  tests  must  be  furnished 
by  the  plumber.     Where  the  peppermint  test  is  used,  2  ozs.  of 
oil  of  peppermint  must  be  provided  for  each  line  up  to  five 
stories  and  basement  in  height,  and  for  each  additional  five 
stories  or  fraction   thereof  one  additional  ounce  of  peppermint 
must  be  provided  for  each  line. 

!  Traps. 

A  trap  is  a  device  which  permits  the  free  passage  of  liquids 
through  it,  and  also  of  any  solid  matters  that  may  be  carried 
by  the  liquid,  while  at  the  same  time  preventing  the  passage 
of  air  or  gas  in  either  direction.  Traps  used  for  plumbing 


1270 


PLUMBING— TRAPS. 


purposes  are  shaped  so  that  an  amount  of  water  sufficient  to 
close  the  passage  and  prevent  the  passage  of  air  will  stand  in 
them  at  all  times.  The  principle  of  the  common  trap  is  shown 
by  Fig.  A.  The  pipe  T  receives  the  waste  from  a  sink  or  wash- 
basin, while  the  lower  end  B  connects  with  the  sewer.  Sewer-gas 
rises  in  pipe  B,  out  is  prevented  from  passing  to  the  fixture  by 
the  water  which  stands  in  the  trap.  The  depth  of  water  through 
which  gas  must  pass  to  effect  a  passage  is  termed  the  "  water- 
seal."  The  water-seal  in  the  trap,  Fig.  A,  is  the  distance  S. 

All    plumbing   pipes  which  connect  with  a  sewerage  system 
require  to  be  trapped  to  prevent  sewer-gas  from  passing  through 


Fig.  B 

them  to  the  fixture  and  into  the  room  in  which  the  fixture  is 
located. 

Ventilation  of  Traps. — When  a  considerable  body  of 
water  rushes  down  through  a  pipe  it  forms  a  suction,  and  if  the 
pipe  is  made  air-tight,  this  suction  is  often  sufficient  to  prevent 
enough  water  remaining  in  the  trap  to  form  a  seal,  thus  leaving 
an  opening  for  the  passage  of  sewer-gas  as  in  Fig.  B.  By  connect- 
ing the  upper  bend  of  a  trap  wi.h  the  outside  air  by  means  of  a 
pipe,  as  at  V,  Fig.  A,  the  suction  will  be  stopped,  and  the  water 
in  the  pipe  T  will  not  fall  below  the  level  of  the  outlet  at  6. 

Several  non-si  phoning  traps  have  been  patented  for  the 
purpose  of  obviating  the  necessity  of  back  venting,  but  they 
are  used  to  a  comparatively  limit  d  extent. 

There  are  also  several  varieties  of  back-pressure  traps,  de- 


PLUMBING— TRAPS. 


1271 


signed  to   prevent    the   sewage   from   flowing    back    into    the 
house   drain.     These   are   in   the   nature   of   check- valves,   and 


Bag 


Fig.  C 

Different  Shapes  of  Traps. 

are  used  principally  in  seaport  towns   where   tide-water  might 
possibly  force  the  sewage  back. 

The  more  common  shapes  of  lead  traps  used  in  plumbing, 
with  their  trade  names,  are  shown  in  Figure  C.  The  same 
shapes  are  also  made  in  cast  iron. 
The  pipes  marked  V  are  the  vent 
connections.  The  drum  trap  shown 
by  Fig.  D  has  a  deeper  seal  than  those 
shown  in  Fig.  C,  and  is  commonly  used 
under  kitchen  sinks,  bath-tubs,  and 
wash-trays.  Drum  traps  are  not  easily 
siphoned,  even  when  not  vented.  The 
traps  for  water-closets  are  commonly 
formed  in  the  fixture. 

Grease  Traps. — The  waste  water 
from  kitchen  sinks  always  contains  con- 
siderable grease,  which  if  permitted  to 
enter  the  soil-pipe  system  is  liable  to  clog  the  pipes  by  adhering 
to  the  walls.  In  certain  localities  grease  gives  much  more 
trouble  than  in  others,  due  to  the  chemical  composition  of  the 
water. 


Fig.  D 

Round  Trap. 


1272 


PLUMBING— TRAPS. 


In  Colorado  and  many  other  places  it  is  necessary  to  con- 
nect the  waste  from  kitchen  sinks  with  a  large  grease  trap, 
which  collects  and  holds  the  grease,  but  permits  the  water  to 
pass  into  the  sewer  system.  After  a  time  the  accumulated 
grease  fills  the  trap  and  must  be  removed.  On  account  of  this 
it  is  desirable  to  use  a  large  trap,  and  whenever  possible  it  should 
be  placed  underground,  just  outside  the  house,  and  as  near  to 
the  sink  as  practicable. 

Grease  traps  to  be  placed  underground  are  commonly  made 
of  24-inch  vitrified  drain-tile  or  cement  pipe,  and  should  be 
about  4  ft.  deep.  They  may  also  be  built  of  brick  in  cement 


Fig.  E 

Outdoor  Grease  Trap. 


mortar.    Fig.  E  shows  a  section    through  such  a  grease  trap 
and  the  inlet  and  outlet  pipes. 

When  the  sink  is  in  a  basement  or  an  upper  story,  or  when 
the  building  occupies  the  entire  lot,  the  grease  trap  must  be 
placed  under  the  sink.  When  so  placed,  a  round  lead  trap 
12  or  14  ins.  in  diameter  may  be  used,  with  a  large  trap  screw 
in  the  top  for  removing  the  grease.  Fig.  F  shows  a  section 
through  such  a  trap  and  the  way  in  which  the  connections 
should  be  made.  A  better  form  of  grease  trap  is  made  of  cast 
iron.  Some  city  ordinances  require  that  inside  grease  traps 


PLUMBING— SUPPLY-PIPES. 


1273 


shall  have  a  chilling  jacket  for  the  purpose  of  more  perfectly 
separating  the  grease  and  thus 
preventlig    any    of    it    from 
entering  the  waste-pipes. 

Supply  -  pipes.  —  These 
may  be  of  lead,  brass,  galvan- 
ized iron,  tin-lined  lead,  or 
block  tin.  Lead  pipe  offers 
the  least  resistance  to  the  flow 
of  water,  is  easily  bent  to  suit 
any  situation,  and  easy  curves 
are  readily  made.  It  is  gener- 
ally considered  more  durable 
underground  than  galvanized- 


Fig.  F 

Lead  Grease  Trap. 


iron  pipe.  The  grade  known 
as  A,  or  " strong,"  is  the  lightest  that  should  ever  be  used,  and 
when  the  supply  is  taken  from  city  mains,  in  which  there  is  a 
considerable  pressure,  A  A,  or  extra  strong  pipe,  should  be  used. 

Galvaiiized-iron  pipe  is  probably  more  extensively  used  than 
any  other  material  for  water-supply  pipes  in  buildings,  except 
where  nickel-plated  pipe  is  required,  in  which  case  brass  piping 
is  commonly  used.  Brass  pipe  used  for  water-supply  should 
be  what  is  known  as  iron- pipe  size. 

Brass  piping  is  preferable  to  galvanized  iron  or  lead  for  con- 
veying hot  water,  and  is  largely  used  in  the  better  class  of  build- 
ings. 

Tin-lined  iron  and  lead  pipes  and  pipes  of  block  tin  are 
usually  considered  as  offering  the  greatest  resistance  to  cor- 
rosion or  chemical  action,  and  should  always  be  used  for  con- 
veying ale,  beer,  and  other  liquors. 

Tin-lined  iron  pipe  is  made  by  pouring  melted  tin  into  a 
wrought-iron  pipe.  While  in  a  fluid  state  the  tin  is  inseparably 
united  to  the  iron,  and  the  result  is  one  solid  pipe  composed  of 
two  metals  which  can  not  be  torn  apart.  It  is  essentially  different 
from  iron  pipe  merely  dipped  in  tin,  and  immeasurably  superior 
to  iron  pipe  lined  with  a  separate  tin  pipe  that  will  become 
detached.  Its  fittings  are  lined  with  tin  to  match.  Hot  water 
will  not  injure  it,  rats  will  not  gnaw  it,  and  thieves  will  not  cut 
it  out.  Either  hot  or  cold  water  may  stand  in  block-tin  pipes 
and  yet  b3  drawn  from  them  pure  and  free  from  poison  or 
rust. 

Lead-lined  pipe  is  made  in  the  same  way  and  insures,  deliver- 


1274  PLUMBING— WATER-SUPPLY. 

ing  the  water  to  the  house  just  as  it  comes  from  the  mains  un- 
changed by  the  chemical  action  which  often  results  from  contact 
with  wrought-iron  pipe. 

Seamless-drawn  nickel-silver  tubing  is  used  to  some  extent  for 
the  exposed  plumbing  pipes  in  high  class  residences,  office  and 
public  buildings.  Being  pure  white  metal  throughout  it  can  not 
rub  or  wear  "  brassy  "  or  become  discolored.  It  is  made  in  all 
the  regular  iron  pipe  sizes,  and  necessary  fittings  are  supplied  of 
the  same  metal.* 

House  Tanks. — Where  the  pressure  in  the  street  mains 
is  not  great  enough  to  furnish  a  sufficient  volume  of  water  for 
supplying  the  fixtures  at  all  times,  or  in  cases  of  a  private 
water-supply,  a  tank  should  be  placed  in  the  attic,  or  elevated  at 
least  6  ft.  above  the  highest  fixture  to  be  supplied.  In  some 
cases  the  fixtures  in  the  lower  story  are  supplied  direct  from 
the  street  mains,  while  those  in  the  upper  story  are  supplied 
from  a  tank.  The  advantage  of  a  tank  is  that  it  will  fill  gradu- 
ally from  a  very  small  stream,  and  thus  form  a  reservoir  from 
which  a  larger  volume  can  be  drawn  in  a  shorter  space  of  time 
than  could  be  obtained  direct  from  the  service  pipes. 

Storage-tanks  should  always  be  provided  with  an  overflow 
pipe  of  ample  size  and  when  supplied  from  the  street  mains 
the  supply  should  be  controlled  by  a  ball  cock  and  float. 

Storage-tanks  of  moderate  size  are  preferably  made  of  wood 
lined  with  planished  or  tinned  copper. 

Sheet  lead,  zinc,  or  galvanized  iron  should  not  be  used  for 
lining  tanks  containing  water  for  drinking  or  cooking  purposes, 
and  are  not  as  durable  as  copper,  even  when  the  effect  on  the 
water  need  not  be  considered. 

The  size  of  tank  required  will  depend  largely  upon  the  char- 
acter of  the  supply.  Tanks  supplied  from  the  street  main  in 
which  the  pressure  is  fairly  constant  need  not  have  a  capacity 
exceeding  160  gallons.  Where  the  water  is  pumped  into  the 
tank  by  a  windmill  or  hot-air  engine,  the  tank  should  have  a 
capacity  sufficient  for  a  three  or  four  days'  supply  at  least. 

Amount  of  Water  Required  for  Various  Pur- 
poses.— The  amount  of  water  required  for  household  pur- 
poses has  been  found  to  be  about  25  gallons  for  each  person, 
large  or  small. 

*For  further  information  consult  the  Benedict  &  Burnham  Mfg.  Co... 
Waterbury,  Conn, 


PLUMBING— SIZE  OF   PIPES. 


1275 


A  horse  will  drink  about  7  gallons  per  day  and  a  cow  5  to 
6  gallons  per  day. 

A  carriage  requires  from  9  to  16  gallons  for  washing. 

Size  of  Supply-pipes. — The  proper  diameter  of  supply- 
pipes  depends  upon  several  considerations,  such  as  the  number 
and  size  of  faucets  that  are  likely  to  be  discharging  water  at 
the  same  time,  the  urgency  of  the  demand,  the  length  of  the 
pipes  and  number  of  angles,  and  upon  the  pressure. 

There  is  no  objection  to  having  a  pipe  larger  than  is  really 
necessary,  except  from  the  standpoint  of  cost.  Service-pipes 
should  always  be  one  size  larger  than  the  tap  in  the  street  main. 

The  following  table  affords  a  fair  guide  for  proportioning 
the  supply  branches  to  plumbing  fixtures.  If  the  pressure 
is  less  than  20  Ibs.  per  square  inch  the  system  may  be  rated 
as  low  pressure,  and  if  above  20  Ibs.  as  high  pressure. 


Supply  Branches. 

Low 
Pressure. 

High    . 
Pressure. 

To  Bath-cocks 

Inch. 
£  to  1 

Inch. 

^  to  £ 

Basin-cocks  

| 

W.  C  flush-tank 

I 

W.  C.  flush-  valve  

1  to  li 

I  to  1 

Sitz  or  foot-bath  

*  to  f 

i 

Kitchen  sinks  

£  to  £ 

i  to  4 

Pantry  sinks 

1 

Slop-sinks  

|  to  £ 

^  to  f 

Urinals  '.  

i  tof 

J  to  f 

With  high-pressure  systems,  dwellings  of  five  or  six  rooms 
are  sometimes,  for  economy,  supplied  entirely  through  J-inch 
pipe. 

.Minimum  Diameter  of  Waste-pipes. — The  following 
are  considered  as  the  smallest  diameters  allowable  for  waste- 
pipes.  The  diameters  required  in  New  York  City  are  given 
on  p.  1264. 

Bath  and  sink  wastes,  1 J  ins. 

Basin  and  urinal  wastes,  1 J  ins. 

Wash  trays,  1^  ins.  from  each  compartment,  entered  into 
1-inch  round  trap  and  2-inch  outlet  from  trap. 

Water-closet  trap,  3^  ins. 


1276  PLUMBING— LEAD  PIPES. 

APPROXIMATE  SPACING  FOR  TACKS  ON  LEAD  PIPES. 


Vertical  Pipe. 

Horizontal  Pipe. 

Size  of  Pipe, 
Inches. 

Distance  Apart,  Inches. 

Distance  Apart,  Inches. 

Hot. 

Cold. 

Hot. 

Cold. 

J 

19 

25 

14 

17 

20 

26 

15 

18 

f 

21 

27 

16 

19 

1 

22 

28 

17 

20 

H 

23 

29 

18 

21 

li 

24 

30 

18 

22 

Designation  of  J^ead.  Pipe. — The  different  thicknesses 
of  lead  pipe  were  formerly  designated  by  letters  as  in  Table  B, 
but  are  now  more  commonly  designated  as  in  Table  A,  follow- 
ing, which  may  be  considered  as  generally  accepted  by  dealers. 

TABLE  A.— WEIGHTS  AND  SIZES  OF  LEAD  PIPE. 


Calibre. 

Weight 
per  Foot. 

Calibre. 

Weight 
per  Foot. 

Lbs, 

Ozs. 

Lbs. 

Ozs. 

^-in.  Tubing.     .  .    . 

6 
15 
8 
10 
12 

8 

10 
12 

4 
12 

8 

12 
4 
12 

8 

f-in.  Ex.  ex.  Strong 
f-in.  Aqueduct  
Ex.  Light  
Light  .  .    . 

3 
1 
1 
2 
2 
3 
3 
4 
1 
2 
2 
1 
2 
2 
3 
4 
4 
5 
2 
2 
3 
3 

8 
8 
4 
8 
8 

8 
8 

8 
4 

12 

8 

8 
12 

Fish  Seine  

f-in.  Aqueduct  

Ex.  Light.  .  .  . 

Light  

Medium  

Medium 

1 
1 
2 

Strong  • 

Strong  

Ex.  Strong.  .  .  . 
Ex.  ex.  Strong, 
^-in  Aqueduct.  . 

Ex.  Strong.  .  .  . 
^-in  Aqueduct 

Ex.  Light  
Light 

i' 

1 
1 
2 
2 
3 

Ex.  Light  
Light 

Medium  

1-in.    Aqueduct  
Ex.  Light  
Light  

Strong  

Ex.  Strong.  .  .  . 
Ex.  ex.  Strong. 
|[-in.  Aqueduct. 

Medium  

Strong 

Ex.  Strong,  .  .  . 
Ex.  ex.  Strong. 
IJ-in.  Aqueduct  
Ex.  Light  
Light  

Ex.  Light  
Light 

1 
1 
2 
2 
3 

Medium.      .  .  . 

Strong 

Ex.  Strong.  .  .  . 

Medium  

% 

PLUMBING—  LEAD  PIPES. 


1277 


Calibre. 

Weight 
per  Foot. 

Calibre. 

Weight 
per  Foot. 

Lbs. 

Ozs, 

Lbs. 

Ozs. 

1  J-in.  Strong  
Ex.  Strong.  . 
Ex.  ex.  Strong 
IJ-in.  Aqueduct.  .  . 
Ex.  Light.  .  . 
Light 

4 
6 
6 
3 
3 
4 
5 
6 
7 
9 
3 
4 
5 
6 
8 
3 
4 
5 
7 
8 
9 
10 

12 
12 

8 

8 

12 

8 
8 
8 

8 

2^-in  Waste               

4 
6 
8 
11 
14 
17 
3 
6 
9 
12 
16 
20 
5 
15 
18 
5 
10 
16 
22 
25 
8 

8 
3 

Light  

Medium,  %        thick 
Strong,  i 
Ex.  Strong,  %      " 
Ex.  ex.  Strong,  f  " 
3-in.    Waste  

Medium 

Strong 

Light  

Ex.  Strong.  . 
Ex.  ex.  Strong 
If-in,  Ex.  Light.  .  . 
Light  

Medium,  %        thick 
Strong,  } 
Ex.  Strong,  %      " 
Ex.  ex.  Strong,  f  " 
3  J-in  Waste 

Medium  
Strong  

Strong,  J            thick 
Ex.  Strong,  %      " 
4-in     Waste 

Ex.  Strong.  . 
2  in    Waste 

Ex.  Light.  .  . 
Light  
Medium 

Medium   

Strong,  J            thick 
Ex.  Strong,  %>      " 
Ex.  ex.  Strong,  J  " 
5-in     Waste  

Strong  

Ex.  Strong.  . 
Ex.  ex.  Strong 

Coils  of  supply-pipe  weigh  about  200  Ibs. ;  Aqueduct  about 
90  Ibs. ;  Suction-pipe,  100  to  180  Ibs.  each. 

Block-tin  pipe  is  stronger  for  a  given  weight  per  foot  than 
lead-  or  tin-lined  lead  pipe.  As  compared  with  lead  pipe  its 
strength  is  as  3  J  to  1. 

Tin-lined  and  lead-lined  iron  pipe  is  made  with  inside  diame- 
ters of  J,  },  1,  IJ,  1J,  and  2  ins.,  and  in  10-ft.  lengths,  threaded 
without  couplings.  Tin-  and  lead-lined  fittings  are  also  made 
(see  p.  1273). 

WEIGHTS  AND  SIZES  OF  SHEET  LEAD. 


Thickness,  inches  
Pounds,  per  sq.  ft  

%4 

VA 

y2o 

3 

Ms 

3^ 

Me 
4 

M4 

4M 

Vl2 

5 

Mo 
6 

Ve 

u 

8 

%4 

9 

Ve 
10 

3/ie 
11 

% 
12 

1278 


PLUMBING— LEAD  PIPES. 


TABLE     B.—  THICKNESS    AND    STRENGTH    OF    LEAD 
PIPES. 


*g 

W) 
d 

-^  £ 

g 

8, 

<a 

3    g 

'S  ® 

1 

B 

%  m 

"B  d 

<B 

PQ  o3 

o  55 

CD 

PQ  | 

O     *H 

I  ' 

•^ 

IB 

| 

c£ 

«  I 

1 

i 

iM 

1 

c£ 

tfl 

'i 

« 

&& 

H 

0 

S 

£ 

H 

£.a 

02 

d 

I* 

H 

s>rH 

02 

Ins. 

lb.    oz. 

ins. 

Ibs. 

Ibs. 

ins. 

lb.  oz. 

ins. 

Ibs. 

Ibs. 

3-^ 

AAA 

1   12 

0.18 

1968 

492 

|  1 

A 

4     0 

0.21 

857 

214 

H 

AA 

1     5 

0.15 

1627 

406 

1 

B 

3     4 

0.17 

745 

186 

H 

A 

1     2 

0.13 

1381 

347 

[  1 

C 

2     8 

0.14 

562 

140 

y% 

B 

1     0 

0.125 

1342 

335 

1 

D 

2     4 

0.125 

518 

129 

H 

C 

0  14 

0.11 

1187 

296 

1 

E 

2     0 

0.10 

475 

118 

0  10 

0.087 

1085 

271 

1 

1     8 

0  09 

325 

81 

7/lo 

0     9i 

0.08 

775 

193 

l¥ 

AAA' 

6  12 

0.275 

962 

240 

1^ 

'AAA' 

3     0 

0.25 

1787 

446 

AA 

5  12 

0.25 

823 

205 

^2 

2     8 

0.225 

1655 

413 

l1^ 

A 

4  11 

0.21 

685 

171 

% 

'  AA  ' 

2     0 

0.18 

1393 

343 

IX 

B 

3  11 

0.17 

546 

136 

% 

A 

1   10 

0.16 

1285 

321 

C 

3     0 

0.135 

420 

105 

1^2 

B 

1     3 

0.125 

980 

245 

lx/| 

D 

2     8 

0.125 

350 

87 

1^ 

C 

1     0 

0.10 

782 

195 

1M 

2     0 

0.095 

322 

80 

1^ 

D 

0     9 

0.065 

468 

117 

l/^ 

'AAA' 

8     0 

0.29 

742 

185 

IX 

0  10 

0.07 

556 

139 

]i2 

AA 

7     0 

0.25 

700 

175 

JX 

0  12 

0.09 

625 

156 

-j  i/ 

A 

6     4 

0  22 

628 

157 

£^ 

AAA 

3     8 

0.23 

1548 

387 

\y^ 

B 

5     0 

0.18 

506 

126 

^ 

AA 

2  12 

0.21 

1380 

345 

i^ 

C 

4     4 

0.15 

430 

107 

£| 

A 

2     8 

0.18 

1152 

288 

^ 

D 

3     8 

0.14 

315 

78 

% 

B 

2     0 

0.16 

987 

246 

1^2 

3     0 

0.12 

245 

61 

% 

C 

1     7 

0.117 

795 

198 

1/4 

"  B  " 

5     0 

116 

% 

D 

1     4 

0.10 

708 

177 

1  /€ 

C 

4     0 

93 

M 

AAA 

4  14 

0.29 

1462 

365 

l/€ 

D 

3  10 

6!i25 

318 

79 

M 

AA 

3     8 

0.225 

1225 

306 

2 

AAA 

10  11 

0.30 

611 

152 

/€ 

A 

3     0 

0.19 

1072 

268 

2 

AA 

8  14 

0.25 

511 

127 

M 

B 

2     3 

0.15 

865 

216 

2 

A 

7     0 

0.21 

405 

101 

^ 

C 

1   12 

0.125 

782 

195 

2 

B 

6     0 

0.19 

360 

90 

M 

D 

1     3 

0.09 

505 

126 

2 

C 

5     0 

0.16 

260 

65 

AAA 

6     0 

0.30 

1230 

307 

2 

D 

4     0 

0.09 

200 

50 

1 

AA 

4     8 

0.23 

910 

227 

WEIGHT  AND  SIZES  OF  PURE  BLOCK-TIN  PIPE. 


ize  Inside 
Lameter  in 
Inches. 

Weight  per  Foot, 
Ounces. 

Size  Inside 
Diameter  in 
Inches. 

Weight  per  Foot, 
Pounds. 

%, 

4 

i 

9,  12,  16 

\ 

4,5,6 

i 

12,  16 

% 

4,5,6,8 

1J 

20,28 

4,  5,  6,  8 

li 

24  and  upwards 

1 

5,6,8,  10 

2 

32  and  upwards 

f 

9,  12,  16 

SEWER-PIPE.  1279 

Sewer-pipe. 

There  are  three  kinds  of  sewer-  or  drain-pipe  offered  in  the 
market,  viz.,  "gait  Glazed  Vitrified  Clay-pipe,"  "Slip  Glazed 
Clay-pipe/'  and  "Cement  Pipe."  The  name  of  the  latter  suf- 
ficiently indicates  what  it  is  without  any  description. 

The  "Slip  Glazed  Clay-pipe "  is  made  of  what  is  known  as 
"fire"  (such  as  fire-brick)  clay,  which  retains  its  porosity  when 
subjected  to  the  most  intense  heat.  It  is  glazed  with  another 
kind  of  clay,  known  as  "slip,"  which,  when  subjected  to  heat, 
melts,  creating  a  very  thin  glazing,  which,  being  a  foreign  sub- 
stance to  the  body  of  the  pipe,  is  liable  to  wear  or  scale  off. 

"Salt  Glazed  Clay-pipe  "  is  made  of  a  clay,  which,  when  sub- 
jected to  an  intense  heat,  becomes 'vitreous  or  glass-like;  and 
is  glazed  by  the  vapors  of  salt,  the  salt  being  thrown  in  the  fire, 
thereby  creating  a  vapor  which  unites  chemically  with  the  clay, 
and  forms  a  glazing,  which  will  not  scale  or  wear  off,  and  is 
impervious  to  the  action  of  acids,  gases,  steam,  or  any  other 
known  substance.  It  unites  with  the  clay  in  such  a  manner 
as  to  form  part  of  the  body  of  the  pipe,  and  is  therefore  inde- 
structible. 

Salt-glazed  pipe  can  only  be  made  from  clay  that  will  vitrify, 
that  is,  when  subjected  to  an  intense  heat  will  come  to  a  hard, 
compact  body,  not  porous.  And  it  should  be  borne  in  mind  that 
"slip  glazing"  is  only  resorted  to  when  the  clays  are  of  such  a 
nature  that  they  will  not  vitrify. 

The  material  of  drain-pipes  should  be  a  hard,  vitreous  sub- 
stance; not  porous,  since  this  would  lead  to  the  absorption  of 
the  impure  contents  of  the  drain,  would  have  less  actual  strength 
to  resist  pressure,  would  be  more  affected  by  the  frost,  or  by 
the  formation  of  crystals  in  connection  with  certain  chemical 
combinations,  or  would  be  more  susceptible  to  the  chemical 
action  of  the  constituents  of  the  sewerage. 

Sewer-pipes  should  be  salt  glazed,  as  this  requires  them  to  be 
subjected  to  a  much  more  intense  heat  than  is  needed  for  "slip  " 
glazing,  and  thus  secures  a  harder  material. 

Cement  pipes  made  without  metal  reinforcement  have  not 
proven  sufficiently  strong  and  durable  to  be  used  with  confi- 
dence in  any  important  work.  When  reinforced  with  metal, 
however,  they  have  ample  strength,  and  reinforced  cement 
sewer-pipes  of  large  diameter  are  used  to  a  considerable  extent, 
in  Europe,  ^ 


1280 


SEWER-PIPE. 


CARRYING  CAPACITY  OF  SEWER-PIPE. 

(Gallons  per  minute.) 


Size 
of 
Pipe. 

Fall  per  100  Feet. 

1  Inch. 

2  Inch. 

3  Inch. 

6  Inch. 

9  Inch. 

1  Foot. 

2  Feet. 

3  Feet. 

Inch. 

3 

13 

19 

23 

32 

40 

46 

64 

79 

4 

27 

38 

47 

66 

81 

93 

131 

163 

6 

75 

105 

129 

183 

224 

258 

364 

450 

8 

153 

216 

265 

375 

460 

527 

750 

923 

9 

205 

290 

355 

503 

617 

712 

1,006 

1,240 

10 

267 

378 

463 

755 

803 

926 

1,310 

1,613 

12 

422 

596 

730 

1,033 

1,273 

1,468 

2,076 

2,554 

15 

740 

1,021 

1,282     1,818 

2,224 

2,464 

3,617 

4,467 

18 

1,168 

1,651 

2,022 

2,860 

3,508 

4,045 

5,704 

7,047 

24 

2,396 

3,387 

4,155 

5,874 

7,202 

8,303 

11,744 

14,466 

27 

4,407 

6,211 

7,674;  10,883 

13,257 

15,344 

21,771 

26,622 

30 

5,906 

8,352 

10,223  14,298 

17,714 

20,204 

28,129 

35,513 

36 

9,707 

13,769 

16,816 

23,763 

29,284 

33,722 

47,523 

58,406 

For  determining  the  diameter  of  house  sewers,  the  table  on 
p.  1265  will  serve  as  a  good  guide.  Storm  sewers  should  be 
proportioned  to  the  area  drained. 

QUANTITIES    OF    CEMENT,    SAND,    AND    OF    CEMENT 
MORTAR   FOR  SEWER-PIPE   JOINTS. 

(Prepared  by  J.  N.  Hazlehurst,  C.E.) 
For  each  100  ft.  of  sewer  (with  Portland  cement,  375  Ibs.  net  per  bbl.) 


Proportions:  1  Cement  to 

Size 

M 

1  Sand. 

2  Sand. 

of 

L'gth, 

r*    u  • 

Pipe, 

Feet. 

UUDIC 

Yards  . 

Inch. 

Cement, 
Barrels. 

Sand, 
Cubic 
Yards. 

No. 
Ft.  to 
Bbl. 
Cem't. 

Cement, 
Barrels. 

Sand, 
Cubic 
Yards. 

No. 
Ft.  to 
Bbl. 
Cement. 

6 

y/2 

0.003 

0.01248 

0.00201 

803 

0.00855 

0  .  00252 

1,168 

8 

VA 

0.038 

0.15808 

0.02546 

633 

0.10830 

0.03192 

923 

10 

2K 

0  .  058 

0.24128 

0.03886 

410 

0.16530 

0.04872 

605 

12 

21A 

0.089 

0.37024 

0.05963 

270 

0.25365 

0.07476 

394 

15 

VA 

0.123 

0.51268 

0.08241 

195 

0.35055 

0.10332 

285 

18 

VA 

0.167 

0.69472 

0.11189 

144 

0.47595 

0.14018 

210 

20 

&A 

0.237 

0  .  98592 

0.15879 

101 

0.67545 

0.19908 

148 

24 

21A 

0.299 

1  .  24384 

0.20033 

80 

0.85215 

0.25116 

117 

27 

3 

0.492 

2  04672 

0  .  32964 

49 

1.40220 

0.41328 

71 

30 

3 

0  548 

2.27968 

0.36716 

44 

1.56380 

0.46032 

64 

36 

3 

0.849 

3.53184 

0  .  56883 

• 

29 

2.41965 

0.71316 

41 

PLUMBING  SPECIALTIES.  1281 

The  maximum  rainfall,  as  shown  by  statistics,  is  about  an 
inch  per  hour  (except  during  very  heavy  storms),  equal  to 
22,633  gallons  per  hour  for  each  acre,  or  377  gallons  per  minute 
per  acre. 

Owing  to  various  obstructions,  not  more  than  fifty  to  seventy- 
five  per  cent,  of  the  rainfall  will  reach  the  drain  within  the  same 
hour,  and  allowance  should  be  made  for  this  fact  in  determin- 
ing size  of  pipe  required. 

Plumbing  Specialties. 

The  Kenney  Flusliometer. — This  is  a  gravity  valve 
designed  for  flushing  all  water-closets,  urinals,  and  slop-sinks 
in  a  building  direct  from  one  tank  situated  in  the  attic  or  where 
most  desirable,  thus  dispensing  with  the  individual  overhead 
tank. 

The  pipe  from  the  main  tank  is  run  down  to  the  different 
floors  either  exposed  or  concealed  and  branches  taken  off  from 
there  to  the  flushometer. 

The  operation  of  the  flushometer  is  to  pull  the  handle  for- 
ward, which  raises  the  main  valve  off  its  seat,  making  a  direct 
connection  from  the  flushometer  to  the  tank.  After  the  handle 
is  released  the  valve  closes  slowly  of  its  own  accord  against  a 
high  or  low  pressure. 

It  is  constructed  without  springs  or  cup  leathers  and  closes 
by  gravity;  is  built  to  stand  the  hardest  of  service,  and  yet  so 
simple  in  construction  and  operation  that  the  same  valve  is 
used  for  all  requirements,  the  only  difference  being  whether 
it  is  to  work  on  high  or  low  pressure. 

The  flushometer  is  extensively  used  in  the  better  class  of 
buildings  in  the  Eastern  States,  including  the  largest  office 
buildings,  factories,  schools,  hospitals,  and  the  better  class  of 
residences,  also  on  steamships  and  yachts. 

Filters. — There  are  few  cities  in  which  the  public  water- 
supply  is  not  greatly  improved  in  wholesomeness  by  being 
filtered,  and  in  many  places  filtering  is  absolutely  necessary. 

The  filter  should  be  large  enough  so  that  the  velocity  of  the 
water  passing  through  it  will  be  low  and  should  be  so  arranged 
that  the  flow  of  water  can  be  reversed  and  the  accumulated 
impurities  washed  into  a  waste-pipe.  In  the  country  a  filter 
suitable  for  rain-water  may  be  built  underground,  the  filtering 
process  being  accomplished  by  beds  of  sand  and  gravel.  For 


1282  PLUMBING  SPECIALTIES. 

city  buildings,  however,  a  portable  filter  located  in  the  basement 
should  be  used.  An  excellent  line  of  niters  is  made  by  Wm.  B. 
Scaife  &  Sons  Co.,  of  Pittsburg.  These  filters  have  capacities 
ranging  from  150  to  5,000  gallons  per  hour.  The  same  com- 
pany also  manufactures  a  line  of  patent  tripoli  niters,  espe- 
cially for  drinking  and  cooking  purposes,  and  ranging  in  cost 
from  $15  to  $200. 

Those  so-called  niters  which  are  made  to  screw  onto  the 
nozzle  of  an  ordinary  faucet  should  be  considered  merely  as 
strainers,  and  even  for  that  purpose  they  soon  become  foul. 

Instantaneous  Water-heaters  are  a  great  conve- 
nience for  heating  water  for  baths  and  wash-basins  in  buildings 
in  which  a  constant  supply  of  hot  water  is  not  provided,  and 
especially  in  residences  where  the  cooking  is  done  by  gas.  They 
are  cylindrical  in  shape,  made  of  nickel-plated  copper,  and  are 
usually  set  on  a  nickel-plated  shelf  attached  to  the  wall  close 
to  the  fixture  to  be  supplied.  A  heater  10J  ins.  in  diameter 
and  30  ins.  high  will  heat  20  gallons  of  water  in  eight  minutes 
at  a  cost  of  1J  to  2  cents  with  gas  at  $1  per  1,000  cu.  ft.  A 
large  line  of  these  heaters  are  made  by  the  Humphry  Manufactur- 
ing and  Plating  Co.,  Kalamazoo,  Michigan,  for  both  gas  and 
gasolene,  although  gas  is  preferable  when  it  can  be  had. 

The  cost  of  heaters  varies  from  $15  to  $45  according  to  size. 

An  Automatic  Water  Heater  which  maintains  water 
at  any  desired  temperature  without  attention,  provided  the 
building  has  a  supply  of  live  steam,  is  made  by  James  B.  Clow  & 
Sons,  the  supply  of  steam  being  automatically  regulated  by  a 
thermostat.  It  will  be  found  especially  desirable  in  hospitals, 
hotels,  apartment-houses,  and  public  institutions.  The  heater 
is  made  in  four  sizes,  with  capacities  of  1,500,  2,500,  4,000,  and 
6,500  gallons  per  hour. 

The  Climax  Cellar  Drainer  *  is  a  simple  device  for  rais- 
ing water  from  6  to  10  ft.  without  attention  or  power,  except  a 
supply  of  steam  or  water.  It  is  used  principally  for  draining 
cellars,  wheel-pits,  furnace-pits,  etc.,  when  the  same  are  too 
low  to  drain  into  the  sewer.  For  such  places  a  box  or  barrel 
is  sunk  so  that  all  of  the  water  will  run  into  it,  and  the  drainer 
is  set  in  this  receiver  and  the  discharge  pipe  run  to  a  sink  or 
open  drain.  The  drainer  performs  its  functions  by  passing 
water  or  steam  under  pressure  through  the  drainer  point  or  jet, 

*  Manufactured  by  Jas.  B.  Clow  &  Sons. 


PLUNGE-BATHS.  1283 

thus  creating  a  suction  which  draws  the  water  from  the  receiver 
in  which  it  is  placed  into  the  discharge-pipe,  and  both  the  jet 
water  and  cellar  water  are  discharged  together.  As  long  as 
the  city  water  or  steam  passes  through  the  drainer-pipe,  this 
suction  and  discharge  continues.  The  supply  of  water  or 
steam  is  turned  on  or  off  automatically,  so  that  there  is  no 
consumption  of  city  water  or  steam  except  when  the  drainer 
is  removing  water.  This  drainer  will  operate  with  pressure  of 
15  Ibs.  or  more,  the  heavier  the  pressure  the  greater  the  amount 
of  dead  water  discharged.  •  When  the  drainage  water  does 
not  have  to  be  raised  more  than  10  ft.,  this  is  the  most  economi- 
cal apparatus  that  can  be  used,  as  the  amount  of  city  water 
consumed  is  very  small. 

The  Climax  Drainer  is  made  in  six  sizes,  costing  from  $25  to 
$160. 

Plunge-baths. 

As  an  example  of  the  construction  and  details  of  a  small 
plunge-  or  swimming-bath,  we  give  the  following  description 
and  illustrations  of  the  bath  in  the  house  of  the  Racquet  and 
Tennis  Club  on  Forty-third  Street,  New  York  City.* 

"  The  swimming-bath  has  inside  dimensions  of  15X22  ft.  and  is 
about  9  ft.  in  total  depth.  It  was  built  in  a  pit  about  19X26  ft, 
and  about  8  ft.  deep  below  the  main  excavation,  which  was 
blasted  out  of  solid  rock.  A  concrete  invert  a  foot  or  more 
in  thickness  was  laid  over  the  bottom,  serving  as  a  footing  on 
which  the  12-inch  walls  of  common  red  brick  were  laid  in  cement. 
They  were  built  close  to  the  rough  vertical  faces  of  the  excava- 
tion, and  the  spaces  behind  them  were  filled  with  concrete  or 
cement  mortar  or  were  flushed  with  grout.  Then  on  the  inner 
surface  of  the  walls  and  on  top  of  the  concrete  bottom  lining 
a  waterproofing  of  six  layers  of  felt  with  lapped  joints  was 
mopped  on  with  hot  tar  and  flashed  around  the  iron  outlet  pipe, 
which  also  had  a  wide  calked  lead  flange  extending  between 
the  layers  of  felt.  On  the  bottom  of  this  water-proof  coat  an 
8-inch  inverted  segmental  flat  floor  arch  of  common  brick  was 
laid,  and  on  its  skewbacks  4-inch  vertical  brick  walls  were 
built  against  the  water-proofed  sides.  The  bottom  was  then 
lined  with  vitrified  white  tile  and  the  sides  were  faced  with 


*  The   illustrations  and  accompanying    descriptions    are    taken    by    per- 
mission from  the  Engineering  Record  of  Nov.  3,  1900. 


1284 


PLUNGE-BATHS. 


English  white  enamelled  brick.  The  tops  of  the  walls  were 
coped  with  bevelled  and  moulded  white  marble  slabs  which  are 
about  2  ft.  above  the  floor-level  and  are  surmounted  at  one 
side  and  one  end  by  a  low  heavy  rail  with  twisted  ornamental 
posts,  all  of  brass.  A  similar  horizontal  hand-rail  is  carried 


9',  ¥.4'.  ?',?.¥ 

.z.t^z~~iiiirrrrrr 

ELEVATION 


along  the  inside  wall  of  the  bath  just  above  water-level 
and  a  curved  brass  hand-rail  is  fastened  to  the  wall  above  the 
narrow  brick  and  marble  stairs  at  one  end.  The  swimming- 
bath  occupies  one  corner  of  the  room  and  its  elevated  marble 
platform  extends  entirely  across  it,  forming  a  diving  platform 
which  is  reached  by  two  marble  steps. 

*  '  All  the  water-supply  is  filtered  and  it  can  be  warmed  by 
injecting  steam  into  the  delivery-pipe  at  the  filter.     The  water 


ILLUMINATING-GAS.  '  1285 

enters  through  the  open  upturned  end  of  a  2-inch  brass  pipe 
projecting  a  foot  or  more  through  the  wall  above  the  top  of 
the  bath  and  delivering  a  solid  jet  unless  it  is  reduced  by  the 
regulating  valve  or  is  formed  into  a  fan-shaped  cascade  by 
means  of  a  special  nozzle  which  can  be  screwed  in  the  open 
end  of  the  pipe.  When  the  bath  is  much  used  a  small  stream  of 
water  is  constantly  admitted  and  causes  a  continual  gentle 
circulation  and  corresponding  overflow,  and  the  entire  con- 
tents are  pumped  out  and  the  bath  cleaned  every  two  or  three 
days.  There  are  two  overflows,  an  open  one  about  8  ft.  above 
the  bottom  and  a  valved  one  a  foot  lower.  Mr.  C.  L.  W.  Eid- 
litz  was  the  architect  of  the  house  and  the  waterproofing  was 
done  by  the  T.  New  Construction  Company." 

Ilium  inating-gas. 

Varieties  of  Gas. — Five  varieties  of  gas  are  now  commonly 
used  for  lighting  and  cooking,  viz. : 

1.  Coal-gas,  which  is  made  by  heating  bituminous  coal  in  air- 
tight retorts.     This  is  the  most  common  variety  of  gas  furnished 
for  the  lighting  of  cities  and  towns. 

2.  Water-gas,  which  is  made,  usually  from  anthracite  coal  and 
steam,  and  is  quite  extensively  used  in  Eastern  cities.     Gas  made 
by  this  process  contains  less  carbon  than  good   coal-gas,   and 
consequently  does  not  give  as  bright  a  light,  although  it  burns 
perfectly  in  heating  burners.     When  used  for  lighting  purposes 
it  is  enriched  in  carbon  by  vaporizing   a   quantity  of  petroleum 
by  heat  and    injecting  it  into  the  hot  gas  before  it  leaves  the 
generator. 

Pure  water-gas  is  lighter  and  has  less  odor  than  coal-gas. 

3.  Natural  gas  is  obtained  from  holes  or  wells  which  are  drilled 
in  the  ground.     In  localities  where  it  can  be  obtained  it  furnishes 
cheap  light  and  fuel.     The  natural  gas  obtained  in  the  hard-coal 
regions  develops  more  heat  per  cubic  foot  in  burning  than  any 
other  kind   of    gas    except    acetylene.     Natural  gas   is    usually 
under  greater  pressure  in  the  street  mains  and  house  pipes  than 
manufactured  gas. 

4.  Acetylene-gas, — Used  almost  exclusively  for  the  lighting  of 
isolated   buildings,   or  for  public   buildings   in   towns   or  cities 
where  there  is  no  public  gas  supply,  and  commonly  generated 
on  the  premises. 

It  is  formed  by  bringing  water  and  calcium  carbide  in  contact. 
Calcium  carbide  is  produced  by  the  electrical  fusion  of  coke  and 


1286  ACETYLENE-GAS. 

lime.  It  is  now  a  commercial  article  produced  in  large  quantities 
and  sold  at  a  moderate  price.  It  is  a  very  hard  substance  like 
dark  granite,  has  a  very  slight  odor,  will  not  burn  or  explode, 
and  can  be  handled  in  any  quantity  with  perfect  safety. 

The  fact  that  carbide  begins  to  disintegrate  and  give  off  acety- 
lene at  the  slightest  touch  of  moisture  makes  it  practicable  to 
generate  the  gas  in  small  quantities  for  single  buildings. 

Process  of  Generating'  Acetylene-gas. — The  satis- 
factory production  of  acetylene-gas  requires  a  generator  which 
shall  feed  carbide  of  sufficient  size  and  weight  to  be  plunged  a 
sufficient  depth  under  the  water  in  the  generator- chamber  to 
insure  coolness  and  proper  washing.  The  carbide-chamber  must 
be  so  arranged  and  protected  that  no  gas  can  return  to  it  to  be 
wasted  when  the  chamber  is  refilled  and  permeate  the  house  with 
its  smell. 

It  must  feed  carbide  loosely  and  in  very  small  quantities,  in 
order  to  provide  for  perfect  coolness  by  free  access  of  water  to 
all  of  the  carbide.  It  must  work  automatically  and  with  abso- 
lute certainty. 

Acetylene-gas  to  be  pure  must  be  thoroughly  washed.  Impure 
acetylene,  as  with  any  other  illuminating-gas,  means  a  discolora- 
tion of  the  flame,  diminished  illuminating  power,  clogging  of  pipes 
and  burners  with  carbon  and  other  foreign  matter,  and  smoky 
burners,  causing  blackening  of  ceilings  and  tarnished  and  soiled 
woodwork  and  upholstery. 

It  is  now  generally  agreed  that  the  requirements  above  out- 
lined can  be  attained  only  by  a  generator  of  the  plunger  type. 

Portable  generators  which  may  be  set  in  the  cellar  or  basement 
of  any  building  are  manufactured  in  great  variety;  it  is  esti- 
mated that  100,000  acetylene-gas  generators  are  now  in  use  in 
the  United  States.  They  are  made  in  sizes  of  5,  10,  15,  20,  and 
up  to  500  lights  capacity. 

In  all  machines  dropping  carbide  into  water  there  should  be 
a  connection  open  from  the  carbide-holding  receptacle  to  the 
safety-vent  run  out  of  doors  from  the  gasometer. 

It  is  claimed  that  for  a  given  degree  of  illumination,  acetylene 
is  cheaper  than  "dollar  gas."  A  large  residence  may  be  lighted 
for  about  $2.50  a  month. 

To  develop  the  full  illuminating  power  of  the  gas  it  is  neces- 
sary to  use  a  burner-tip  having  the  thinnest  slit  obtainable,  the 
illuminating  power  of  the  gas  being  about  15  times  that  of  coal- 
gas,  for  the  same  consumption. 


GAS-FITTING.  1287 

The  light  is  a  clear  white,  very  nearly  resembling  sunlight  in 
color  and  diffusiveness,  with  none  of  the  red  of  the  incandescent 
lamp,  the  orange  of  the  ordinary  gas-flame,  or  the  green  tone 
of  the  incandescent  mantle;  and  it  possesses  the  quality,  unique 
among  artificial  illuminants,  of  reproducing  even  the  most  deli- 
cate shades  of  color  as  faithfully  as  sunlight.  Even  when  used 
with  mantle  burners,  as  it  may  be  with  great  economy,  acetylene 
light  presents  a  strong  dissimilarity  from  ordinary  gas  under  the 
same  conditions.  Acetylene  corrodes  silver  and  copper,  but 
does  not  affect  brass,  iron,  lead,  tin,  or  zinc. 

A  government  specification  for  a  complete  apparatus  for  acety- 
lene gas  was  published  in  Engineering  News  of  Feb.  4,  1904. 

5.  Gasolene-gas  is  a  mixture  of  gasolene  vapor  with  air.  It 
is  never  piped,  but  is  generated  close  to  the  burner,  and  is  seldom 
used  for  lighting  except  for  street  stands,  and  the  like.  It  is 
much  used  for  fuel,  however. 

Gasolene  changes  from  the  liquid  to  the  gaseous  form  under 
ordinary  atmospheric  pressure,  at  temperatures  above  40°,  the 
evaporation  being  very  slow  at  40°,  quite  rapid  at  70°,  and  furious 
at  212°. 

If  a  tank  containing  liquid  gasolene  be  left  open  to  the  air, 
the  liquid  will  all  pass  away  in  the  form  of  gas.  If  a  match 
be  lighted  near  an  open  can  of  gasolene,  the  escaping  gas  at  once 
takes  fire  and  communicates  the  fire  to  the  liquid,  causing  it  to 
explode  with  great  violence.  Although  generally  considered  as 
dangerous,  it  is  only  so  when  carelessly  or  ignorantly  handled. 

To  produce  1,000  cu.  ft.  of  gas  of  good  quality  requires  about 
4J  gallons  of  the  best  grade  of  gasolene. 

An  ordinary  burner  consumes  about  5  cu.  ft.  per  hour. 

PIPING  A   HOUSE  FOB  G-AS. 

[Circular  issued  by  the  Gilbert  &  Barker  Manufacturing  Company.] 
Ordinary  wrought-iroii  pipe,  such  as  is  used  for  steam  or  water, 
is  suitable  arid  proper  for  all  kinds  of  gas.  Galvanized  malleable 
iron  fittings,  in  distinction  from  plain  iron,  are  very  superior. 
The  coating  of  zinc  inside  and  out  effectually  and  permanently 
covers  all  blow-holes,  makes  the  work  solid  .?--nd  durable,  and 
avoids  the  use  of  perishable  cement.  Before  the  pipe  is  placed 
in  position  it  should  be  looked  and  blown  through.  It  is  not 
infrequent  that  it  is  obstructed,  and  this  precaution  will  save 
much  damage  and  annoyance.  What  is  known  as  gas-fitters' 
cement  never  should  be  used.  It  cracks  off  easily,  in  warm 


1288  GAS-FITTING. 

places  it  will  melt,  and  it  can  be  dissolved  by  several  different 
kinds  of  gas.  Nothing  but  solid  metals  is  admissible  for  con- 
fining gas  of  any  kind.  When  pipes  under  floors  run  across 
floor  timbers,  the  latter  should  be  cut  into  near  their  ends,  or 
where  supported  on  partitions,  in  distinction  from  being  cut 
in  or  near  the  centres  of  rooms.  It  is  evident  that  a  10-inch 
timber  notched  2  ins.  in  the  middle  is  no  stronger  than  an 
8-inch.  All  branch  outlet-pipes  should  be  taken  from  the  sides 
or  tops  of  running  lines.  Bracket-pipes  should  run  up  from 
below,  in  distinction  from  dropping  from  overhead.  Never 
drop  a  centre  pipe  from  the  bottom  of  a  running  line.  Always 
take  such  outlet  from  the  side  of  the  pipe.  The  whole  system 
of  piping  must  be  free  from  low  places  or  traps,  and  decline 
toward  the  main  rising  pipe,  which  should  run  up  in  a  partition 
as  near  the  centre  of  the  building  as  is  practicable.  It  is  ob- 
vious that  where  gas  is  distributed  from  the  centre  of  a  build- 
ing, smaller  running  lines  of  pipe  will  be  needed  than  when 
the  main  pipe  runs  up  on  one  end.  Hence,  timbers  will  not 
require  as  deep  cutting,  and  the  flow  of  gas  will  be  more  regu- 
lar and  even.  For  the  same  reason  in  large  buildings,  more 
than  one  riser  may  be  advisable.  When  a  building  has  different 
heights  of  post,  it  is  always  better  to  have  an  independent 
rising  pipe  for  each  height  of  post,  in  distinction  from  dropping 
a  system  of  piping  from  a  higher  to  a  lower  post,  and  grading 
to  a  low  point  and  establishing  drip-pipes.  Drip-pipes  in 
a  building  should  always  be  avoided.  The  whole  system  of 
piping  should  be  so  arranged  that  any  condensed  gas  will  flow 
back  through  the  system  and  into  the  service-pipe  in  the  ground. 
All  outlet-pipes  should  be  so  securely  and  rigidly  fastened  in 
position  that  there  will  be  no  possibility  of  their  moving  when 
the  gas-fixtures  are  attached.  Centre  pipes  should  rest  on  a 
solid  support  fastened  to  the  floor  timbers  near  their  tops.  The 
pipa  should  be  securely  fastened  to  the  support  to  prevent 
lateral  movement.  The  drop-pipe  must  be  perfectly  plumb, 
and  pass  through  a  guide  fastened  near  the  bottom  of  the  tim- 
bers, which  will  keep  them  in  position  despite  the  assaults 
of  lathers,  masons,  and  others.  In  the  absence  of  express 
directions  to  the  contrary,  outlets  for  brackets  should  generally 
be  5  ft.  and  6  ins.  high  from  the  floor,  excepting  that  it  is 
usual  to  put  them  6  ft.  in  halls  and  bathrooms.  The  up- 
right pipes  should  be  plumb,  so  that  the  nipples  that  project 
through  the  walls  will  be  level.  The  nipples  should  project 


GAS-FITTINGS.  1289 

not  more  than  f  in.  from  the  face  of  the  plastering.  Laths 
and  plaster  together  are  usually  f  in.  thick;  hence  the  nipples 
should  project  1J  ins.  from  the  face  of  the  studding.  Drop 
centre  pipes  should  project  1J  ins.  below  the  furring,  or  timbers 
if  there  be  no  furring,  where  it  is  known  that  there  will  be  no 
stucco  or  centre-pieces  used.  Where  centre-pieces  are  to  be 
used,  or  where  there  is  a  doubt  whether  they  will  be  or  not, 
then  the  drop-pipes  should  be  left  about  a  foot  below  the  furring. 
All  pipes  being  properly  fastened,  the  drop-pipe  can  be  safely 
taken  out  and  cut  to  the  right  length  when  gas-fixtures  are  put 
on.  Gas-pipes  should  never  be  placed  on  the  bottoms  of  floor 
timbers  that  are  to  be  Bathed  and  plastered,  because  they  are 
inaccessible  in  the  contingency  of  leakage,  or  "when  alterations 
are  desired,  and  gas-fixtures  are  insecure.  The  whole  system 
of  piping  should  be  proved  to  be  air-  and  gas-tight  under  a 
pressure  of  air  that  will  raise  a  column  of  mercury  6  ins.  high 
in  a  glass  tube.  The  pipes  are  either  tight  or  they  leak.  There 
is  no  middle  ground.  If  they  are  tight  the  mercury  will  not 
fall  a  particle.  A  piece  of  paper  should  be  pasted  on  the  glass 
tube,  even  with  the  mercury,  to  mark  its  height  while  the 
pressure  is  on.  The  system  of  piping  should  remain  under  test 
for  at  least  a  half-hour.  It  should  be  the  duty  of  the  person 
in  charge  of  the  construction  of  the  building  to  thoroughly 
inspect  the  system  of  gas-fitting;  surely  as  much  so  as  to  in- 
spect any  other  part  of  the  building.  He  should  know  from 
personal  observation  that  the  specifications  are  complied 
with.  After  being  satisfied  that  the  mercury  does  not  fall  he 
should  cause  caps  on  the  outlets  to  be  loosened  in  different 
parts  of  the  building,  first  loosening  one  to  let  some  air  escape, 
at  the  same  time  observing  if  the  mercury  falls,  then  tighten 
it  and  repeat  the  operation  at  other  points.  This  plan  will 
prove  whether  the  pipes  are  free  from  obstruction  or  not.  When 
he  is  satisfied  that  the  whole  work  is  properly  and  perfectly 
executed,  he  should  give  the  gas-fitter  a  certificate  to  that 
effect. 

The  following  requirements  from  specifications  published 
by  the  Denver  Gas  and  Electric  Company  are  worthy  of  atten- 
tion : 

Always  use  fittings  in  making  turns;  do  not  bend  pipe. 
Do  not  use  unions  in  concealed  work;  use  long  screws  or  right- 
and-left  couplings.  Long  runs  of  approximately  horizontal 


1290  GAS-FITTING. 

pipe  must  be  firmly  supported  at  short  intervals  to  prevent 
sagging. 

Rules    and    Table    for    Proportioning    Sizes     of 
House  Pipes.* 

The  table  on  the  opposite  page  is  based  011  the  well-known 
formula  for  the  flow  of  gas  through  pipes.  The  friction,  and 
therefore  the  pressure  necessary  to  overcome  the  friction,  increases 
with  the  quantity  of  gas  that  goes  through,  and  as  the  aim  of 
the  table  is  to  have  the  loss  in  pressure  not  exceed  -^  in.  water 
pressure  in  30  ft.,  the  size  of  the  pipe  increases  in  going  from 
an  extremity  toward  the  meter,  as  each  section  has  an  increas- 
ing number  of  outlets  to  supply.  The  quantity  of  gas  the 
piping  may  be  called  on  to  pass  through  is  stated  in  terms 
of  | -in.  outlets,  instead  of  cubic  feet,  outlets  b'eing  used  as  a 
unit  instead  of  burners,  because  at  the  time  of  first  inspection 
the  number  of  burners  may  not  be  definitely  determined.  In 
designing  the  table,  each  f-in.  outlet  was  assumed  as  requiring 
a  supply  of  10  cu.  ft.  per  hour. 

In  using  the  table  observe  the  following  rules: 

1.  No  house  riser  shall  be  less  than  f  in.     The  house  riser 
is  considered  to  extend  from  the  cellar  to  the  ceiling  of  the 
first,  story.     Above  the  ceiling  the  pipe  must  be  extended  of 
the  same  size  as  the  riser,  until  the  first  branch  line  is  taken  off. 

2.  No  house  pipe  shall  be  less  than  f  in.     An  extension  to 
existing  piping  may  be  made  of  J-in.  pipe  to  supply  not  more 
than  one  outlet,  provided  said  pipe  is  not  over  6  ft.  long. 

3.  No  gas-range  shall  be  connected  with  a  smaller  pipe  than 
fin. 

4.  In  figuring  out  the  size  of  pipe,  always  start  at  the  ex- 
tremities of  the  system  and  work  toward  the  meter. 

5.  In  using  the  table,  the  lengths  of  pipe  to  be  used  in  each 
case  are  the  lengths  measured  from  one  branch  or  point  of  junc- 
ture to  another,   disregarding  elbows  or  turns.     Such  lengths 
will  be  hereafter  spoken  of  as  "sections."     No  change  in  size 
of  pipe  may  be  made  except  at  branches  or  outlets,  each  "  sec- 
tion" therefore  being  made  of  but  one  size  of  pipe. 

6.  If  any  outlet  is  larger  than  J  in.  it  must  be  counted  as 
more  than  one,  in  accordance  with  the  schedule  below: 

Size  of  outlet  (inches) \     f     1     1J     1J      2      2J      3 

Value  in  table 2     4     7     11     16     28     44     64 

*  The  Denver  Gas  and  Electric  Company. 


GAS-FITTING. 


1291 


TABLE  SHOWING  THE  CORRECT  SIZES  OF  HOUSE 
PIPES  FOR  DIFFERENT  LENGTHS  OF  PIPES  AND 
NUMBER  OF  OUTLETS. 


Number 
of 
Outlets. 

Lengths  of  Pipes  in  Feet. 

H-in. 

Pipe. 

&-in. 
Pipe. 

?4-in. 
Pipe. 

50 
50 
50 
50 
33 
24 
13 

l-in. 
Pipe. 

70 

70 
70 
70 
70 
70 
50 
35' 
21 
16 

IM-in. 
Pipe. 

l#-in. 
Pipe. 

150 
150 
150 
150 
150 
150 
150 
150 
150 
120 
65 
42 
30 
22 
17 
13 

2-in. 
Pipe. 

200 
200 
200 
200 
200 
200 
200 
200 
200 
200 
200 
175 
120 
90 
70 
55 
45 
27 
20 

2H-in. 
Pipe. 

300 
300 
300 
300 
300 
300 
300 
300 
300 
300 
300 
300 
300 
270 
210 
165 
135 
80 
60 
33 
22 
15 

3-in. 
Pipe. 

400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
400 
330 
200 
150 
80 
50 
35 
28 
21 
17 
14 

1 
2 

3 
4 
5 
6 
8 
10 
13 
15 
20 
25 
30 
35 
40 
45 
50 
65 
75 
100 
125 
150 
175 
200 
225 
250 

20 

30 

27 
12 

100 
100 
100 

100 
100 
100 
100 
100 
60 
45 
27 
17 
12 

7.  If  the  exact  number  of  outlets  given  cannot  be  found  in 
the  table,  take  the  next  larger  number.     For  example,  if  seven- 
teen outlets  are  required,  work  with  the  next  larger  number 
in  the  table,  which  is  20. 

8.  If,  for  the  number  of  outlets  given,  the  exact  length  of  the 
"section"   which  feeds  these  outlets  cannot  be  found  in  the 
table,  the  next  larger  length  corresponding  to  the  outlets  given 
must  be  taken  to  determine  the  size  of  pipe  required.     Thus, 
if  there  are  eight  outlets  to  be  fed  through  55  ft.  of  pipe,  the 
length  next  larger  than  55  in  the  eight-outlet  line  in  the  table 
is  100,  and  as  this  is  in  the  IJ-in.  column,  that  size  pipe  would 


1292  GAS-FITTING. 

be  required.     Under  Rule  7  the  same  size  pipe  would  be  re- 
quired for  seven  outlets. 

9.  For  any  given  number  of  outlets,  do  not  use  a  smaller  size 
pipe  than  the  smallest  size  that  contains  a  figure  in  the  table  for 
that  number  of  outlets.     Thus,  to  feed  15  outlets,  no  smaller  size 
pipe  than  1  in.  may  be  used,  no  matter  how  short  the  " section" 
may  be. 

10.  In  any  piping  plan,  in  any  continuous  run  from  an  ex- 
tremity to  the  metre,  there  may  not  be  used  a  longer  length 
of  any  size  pipe  than  found  in  the  table  for  that  size,  as  50  ft. 
for  f  in.,  70  ft.  for  1  in.,  etc.     If  any  one  " section  "  would  exceed 
the  limit  length,  it  must  be  made  of  larger  pipe.     Thus,  6  outlets 
could  not  be  fed  through  75  ft.  of  1-in.  pipe,  but  1 }  in.  would  have 
to  be  used.     When  two  or  more  successive  "sections/'  work  out  to 
the  same  size  of  pipe  and  their 'total  length  or  sum  exceeds  the 
longest  length  in  the  table  for  that  size  pipe,  make  the  "section  " 
nearest  the  metre  of  the  next  larger  size.      For  example,  if  we 
have  5  outlets  to  be  supplied  through  45  ft.  of  pipe,  and  these  5 
and  5  more,  making  10  in  all,  through  30  ft.  of  pipe,  we  should 
find  by  the  table  that  10  outlets  through  30  ft.  would  require 
1-in.  pipe,  and  that  5  outlets  through  45  ft.  would  also  require 
1-in.  pipe,  but  as  the  sum  of  the  two  sections,  30  plus  45  equals 
75  ft.,  is  longer  than  the  amount  of  1  in.  that  may  be  used  in 
any  continuous  run.  the  30-ft.  section,  being  the  one  nearer  the 
metre,  must  be  made  of   IJ-in.   pipe.     The  application  of  the 
limit  in  length  of  any  one  size  in  a  continuous  run  may  also  be 
shown  as  follows:   Eight  outlets  will  allow  of  13  ft.  of  J-in.  pipe 
in  the  section  between  the  eighth  and  ninth  outlet  (counting  from 
the  extremity  of  the  system  toward  the  metre) ,  provided  that 
this  13  ft.  added  to  the  total  length  of  f-in.  pipe  that  may  have 
been  used  between  the  extremity  of  the  run  and  the  eighth  outlet 
does  not  exceed  50  ft.,  which,  according  to  the  table,  is  the 
greatest  length  of  f  in.  allowable  in  any  one  branch  of  the  system. 
Therefore,  up  to  the  eighth  outlet,  37  ft.   of  J-in.   pipe  could 
have  been  used,  and  yet  allow  13  ft.  of  J  in.  to  be  used  in  the 
section   between   the   eighth   and   ninth   outlet.     If   more   than 
37  ft,  had  been  used,  then  the  entire  13  ft.  between  the  eighth 
and  ninth  outlets  would  have  to  be  of  1-in.  pipe. 

11.  Never  supply  gas  from  a  smaller  size  pipe  to  a  larger 
one.     If  we  have  25  outlets  to  be  supplied  through  200  ft.  of 
pipe,  and  these  25  and  5  more,  making  30  in  all,  through  100 
ft.  of  pipe  we   should  find  by  the  table  that  25  outlets  through 


GAS-FITTING. 


1293 


200  ft.  would  require  2J-in.  pipe,  and  30  outlets  through  100  ft. 
would  require  2-in.  piping,  but  as  under  this  condition  a  2-in. 
pipe  would  be  supplying  a  2J-in.,  the  100  ft.  section  must  be 
made  2J  in. 


Main  : 


•0 

a 


The  sizes  of  pipes  in  the  above  diagram  are  in  accordance  with 
the  foregoing  rules  and  table. 


1294  LIGHTING  AND  ILLUMINATION. 

Notes  on  Lighting  and  Illumination.* 

When  we  say  that  we  see  an  object,  we  mean  that  the  light 
which  is  reflected  from  its  surface  strikes  our  eye.  When  we 
see  an  object  twice  as  clearly,  this  is  because  twice  as  much  light 
is  being  reflected  from  that  object  into  our  eye.  Our  seeing 
objects,  therefore,  depends  on  two  things:  on  the  amount  of  light 
shining  on  the  surface  and  on  the  quantity  of  light  reflected 
back  from  the  surface  of  the  eye. 

A  room  may  appear  brilliantly  lighted  and  yet  objects  looked 
at  not  be  sufficiently  well  illuminated  for  reading  or  for  working 
purposes.  These  lights  appear  brilliant  to  the  eye,  but  because 
they  throw  their  strongest  rays  in  other  directions  than  those  in 
which  they  are  needed  for  use,  they  do  not  give  efficient  illu- 
mination. 

Distinction  between  Light  and  Illumination. — There  is  not  only 
a  great  difference  between  light  and  illumination,  but  there  is  a 
great  difference  between  a  brilliantly  lighted  room  and  a  well 
illuminated  one. 

When  anybody  is  asked  whether  a  room  is  well  illuminated  or 
not,  the  chances  are  ten  to  one  that  he  at  once  looks  at  the  light 
itself.  If  the  light  appears  to  him  to  be  brilliant  and  dazzling,  he 
will  invariably  say,  "Why,  of  course,  the  room  is  well  lighted." 
He  should  first  look  away  from  the  light  at  the  objects  around 
the  room  or  underneath  the  light.  If  these  can  be  seen  clearly 
and  easily,  then  the  room  is  well  illuminated.  Afterwards  he 
should  look  at  the  lights  themselves,  and  if  they  appear  soft 
and  pleasing  to  his  eyesight  the  room  is  well  lighted.  A  room 
in  which  the  lights  appear  soft  to  the  eye  and  yet  the  eye  can 
distinguish  objects  clearly  is  both  well  lighted  and  well  illu- 
minated. A  room  in  which  the  objects  appear  clear  to  the  eye 
while  the  lights  remain  dazzling  is  well  illuminated  but  badly 
lighted.  A  room  in  which  the  lights  appear  soft  to  the  eye 
and  the  objects  not  clearly  illuminated,  is  well  lighted,  but  badly 
illuminated.  A  room  in  which  the  lights  appear  dazzling  to  the 
eye  and  the  surrounding  objects  or  those  underneath  not  clear 
to  the  eyesight  is  both  badly  lighted  and  badly  illuminated. 

An  axiom  in  good  artificial  illumination  is  to  keep  the  illumina- 
tion of  objects  around  as  strong  as  possible,  but  the  intensity 
or  brilliancy  of  the  lights  as  low  as  possible.  By  doing  the  first 

*  Compiled  from  papers  by  Wm.  Lincoln  Smith,  Van  Renssellaer  Lan- 
singh,  and  a  pamphlet  published  by  the  Holophane  Glass  Co, 


LIGHTING  AND  ILLUMINATION.  1295 

we  enable  the  eye  to  see  better,  by  doing  the  second  we  enable 
the  eye  to  feel  better,  and  suffer  less  from  temporary  discomfort 
or  permanent  injury. 

It  is  not  generally  understood  that  a  light  which  is  dazzling  and 
brilliant  to  the  eyesight  may  not  be  giving  as  much  illumination 
as  another  source  of  light  which  appears  soft,  or  even  dim,  by 
comparison.  A  bare  50-candle-power  incandescent  gas-light 
put  next  to  a  100-candle-power  light  inside  of  an  opal  globe  will 
appear  more  brilliant  and  olazzling  than  the  second,  but  will  not  be 
giving  as  efficient  an  illumination.  The  actual  illuminating 
power  of  the  two  lights  is  about  equal,  but  the  intensity  or  daz- 
zling quality  of  the  bare  50-candle-power  light  is  twenty  times 
that  of  the  100-candle-power  light  in  the  opal  globe. 

Relative  Intensity  of  Artificial  Lights.  —  The 
present  legal  standard  of  light  in  this  country  is  the  British 
standard  candle  weighing  six  to  the  pound  and  burning  at  the 
rate  of  120  grains  per  hour.  Owing  to  the  very  wide  variations 
from  various  causes  in  the  light  of  candles,  measurements  of 
brilliancy  are  frequently  made  against  the  Hofner  Alteneck 
lamp  burning  acetate  of  amyl  and  certified  by  the  Reichan- 
stalt.  It  may  be  assumed  to  equal  0.88  standard  candle. 

The  following  table  gives  the  candle-power  per  square  inch 
for  the  older  and  newer  illuminants :  * 

Flat  gas-flame 4  to  8  candles  per  sq.  in. 

Oil-lamps 3  to  8  "  "  "  " 

Candle 2  to  4  "  "  "  " 

Welsbach  mantle 20  to  25  "  "  "  " 

Acetylene-gas 75  to  125  "  "  "  " 

Incandescent-lamp 100  to  200  "  "  "  " 

Nernstlamp 1,000  to  1,500  "  "  "  " 

Crater  open  arc 25,000  to  50,000       "  "  "  " 

Sun  on  the  horizon 2,000f  "  "  "  " 

Sun  in  zenith 190,000  "  "  "  " 

From  these  figures  it  will  be  readily  seen  that  much  greater 
care  is  necessary  than  formerly  in  fixing  the  location  of  lights, 
especially  when  it  is  remembered  that  the  average  eye  is  liable 
to  be  more  or  less  seriously  disturbed  if  subjected  for  any  length 
of  time  to  the  direct  rays  of  a  light  source  of  much  higher  in- 
trinsic brilliancy  than  an  ordinary  gas-flame  of  about  five 

*  Wm.  Lincoln  Smith,  engineer. 

t  Van  Renssellaer  Lansingh,  engineer. 


1296 


LIGHTING  AND  ILLUMINATION. 


candles  per  square  inch.  From  this  consideration  it  at  once 
follows  that  naked  lights  of  the  more  modern  type  should  be 
kept  carefully  out  of  range  of  direct  vision,  or  if  necessity 
requires  that  they  should  fall  within  the  range  of  vision  they 
should  be  so  screened  as  to  reduce  the  intrinsic  brilliancy  to 
within  proper  limits. 

Another  measurement  of  the  intensity  of  illumination  is  the 
"candle-foot,"  which  is  the  illumination  given  by  one  candle 
at  a  distance  of  1  ft. 

A  candle-foot  light  is  considered  a  good  intensity  for  reading 
purposes.  The  intensity  of  light  varies  inversely  as  the  square 
of  the  distance,  or  candle-feet  =  candle-power  divided  by  square 
of  distance  in  feet. 

Thus  a  16-candle-power  lamp  has  an  intensity  of  16  candle- 
feet  at  a  distance  of  1  ft.,  4  candle-feet  at  a  distance  of  2  ft., 
and  1  candle-foot  at  a  distance  of  4  ft. 

Quantity  of  laght  Kequired.*  —  The  quantity  of 
light  to  be  supplied  is  usually  estimated  in  candle-power  per 
square  feet  of  area,  or  per  cubic  foot  of  space.  Fontaine  showed 
that  the  latter  method  is  in  the  majority  of  instances  more 
nearly  correct.  In  a  drawing-room  with  medium-tinted  walls, 
for  instance,  0.015  candle-power  per  cubic  foot  is  about  right 
and  in  larger  halls  it  is  advisable  to  figure  about  0.02  to  0.03 
candle-power  per  cubic  foot.  The  following  table  will  give 
some  idea  of  tne  values  to  be  found  in  practice: 


Apartment. 

Volume. 
Cubic 
Feet. 

Candle- 
power. 

Candle- 
power 
per  Cubic 
Foot. 

1    Museum                       .  .          .    . 

330,000 

8,000 

024 

2.  Public  hall     

12,425 

1,000 

.080 

3    Town  hall 

48,000 

1,376 

028 

4    Legislative  hall  

143,560 

7,560 

.052 

5.  Body  opera-house  

324,760 

11,400 

.034 

6    Theatre                              

125,550 

2,340 

.019 

7.  Colonial  church  

80,000 

1,600 

.020 

In  this  list  the  second  is  wastefully  bright,  the  others  are  all 
about  right. 

It  must  be  remembered  that  all  globes  and  shades  absorb  a 


*  Wm.  Lincoln  Smith,  engineer. 


LIGHTING  AND  ILLUMINATION.  1297 

certain  amount  of  light  and  that  it  is  advisable  to  increase  the 
allowance  as  figured  so  as  to  correct  for  this  loss, 

"Assuming  the  16-candle-power  lamp  as  the  standard,  it  is 
generally  found  that  two  16-candle-power  lamps  per  100  sq.  ft. 
of  floor  space  give  good  illumination,  three  very  bright,  and  four 
brilliant.  These  general  figures  will  be  modified  by  the  height 
of  ceiling,  color  of  walls  and  ceiling,  and  other  local  conditions."  * 

SPACE   ILLUMINATED   BY   ENCLOSED   ARC   LAMPS.f 


Space  to  be  Illuminated. 

Square  Yards 
per  450-Watt 
Lamp. 

Outdoor  areas  

2000-2500 

Train  sheds.  . 

1400-1600 

Foundries  (general  illumination)  

600-  800 

Machine  shops  

200-  250 

Thread  and  cloth  mills  

200-  230 

Means  for  Reducing  Intrinsic  Brilliancy  — 
Globes. — In  practically  all  cases  of  interior  illumination  it  is 
necessary  to  reduce  the  intrinsic  brilliancy  by  the  use  of  some 
type  of  diffusing  shade  or  globe,  and  frequently  to  further  alter 
the  direction  of  the  rays  of  light  by  some  type  of  reflector,  etc. 
There  are  on  the  market  shades  and  globes  which  aim  to  accom- 
plish each  of  these  two  results  independently  of  the  other, 
one  or  two  forms  which  aim  to  do  both  at  once,  and  a  great 
number  which  accomplish  neither  result  to  any  degree  of  satis- 
faction are  wasteful  of  light  and  many  of  them  cannot  even 
claim  to  be  ornamental. 

Opal,  opaline,  or  ground  glasses  are  very  good  diffusers, 
but  they  waste  from  30  to  60  per  cent,  of  the  light.  After 
diffusing  the  light  they  cannot  deflect  or  direct  the  rays  in 
such  directions  as  they  may  be  needed  for  use.  Their  only 
use,  therefore,  is  in  softening  the  source  of  light  so  as  to  render 
it  less  injurious  to  the  eyesight,  for  they  have  no  power  to  in- 
crease the  efficient  illumination  in  any  special  direction.  By 
a  properly  calculated  and  worked-out  system  of  prism  glass 
globes  any  light  may  be  diffused  over  a  large  surface  and  its 
intensity  softened,  while  at  the  same  time  these  diffused  or 

*  H.  C.  Gushing,  Jr.,  in  "Practical  Lessons  in  Electricity." 
t  International  Library  of  Technology,  Vol.  13. 


1298 


LIGHTING    4ND  ILLUMINATION. 


softened  rays  are  deflected  into  directions  where  they  art 
needed  for  use,  thereby  increasing  the  efficient  illumination. 

At  present  there  is  only  one  system  of  prism  glass  globes 
known  to  the  author  that  carries  out  these  purposes.  This 
is  the  invention  of  Messrs.  Blondel  and  Psaroudaki  of  Paris, 
who  have  called  it  the  Holophane  system  of  compound  prism 
glass. 

Absolutely  transparent  glass  is  used.  The  inner  surface  of 
the  glass  is  given  over  to  carefully  calculated  flutings  or  prisms 
used  solely  for  diffusing  or  softening  the  light  without  loss  of 
power.  On  the  outside  surface  are  prisms  calculated  for  de- 
flecting these  diffused  rays  into  directions  where  needed. 

In  practice,  Holophane  glass,  made  into  globes  and  shades, 
when  placed  over  a  light,  will  render  a  dazzling  light  soft  and 
healthful,  while  increasing  its  effective  illuminating  power. 

These  globes  are  made  of  three  classes,  or  of  three  different 
shapes,  each  shape  designed  for  a  separate  purpose,  as  for 
desk,  general,  or  large  interior  illumination. 

The  Meridian  Lamp. — The  General  Electric  Company 
has  introduced  a  new  lamp,  which  they  have  named  the  "Merid- 
ian Lamp,"  which  is  a  specially  designed  incandescent  lamp 

ILLUMINATING  DATA  FOR  MERIDIAN  LAMPS. 


Class 
Service. 

Light 
Intensity 
in  Candle- 
feet. 

No.  1  Lamp  (60  Watts). 

No.  2  Lamp  (120  Watts). 

Height  of 
Lamp  and 
Diameter  of 
Uniformly 
Lighted 
Area. 

Distance 
between 
Lamps 
when  Two 
or  More 
are  Used. 

Height  of 
Lamp  and 
Diameter  of 
Uniformly 
Lighted 
Area. 

Distance 
between 
Lamps 
when  Two 
or  More 
are  Used. 

Desk  or 
reading- 
table 

/        3 

r    2 

)      14 

Feet. 
2.9 
3.5 
4 

Feet. 
4.9 
6 

7      * 

Feet. 
4 
5 
5.75 

Feet. 

7 
8.5 
9.8 

General 
lighting 

l! 

5 
5.75 

7 

8.5 
9.8 
12 

7 
8.2 
10 

12 
13.9 
11 

with  a  suitable  reflector  and  ornamental  collar  detachable 
from  the  lamp.  The  lamp  bulb  is  spherical  in  shape,  and 
usually  frosted.  The  light  from  the  lamp  is  of  high  brilliancy, 
rendered  soft  and  white  by  the  diffusing  action  of  the  sand- 


LIGHTING  AND  ILLUMINATION.  1299 

blasted  bulb  and  reflector.  The  illumination  is  uniform  over 
an  area  having  a  diameter  equal  to  the  height  from  the  plane 
on  which  the  illumination  is  measured.  The  lamp  is  made 
in  two  sizes,  No.  1,  3J"-bulb,  25  candle-power,  consuming 
60  watts,  and  No.  2,  5"~bulb,  50  candle-power,  consuming 
120  watts.  The  prices  of  the  bulbs  for  renewal  are  40  and  60 
cents  respectively.  The  lamps  should  always  be  suspended, 
preferably  from  the  ceiling. 

The  Nernst  Lam  p. — This  is  a  new  form  of  incandescent 
lamp  which  derives  its  name  from  the  inventor,  Dr.  Walther 
Nernst,  an  eminent  German  scientist.  The  distinguishing 
features  of  the  Nernst  lamp  are  its  filament  or  glower,  and 
the  means  for  making  the  glower  conductive.  The  glower 
operates  in  the  open  air,  its  removal  and  replacement  may  be 
readily  accomplished,  and  at  ordinary  temperatures  it  is  a 
non-conductor  of  electricity.  A  heater,  separate  therefrom, 
is  therefore  provided  for  giving  it  an  initial  temperature  suffi- 
cient to  make  it  conductive.  When  it  becomes  conductive 
by  external  heat  the  current  traversing  the  glower  not  only 
causes  it  to  emit  light,  but  also  to  develop  internally  sufficient 
heat  to  maintain  it  in  a  conductive  condition,  the  action  of 
the  preliminary  heater  being  discontinued.  For  a  given  illu- 
mination the  Nernst  lamp  requires  only  about  one  half  the 
amount  of  electrical  energy  required  by  ordinary  incandescent 
lamps,  and  about  the  same  as  that  of  the  enclosed  arc  lamp. 

Nernst  lamps  are  made  in  two  types,  viz.:  the  110- volt  type, 
adjustable  for  any  voltage  from  100  to  120,  and  the  220- volt 
type,  adjustable  for  any  even  voltage  from  200  to  240.  The 
former  type  is  made  in  two  sizes  and  the  latter  type  in  five  sizes.* 

Color  of  Illuminants.t 

The  question  of  color  plays  an  important  part  in  the  study  of 
illumination.  For  some  purposes,  where  it  is  desired  to  produce 
the  effects  of  daylight  as  nearly  as  possible,  the  arc  lamp,  when  the 
violet  rays  are  properly  filtered  out,  plays  an  important  part. 
In  general,  however,  the  color  of  the  arc  is  cold,  and  for  a  room 
where  the  effect  is  to  produce  a  cheerful  and  warm  appearance, 
an  illuminant  with  more  of  the  red  rays,  such  as  the  incandescent 

*  Additional  data  may  be  obtained  from  the  Nernst  Lamp  Company, 
Pittsburg,  Pa. 

t  Van  Ilenssellaer  Lansingh. 


1300  LIGHTING  AND  ILLUMINATION. 

lamp  or  ordinary  gas,  is  very  much  to  be  preferred.  The  pre- 
dominant color  in  a  few  of  the  most  important  illuminants  is: 

Sun  at  noon — white. 

Sun  near  sunset — reddish. 

Enclosed  arc,  low  voltage — white. 

Open  arc — bluish  white  to  violet. 

Nernst  lamp — white. 

Acetylene — white. 

Incandescent  electric — yellowish  white. 

Mantle  burner — white  with  a  tinge  of  green. 

Open-flame  gas — orange- white. 

Kerosene  lamp — orange- white. 

Candle — orange-yellow. 

The  amount  of  light  reflected  from  surfaces  is  also  largely 
dependent  on  the  condition  and  color  of  such  surfaces.  It  is 
very  necessary  in  calculations,  where  the  walls  or  decorations 
play  any  part,  to  know  the  character  of  the  same;  thus  white 
paper  reflects  from  70  to  80  per  cent.;  yellow  wall-paper  gives 
only  about  half  that  amount;  emerald-green  about  18  per  cent.; 
black  paper  about  5  per  cent.,  deep-blue  paper  about  3  per  cent., 
while  black  velvet  gives  only  about  -fa  of  1  per  cent.  As  these 
coefficients  of  diffuse  reflections  play  an  important  part  in  all 
attempts  at  calculation,  it  is  necessary,  in  order  to  do  the  best 
work,  to  know  rather  closely  the  character  of  the  decorations. 

The  Diffusion  of  LJglit  through  Windows. 

Abstracts  from  report  of  Mr.  Charles  L.  Norton,  on  an  elaborate 
series  of  tests  made  at  the  Mass.  Institute  of  Technology.* 

The  results  of  the  tests  on  a  score  or  more  of  different  glasses 
may  be  stated  briefly  as  follows: 

We  may  increase  the  light  in  a  room  30  ft.  or  more  deep  to 
form  three  to  fifteen  times  its  present  effect  by  using  "Factory 
Ribbed"  glass  Instead  of  plane  glass  in  the  upper  sash.  By 
using  prisms  we  may,  under  certain  conditions,  increase  the  effect- 
ive light  to  fifty  times  its  present  strength.  The  gain  in  effective 
light  on  substituting  ribbed  glass  or  prisms  for  plane  glass  is 
much  greater  when  the  sky-angle  is  small,  as  in  the  case  of  win- 
dows opening  upon  light  shafts  or  narrow  alleys.  The  increase  in 
the  strength  of  the  light  directly  opposite  a  window  in  which 

*  From  Report  No.  Ill,  Insurance  Engineering  Experiment  Station, 
Sept.,  1902. 


DIFFUSION   OF  LIGHT.  1301 

ribbed  glass  or  prisms  have  been  substituted  for  plane  glass  is  at 
times  such  as  to  light  a  desk  or  table  50  ft.  from  the  window 
better  than  one  20  ft.  from,  the  window  had  previously  been 
lighted. 

The  kinds  of  glass  tested  were  as  follows: 

1.  Ground  glass  of  different  degrees  of  fineness. 

2.  Rough  plate  or  hammered  glass. 

3.  Ribbed  or  corrugated  glass,  with  five,  and  eleven  and  twenty- 
one  ribs  to  the  inch,  the  corrugations  being  sinusoidal  in  outline 
(as  in  Fig.  A)  and  the  back  of  the  plate  smooth. 

4.  Glass   known  as   "Maze,"   " Florentine"   or  " Figured,"   in 
which  a  raised  pattern   is  worked  upon   one   side,   practically 
roughening  the  whole  surface. 

5.  "Wash-board"  glass,  corrugated,  with  twenty-one  ribs  to  the 
inch  on  one  side  and  five  ribs  to  the  inch  on  the  other  side,  the 
ribs  being  parallel. 

6.  "Skylight"  glass,  which  has  five  ribs  to  the  inch  on  each 
side,  groove  on  one  side  being  opposite  the  rib  on  the  other, 
giving  a  sinuous  section  (Fig.  B). 

7.  "Ripple  glass,"   with  rippled  surfaces  on  both  sides;    of 
very  beautiful  appearance  and  a  clear  white  color. 

8.  Glass  ribbed  on  one  side  and  figured  on  the  other. 

9.  Ribbed  glass  with  a  wire  net  pressed  into  it,  to  increase  its 
resistance  to  fire. 

Of  these  several  specimens,  one  or  two  may  be  dismissed 
with  brief  mention.  Ground  glass  is  of  little  value,  except  as  a 
softening  medium  for  bright  sunlight.  Its  rapidly  increasing 
opaqueness  with  moisture  and  dust  makes  it  undesirable  as  a 
window  glass.  The  common  rough  plate  has  very  little  action 
as  a  diffusing  medium,  giving  no  perceptible  change  in  the  effect- 
ive light.  "Ripple  glass"  has  great  value  as  a  diffusing  medium 
in  small  rooms  with  nearly  open  horizon.  Of  the  ribbed  glasses, 
the  fine  "Factory  Ribbed,"  with  twenty-one  ribs  to  the  inch, 
is  distinctly  the  best,  not  in  all  probability  because  of  the  fine- 
ness, but  because  of  the  greater  sharpness  of  the  corrugation. 
The  "Ribbed  Wire"  glass  is  about  twenty  per  cent,  less  effective 
than  the  ordinary  "Factory  Ribbed"  glass.  The  addition  of  a 
second  corrugation  upon  the  back  of  the  plate  giving  the  "Sky- 
light" and  "Wash-board"  glass  is  of  no  apparent  value.  The 
raised  pattern  imprinted  upon  one  surface  of  the  glass,  as  in 
the  case  of  the  "Maze,"  gives  the  widest  diffusion,  especially  in 
bright  sunlight.  A  raised  figure,  when  worked  upon  the  back 


1302 


LIGHTING  AND  ILLUMINATION. 


of  the  "Ribbed"  glass,  renders  it  less  offensive  to  the  eye  in 
bright   sunlight,   but   less   effective   in   deep   rooms.      The  only 


Fig.  A      Fig.  B         Fig.  C  Fig.  D 


glasses  of  this  group  which  it  is  worth  while,  then,  to  discuss 
further  are  the  "Factory  Ribbed"  and  the  "Maze"  glass. 
The  second  group  comprises  the  following  glasses: 

1.  The  Luxfer  prisms. 

2.  The  Solar  prisms. 

3.  The  Daylight  prisms. 

4.  The   glass   of   prismatic   section   made   by   the   Mississippi 
Glass  Company. 

5.  Three-way  prisms. 

6.  Maltby  prisms. 

The  Luxfer  prism  consists  of  a  plate  smooth  upon  one  side 
and  deeply  notched  upon  the  other  (Fig.  C),  the  teeth  or  prisms 
being  of  very  flat,  smooth  faces  and  of  brilliant  appearance.  The 
glass  is  clear  white,  and  the  prisms  used  in  canopies  and  in  the 
major  part  of  the  vertical  glazing  are  made  in  tiles  or  plates 
about  4  ins.  square.  Tiles  are  built  up  in  large  sheets  in  frames 
of  copper  or  brass,  so  made  as  to  give  to  the  sheets  of  tiles  a 
strength  and  durability  far  in  excess  of  a  single  sheet  of  the  same 
size.  The  Luxfer  prisms  are  now  being  made  for  factory  use 
in  large  sheets,  as  well  as  in  the  small  tiles.  The  Solar  prisms  are 
made  in  small  tiles,  which  are  held  together  in  a  metal  frame  to 
make  large  sheets.  The  main  difference  between  the  Solar  and 
Luxfer  prisms  is  that  the  under  face  of  the  former  prism  is 
curved  instead  of  plane,  as  in  Fig.  D.  The  Daylight  prisms 
tested  were  made  in  large  sheets  and  of  approximately  the  same 
cross-section  and  general  appearance  as  the  Luxfer  prisms  for 
factory  use.  No  tiles  of  Daylight  prisms  were  tested,  as  none 
came  to  hand  in  time  for  the  test.  The  Mississippi  prism  glass  is 


DIFFUSION   OF  LIGHT. 


1303 


much  like  the  other  prisms  in  cross-section,  but  the  ridges  or  prisms 
do  not  run  across  the  plate  in  a  straight  line,  but  in  a  wavy  or 
sinuous  line.  I  cannot  detect  any  advantage  arising  from  this  over 
the  straight-edge  prism. 

Conclusions. — First.  The  conditions  in  a  room  less  than 
15  ft.  deep  are  such  that,  except  with  a  skylight  of  less  than  45°, 
it  is  not  advisable  to  alter  the  general  course  of  the  light  by 
using  a  prismatic  or  ribbed  glass.  A  nearly  hemispherical 
diffusion,  such  as  is  given  by  the  "Maze"  or  "Ripple,"  is  ordi- 
narily preferable. 

Second.  When  a  room  is  from  20  ft.  to  60  ft.  deep,  or  even 
more,  and  has  a  skylight  of  60°  or  less,  the  ribbed  and  prismatic 
glass  gives  a  very  great  gain  in  effective  light.  The  gain  in 
brilliancy  is  such  as  to  make  a  basement  with  prism  canopies 
as  light  as  a  second  story  with  plane  glass. 

Rooms  with  windows  opening  upon  light-shafts  and  narrow 
alleys  with  very  limited  sky,  where  the  available  light  is  now 
small,  may  have  the  light  20  ft.  back  from  the  window  increased 


FI9.E 


Fig.  F 


ten  or  twenty  times  by  using  prisms]  and,  by  using  canopies 
of  prisms,  it  is  sometimes  possible  to  strengthen  the  light  from 
fifty  to  one  hundred  times. 

With  sky-angles  of  30°,  or  less,  and  in  deep  rooms,  the  relative 
efficiency  of  the  prism  tile  increases  greatly. 


1304 


LIGHTING  AND  ILLUMINATION. 


The  refraction  of  the  incident  ray  in  a  case  of  the  ribbed  glass 
and  prism  is  shown  by  Figs.  E  and  F. 

"Ribbed  "  and  "Maze  "  glass  are  of  very  great  value  in  soften- 
ing the  light,  especially  in  the  case  of  such  windows  as  are  exposed 
to  the  direct  sun,  aside  from  their  effectiveness  in  strengthening 
the  light  at  distant  points.  With  the  "Maze"  glass,  the  artist 
may  have,  in  all  weather  and  in  all  directions,  what  is  in  effect  a 
much-desired  "north  light."  The  photographer  may  have  in 
this  way  as  well  diffused  a  light  as  he  now  has  with  cloth  screens 
or  shades,  with  a  much  greater  intensity.  To  be  efficient  in 
rooms  20  ft.  deep  or  more,  ribbed  glass  should  be  set  with  its 
ribs  horizontal,  and  where  the  sunlight  falls  upon  it,  it  should 
be  provided  with  thin  white  shades.  All  inferences  drawn  from 
the  test  are  made  upon  the  assumption  that  the  windows  are  to 
be  glazed  with  diffusing  glass  only 
in  the  upper  half,  which  is  the  com- 
mon practice.  If  the  lower  sash  is 
to  be  glazed  with  diffusing  glass  as 
'  well,  a  further  increase  of  about 
twenty-five  per  cent,  may  be  ex- 
pected. 

Considering  both  expense  and 
efficiency,  the  following  general  sug- 
gestions are  given : 

Use  "Maze"  or  "Ripple"  glass 
in  small  rooms  or  offices  not  more 
than  15  or  20  ft.  deep. 

Use   "Factory  Ribbed"   glass  in 
rooms  30  to  50  ft.  deep,  with  sky- 
angles  of  60°  or  more. 
Use    prisms  or   "Factory    Ribbed"    glass,   in   sheets,    in   all 
vertical  windows  in  rooms  more  than  50  to  60  ft.  deep,  with  sky- 
angle  of  less  than  45°.     With  a  sky-angle  of  less  than  30°  use 
prisms  in  canopies. 

Fig.  G  shows  an  effective  method  of  lighting  the  basement  and 
first  story  where  the  light  must  come  from  a  court. 


ELECTRICITY— DEFINITIONS.  1305 


ELECTRICITY.* 

Definitions. — Electricity  \$  the  name  given  to  that  invisible 
agent  which  causes  all  electrical  phenomena.  Just  what  this 
agent  is,  is  unknown.  It  seems  probable  that  all  electrical 
phenomena  are  due  to  a  peculiar  state  or  stress  of  a  medium 
called  ether. 

Electrical  science  is  founded  upon  the  effects  produced  by 
the  action  of  certain  forces  upon  matter. 

Electricity  may  appear  either  to  reside  upon  the  surface  of 
bodies  as  a  charge  under  high  pressure  or  to  flow  through  their 
substance  as  a  current  under  comparatively  low  pressure. 

The  former  is  called  static  electricity  and  the  latter  dynamic 
electricity. 

That  branch  of  electrical  science  which  treats  of  static  elec- 
tricity is  termed  electrostatics  and  that  which  treats  of  the 
action  of  electric  currents  is  termed  electrodynamics. 

Static  electricity  is  produced  by  friction  and  is  used  prin- 
cipally in  medicine. 

An  electrostatic  battery  consists  of  a  number  of  Ley  den  jars 
whose  inside  coatings  are  all  connected  together  and  whose 
outside  coatings  are  all  connected  to  the  earth. 

Voltaic  electricity  is  a  term  applied  to  electricity  developed 
by  chemical  action  in  a  voltaic  cell,  or  battery.  Such  batteries 
develop  a  continuous  current  of  electricity,  and  hence  voltaic 
electricity  is  but  a  sub-branch  of  dynamic  electricity.  Electric 
currents  may  be  obtained  by  chemical  action,  heat,  or  induction. 

The  Electromagnet. — When  an  electric  current  is  passed 
through  a  coil  of  wire,  the  coil  becomes  equivalent  to  a  magnet 
and  possesses  the  same  properties. 

When  a  core  of  soft  iron  is  inserted  in  such  a  coil  it  becomes 
an  electromagnet.  The  core  is  magnetized  only  when  the 
current  is  flowing  in  the  coil,  and  it  is  to  this  fact  that  the  prac- 
tical value  of  the  electromagnet  is  due.  The  principle  of  the 
electromagnet  is  employed  in  the  construction  of  telegraphic 
instruments,  dynamos,  electric  bells,  etc.  Electric  clocks  are 
also  governed  by  the  action  of  electromagnets. 

Dynamos  generate   current  by  the  revolving  of  their  arma- 

*  In  the  preparation  of  this  subject  the  author  has  had  the  valued  assist- 
ance of  Mr.  Geo.  A.  Stiles.  Electrical  Ensdneer.  Denver. 


1 306  ELECTRICITY— DEFINITIONS. 

tures  in  a  magnetic  field.  The  armature  is  an  electromagnet 
with  the  wire  wound  parallel  to  its  axis  and  so  connected  to 
a  commutator  in  direct-current  machines  and  to  collector 
rings  in  alternators  that  the  current  may  be  taken  off  by 
brushes  applied  to  the  commutator  or  collecter  rings  as  the 
case  may  be. 

Types  of  dynamos  may  be  divided  into  two  divisions,  being 
distinguished  by  the  nature  of  the  current  they  are  to  supply — • 
the  one  type  continuous  or  direct  current,  the  other  alternating 
or  rapidly  reversing  the  directions  of  current. 

Flow  of  Electricity. — Electricity,  although  commonly 
described  and  referred  to  as  flowing  through  a  circuit,  does  not 
actually  flow.  There  is  no  transfer  of  matter  along  the  circuit. 
A  wire  carrying  a  current  looks  the  same  as  one  that  is  not, 
and  that  electricity  is  present  is  only  evident  by  the  heating, 
chemical,  or  magnetic  effects  produced.  For  practical  pur- 
poses, however,  it  is  convenient,  to  consider  electricity  as  flow- 
ing. 

As  -water  flows  from  a  higher  to  a  lower  level,  so  electricity 
flows  from  a  high  potential  to  a  lower  potential. 

Potential  is  the  electrical  difference  between  the  plates  of  a 
battery  or  the  poles  of  a  dynamo  or  induction  coil;  it  is  analo- 
gous to  "head,"  or  "pressure,"  in  hydraulics. 

Electromotive  Force. — As  stated  above,  whenever  a 
difference  of  electrical  potential  exists  between  two  points  of  a 
circuit  it  causes  a  current  to  flow,  and  this  difference  of  potential, 
or  the  force  to  which  it  gives  rise,  is  called  electromotive  force, 
commonly  designated  by  the  letters  E.M.F.  or  simply  E. 

The  terms  potential  difference  and  electromotive  force  are 
commonly  used  with  the  same  meaning. 

The  unit  of  electromotive  force  is  the  volt,  and  the  head,  or 
pressure,  which  produces  the  current  is  the  voltage,  high  or  low 
voltage  meaning  that  the  E.M.F.  is  measured  by  a  large  or 
small  number  of  volts.  In  common  language  the  terms  pressure, 
voltage,  difference  of  potential,  and  electromotive  force  are 
synonymous. 

The  strength  of  current  in  a  conductor,  corresponding 
to  rate  of  flow,  for  air  or  water  is  the  quantity  of  electricity  which 
passes  any  point  in  the  circuit  in  a  second  and  is  measured 
in  amperes.  The  quantity  of  electricity  conveyed  in  a  given 
time  is  the  product  of  the  strength  of  the  current  by  the  time 
it  continues. 


ELECTRICAL  UNITS,  DEFINED.  1307 

The  quantity  of  electricity  which  passes  any  cross-section 
of  the  conductor  in  one  second  when  the  current  strength  is 
one  ampere  is  called  a  coulomb. 

The  quantity  or  amount  of  electricity  in  coulombs  is  equal 
to  the  current  strength  in  amperes  multiplied  by  the  time  in 
seconds.  Thus  with  a  current  of  4  amperes  flowing  for  three 
seconds  the  quantity  delivered  is  12  coulombs. 

The  coulomb  is  also  called  the  ampere-second. 

An  ampere-hour  represents  an  amount  of  electricity  equal  to 
1  ampere  flowing  one  hour,  or  3,600  seconds,  and  is  consequently 
equal  to  3,600  coulombs. 

Jjoad. — The  term  load  as  used  in  electricity  generally  refers 
to  the  current  that  is  required  either  for  supplying  lamps  or 
motors.  The  load  of  a  motor  is  the  mechanical  energy  required 
of  it. 

Resistance  is  that  property  of  matter  in  virtue  of  which 
bodies  oppose  or  resist  the  free  flow  of  electricity  and  is  analo- 
gous to  friction  or  obstructions  in  water-pipes. 

The  specific  resistance  of  a  substance  is  the  resistance  of  a 
portion  of  that  substance  of  unit  length  and  cross-section  at  a 
standard  temperature,  and  is  an  inherent  property  of  the  sub- 
stance or  material.  The  specific  resistance  of  any  material 
must  first  be  determined  by  experiment. 

The  resistance  of  a  conductor  varies  directly  as  the  length, 
inversely  as  the  cross-sectional  area  or  as  the  square  of  the 
diameter,  if  the  conductor  is  in  the  shape  of  a  wire,  and  depends 
upon  the  specific  resistance  of  the  material. 

Thus  the  resistance  of  a  wire  100  ft.  long  is  twice  as  great 
as  another  of  the  same  cross-section  and  material  50  ft.  long; 
but  if  the  sectional  area  of  the  first  is  twice  that  of  the  second, 
then  both  wires  will  have  the  same  resistance. 

If  a  circuit  is  made  up  of  several  different  materials  joined 
in  series  with  each  other,  the  resistance  of  the  circuit  is  equal 
to  the  sum  of  the  resistances  of  its  several  parts. 

The  unit  of  resistance  is  the  oil  ill,  which  is  the  resistance  of 
a  uniform  column  of  mercury  106.3  centimeters  long  and  14.4521 
grams  in  mass  at  the  temperature  of  melting  ice. 

The  resistance  of  a  piece  of  round  copper  wire  .001  in.  in 
diameter  and  1  ft.  long  is  10.8  ohms. 

All  metals  have  their  resistance  increased  by  a  rise  of  tem- 
perature. 


1308  ELECTRICAL   UNITS— NOTATION. 

Heating  Effects  of  Current. — The  passage  of  electricity 
through  a  circuit  raises  the  temperature  of  the  circuit  a  certain 
amount. 

Joule's  law  is  as  follows:  "  The  heating  power  of  a  current  is 
proportional  to  the  product  of  the  square  of  its  strength  and 
the  resistance  of  the  circuit  through  which  it  passes." 

The  heating  of  a  wire  carrying  a  current  is  made  use  of  for 
lighting,  for  electric  heaters,  for  exploding  charges  of  powder, 
dynamite,  etc.  The  use  of  fuses  for  the  protection  of  electric 
circuits  is  also  based  on  this  principle. 

Electric  welding  is  accomplished  by  passing  a  powerful 
current  through  two  bars  pressed  together.  The  heating  of 
the  junction  fuses  the  metal  and  the  rods  become  welded. 

Energy. — The  unit  of  mechanical  energy  is  the  raising  of 
1  Ib.  1  ft.  The  unit  of  electrical  work  is  the  energy  expended 
by  1  ampere  in  1  second  in  overcoming  the  resistance  of  1  ohm 
and  is  called  the  joule.  The  joule  may  also  be  denned  as  the 
energy  expended  when  1  coulomb  is  carried  through  a  distance 
between  which  the  difference  of  potential  is  1  volt. 

Electrical  Power. — The  unit  of  mechanical  work  is  the 
foot-pound  per  minute.  In  electrical  work  the  unit  is  the  joule 
per  second  =  1  watt.  The  watt  is  also  sometimes  called  the 
volt-ampere.  One  kilowatt  =  1,000  watts. 

The  'kilowatt-hour  is  a  unit  of  energy  and  is  the  energy 
expended  in  one  hour  when  the  power  is  1  kilowatt. 

746  watts  =  1  electrical  horse-power  and  is  equivalent  to 
1  mechanical  horse-power. 

Notation  of  Electrical  Units. — The  various  electrical 
units  are  commonly  represented  by  the  letters  given  in  the 
following  table,  those  in  parenthesis  being  sometimes  used  in- 
stead of  the  letter  which  precedes : 
Volt,  the  electro-  )  ^        -^  ,,  ,?      Watt,  the  unit  of  power,  W  (P). 

motive  force      )  1  kilowatt  =  1 ,000  watts  =  kw. 

Ampere,  unit  of  current  or  rate     Joule,  the  unit  of  work,  J  (W). 

of  flow,  C  (7).  H. P.  =  horse-power. 

Ohm,  unit  of  resistance,  R.  t  =  one  second. 

Coulomb,  unit  of  quantity,  Q.  T=one  hour. 

Ampere-hour  =  3,600Q  =  Q'. 

Electrical  Equations. — Using  the  above  notation  the 
relation  between  the  various  units  may  be  expressed  by  the 
following  equations,  which  may  be  transposed  in  the  same 
mariner  as  any  algebraic  equation: 


ELECTRICAL  EQUATIONS. 


1309 


E=CR 


CE 
C2 

E* 


J= 


QE 

orCEt 
or  C2Rt 

EH 


H.P. 


W 

746 


kw. 
.746 


746 


EXAMPLES  SHOWING  APPLICATIONS  OF  ABOVE  FORMULAS. 

Example  1. — What  voltage  is  required  to  send  a  current 
of  22  amperes  through  a  wire  having  a  resistance  of  5  ohms? 

Ans.  #=22X5=110  volts. 

Example  2. — How  many  amperes  will  flow  through  a  copper 
wire  having  a  resistance  of  5  ohms,  the  voltage  being  110? 

Ans.  C=— —-=22  amperes, 
o 

Example  3. — The  pressure  on  a  circuit  is  110  volts,  and  it  is 
desired  to  supply  current  sufficient  for  twelve  16-c.p.  lamps  (6 
amperes),  what  should  be  the  resistance  of  the  circuit? 

Ans.  R=— -=18.33  ohms. 

Example  4. — The  common  110-volt  incandescent  lamp  has  a 
resistance  of  about  216  ohms.  (1)  What  current  is  required 

with  a  pressure  of  110  volts?  Ans.  C=^-—=.51  ampere. 

(2)  How  many  watts  does  it  consume?  Ans.  W=  CE=  .51 
X 110=  56.1  watts.  (3)  How  many  such  lamps  can  be  sup- 
plied by  1  electrical  H.P.?  Ans.  1  H.P.=  746  watts.  If  one 
lamp  requires  56.1  watts,  the  number  of  lamps  that  can  be 

746 
supplied    by    746   watts  =          =  13.3    lamps.     (4)  How    many 

OD.  1 

such  lamps  will  10  kw.  suffice?     Ans.  10kw.=  10X1,000  watts 

1  o  000 

=  10,000  watts.         ^  =  178  lamps, 
oo.l 

Example   5. — How   many   H.P.   will   10   kw.    furnish?     Ans. 

H.P.=  -^75=  13.4  horse-power. 
.74o 

Dynamo-electric  Machines. — There  are  three  classes 
of  dynamo-electric  machines,  viz. : 

1.  Generators  for  generating  an  electric  current. 

2.  Motors  for  converting  electrical  into  mechanical  energy. 

3.  Rotary  converters  for  changing  the  voltage   of  direct   cur- 
rents, or  the  voltage,  phase,  or  frequency  of  alternating  currents, 
and  also  for  changing   alternating  currents  to  direct  or  vice 
versa,  and 

3a.  Transformers  for  converting  one  voltage  into  a  higher  or 
lower  voltage.  Converters  and  transformers  belong  to  the  same 
class. 


1310  ELECTRICAL  CURRENTS. 

A  motor  is  the  same  machine  as  a  dynamo,  but  with  the 
nature  of  its  operation  reversed. 

Generators  are  of  two  general  classes,  viz.,  continuous-cur- 
rent and  alternating-current  machines ;  the  former  are  commonly 
called  dynamos  and  the  latter  alternators. 

Generators  and  motors  of  all  kinds  vary  in  voltage,  current, 
and  speed,  according  to  the  purpose  for  which  they  are  de- 
signed. 

A  transformer  consists  essentially  of  two  coils  of  wire,  one 
coarse  and  one  fine,  wound  upon  an  iron  core.  Its  function 
is  to  convert  electrical  energy  from  one  voltage  to  another. 
If  it  reduces  the  voltage  it  is  known  as  a  "step-down"  trans- 
former, and  if  it  raises  it,  it  is  known  as  a  " step-up"  trans- 
former. 

Kinds  of  Currents  Produced. — There  may  be  said 
to  be  four  kinds  of  electrical  currents,  viz. :  (1)  Direct  currents, 
constant-potential,  or  pressure.  (2)  Direct  currents,  constant 
current.  (3)  Alternating  currents,  constant-potential.  (4) 
Alternating  currents,  constant  current. 

Alternating  currents  may  be  single-phase,  two-phase,  three- 
phase,  five-phase,  or  any  other  number,  depending  upon  the 
number  of  poles  and  armature  winding  of  the  generator. 

A  current  used  for  either  lighting  or  power  cannot  be  constant 
in  both  pressure  and  rate. 

Both  for  lighting  and  power  a  constant  pressure  is  more  de- 
sirable than  a  constant  current  with  varying  pressure. 

"A  direct  current  is  uniform  in  strength  and  direction,  while 
an  alternating  current  rapidly  rises  from  zero  to  a  maximum, 
falls  to  zero,  reverses  its  direction,  attains  a  maximum  in  the 
new  direction  and  again  returns  to  zero.  The  advantages  of 
alternating  over  direct  currents  are:  1.  Greater  simplicity  of 
dynamos  and  motors,  no  commutators  being  required;  2.  The 
feasibility  of  obtaining  high  voltages  by  means  of  transformers 
for  cheapening  the  cost  of  transmission;  3.  The  facility  of 
transforming  from  one  voltage  to  another,  either  higher  or 
lower,  for  different  purposes."  (Kent,  p.  1063.) 


ELECTRIC  LIGHTING.  1311 

Electric  Lighting. 

SYSTEMS   COMMONLY   USED   FOR   SUPPLYING  THE   ELECTRICAL 
ENERGY  TO  LAMPS. 

Direct-current,    Constant-potential    Systems. — • 

a.  Two-wire  system  largely  used  for  incandescent  lighting 
from  small  plants,  as  for  a  large  office  building  or  factory;  it 
is  usually  operated  at  110  volts. 

b.  Three-wire  system  used  in  small  towns  for  the  lighting  of 
buildings  from  the  public  mains,  usually  operated  at  220  volts. 
Also  in  large  cities  with  underground  conduit  system. 

The  ordinary  three-wire  system  requires  two  dynamos  to 
balance  the  load. 

Five-wire  and  seven-wire  systems  with  high  voltage  have 
been  used  in  Europe,  but  very  little  in  America. 

Direct-current,  Constant-current  System.  —  This 
system  is  largely  used  for  municipal  and  commercial  arc  lights, 
but  is  rarely  used  for  incandescent  lighting. 

Alternating-current,  Constant-potential  Sys- 
tems.— a.  Single-phase  System. — Current  transmitted  to  build- 
ing at  1,000  to  2,000  volts  and  reduced  to  50  to  110  volts  by  a 
transformer. 

b.  Two-phase  System. — Two  or  three  wires;    most  used  for 
lighting    from    public    plants,    principally    because    it    enables 
both  lights  and  motors  to  be  operated  from  the  public  dynamo. 

c.  Three-phase  System. — Three  or  four  wires;    used  for  same 
purpose  as  the  two-phase  system. 

All  three  of  these  systems  are  used  both  for  incandescent 
lighting  and  power  from  central  stations. 

An  alternating  current  may  be  changed  to  direct  current  at  a 
sub-station  by  a  rotary  converter. 

Alternating-current,  Constant-current  System, 
practically  if  not  wholly  obsolete. 

Fuses,  Cut-outs,  and  Circuit-breakers. — The  fuse 
consists  of  an  easily  fusible  metal,  generally  a  mixture  of  lead 
and  bismuth,  which  is  inserted  in  the  circuit.  .  The  passage  of 
an  excesssive  or  dangerously  large  current  from  any  cause  melt 
the  fuse  and  breaks  the  circuit.  The  cause  of  the  large  currents 
may  then  be  removed  and  a  new  fuse  inserted  'in  place  of  the 
old  one. 


1312  ELECTRIC  LIGHTING. 

TABLE  L— RELATIVE  WEIGHT  OF  COPPER  REQUIRED 
IN  DIFFERENT  SYSTEMS  FOR  EQUAL  EFFECTIVE 
VOLTAGE  (KENT). 

Direct-current,  ordinary  two-wire  system 1 .000 

Direct-current,  three-wire  system,  all  wires  of  same  size.  .      .375 

Direct-current,  three  wires,  neutral,  one-half  size 313 

Alternating-current,     single-phase    two-wire     and     two- 
phase  four-wire 1 . 000 

Two-phase  three-wire,  voltage  between  outer  and  middle 

wire  same  as  in  single-phase  two-wire 729 

voltage  between  two  outer  wires  same 1 . 457 

Three-phase  three-wire 750 

Three-phase  four-wire 333 

Cut-outs  and  circuit-breakers  are  automatic  safety  devices 
required  for  the  protection  of  all  constant-potential  systems 
whatever  the  voltage.  Both  are  for  the  purpose  of  protecting 
the  wires  from  damage  due  to  the  presence  of  too  much  current 
from  any  cause  whatever. 

The  ordinary  cut-out  consists  of  a  porcelain  base  that  has 
suitable  terminals  for  inserting  a  fuse  between  the  ends  of  the 
wire.  It  must  be  constructed  so  that  the  blowing  out  of  a 
fuse  can  do  no  damage,  i.e.,  set  anything  on  fire,  and  placed 
where  it  can  easily  be  reached  to  replace  the  fuse. 

Formerly  a  piece  of  fuse  wire  was  used  in  cut-outs,  but  the 
underwriters  now  require  enclosed  fuses  (Fig.  1)  or  fusible  plugs 


Fig.  I 

Enclosed  Fuse. 

which  screw  into  a  receptacle.  Fuse  plugs  may  be  used  for 
currents  up  to  30  amperes;  above  that  enclosed  fuses  must  be 
used.  Fuse  plugs  and  enclosed  fuses  are  somewhat  more  ex- 
pensive than  the  link  fuse,  but  are  considered  safer.  A  cut- 
out or  circuit-breaker  is  required  at  or  near  the  place  where 
the  wires  enter  a  building,  and  every  circuit  of  twelve  16-c.p. 
lights  must  be  protected  by  a  cut-out. 


INCANDESCENT  LAMPS.  1313 

Circuit-breakers  are  automatic  switches  controlled  by  an 
electromagnet  and  are  made  in  a  variety  of  styles. 

They  are  more  expensive  than  fusible  cut-outs,  and  are 
generally  used  only  on  switchboards  for  large  installations 
and  where  it  is  desirable  to  open  the  circuit  instantly  on  cer- 
tain loads,  wrhich  a  fuse  cannot  be  depended  on  to  do  with  any 
degree  of  accuracy,  owing  to  both  time  and  surrounding  tem- 
perature factors. 

Also  used  largely  on  installations  where  the  variation  in 
load  is  large  and  often  and  the  frequent  burning  out  of  fuse 
would  become  expensive  both  for  renewals  and  time  required 
to  replace  them. 

Lamps. — Two  kinds  of  lamps  are  used  for  electric  lighting — 
incandescent  lamps  and  arc  lamps.  The  former  are  used 
principally  for  interior  illumination,  although  sometimes  used 
for  street  lighting,  especially  where  the  streets  are  thickly 
shaded  by  trees.  Arc  lamps  are  especially  adapted  for  street 
lighting  and  for  large  interiors  where  they  can  be  kept  above 
the  range  of  the  eye,  as  in  railway  stations,  stores,  etc. 

Incandescent  lamps  as  commonly  made  consist  of  a  glass 
bulb  containing  a  simple  carbon  conductor  the  ends  of  which 
are  connected  to  the  source  of  the  electric  current.  When 
the  current  flows  through  the  carbon  filament  it  heats  it  to 
such  a  degree  that  it  becomes  incandescent;  hence  the  name 
of  the  lamp. 

Voltages. — In  order  that  the  current  shall  cause  the  lamp  to 
give  its  rated  candle-power,  it  must  be  designed  for  the  voltage 
at  which  the  system  is  run.  If  the  voltage  of  the  current  is 
much  greater  than  that  for  which  the  lamp  is  designed  it  will 
quickly  burn  out  the  carbon  filament,  while  if  the  voltage  of 
the  current  is  below  that  of  the  lamp,  it  will  not  give  its  rated 
candle-power,  a  voltage  10  per  cent,  lower  reducing  the  candle- 
power  about  one  half. 

The  voltage  most  commonly  used  for  16-c.p.  lamps  is  from 
104  to  110. 

Lamps  are  also  made  for  voltages  of  45  to  250,  and  1-c.p. 
lamps,  for  illuminating  signs  or  decorative  purposes,  are  made 
for  12.5  and  15  volts,  these  lamps  being  commonly  used  in 
series,  eight  lamps  on  a  110- volt  circuit.  Two  4-c.p.  lamps, 
52  volts,  are  also  often  used  in  series  on  a  110- volt  circuit. 

Candle-pouer. — Incandescent  lamps  of  110  volts  are  commonly 
made  4,  8,  10,  12,  16,  24,  and  32  candle-power.  Table  II 


1314 


ELECTRIC  LIGHTING. 


shows  the  standard    candle-powers,  voltages,   and  current  re- 
quired for  incandescent  lamps. 

For  data  pertaining  to  the  Meridian  and  Nernst  lamps,  see 
pp.  1298,  1299. 

TABLE  II.— INCANDESCENT-LAMP  DATA.* 


Volts. 

Candle-power. 

Current, 
Amperes. 

Watts 
per  Lamp. 

52 

4 

.39 

20 

" 

8 

.61 

32 

« 

10 

.67 

35 

(t 

16 

1.08 

56 

a 

20 

1.34 

70 

(( 

24 

1.62 

84 

11 

32 

2.15 

112 

104 

10 

.34 

35 

u 

16 

.54 

56 

u 

20 

.67 

70 

(( 

24 

.81 

84 

u 

32 

1.08 

112 

110 

8 

.27 

30 

(t 

10 

.32 

35 

(( 

16 

.51 

56 

11 

20 

.64 

70 

u 

24 

.76 

84 

It 

32 

1.02 

112 

(( 

50 

1.59 

175 

(( 

100 

3.18 

350 

(( 

150 

4.77 

525 

220 

16 

.291 

64 

n 

32 

.582 

128 

*  H.  C.  Gushing,  Jr.,  in  Practical  Lessons  in  Electricity. 

Arc  Lamps. — These  are  of  two  kinds,  open  arc  lamps  and 
enclosed  arc  lamps,  the  latter  being  generally  used  for  interior 
illumination.  The  light  from  the  enclosed  arc  is  much  softer 
and  steadier  than  that  from  the  old-style  open  arc,  there  are 
no  sparks,  and  the  life  of  the  carbon  is  from  twelve  to  fifteen 
times  as  great  as  in  the  open  arc. 

"Current  for  arc  lighting  is  furnished  either  on  the  series 
constant-current  or  on  the  parallel  constant-potential  system. 
In  the  latter  the  voltage  of  the  circuit  is  usually  110.  In  cur- 


ELECTRIC-LIGHT  WIRING.  1315 

rents  with  higher  voltages  lamps  are  used  in  series,  for  instance 
5  to  10  with  a  500- volt  circuit. 

"  Direct-current  open  arcs  usually  require  about  10  amperes 
at  45  volts,  or  450  watts.  The  range  of  voltage  is  from  42 
to  52  for  ordinary  constant-current  arcs.  The  most  satis- 
factory light  is  given  by  45  to  47  volts. 

"  Alternating- current  open  arcs  usually  take  about  15  amperes 
at  30  to  35  volts,  but  are  not  much  used.  With  the  same 
energy  and  carbons,  the  mean  spherical  candle-power  is  about 
one  half  that  of  the  continuous-current  open  arc. 

"  Direct-current  enclosed  arcs  consume  about  5  amperes  at 
80  volts,  or  400  watts.  Alternating-current  enclosed  arcs 
usually  take  a  current  of  6  amperes  at  70  or  75  volts."  * 

Arc  lamps  generally  require  a  resistance  in  series  with  the 
arc  in  order  to  regulate  properly.  This  resistance  is  usually 
placed  within  the  structure  of  the  lamp,  and  is  adjustable  so 
that  a  single  lamp  can  be  made  to  burn  well  on  any  circuit 
from  105  to  120  volts. 

Methods  of  Connecting  Lamps. 

There  are  three  ways  of  connecting  lamps  to  the  distribution 
wires,  viz.:  (1)  in  series,  (2)  in  parallel,  and  (3)  in  parallel 
series. 

Lamps  in  Series. — Lamps  are  said  to  be  connected  in 
series  when  they  are  arranged  one  after  the  other,  so  that  the 
same  current  flows  through  all  the  lamps. 

The  lamps  shown  by  Fig.  2  are  in  series.  When  conductors 
are  arranged  in  series  the  total  resistance  of  the  circuit  is  the 


Fig.  2 

Lamps  in  Series. 

sum  of  the  resistances  of  the  several  parts,  and  the  pressure 
required  to  force  the  current  through  a  number  of  lamps  in 
series  is  the  sum  of  the  voltages  required  for  the  separate  lamps. 
Thus  the  voltage  required  to  supply  the  proper  current  for 
four  52-volt  lamps  is  4X52=208  volts.  Arc  lamps  for  street 

*  Kent,  p.  1044. 


1316 


ELECTRIC-LIGHT  WIRING. 


Distributing 

*-  -Wires-  * 


lighting  are  often  connected  in  series,  but  incandescent  lamps 
are  almost  never  connected  in  series  except  for  decorative 
purposes  and  in  electric  signs.  Where  lamps  of  low  voltage 
are  used  on  110- volt  systems  it  is  necessary  to  connect  them 
in  series.  The  underwriters  do  not  approve  connecting  in- 
candescent lamps  in  series.  The  series  system  requires  a 
constant  current  with  varying  pressure,  and  if  one  lamp  burns 
out  the  circuit  is  broken  and  all  of  the  lamps  will  go  out, 
unless  some  provision  is  made  for  maintaining  the  circuit 
around  the  lamps. 

Lamps  in  Parallel. — This  is  the  common  method  of  con- 
necting incandescent  lamps.  It  is  illustrated 
by  Fig.  3.  With  this  system  the  pressure  in 
each  lamp  is  the  same  as  in  the  distributing 
lines,  and  any  lamp  may  be  turned  on  or  off 
without  affecting  the  other  lamps.  For  this 
system  the  pressure  or  voltage  must  be  kept 
constant,  while  the  current  or  quantity  of 
electricity  flowing  in  the  lines  will  depend  upon 
the  number  of  lamps  that  are  burning.  Thus 
with  twelve  16-c.p.  lamps  of  110  voltage  on  a 
parallel  circuit,  each  lamp  requiring  .51  ampere 
(see  Table  II),  when  all  the  lamps  are  burning, 
a  current  of  6.12  amperes,  or  673. 2*  watts,  will 
be  required,  but  with  but  one  lamp  burning,  a 
current  of  only  .51  ampere  will  flow.  The 
voltage,  however,  must  be  the  same  for  one 
lamp  as  for  the  twelve.  For  lamps  in  parallel, 
therefore,  a  constant-potential  system  is  required. 
The  current  for  lamps  in  parallel  may  be 
turned  on  or  off  at  the  lamp,  or  a  switch  loop  may  be  run  any 
distance  and  the  contact  made  by  a  switch  (S)  as  for  the  lower 
lamp  (Fig.  3). 

Lamps  in  Parallel  Series. — This  method  is  a  combination 
of  the  other  two..  Parallel  lines  are  run  as  in  the  parallel 
system,  but  two  or  more  lamps  are  connected  in  series  between 
them  as  in  Figs.  4  and  5.  This  method  of  connecting  lamps 
is  used  principally  in  places  where  it  is  desired  to  operate  lamps 
on  a  power  system.  Fig.  4  shows  series  of  five  lamps  operated 
on  a  500- volt  system,  and  Fig.  5  series  of  two  lamps  on  a  110- 


I 
Fig.   3 


*  Watts  being  equal  to  amperes  times  voltage. 


ELECTRIC-LIGHT   WIRING. 


1317 


or  220- volt  system  using  52-  or  110-volt  lamps  respectively. 
Any  number  of  series  may  be  connected  across  the  mains,  each 
series  being  independent  of  the  others.  But  in  each  series  if 
one  light  burns  out,  the  others  will  go  out,  and  one  lamp  cannot 


< r500-Volts 

aoo-v-4ioo- ' 


<-  •  220-Volts-  -  • 


Fig.  4  Fig.  5 

Lamps  in  Parallel  Series. 

be  used  without  using  the  others.  The  sum  of  the  voltages 
of  the  lamps  in  series  must  be  approximately  equal  to  the 
voltage  between  the  mains.  There  are  a  number  of  special 
cases  in  which  this  method  of  connection  may  be  used. 

[Note. — Although  the  lamps  in  Figs.  3,  4,  and  5  are  connected 
directly  across  the  wires,  this  is  not  necessary  in  practice  so 
long  as  the  lamp  wires  are  connected  to  the  distributing  wires 
or  mains.  Thus  five  lamps  in  series  on  a  500-volt  circuit  may 
be  connected  as  in  Fig.  6.] 


na 

L    l<-100-VrH<-100-V 

±H=J    ' 

r 

©.,_©       © 

(°) 

Fig.  6 

The  Edison  Three-wire  System.— Figs.  3,  4,  and  5 
are  examples  of  the  two-wire  system  of  distribution,  which  is 
the  system  recommended  for  average  sized  office  buildings, 
apartment  houses,  'theatres,  and  stores. 

Where  power  is  to  be  taken  from  the  same  plant  and  is  not 


1318  ELECTRIC-LIGHT  WIRING. 

too  great  a  portion  of  the  capacity  of  the  installation  this  sys- 
tem may  also  be  used,  but  separate  mains  should  under  all 
circumstances  be  run  for  the  motors,  as  the  variation  in  load 
and  consequently  the  current  demand  on  the  mains  would 
cause  a  very  appreciable  fluctuation  in  candle-power  of  the 
lamps  if  on  the  same  mains  with  the  motors. 

Where  comparatively  long  lines  are  required  and  the  amount 
of  current  to  be  supplied  is  large  the  three-wire  system  is  used. 

By  this  system  we  can  supply  two  voltages  or  pressures, 
110  and  220  volts  being  those  generally  adopted,  the  110-volt 
circuit  supplying  the  arc  and  incandescent  lights  and  the  220- 
volt  circuit  the  motors.  Fig.  7  shows  how  the  wires  are  run 
and  connections  made. 


o    + "^  r '   '  ^ 
g*  NeutraK^jr^  « 


Fig.  7 

The  pressure  between  the  two  outside  wires  is  the  full  voltage 
transmitted  from  the  dynamos  or  transformer,  usually  220 
volts  for  interior  wiring.  The  current  in  these  two  wires  flows 
in  opposite  directions.  The  middle  wire,  called  the  neutral 
wire,  forms  one  side  of  two  circuits,  the  current  from  one  circuit 
tending  to  flow  in  one  direction  and  that  from  the  other  circuit 
in  the  opposite  direction;  consequently  when  currents  of  the 
same  strength  (in  amperes)  are  flowing  in  both  circuits  they 
neutralize  each  other  in  the  middle  wire  and  there  will  be  no 
current  flowing  in  this  wire. 

With  a  current  of  10  amperes  flowing  in  one  circuit  and  one 
of  6  amperes  in  the  other  circuit,  the  current  flowing  in  the 
neutral  wire  will  be  4  amperes.  To  obtain  the  greatest  benefit 
from  this  system,  it  should  always  be  installed  so  that  there 
will  be  nearly  the  same  load  or  number  of  lamps  on  each  side 
of  the  neutral  wire.  Even  then  there  will  be  times  when  more 
lamps  will  be  burning  on  one  side  than  on  the  other,  so  that 
it  is  necessary  to  give  some  size  to  the  neutral  wire. 

The  neutral  wire  is  seldom  made  less  than  one  half  the  cross- 
section  of  the  outer  wires.  For  distributing  mains  in  build- 


THREE-WIRE  SYSTEM  OF  WIRING. 


1319 


ings  carrying  lamps  only,  the  neutral  wire  should  be  of  the 
same  size  as  the  outer  wires. 

From  Table  I  it  will  be  seen  that  the  three-wire  system  effects 
a  considerable  saving  in  copper,  amounting  to  fully  GO  per  cent, 
of  the  ordinary  two-wire  110-volt  system. 

As  a  rule  in  supplying  current  for  light  and  power  from  one 
plant,  the  main  wires  only  are  arranged  on  the  three-wire 
system  and  the  distributing  wires  are  run  on  the  two-wire 
system  as  in  Fig.  8. 


'D.  denotes  Dynamo 
C.O.      »        Cut-out 
£.       "        Lamp 
M.      »        Motor 


no  v 


C.O. 

Fig.  8 

Example  of  Three-wire  System  of  Wiring. 

When  using  the  three-wire  system  for  lighting  only,  the  three 
wires  are  usually  run  no  farther  within  the  building  than  to 
the  centres  of  distribution,  and  from  these  centres  two  wires 
are  run  for  each  circuit,  the  circuits  being  divided  as  equally  as 
:  possible  on  the  two  sides  of  the  three-wire  system  as  showrn  by 
Fig.  9.  Three-wrire  mains  are  now  very  commonly  used  where 
:the  current  exceeds  100  amperes. 

When  motors  are  operated  from  the  three-wire  system  they 
i  are  usually  connected  only  to  the  outside  wires. 

Motors  used  on  three-wire  incandescent-lighting  systems 
should  be  wound  for  220  volts. 


1320 


ELECTRIC-LIGHT   WIRING. 


WIRE    CALCULATIONS. 

Wire  Gauges. — As  the  diameter  of  wires  are  ordinarily 
designated  by  the  numbers  of  a  wire  gauge,  and  as  there  are 
a  number  of  wire  gauges  in  common  use,  some  knowledge  of 
those  used  for  copper  wire  is  necessary. 

The  Brown  &  Sharp,  or  B.  &  S.,  gauge  is  almost  exclusively 
used  in  America  in  connection  with  electrical  work,  except 


To  Cut-out  Cabinet 
.Second  Story 


where  the  size  of  the  wire  is  designated  in  circular  mils.  The 
sizes  of  wire  given  by  this  gauge  range  from  No.  0000  (.46  in.) 
to  No.  40  (.0031  in.),  but  No.  14  is  the  smallest  size  permitted 
for  interior  wiring.  The  No.  10  wire  has  a  diameter  of  very 
nearly  TV  of  an  inch,  and  its  resistance  per  1,000  ft.  is  very  nearly 
1  ohm.  For  any  given  number  of  this  gauge  a  wire  three 
numbers  higher  has  very  nearly  half  the  cross-section,  ana  one 
three  numbers  lower  has  twice  the  cross-section;  thus  a  No.  13 
wire  has  very  nearly  one  half  the  cross-section  of  a  No.  10  wire, 
and  a  No  7  has  twice  the  cross-section  of  a  No.  10,  or  four 
times  that  of  a  No.  13. 

The   Circular-mil  Wire    Gauge. — This    gauge    was 
designed  by  the  engineering  department  of  the  Edison  Company 


WIRE  CALCULATIONS.  1321 

especially  for  the  designation  of  copper  wire  for  electrical  work, 
and  is  now  in  universal  use  in  this  country.  •  In  practice  the 
B.  &  S.  gauge  is  commonly  used  for  designating  wires  up 
to  No.  0  or  No.  00,  and  all  wires  above  that  size  are  designated 
by  circular  mils  (c.m.). 

The  size  of  wire  required  is  often  determined  in  circular  mils 
and  designated  by  the  corresponding  B.  &  S.  gauge  number, 
which  is  readily  done  by  means  of  Table  III. 

Copper  wire  is  sold  by  the  pound  if  bare  or  of  the  numerous 
weather-proof  varieties,  but  rubber-covered  wire  is  sold  by  the 
1,000  ft 

The  basis  of  the  circular-mil  gauge  is  the  area  of  a  wire 
ig\nF  of  an  inch  in  diameter  (1  mil=  .001  in!),  consequently 
1  c.m.  =  .0000007854  sq.  in.  As  the  area  of  circles  is  directly 
as  the  square  of  their  diameter,  it  follows  that  the  sectional 
area  of  a  wire  2  mils  in  diameter=4  c.m.,  of  a  wire  10  mils  in 
diameter  100  c.m.,  and  so  on. 

When  wires  are  designated  by  circular  mils,  the  sectional 
area  and  not  the  diameter  is  generally  given,  c.m.  always  re- 
ferring to  sectional  area. 

The  diameter  of  a  wire  in  mils  or  in  thousands  of  an  inch= 
square  root  of  its  area  in  circular  mils. 

Thus  the  diameter  of  a  wire  of  3,600  c,m.=  60  mils,  or  .060  in. 

The  diameter  of  a  wire  14,400  c.m.=  120  mils=  .12  in. 

The  area  of  a  wire  .162  in.  in  diameter,  or  162  mils,=  1622 
=  26,244. 

To  reduce  circular  mils  to  square  inches  multiply  by  7,854  and 
point  off  ten  places  of  decimals.  Thus,  5,000  c.m.  =  7, 854 
X  5,000- .0039270000  sq.  in. 

To  obtain  the  sectional  area  of  a  square  or  rectangular  bar  in 
circular  mils  multiply  together  its  dimensions  in  mils  and  the 
product  by  1.273. 

Example  6. — What  :s  the  sectional  area  in  circular  mils  of  a 
bar  -J  in.  X  J  in.?  Ans.  J  in.=  .125  in.=  125  mils,  \  in.=  .250  in. 
-250  mils;  125X250X1.273=39,781.25  c.m. 

The  weight  of  bare  copper  wire  per  1,000  ft.=  c.m.  X  .003027  Ibs. 
Thus  the  weight  of  1,000  ft.  of  copper  wire  having  a  sectional 
area  of  2,000  c.m.  =  .003027X2,000=6.054000  Ibs. 

Table  IV  gives  the  dimensions  and  weights  of  bare  copper 
wire  from  No.  1 8  to  No.  4-0  B.  &  S.  gauge. 

Carrying  Capacity  of  Copper  Wire.— The  safe  carry- 
ing capacity  of  copper  wire  for  interior  wiring  is  practically 


1322  ELECTRIC-LIGHT  WIRING. 

fixed  by  the  underwriters,  and  if  the  capacity  limits  given 
by  the  table  published  by  them  are  exceeded  it  would  tend 
to  destroy  the  right  to  recover  insurance  in  case  of  fire. 

The  safe  carrying  capacity  of  rubber-covered  and  weather- 
proof wires  given  by  the  National  Board  of  Fire  Underwriters 
is  shown  by  Table  III. 

The  lower  ampere  capacity  assigned  to  rubber-covered  wires 
is  due  to  the  fact  that  the  rubber  insulation  would  deteriorate 
in  quality  under  a  temperature  as  high  as  that  allowed  for 
weather-proof  wire;  i.e.,  the  rubber  covering  makes  necessary 
a  lower  rate  of  heat  development  than  is  required  for  safety 
from  fire. 

No  smaller  than  No.  14  wire  may  be  used  under  insurance 
rules,  except  that  No.  16  may  be  used  for  flexible  cord  and 
No.  18  for  fixture  wiring.  Nos.  13,  11,  9,  and  7  are  not  usually 
carried  in  stock  and  can  only  be  purchased  on  special  order. 

Rubber-covered  wire  must  be  used  for  service  wires,  for 
moulding  work,  and  in  damp  places ;  it  is  more  expensive  than 
weather-proof  wire.  The  latter  wire  may  be  used  in  open  or 
exposed  places  and  for  outside  line  wires. 

Drop  of  Potential. — When  an  electric  current  flows 
through  a  wire  of  any  appreciable  length  the  pressure  becomes 
reduced  by  the  resistance  of  the  wire,  so  that  if  the  current  enters 
the  wire  at,  say,  110  volts,  at  the  extreme  end  of  the  circuit  it 
will  be  somewhat  less,  depending  upon  the  length  and  sectional 
area  of  the  wire.  Drop  of  potential  corresponds  to  loss  of 
head  in  hydraulics.  As  a ,  drop  of  voltage  materially  below 
that  for  which  the  lamps  are  designed  means  diminished  candle- 
power,  it  is  very  important  that  the  wires  be  proportioned  so 
that  the  drop  shall  not  be  sufficient  to  affect  the  illumination. 

Mains  and  distributing  wires  may  be  capable  of  carrying 
the  number  of  amperes  in  accordance  with  Table  III,  arid  yet 
cause  a  drop  of  potential  of  such  magnitude  that  the  most  distant 
lamps  will  burn  only  at  a  dull  red. 

An  excessive  drop  in  voltage  also  means  increased  cost  for 
light  and  not  enough  copper  in  the  wires. 

Where  the  current  is  supplied  from  the  public  mains  it  is 
usual  to  specify  a  2  per  cent,  drop,  but  where  the  current  is 
produced  cheaply,  as  by  a  dynamo  on  the  premises,  a  3  per  cent, 
or  5  per  cent,  drop  may  be  allowed.  Not  more  than  a  5  per  cent, 
drop  on  short  distances  should  be  permitted,  even  where  very 
cheap  work  is  desired. 


WIRE  CALCULATIONS. 


1323 


The  drop  in  volts  (not  in  percentage)  =  current  in  line  X  re- 
sistance of  line,  or  drop  in  volts  =  amperes  X ohms. 

Example. — What  will  be  the  drop  in  a  circuit  of  No.  14  copper 
wire  280  ft.  long,  supplying  nine  lamps,  requiring  4.5  amperes? 
Ans  From  Table  V  we  find  that  the  resistance  of  No.  14  wire 
is  2.527  ohms  per  1,000  ft.,  hence  for  280  ft.  it  will  be  2.527 X 
.280=. 7075  ohm,  and  drop  in  volts=4.5X.7075=3.1837  volts. 
The  voltage  for  this  current  (.5  ampere  per  lamp)  will  be  about 

3  1837 
110,    consequently    the    percentage    of    drop=    "1in    =2JG  per 


cent.,  nearly. 
is  2.2  volts. 


110 
Two  per  cent,  drop  on  a  pressure  of  110  volts 


Centre  of  Distribution. — The  meaning  of  this  term  may 
best  be  illustrated  by  an  example.     Let  Fig.  10  represent  a  circuit 


4 


—40- 


-70— 


Fig.  10 

carrying  six  lamps,  the  first  lamp  being  40  ft.  from  the  cut-out,  or 
source  of  supply.  The  whole  of  the  current  must  be  transmitted 
through  this  40  ft.,  but  from  that  point  it  will  gradually  fall 
off,  and  the  average  current  will  only  extend  to  the  point  CD, 
half  way  between  the  extreme  lamps.  Or,  in  other  words,  the 
centre  of  distribution  is  analogous  to  the  centre  of  gravity  of 
the  lamps  on  the  circuit. 

The  centre  of  distribution  determines  the  length  of  the  line 
in  the  rules  for  finding  the  necessary  size  of  wire. 

Distributing  centres  are  the  points  in  a  building  where 
the  cut-out  cabinets  are  located  and  the  branch  circuits  taken 
off. 

Calculations  for  Size  of  Wire  for  Incandescent 
Lighting. — The  sizes  of  wires  for  interior  lighting  are  or  should 
be  always  determined  on  a  basis  of  a  fixed  drop  of  potential, 


1324  ELECTRIC-LIGHT  WIRING. 

usually  2  volts  on  the  distributing  circuit  and  2  to  3  volts  on 
the  feeders  or  mains.*  The  size  of  wire  may  be  determined 
either  in  terms  of  its  sectional  area  in  circular  mils  or  in  terms 
of  its  resistance  in  ohms  per  1,000  ft. 

Knowing  the  sectional  area  in  circular  mils  the  corresponding 
gauge  number  may  be  found  from  Table  III,  or  if  we  have  the 
resistance  in  ohms  per  1,000  ft.,  we  may  find  the  corresponding 
gauge  number  from  Table  IV. 

The  formula  for  circular  mils  is  as  follows: 


.,  . 

Circular  mils=  —  —  ....     (A) 


v 


The  formula  for  resistance  per  1,000  ft.  of  wire  is 

l,000t> 


In  both  these  formulas  d=  distance  in  feet,  one  way,  from 
cut-out  to  centre  of  distribution  (see  p.  1323)  for  distributing 
wires,  or  from  entrance  cut-out  or  source  of  current  to  dis- 
tributing centre  for  main  lines  or  feeders.  c=  current  in  am- 
peres per  lamp  (Table  II).  N=  number  of  lamps  supplied. 
v=  drop  in  volts. 

Both  formulas  apply  to  any  voltage  and  to  any  two-wire 
system. 

To  use  these  formulas  for  the  ordinary  three-wire  system, 
let  N=  maximum  number  of  lamps  on  one  side  of  the  neutral 
wire  and  double  the  drop  in  volts.  The  neutral  or  middle  wire 
should  be  of  the  same  size  as  the  outside  wires  (see  top  of  p.  1319). 

Exo.mple  7.  —  The  distance  from  the  cut-out  to  centre  of 
distribution  of  a  circuit  carrying  twelve  16-c.p.  110-volt  lamps 
is  50  ft  What  size  of  wire  should  be  used  for  a  drop  of  2  volts? 
'  Ans.  d=50;  Ar=12;  c  (Table  II)-.  51,  and  v=2. 

By  formula  (A), 

..       10.8  X  100  X  12  X.  51 
Circular  rmls=  —          —  ~  —  =  3,605. 

Zi 

From  Table  III,  we  see  that  the  next   larger   size  of  wire 
is  4,107  c.m.,  equivalent  to  a  No.  14  wire. 
By  formula  (5), 

Resistance  per  1,000  ft.= 


*  Many   municipal   lighting   companies   require   that   there   shall    be   no 
more  than  2  per  cent,  total  drop  in  the  wiring  for  interior  lighting. 


WIRE  CALCULATIONS.  1325 

which  we  see  from  Table  IV  is  about  the  resistance  of  a  No.  15 
wire,  but  as  No.  14  is  the  smallest  wire  permitted  we  must  use 
that  size. 

Example  8. — The  distance  from  the  entrance  cut-out  (where 
the  wires  enter  the  building)  to  the  main  distributing  centre 
of  a  building  is  100  ft.  The  total,  number  of  16-c.p.  110-volt 
lamps  supplied  is  ninety.  What  size  mains  should  be  used  on 
the  two-wire  system  with  a  drop  of  two  volts? 

Ans.  d-100;  N=90;  c=.51;  v=2. 

By  formula  (A), 

.,       10.8X200X90X.51      ,n  _,_0 
Circular  mils= —       — = —         — =49,572. 

Looking  in  Table  III,  we  see  that  we  must  use  No.  3  wire. 
If  we  allow  a  drop  of  3  volts  the  sectional  area  required  will  be 
33,048  c.m.,  which  requires  a  No.  5  wire.  The  weight  per 
1,000  ft.  of  No.  3  weather-proof  wire  (Table  IV)  is  200  Ibs.  and 
of  No.  5  wire  125  Ibs.,  consequently  the  saving  in  weight  of  wire 
by  using  a  drop  of  3  volts  instead  of  2  is  75  Ibs.,  or  37 J  per  cent, 
of  200,  and  as  wire  is  sold  by  the  pound,  the  saving  in  cost  with 
a  3  per  cent,  drop  ranges  from  30  to  40  per  cent,  of  a  2  per  cent, 
drop. 

Example  9. — With  the  same  conditions  as  given  in  Ex.  8, 
what  size  of  wire  will  be  required  for  the  ordinary  three-wire 
system  with  2  per  cent,  drop?  Ans.  In  this  case  we  use  one 
half  of  N,  or  45,  and  2v  instead  of  v;  then 

.,       10.8X200X45X.51 
Circular  mils=  — - —         — =  12,392, 

or  just  one  fourth  the  section  required  for  the  two-wire  system. 
The  size  of  wire  required  is  No.  8  (a  No.  9  would  answer  if  it 
could  be  had).  Comparing  the  weight  of  wire  required  with 
the  two-wire  system,  we  have  two  No.  3  wires  weighing  400  Ibs. 
per  1,000  ft.,  and  with  the  three-wire  system  three  No.  8  wires 
weighing  207  Ibs.,  hence  the  saving  in  cost  is  nearly  50  per  cent., 
and  if  No.  9  wire  were  obtainable  the  saving  would  be  55  per  cent. 

With  a  drop  of  3  per  cent.   (3.3  volts)  the  circular  mils  re- 

10.8  X  200  X  45  X. 51 
quired   for  the  three-wire  system=  —        — ^ —     —  =  7,510, 

requiring  No.  10  wires. 

The  current  in  amperes  in  the  two-wire  system=  ArXc=45.9, 
and  in  the  three-wire  system  JA^Xc— 22.95. 

Referring  to  Table  III,  we  see  that  the  smallest  size  of 
weather-proof  wire  permitted  for  45.9  amperes  is  No.  8;  con- 
sequently we  could  use  No.  8  wire  with  the  two-wire  system 


1326 


ELECTRIC-LIGHT  WIRING. 


and  comply  with  the  underwriters7  rules,  but  the  drop  in  poten- 
tial would  be  45.9 X. 2 X. 6285  (amperes X resistance  of  line) 
=  5.77  volts',  or  over  5  per  cent. 

TABLE    III.— CARRYING    CAPACITY    OF    WIRES    AND 

CABLES. 

For  interior  conductors,   all  voltages. 
(From  the  National  Electrical  Code.) 


Wires, 

No.  B.  &  S. 
Gauge. 

Circular 
Mils. 

Capacity  in  Amperes. 

Rubber- 
covered. 

Weather- 
proof. 

18 

1,624 

3 

5 

16 

2,583 

6 

8 

14 

4,107 

12 

16 

12 

6,530 

17 

23 

10 

10,380 

24 

32 

8 

16,510 

33 

46 

6 

26,250 

46 

65 

5 

33,100 

54 

77 

4 

41,740 

65 

92 

3 

52,630 

76 

110 

2 

66,370 

90 

131 

1 

83,690 

107 

156 

0 

105,500 

127 

185 

00 

133,100 

150 

220 

000 

167,800 

177 

262 

0000 

211,600 

210 

312 

Cables 

200,000 

200 

300 

300,000 

270 

400 

400,000 

330 

500 

500,000 

390 

590 

600,000 

450 

680 

700,000 

500 

760 

800,000 

550 

840 

900,000 

600 

920 

1,000,000 

650 

1,000 

1,100,000 

690 

1,080 

1,200,000 

730 

1,150 

1,300,000 

770 

1,220 

1,400,000 

810 

1,290 

1,500,000 

850 

1,360 

1,600,000 

890 

1,430 

1,700,000 

930 

1,190 

1,800,000 

970 

1  ,550 

1,900,000 

1,010 

1,610 

2,000,000 

1,050 

1,670 

A  current  of  one  ampere  will  supply  two  16-c.p.  lamps. 


WIRE  CALCULATIONS, 


1327 


For  the  three-wire  system,  the  current  being  23  amperes t 
the  smallest  weather-proof  wire  permitted  by  Tabl9  III  is 
No.  12,  which  would  give  a  drop  of  7.4  volts,  or  3.8  volts  on 
each  side,  or  about  3J  per  cent,  of  the  lamp  voltage.  Except 
on  very  short  lines  a  2  per  cent,  drop  will  always  demand  larger 
wires  than  required  by  the  underwriters,  and  this  is  also  usually 
true  of  a  3  per  cent.  drop. 

TABLE  IV.— DIMENSIONS,  WEIGHT,  AND  RESISTANCE 
OF  COPPER  WIRE. 


Gauge 

Weight  ir 
1,000 

i  Lbs.  per 
Feet. 

Resistance 

No. 
B.  &S. 

in  Mils. 

Cir.  Mils. 

Sq.  Ins. 

Bare 
Wire. 

Weather- 
proof * 
Wire. 

in  Ohms  t 
per 
1,000  Ft. 

0000 
000 
00 
0 

1 

2 

3 

4 
5 
6 
7 
8 
9 

460 
410 
365 
325 
289 
258 
229 
204 
182 
162 
144 
128 
114 

211,600 
167,800 
133,100 
105,500 
83,690 
66,370 
52,630 
41,740 
33,100 
26,250 
20,820 
16,510 
13,090 

.166190 
.131790 
.  104520 
.082887 
.065732 
.052128 
.041339 
.032784 
.025999 
.020618 
.016351 
012967 
.010283 

640.73 
508.12 
402.97 
319.74 
253.43 
200.98 
159.38 
126.40 
100.23 
79.49 
63.03 
49.99 
39.65 

800 
666 
500 
363 
313 
250 
200 
144 
125 
105 
87 
69 

.04904 
.06184 
.07797 
.09827 
.12398 
.15633 
.19714 
.24858 
.31346 
.39528 
.49845 
.62849 
79242 

10 
11 

102 
91 

10,380 
8,234 

.008155 
.006466 

31.44 
24.93 

50 

.99948 
1  2602 

12 
13 

81 

72 

6,530 
5,178 

.005129 
.004067 

19.77 
15.68 

31 

1.5890 
2  0037 

14 
15 

64 
57 

4,107 
3,257 

.003225 
.002558 

12.44 

9.86 

22 

2.5266 
3  1860 

16 
17 

51 
45 

2,583 

2,048 

.002028 
.001608 

7.82 
6.20 

14 

4.0176 
5  0660 

18 

40 

1,624 

.001275 

4.92 

11 

6.3880 

*  Approximate  weight  of  weather-proof  line  wire  for  outdoor  work  is 
10  per  cent,  less  than  here  given. 

t  Values  given  by  H.  C.  Gushing,  Jr.,  in  Practical  Lessons  in  Elec- 
tricity. The  author  has  been  unable  to  find  any  two  tables  that  give 
exactly  the  same  resistance. 

To  find  the  smallest  size  of  wire  that  will  comply  with  the 
underwriters'  rules  it  is  only  necessary  to  compute  the  total 
current  in  amperes,  and  from  Table  III  select  the  wire  having 


1328 


ELEC TRIG-LIGHT  WIRING. 


a  capacity  equal  to  or  next  above  the  required  number  of 
amperes.  Table  VI  shows  at  a  glance  the  maximum  number  of 
16  c.p.  110  volt  lamps  permitted  by  the  National  Code. 

TABLE  V.— MAXIMUM  LENGTH  OF  LINE  FOR  GIVEN 
NUMBER  OF  LAMPS  THAT  CAN  BE  USED  WITH  A 
2  PER  CENT.  DROP.  TWO-WIRE  SYSTEM. 

Based   on  %  ampere  per  lamp.      One   32-c.p.   lamp  =  two    16-c.p.    lamps 
Two  24-c.p.   lamps  =  three   16-c.p.   lamps. 


No.  of 
Wire, 
B.  &S. 
Gauge. 

Number  of  16-c.p.  110-volt  Lamps. 

4 

6 

8 

10 

11 

12 

16 

20 

24 

Maximum  Length  of  Line,  One  Side,  in  Feet. 

14 
12 
10 
8 
6 

12 

10 
8 
6 
5 
4 
3 
2 
1 

209 

139 
221 

104 
166 
264 

83 
133 
211 
326 

76 
120 
192 
297 

70 
110 
176 

272 
440 

52 

83 
132 
204 
334 

42 
66 
105 
163 

267 

35 
55 

88 
136 
220 

Number  of  16-c.p.  110-volt  Lamps. 

30 

36 

40 

50 

60 

70 

80 

90 

100 

Maximum  Length  of  Line,  One  Side,  in  Feet. 

44 
70 
109 
178 
225 

37 

58 
91 
148 
187 
236 

52 

81 
133 
168 
212 

268 

42 
65 
107 
135 
170 
214 
270 

54 
89 
112 
141 
180 
225 
285 

37 
76 
96 
121 
153 
193 
243 

40 
66 
84 
106 
134 
169 
213 

59 
75 
94 
119 
150 
190 

53 
67 
85 
107 
135 
170 

For  three- wire  mains  with  220  volts  between  outer  wires  and  same  num- 
ber of  lamps  on  each  side  length  of  wire  may  be  increased  four  times. 

Formulas  (A)  and  (B)  may  also  be  used  for  motor  wiring,  if 
the  required  current  in  amperes  is  known,  by  substituting  the 
given  number  of  amperes  for  NXc. 

Example  10. — What  size  of  wires  should  be  run  to  a  motor 
that  requires  30  amperes  and  220  volts  and  is  situated  200  ft. 


EXAMPLE  OF  LIGHT  WIRING. 


1329 


from  the  distributing  pt>le,  the  drop  in  volts  not  to  exceed  2  per 
cent.?  Ans.  Using  formula  (A),  and  substituting  30  for  JVXc, 
we  have 

.,       10.8X400X30     on/IEr, 
Circular  mils=  -    — -j-j =  29,454, 

which  requires  a  No.  5  wrire. 

The  current  either  in  watts  or  amperes  is  stamped  on  every 
motor.  If  watts  are  given,  the  current  in  amperes  may  be 
found  by  dividing  the  watts  by  the  voltage.  If  kilowatts  are 
given,  multiply  by  1,000  and  then  divide  by  the  voltage. 

TABLE  VI.— MAXIMUM  CARRYING  CAPACITY  OF  WIRES 
IN  TERMS  OF  16-C.P.  110-VOLT  LAMPS,  HOWEVER 
SHORT  THE  WIRES  MAY  BE. 

Based  on  }4  ampere  per  lamp. 


No.  of 

Number  of  Lamps. 

No.  of 

Number  of  Lamps. 

Wire, 

Wire, 

B.  &S. 

B.  &S. 

Gauge. 

Rubber- 

Weather- 

Gauge. 

Rubber- 

Weather- 

covered. 

proof. 

covered. 

proof. 

14 

24 

32 

4 

130 

184 

12 

34 

46 

3 

152 

220 

10 

48 

64 

2 

180 

262 

8 

66 

92 

1 

214 

312 

6 

92 

130 

0 

254 

370 

5 

'108 

154 

00 

300 

440 

Wiring  Tables. — Several  forms  of  wiring  tables  are  pub- 
lished in  various  books  on  electricity  which  are  very  useful 
to  electricians.  For  oidinary  interior  wiring  for  110- volt 
16-c.p.  lamps,  Table  V,  computed  by  the  author,  will  show 
at  a  glance  the  number  of  wire,  B.  &  S.  gauge,  required  to  supply 
the  given  number  of  lamps  by  first  ascertaining  the  length  of 
line  (one  way)  through  wrhich  the  average  current  flows,  as 
explained  under  Centre  of  Distribution  (p.  1323). 

Simple  Example  of  Wiring:. — To  show  the  method  of 
wiring  an  ordinary  building  for  incandescent  lighting  we  will 
take  a  two-story  building  having  a  floor  plan  as  shown  by 
Fig.  11.  The  light  outlets  are  all  on  the  ceiling  and  are  indi- 
cated by  a  small  circle  and  cross.  The  numbers  1  and  2  beside 
the  outlets  denote  the  number  of  lamps  to  the  outlet. 

Current  to  be  obtained  from  the  wires  of  the  public  lighting 
company,  which  carry  a  current  of  220  volts.  The  feed-wires 


1330 


ELECTRIC-LIGHT  WIRING, 


for  the  building  should  enter  through  the  alley  wall  at  about 
the  level  of  the  second  floor  and  should  drop  in  the  partition 


ALLEY 


)  fFEED'WIRE 


STREET  FRONT 
.SECOND  FLOOR  PLAN 
Fig.  II 

Example  of  Wiring. 

just  inside  the  wall  for  the  main  fuse  block  and  switch  (M .£.), 
which  should  be  in  a  small  cabinet.     The  distribution  cabinet, 


EXAMPLE  OF  LIGHT  WIRING. 


1331 


should  be  located  near  the  centre  of  the  building,  say  at  DC, 
and  there  should  be  a  cabinet  in  each  story.  From  this  cabi- 
net we  will  run  four  circuits  for  each  story,  which  are  indicated 
by  the  letters  A,  B,  C,  and  D.  Circuit  A  shows  the  wires  run 
for  a  switch  on  the  wall  of  each  of  four  rooms  to  control  the 
lights  in  those  rooms.  All  of  the  lights  on  circuit  C  should  be 
controlled  by  a  switch  in  the  cabinet.  The  lights  on  circuits  B  v 
and  D  are  not  switched,  except  the  outlet  at  head  of  stairs, 
which  is  controlled  by  a  snap  or  push-button  switch  at  S. 

For  a  first-class  job  all  of  the  four  circuits  would  be  con- 
trolled by  knife  switches  in  the  cabinet,  as  shown  by  Fig.  12j 
but  this  is  not  absolutely  necessary. 


F..F,  FUSE  PLUGS 


S.6,  KNIFE  SWITCHES 


Fig.  12 


Size  of  Wires. — The  centre  of  distribution  of  circuits  A,  C, 
and  D  would  be  at  about  the  points  marked  X.  For  circuit  B 
take  one  half  the  distance  ab  and  add  to  it  the  distance  from 
c  to  the  cabinet. 

In  figuring  the  length  of  line,  6  ft.  should  be  added  for  the 
drop  from  ceiling  to  the  cabinet.     The  number  of  lamps  and 
length  of  wire  for  each  circuit  are  as  follows: 
Circuit  A,    8  lights,  41  ft.  one  way  to  centre  of  distribution. 
Circuit  B,  12  lights,  52  ft.    "      "     "       "       "  " 

Circuit  C,    4  lights,  37  ft.    "      "     "       "       "  « 

Circuit  D,  12  lights,  59  ft.    "      "     w       "       «  « 

Total  number  of  lamps,  36. 


1332  ELECTRIC-LIGHT  WIRING. 

From  Table  V  we  see  that  the  maximum  length  of  line  one 
way  for  No.  14  wire  carrying  twelve  lamps  is  70  ft.,  consequently 
all  of  the  lamp  circuits  can  be  No.  14  wire,  which  is  the  smallest 
size  permitted. 

Feed-wires. — These  should  be  run  on.  the  three-wire  system. 
Allowing  for  seventy-two  lamps  in  first  and  second  stories 
and  eight  in  basement,  the  feed-wires  must  be  capable  of  supply- 
ing eighty  lamps.  The  distance  from  outside  the  building 
to  distribution  cabinet  is  about  72  ft.,  allowing  for  three  drops. 

Using  formula  (A),  and  assuming  that  there  will  be  forty 
lamps  on  each  side  of  the  three-wire  system,  and  doubling  the 
drop  in  volts,  we  have 

10.8X144X40X.51 
Circular  mils= =7,932  c.m., 

which  calls  for  No.  11  wire;  but  as  this  size  is  not  carried  in 
stock  we  must  use  No.  10.  From  the  second  story  to  the  third 
we  could  use  No.  12  wires. 

For  almost  all  buildings  lighted  from  a  central  station  the 
lamp  circuits  will  not  usually  require  larger  than  No.  14  wire, 
so  that  about  the  only  wires  which  the  architect  needs  to  look 
after  are  the  wires  which  run  to  the  distribution  cabinets. 

Switches, — A  switch  is  a  device  for  opening  or  closing  a 
circuit  at  will  other  than  at  the  fixture. 

In  the  better  class  of  buildings  most  if  not  all  of  the  ceiling 
lights  are  controlled  by  switches  placed  at  a  convenient  place 
on  a  side  wall.  Lights  may  be  controlled  at  any  distance  from 
the  fixture  by  running  a  switch  loop. 

For  controlling  either  a  single  lamp  or  fixture,  or  any  number 
of  lamps,  a  switch  loop  is  run  as  shown  on  circuits  A  and  C, 
Fig.  10,  also  by  Fig.  3;  one  side  of  the  loop  must  be  connected 
with  one  of  the  distributing  wires  and  the  other  side  to  the 
lamp. 

When  a  number  of  lamps  are  to  be  controlled  by  one  switch, 
as  in  the  case  of  hall  lights,  and  the  lamps  in  large  rooms,  such 
as  churches,  theatres,  concert  halls,  etc.,  a  separate  circuit  is 
usually  run  for  those  lamps,  and  a  switch  anywhere  in  one  of 
the  distributing  lines  will  turn  on  or  off  all  of  the  lights. 

As  the  underwriters  do  not  permit  more  than  twelve  16-c.p. 
lamps  on  one  circuit,  not  more  than  twelve  lamps  can  be  con- 
trolled by  one  switch,  except  where  the  switch  is  placed  on  the 
mains. 


SWITCHES  AND  SWITCH  LOOPS. 


1333 


Second  Story 
Eloor 


It  Is  also  practicable  to  control  one  lamp  from  two  or  three 
places.  Thus  by  a  duplex  or  three- 
poirr  switch  and  propei  wiring,  a 
lamp  may  be  lighted  or  turned  off 
fTom  either  the  first  or  second  story 
at  will.  By  means  of  two  three-point 
switches  and  one  four-point  switch  a 
first-story  hall  lamp  may  be  controlled 
at  will  from  either  the  first,  second, 
or  third  stories.  Fig.  13  shows  one 
method  of  wiring  for  controlling  a 
hall  light  from  first  and  second  stories. 
With  the  switches  in  the  position 
shown  the  circuit  is  broken,  as  there 
is  no  connection  between  the  lamps 
and  line  B  By  turning  either  switch 
a  connection  is  made  with  line  B  and 
the  current  will  flow.* 


First  Story 


Fig.  13 


Kinds  of  Switches. — For  controlling  lamps  from  one  point 
three  kinds  of  switches  are  used,  viz.,  snap,  push-button,  and 
knife  switches.  When  less  than  eight  lamps  are  controlled  by 
the  switch,  a  push-button  switch  is  commonly  used  where  a 
neat  appearance  is  desirable,  and  in  places  where  this  is  of  no 
importance,  a  snap  switch  is  used,  as  it  is  the  cheaper. 

Where  a  circuit  of  twelve  or  more  lamps  is  controlled  by  a 
switch,  a  d.p.  (double  pole)  knife 
switch  (Fig.  14)  is  commonly 
used,  being  generally  placed  in  a 
cabinet. 

Knife  switches  should  always 
be  used  on  main  wires.  Snap 
and  push-button  switches  are 
made  both  single  and  double 
pole.  A  single-pole  switch  opens 
only  one  side  of  the  circuit  and 
a  double-pole  switch  both  sides. 

A  d.p.  knife  switch  necessarily  opens  both  sides,  and  when 
used  on  a  three-wire  system  it  must  have  three  poles. 

Double-pole  snap  and  push-button  switches  are  seldom  used 
for  less  than  twelve  lamps. 

*  For  method  of  wiring  for  controlling  lamps  from  three  or  more  points 
see  p.  41,  §  27,  vol.  13-  International  Library  of  Technology. 


Fig.  14 

Common  Knife  Switch. 


1334  ELECTRIC-LIGHT  WIRING. 

Duplex  switches  (sometimes  called  three-point  switches)  are 
usually  of  the  push-button  type. 

Conduit  Systems. — As  weather-proof  or  rubber-covered 
wire  cannot  be  run  in  brick  walls  or  floors  of  brick,  terra-cotta, 
or  concrete  without  some  protection  other  than  the  covering 
of  the  wires,  it  is  necessary  in  such  places  to  run  the  wires  in 
tubes  or  conduits,  and  in  fireproof  buildings  all  of  the  lighting 
wires  are  generally  run  in  a  system  of  conduits. 

Kinds  of  Conduits. — There  are  five  kinds  of  interior  conduits 
now  in  common  use,  viz. : 

1.  Brass-covered  conduit,  which  is  made  of  paper  wound  to 
form  a  tube,  coated  with  tar  on  the  inside,  arid  covered  with  a 
thin  shell  of  brass  on  the  outside. 

2.  Circular-loom  tube,   a  flexible  woven   tube   treated  with 
insulating  material  that  makes  it  hold  its  shape.     Although  it 
has  no  metal  covering,  it  is  stronger  than  the  brass-covered 
conduit  and  is  more  convenient  to  use. 

3.  Unlined  iron  pipe. 

4.  Lined  iron  pipe. 

5.  Flexible   armored   conduit,  made   of   metal   ribbon  wound 
spirally. 

For  regular  conduit  systems  only  iron  piping  of  the  same 
thickness  as  ordinary  gas  piping  is  approved  by  the  under- 
writers. 

The  circular-loom  and  flexible-steel  conduit  may  be  used 
in  dry  places  and  for  outlets  through  plaster  if  it  extends  back 
to  the  nearest  porcelain  knob  holding  the  wire  which  the  con- 
duit covers. 

The  brass-covered  conduit  was  at  one  time  extensively 
used,  but  its  use  is  now  confined  principally  to  protecting 
exposed  risers  on  dry  walls. 

Unlined  iron  pipe  must  be  galvanized,  coated,  or  enamelled 
on  the  inside;  lined  iron  pipe  must  have  an  insulating  lining 
•gV  in.  thick  firmly  secured  to  the  pipe. 

Iron  conduit  whether  lined  or  unlined  is  installed  in  the 
same  manner  as  a  good  job  of  gas  fitting,  except  that  for  con- 
duits the  pipe  may  be  bent  to  a  curve  and  no  elbow  can 
be  used  having  less  than  3J-in.  radius  for  the  inner  edge. 
Wherever  branches  are  taken  off,  junction  boxes  must  be  pro- 
vided, and  every  outlet  must  have  an  approved  outlet  box  or 
plate. 


NATIONAL  ELECTRICAL  CODE.  1335 

National  Electrical  Code. — The  National  Board  of  Fire 
Underwriters,  in  conjunction  with  committees  from  the  national 
associations  of  architects,  electrical,  mechanical,  and  railway 
engineers,  have  prepared  a  code  of  rules  and  requirements  for 
the  installation  of  electrical  lighting  which  is  the  generally 
recognized  standard  and  with  which  all  interior  wiring  must 
comply  if  it  is  desired  to  obtain  insurance  on  the  building. 
This  code  has  also  been  made  a  part  of  the  ordinances  of  most 
of  the  larger  cities. 

The  National  Board  of  Underwriters  also  publish,  semi- 
annually,  a  supplement  to  the  National  Electrical  Code  which 
contains  a  list  of  all  articles  that  have  been  examined  and 
approved  for  use  in  connection  with  the  code,  together  with 
the  names  of  the  manufacturer.  Articles  not  included  in  this 
list  will  not  be  passed  by  the  inspectors.  Copies  of  the  code 
and  supplement  can  be  obtained  from  the  nearest  Under- 
writers' Inspection  Bureau,  or  by  writing  to  the  Underwriters 
Laboratories,  67  East  21st  Street,  Chicago.  The  following 
requirements  apply  to  almost  every  installation,  and  every 
architect  should  be  conversant  with  them. 

EXTRACTS  FROM  THE  NATIONAL  ELECTRICAL  CODE.* 

1.  All  wire  for  concealed  work  must  be  of  the  best  approved 
rubber-covered  brands,  as  shown  in  List  of  Fittings.     No  wire 
smaller  than  No.  14  B.  &  S.  gauge  to  be  used. 

2.  Where  wires  are  concealed  and  run  parallel  to  joists  they 
must  be  supported  on  porcelain  knobs  which  hold  the  wires 
at  least  1  in.  from  woodwork  or  surface  wired  over.     Knobs 
must  be  securely  fastened  and  must  be  placed  every  4J  ft.  apart. 
Where  wires  are  run  through  joists  they  must  be  bushed  with 
porcelain  tubes  the  entire  width  of  joists.     All  wires  must  be 
drawn  tight,  so  as  to  have  all  slack  removed. 

3.  In  concealed  work  all  wires  must  be  separated  from  each 
other  by  at  least  5  ins.      Where  wires  run  down  partitions,  espe- 
cially partitions  formed  by  2X4  studding,  the  wires   must  he 
so  supported  as  to  run  in  centre  of  partition.     If  more  than  two 
wires  are  run   down  partition  between  studs,   they    must    be 
separated  by  at  least  5  ins. 

*  The  numbers  here  given  do  not  correspond  with  those  in  the  code,  and 
several  of  the  rules  are  much  abridged.  They  are  intended  to  give  tha 
substance,  rather  than  the  exact  language. 


1336  /  ELECTRIC-LIGHT  WIRING. 

4.  Where  wires   pass   through  floors   they   must   be  bushed 
with  porcelain  tubes  and  have  a  floor  tube  or  additional  bush- 
ing taped  securely  in  place  at  floor. 

5.  All  joints  must  be  securely  soldered  and  taped.     A  splice 
to  be  approved  must  be  the  regular  W.  U.  telegraph  joint  and 
must  have  at  least  five  turns  of  wire  on  each  side  where  they 
join.     Joints  to  be  properly  taped  require  where  rubber-covered 
wire -is  used,  first  to  be  taped  with  rubber  tape  and  then  with 
friction  tape. 

6.  Where  wires  enter  the  building  they  must  be  provided 
with  a  drip  loop. 

7.  There  must  be  a  main  cut-out  and  switch  installed  in  an 
easily  accessible  place,  as  near  as  possible  to  point  where  wires 
enter   building.      (This   will   require   that    cut-out    and   switch 
be  placed  where  there  is  no  need  of  a  12-ft.  ladder  to  reach 
them.) 

8.  Every  lighting  circuit  of  660  watts  must  be  protected  by 
a  cut-out.     This  will  limit  the  number  to  twelve  16-c.p.  lights 
on  a  two-wire  110- volt  circuit,  or  twenty  16-c.p.  lights  on  a 
three-wire  220-volt  circuit. 

9.  All  cut-outs   must   be  placed  in  an   asbestos-lined  cabinet. 
Asbestos  to  be  at  least  J  in.  in  thickness  and  securely  held  in 
place  by  shellac  and  tacks.     Lumber  of  which  cabinet  is  made 
must  be  at  least  f  in.  in  thickness.     Cabinet  must  be  furnished 
with  snug-fitting  door;    door  to  be  hung  by  strong  hinges  and 
to  be  furnished  with  a  suitable  catch. 

10.  Cut-outs  to  be  approved  must  be  of  the  plug  and  car- 
tridge type. 

11.  Enclosed  arc  lamps  and  incandescent  lamps  must  not  be 
placed  on  same  circuit.     Arcs  must  be  on  separate  circuits  by 
themselves.     Each  arc  light  must  be  protected  by  an  approved 
cut-out.     Cut-out  to  be  placed  in  an  asbestos-lined  cabinet. 

12.  The  practice  of  using  fused  rosettes  will  not  be  approved. 

13.  Where  wires  run  down  side  wall  they  must  be  protected 
from  mechanical  injury. 

14.  All  outlets  must  be  made  to  conform  to  rule  22  e,  p.  24, 
National  Electrical  Code. 

15.  Fans  or  lights  in  series  will  not  be  approved, 

16.  Runs  of  lamp  cord  will  not  be  approved.     Lamp  cord 
is   designed   to   be   used   for   drops   only.     Ordinary   insulated 
wire  must  be  run  to  place  desired. 


GENERAL  SUGGESTIONS.  1337 


General  Suggestions. 

Preface  to  the  National  Electrical  Code. 

In  all  electric  work  conductors,  however  well  insulated,  should 
always  be  treated  as  bare,  to  the  end  that  under  no  conditions, 
existing  or  likely  to  exist,  can  a  grounding  or  short  circuit 
occur,  and  so  that  all  leakage  from  conductor  to  conductor, 
or  between  conductor  and  ground,  may  be  reduced  to  the  mini- 
mum. 

In  all  wiring  special  attention  must  be  paid  to  the  mechanical 
execution  of  the  work.  Careful  and  neat  running,  connecting, 
soldering,  taping  of  conductors,  and  securing  and  attaching 
of  fittings,  are  specially  conducive  to  security  and  efficiency, 
and  will  be  strongly  insisted  on. 

In  laying  out  an  installation,  except  for  constant-current 
systems,  the  work  should,  if  possible,  be  started  from  a  centre 
of  distribution,  and  the  switches  and  cut-outs,  controlling  and 
connected  with  the  several  branches,  be  grouped  together  in  a 


Main  Fuse  Block  Potential  Wire 

Outside  Wall 

Fig.  15 

safe  and  easily  accessible  place,  where  they  can  be  readily  got 
at  for  attention  or  repairs.  The  load  should  be  divided  as 
evenly  as  possible  among  the  branches,  and  all  complicated 
and  unnecessary  wiring  avoided. 

The  use  of  wireways  for  rendering  concealed  wiring  per- 
manently accessible  is  most  heartily  indorsed  and  recommended; 
and  this  method  of  accessible  concealed  construction  is  advised 
for  general  use. 

Architects  are  urged,  when  drawing  plans  and  specifications, 
to  make  provision  for  the  channelling  and  pocketing  of  buildings 
for  electric-light  or  power  wires,  and  in  specifications  for  electric 
gas  lighting  to  require  a  two-wire  circuit,  whether  the  building 
is  to  be  wired  for  electric  lighting  or  not,  so  that  no  part  of  the 
gas  fixtures  or  gas  piping  be  allowed  to  be  used  for  the  gas- 
lighting  circuit. 


1338  ELECTRIC-LIGHT  WIRING. 

Fig.  15  shows  a  common  arrangement  of  main  cut-out, 
switch,  and  metre,  to  comply  with  rule  7,  p.  1336.  The  main 
cut-out  and  switch  should  be  as  near  as  possible  to  the  outside 
wall,  but  the  metre  may  be  at  some  distance  from  the  switch 
if  desirable  for  any  reason. 

Specifications  for  Interior  Wiring. 

Specifications  for  interior  wiring  should  provide: 

1.  That   the   wiring   shall   be   installed   in   accordance   with 
the  latest  rules  and  requirements  of  the  National  Board  of  Fire 
Underwriters,  the  local  ordinances,  and  the  rules  of  the  local 
electric  light  company,  where  current  is  to  be  taken  from  the 
public  mains. 

2.  No  electrical  device  or  material  of  any  kind  to  be  used 
that  is  not  approved  by  the  Underwriters'  National  Electric 
Association,  and  all  articles  must  have  the  name  or  trade  mark 
of  the  manufacturer  and  the  rating  in  volts  and  amperes  or 
other  proper  units  marked  where  they  may  readily  be  observed 
after  the  device  is  installed. 

Requirements  1  and  2  are  sufficient  to  insure  a  safe  installa- 
tion. 

3.  Contractor  must   obtain   a   satisfactory   certificate   of  in- 
spection from  the  city  inspector  or  from  the  inspector  of  the 
local  board  of  fire  underwriters. 

4.  If  the  wires  are  to  run  in  a  conduit  system  it  should  be 
so  specified.     When  a  conduit  system  is  used,  the  wires  should 
not  be  drawn  in  until  after  the  plastering  is  dry. 

5.  Size  of  Wires. — The  best  method  is  to  specify  the  size  of 
all  wires,  no  wire  to  be  less  than  No.  14  B.  &.  S  gauge,  but  if 
the  architect  does  not  care  to  do  this,  the  following  clause  is 
sufficient,  provided  he  can  have  confidence  that  the  contractor 
will  comply  with  it:  "All  wires  must  be  of  such  size  that  the 
drop  in  potential  at  farthest  outlet  shall  not  exceed  2%  under 
maximum  load." 

(Wiring  specifications  for  buildings  having  their  own  generating 
plant  should  be  prepared  by  an  expert.) 

6.  Cut-out  cabinets  and  where  they  are  to  be  placed;    also 
location  of  main-line  cut-out  and  fuse. 

(For  buildings  containing  more  than  forty  lights,  one  dis- 
tributing point  is  generally  sufficient,  although  in  large  houses 
it  is  often  convenient  to  have  a  cut-out  cabinet  on  each  floor.) 


SPECIFICATIONS  AND  COSt.  1339 

7.  Number  and  kind  of  switches.  All  outlets  should  be 
marked  on  the  plans,  and  the  number  of  lights  indicated  by 
figures  1,  2,  3,  4,  etc.,  as  on  Fig.  11.  The  location  of  all  switches 
for  controlling  lights  should  also  be  indicated  on  the  plans. 

Approximate  Cost  of  Wiring  for  Incandescent  Lighting. — 
Approximate  estimates  of  the  cost  of  wiring  buildings  for  electric 
lighting  are  usually  based  on  the  number  of  outlets  (not  lamps). 
The  actual  cost  will  depend  upon  the  number  of  pounds  of  wire 
required,  the  kind  and  number  of  switches,  character  of  cut-out 
cabinets,  etc.,  and  the  time  required  to  do  the  work,  so  that 
a  close  estimate  cannot  be  made  without  plans  and  specifica- 
tions. Again,  wages  and  prices  of  material  vary  to  a  consider- 
able extent  in  different  portions  of  the  country,  so  that  an 
estimate  that  would  be  about  right  for  one  locality  would  not 
suffice  for  another. 

The  following  figures,  however,  will  enable  any  one  to  form  an 
approximate  iclea  of  what  any  proposed  wiring  job  will  cost. 

For  new  houses  of  less  than  seventeen  outlets  or  twenty-five 
lamps,  with  no  switches  except  main  switch  and  a  rough  cut-out 
box  lined  with  asbestos,  allow  $1.50  per  outlet. 

For  same  class  of  work,  25  to  100  lamps,  allow  $1.75  to  $2.00 
per  outlet. 

The  extra  labor  involved  in  wiring  old  buildings  will  add 
from  10  to  50  per  cent,  to  the  above  figures. 

For  each  switch  loop  with  a  single-pole  snap  switch  add 
$1.50  to  $1.75. 

For  each  switch  loop  with  single-pole  push-button  switch 
add  $2.25  to  $2.50. 

For  each  lamp  controlled  by  duplex  switches  add  $5  to  $6. 

For  each  hardwood  cut-out  cabinet  with  door  and  lock  add 
from  $7  up  according  to  number  of  circuits  and  finish. 

Iron  cut-out  cabinets  cost  from  $8.50  up. 

Ordinary  exposed  wiring,  as  in  factories,  can  usually  be  run 
for  $1.00  to  $1.75  per  drop,  including  rosettes,  cord,  and  sockets, 
the  cost  depending  very  largely  upon  how  closely  the  drops 
are  spaced. 

Small  installations  with  iron-armored  conduit  will  probably 
cost  from  $5  to  $6  per  outlet.  Large  installations  will  cost 
somewhat  less. 

A  private  lighting  plant  of  200  lamps,  wired  on  the  concealed 
knob  and  tube  system,  will  cost  from  $1250  to  $1500,  and  a 
similar  plant  with  600  lamps  will  cost  from  $2500  to  $3000 


1340  ELECTRIC-LIGHT  WIRING. 

These  prices  include  engine,  dynamo-switchboard,  etc. ,  complete, 
and  wiring,  but  no  switches  for  controlling  lamps. 

The  iron-armored  conduit  system  will  add  about  $2.75  per 
outlet. 

None  of  the  above  estimates  include  the  cost  of  fixtures  except 
in  the  case  of  exposed  wiring. 

Drop  cord  and  'sockets  cost  about  90  cts.  per  lamp.  Single- 
lamp  fixtures  may  be  purchased  from  $1.25  upwards;  double- 
lamp  fixtures  from  $2.00  upwards.  Combination  fixtures 
cost  about  25  per  cent,  more  than  straight  electric  fixtures. 

The  price  of  rubber-covered  wire  varies  from  $8.00  to  $60.00 
per  1,000  ft.  according  to  size,  and  of  weather-proof  wire  from 
16  cts.  to  25  cts.  per  pound. 


SPECIFIC  GRAVITIES  AND  WEIGHTS.       1341 

SPECIFIC   GRAVITIES   AND   WEIGHTS   OF   VARIOUS 
SUBSTANCES* 


The  Basis  for  Specific  Gravities  is  Pure  Water  at 

62°  Fahr.,  Barometer  30  Inches. 
Weight  of  1  Cubic  Foot,  62.355  Pounds. 


Average 

Sp.  Gr. 

Water  =  1. 


Average 
Weight  of 
1  Cu.  Ft., 

Pounds. 


Air,  atmospheric  at  60°  F.,  under  pressure 
of  one  atmosphere,  or  14.7  Ibs.  per  sq. 

in. ,  weighs  ^th  as  much  as  water 

Aluminum 

Anthracite,  1.3  to  1.84;  of  Penn.,  1.3  to  1.7 

broken,  of  any  size,  loose 

"        moderately  shaken.  .  .  . 
"  "        heaped  bushel,  loose,  77 

to  83  Ibs 

"        a  ton  loose  occupies  40 

to  43  cu.  ft 

Antimony,  cast 

native 

Ash,  perfectly  dry  (see  note  p.  1344) 

"     American  white  dry  (see  note  p.  1344) . . 

Ashes  of  soft  coal,  solidly  packed 

Asphaltum,  1  to  1.8 

Brass  (copper  and  zinc),  cast,  7.8  to  8.4.  . .  . 

"      rolled 

Brick,  best  pressed 

"       common  and  hard 

"       soft  inferior 

Brickwork,  pressed  brick,  fine  joints 

medium  quality 

coarse,  inferior,  soft 

"  at  125  Ibs.  per  cubic  foot,  1  cu. 

yd.   equals    1.507    tons  and 

17.92  cu.  ft.  equal  1  ton 

Bronze,  copper,  8,  tin  1  (gun-metal) 

Cement,  hydraulic.    American,  Rosendale, 

ground,  and  loose  (see  p.  192).  .  . 

hydraulic.    Portland,  loose  (see  p. 

'197) .» 

Charcoal  of  pines  and  oaks 

Chalk 

I  Cherry,  perfectly  dry  (see  note  p.  1344).  .  . . 
Chestnut,  perfectly  dry  (see  note  p.  1344).  . 

/Clay,  potters',  dry,  1.8  to  2.1 

"      dry  in  lump,  loose 


.00123 
2.6 
1.5 


6.70 
6.67 

.752 
.61 


1.4 

8.1 
8.4 


8.5 


2.5 

.672 
.660 
1.9 


.0765 
162 
93.5 
52  to  56 
56  to  60 


418 

416 

47 

38 

40  to  45 
87.3 
504 
524 
150 
125 
100 
140 
125 
100 


529 
56 

85  to  90 

15  to  30 

156 

42 

41 

119 

63 


*  The  values  in  this  table  are  taken  largely  from  a  table  compiled  by 
the  Cambria  Iron  Co. 


1342       SPECIFIC  GRAVITIES  AND  WEIGHTS. 


SPECIFIC   GRAVITIES  AND   WEIGHTS   OF   VARIOUS 
SUBSTANCES.— Continued. 


The  Basis  for  Specific  Gravities  is  Pure  Water  at 

62°  Fahr.,  Barometer  30  Inches. 
Weight  of  1  Cubic  Foot,  62.355  Pounds. 


Average 

Sp.  Gr. 

Water  =  1. 


Coal,  anthracite;  see  Anthracite. 

"      bituminous,  solid,  1.2  to  1.5 1 .35 

"      bituminous,  solid,  Cambria  Co.,  Pa., 

1.27-1.34 

"      bituminous,  broken,  of  any  size,  loose . 

"      bituminous,  moderately  shaken 

"      bituminous,  a  heaped  bushel,  loose, 

70  to  78 

"      bituminous,  1  ton  occupies  43  to  48 

cubic  feet 

Coke,  loose,  good  quality 

loose,  a  heaped  bushel,  35  to  42 

"      1  ton  occupies  SO  to  97  cu.  ft 

Corundum,  pure,  3.8  to  4 3.9 

Copper,  cast,  8.6  to  8.8 8.7 

rolled,  8.8  to  9 8.9 

Cork,  dry  (see  note  p.  1344) 24 

Cypress,  American  (see  note  p.  1344) 55 

Earth,  common  loam,  perfectly  dry,  loose  .  .  . 
perfectly  dry,  shaken  . 
perfectly  dry,  rammed, 
slightly  moist,  loose  .  . 
more  moist,  loose.  .  .  . 
more  moist,  shaken  .  . 
more  moist,  packed  .  . 
as  soft  flowing  mud  .  . 
as  soft  flowing  mud 
well  pressed  .... 

Elm,  perfectly  dry  (see  note  p.  1344) 56 

Flint 2.6 

Glass,  2.5  to  3.45. 2.98 

' '       common  window 2 . 52 

Gneiss,  common,  2.62  to  2.76 2 . 69 

"        in  loose  piles «.  . 

Gold,  cast,  pure  or  24  karat 19  . 258 

"      pure,  hammered 19.5 

Granite,  2.56  to  2.88 2 . 72 

Greenstone,  trap,  2.8  to  3.2 3 .00 

Gypsum,  plaster  of  Paris,  2.24  to  2.30 2.27 

Hay,  loose 

"      in  stacks,  about  512  cu.  ft.  to  ton.  .  .  . 
Hemlock,  perfectly  dry  (see  note  p.  1344).  .  .         .4 

Hickory,          "  "       "      "        "        85 

Ice,  .917  to  .922 92 


SPECIFIC  GRAVITIES  AND  WEIGHTS.        1343 


SPECIFIC   GRAVITIES   AND   WEIGHTS   OF  VARIOUS 
SUBSTANCES  .—Continued. 


The  Basis  for  Specific  Gravities  is  Pure  Water  at 

62°  Fahr.,  Barometer  30  Inches. 
Weight  of  1  Cubic  Foot,  62.355  Pounds. 


Average 

Sp.Gr. 

Water  =  1. 


Iron,  cast,  6.9  to  7.4 

"      gray  foundry,  cold 

"         "  "     "    molten 

"      wrought 

Lead,  commercial 

Lignum- vitse  (dry) 

Limestone  and  marbles 

Lime,  quick 

"      quick,  ground,  well  shaken,  per  struck 

bushel,  80  Ibs 

"      quick,   ground,   thoroughly  shaken, 

per  struck  bushel,  93f  Ibs 

Locust,  dry  (see  note  p.  1344) 

Mahogany,  Spanish,  dry  (see  note  p.  1344).  . 
Honduras,  dry  (see  note  p.  1344) 

Maple,  dry  (see  note  p.  1344) 

Marbles  (see  Limestone). 
Masonry   of   granite   or   limestones,   well- 
dressed 

of  granite,  well-scabbled  mortar 
rubble;  about  i  of  mass  will  be 

mortar 

of  gr'nite,  well-scabbl'd  dry  rubble 
of  granite,  roughly  scabbled  mor- 
tar rubble;  about  I  to  J  of  mass 

will  be  mortar 

of  granite,  scabbled  dry  rubble  .  .  . 
of  sandstone,  J  less  than  granite  .  . 
Masonry  of  brickwork  (see  Brickwork). 

Mercury  at  32°  Fahr 

Mica,  2.75  to  3.1 

Mortar,  hardened,  1.4  to  1.9 

Mud,  dry,  close 

"      wet,  moderately  pressed 

"     fluid 

Oak,  live,  perfectly  dry,  .88-1.02  (see  note 

p.  1344) 

"      white,  perfectly  dry,  .66  to  .88  (see 

note  p.  1344) 

"      red,  black,  perfectly  dry 

Petroleum 

Pine,  white,  perfectly  dry,  .35  to  .45  (see 
note  p.  1344) 


15 
21 


6.94 


7. 
11. 


69 
38 
65-1.33 

2.6 

1.5 


.71 
.85 
.56 
.79 


13.62 
2.93 
1.65 


.95 

.77 


.878 
.40 


Average 
Weight  of 
ICu.  Ft., 
Pounds. 


446 
450 
433 
480 
709 . 6 
41  to  83 
164.4 
95 

64 

75 
44 
53 
35 
49 


165 


154 
138 


150 
125 


849 

183 

103 

80  to  110 
110  to  130 
104  to  120 

59.3 

48 

32  to  45 
54.8 

25 


1344       SPECIFIC  GRAVITIES  AND  WEIGHTS. 

SPECIFIC   GRAVITIES   AND   WEIGHTS   OF  VARIOUS 
SUBSTANCES.— Continued. 


The  Basis  for  Specific  Gravities  is  Pure  Water  at 

62°  Fahr.,  Barometer  30  Inches. 
Weight  of  1  Cubic  Foot,  62.355  Pounds. 


Average 

Sp.  Or. 

Water  =  1. 


Pine,  yellow,  Northern,  perfectly  dry,  .48 

to  .62  (see  foot-note).  . .55 

"      yellow,  Southern,  perfectly  dry,   .64 

to  .8  (see  foot-note) 72 

Pitch 1.15 

Poplar,  dry  (see  foot-note) .47 

Platinum 21.5 

Quartz 2.65 

Rosin 1.10 

Salt,  coarse  (per  struck  bushel,  Syracuse, 

N.  Y.,  561bs.) 

Sand,  of  pure  quartz,  perfectly  dry  and  loose 
"  voids  full  of  water.  .  .  . 
"  very  large  and  small 

grains,  dry 

Sandstone,  2.1  to  2.73,  131  to  171 2.41 

quarried  and  piled,  1  measure 
solid  makes  1J  (about)  piled.  . 

Snow,  fresh  fallen 

"       moistened,  compacted  by  rain 

Sycamore,  perfectly  dry  (see  foot-note) .59 

Shales,  red  or  black,  2.4  to  2.8 2.6 

Silver 10.5 

Slate,  2.7  to  2.9 2.8 

Soapstone,  2.65  to  2.8 2 . 73 

Spruce,  perfectly  dry  (see  foot-note) .4 

Steel 7.85 

Sulphur 2.00 

Tallow 94 

Tar 1 

Tin,  cast,  7.2  to  7.5 7.35 

Walnut,  black,  perfectly  dry  (see  foot-note) .  .         .61 
Water,  pure  rain,  distilled,  at  32°  F.,  bar. 

30  ins 

"          "       "  "  at  62°  F.,bar. 

30  ins 1 

"          "       "  "  at  212°  F.,  bar. 

30  ins 

sea,  1.026  to  1.030 1.028 

Zinc  or  spelter,  6.8  to  7.2 |      7.00 


Note. — Green  timbers  usually  weigh  from  one  fifth  to  nearly  one  half  more 
than  dry;    ordinary  building  timbers,  tolerably  seasoned,  one  sixth  more. 


WIRE  GAUGES,  1345 


Specific  Gravity. 

The  specific  gravity  of  a  substance  is  the  number  which  ex- 
presses the  ratio  that  the  weight  of  a  given  volume  of  the  sub- 
stance bears  to  the  weight  of  the  same  volume  of  distilled  water 
at  a  temperature  of  62°  Fahr. ;  or,  the  specific  gravity  of  a  body 
is  equal  to  its  weight  divided  by  the  weight  of  an  equal  volume 
of  water.  The  specific  gravity  of  a  substance,  multiplied  by  the 
weight  of  a  cubic  foot  of  water,  will  give  the  weight  of  a  cubic 
foot  of  the  given  substance-. 

The  weight  of  a  cubic  foot  of  water,  at  62°  Fahr.  and  at  the 
sea-level,  is  about  62.355  Ibs:* 

The  specific  gravity  of  a  solid  substance  may  be  determined 
by  first  weighing  a  portion  of  it  in  air  and  then  in  water  and 
dividing  the  weight  in  air  by  the  loss  of  the  weight  in  water; 
the  quotient  is  the  specific  gravity  required. 

EXAMPLE. — A  piece  of  granite  weighs  5.32  Ibs.  in  air;  when 
immersed  in  water  it  weighs  3.32  Ibs. 

Weight  in  air  (5.32  Ibs.  divided  by  loss  of  weight  in  water 
(2  Ibs.)  =  2.66,  the  specific  gravity. 

2.66X  62.355  Ibs.  =  165.84  Ibs.  =  weight  per  cubic  foot. 

Wire  Gauges. 

A  "wire  gauge"  is  a  method  of  designating  the  diameter  of 
wires  or  the  thickness  of  sheets  of  metal  by  the  numbers  of  a 
table  arranged  on  a  certain  fixed  basis.  There  are  now  nine  or 
ten  different  gauges,  resulting  in  great  confusion.  The  table  on 
the  following  page  gives  the  diameter  of  the  gauges  in  common 
use.  The  only  legal  gauge  in  this  country  is  the  U.  S.  standard 
gauge,  described  on  p.  1438.  It  is  used  by  most  of  the  manu- 
facturers of  sheet  iron  and  steel  and  tin-plate.  The  Brown  & 
Sharpe  gauge  is  commonly  used  for  designating  size  of  copper 
wires  (see  p.  1320) ;  also  for  sheet  copper  and  brass. 

The  American  Steel  and  Wire  Co.  uses  the  old  Washburn  & 
Moeii  gauge  for  all  their  steel  and  iron  wire  and  also  for  wire 
nails.  The  sectional  areas  for  this  gauge  are  given  on  p.  1349. 

When  placing  orders  for  sheets  and  wire,  it  is  always  best  to 
specify  the  weight  per  square  or  lineal  foot  or  the  thickness  or 
diameter  in  thousandths  of  an  inch. 

*The  text-books  differ  slightly  in  regard  to  this  value. 


1346         WIRE  AND  SHEET  METAL  GAUGES. 


WIRE  AND  SHEET-METAL  GAUGES  COMPARED. 

(In  decimals  of  an  inch.) 


| 

o§ 

M 

1i« 

g«i  £«£  . 

g 

|B 

t-f—i  O 
O  cS  .^ 

oS 

g|£ 

eb 

F§OQ  o 

S  Qi2«fc  §o 

w 

i^ 

^  g>j£ 

O 

e3 

PQ 

...  o   02  o3 

CH   « 

GO 

'C  ,  ~i  , 

•s 

to  2 

(H  0> 

o  a 

^t§*2 

8  bfl 

•51 

S"^  ^ 

Number 

||| 

1:! 

Ja 

a  6  g"C.fa 

CO 

p 

$1 

7-0 

.5 

.500 

6-0 

.  46875 

.4600 

.464 

5-0 

.4375 

4300 

.450 

'432 

4-0 

.454 

.460000 

.40625 

'.  3938 

.400 

!400 

3-0 

.425 

.409642 

.375 

.3625 

.360 

'  '!6315' 

372 

2-0 

.380 

.  364796 

.  34375 

.3310 

.330 

.0447 

.348 

0 

.340 

.324861 

.3125 

.3065 

.305 

.0578 

.324 

1 

.300 

.  289297 

.28125 

.2830 

.285 

.0710 

.300 

2 

.284 

.  257627 

.265625 

.2625 

.265 

.08*12 

.276 

3 

.259 

.229423 

.25 

.2437 

.245 

.0973 

.252 

4 

.238 

.  204307 

.234375 

.2253 

.225 

.  1  105 

.232 

5 

.220 

.  181940 

.21875 

.2070 

.205 

.1236 

.212 

6 

.203 

.  162023 

.203125 

.1920 

.190 

.1368 

.192 

7 

.180 

.  144285 

.1875 

.1770 

.175 

.1500 

.176 

8 

.165 

.  128490 

.171875 

.1620 

.160 

.1631 

.160 

9 

.148 

.114423 

.  15625 

.1483 

.145 

.  1763 

.144 

10 

.134 

.101897 

.  140625 

.1350 

.130 

.1894 

.128 

11 

.120 

.090742 

.125 

.1205 

.1175 

.2026 

.116 

12 

.109 

.080808 

.  109375 

.1055 

.105 

.2158 

.104 

13 

.095 

.071962 

.09375 

.0915 

.0925 

.2289 

.092 

14 

.083 

.064084 

.078125 

.0800 

.0806 

.2421 

.080 

15 

.072 

.057068 

.0703125 

.0720 

.070 

.2552 

.072 

16 

.065 

.050821 

.0625 

.0625 

.061 

.2684 

.064 

17 

.058 

.045257 

.05625 

.0540 

.0525 

.2816 

.056 

18 

.049 

.040303 

.05 

.0475 

.045 

.2947 

.048 

19 

.042 

.035890 

.04375 

.0410 

.040 

.3079 

.040 

20 

.035 

.031961 

.0375 

.0348 

.035 

.3210 

.036 

21 

.032 

.028462 

.034375 

.03175 

.031 

.3342 

.032 

22 

.028 

.025346 

.03125 

.0286 

.028 

.3474 

.028 

23 

.025 

.022572 

.028125 

.0258 

.025 

.3605 

.024 

24 

.022 

.020101 

.025 

.0230 

.0225 

.3737 

.022 

25 

.020 

.017900 

.021875 

.0204 

.020 

.3868 

.020 

26 

.018 

.015941 

.01875 

.0181 

.018 

.4000 

.018 

27 

,016 

.014195 

.0171875 

.0173 

.017 

.4132 

.0164 

28 

.014 

.012641 

.015625 

.0162 

.016 

.  4263 

.0148 

29 

.013 

.011257 

.0140625 

.0150 

.015 

.4395 

.0136 

30 

.012 

.010025 

.0125 

.0140 

.014 

.4526 

.0124 

31 

.010 

.008928 

.0109375 

.0132 

.013 

.4658 

.0116 

32 

.009 

.007950 

.01015625 

.0128 

.012 

.4790 

.0108 

33 

.008 

.007080 

.009375 

.0118 

.011 

.4921 

.0100 

34 

.007 

.006305 

.00859375 

.0104 

.010 

.5053 

.0092 

35 

.005 

.005615 

.0078125 

.0095 

.0095 

.5184 

.0084 

36 

.004 

.005000 

.00703125 

.0090 

.009 

.5316 

.0076 

37 

.004453 

.006640625 

.0085 

.0085 

.5448 

.  0068 

38 

.  003965 

00625 

.0080 

.008 

.  5579 

0060 

39 

.003531 

'.  0075 

.0075 

.0052 

40 

.003144 

.0070 

.007 

1  5842 

.0048 

SHEETS  OF  STEEL,  COPPER,  AND  BRASS.     1347 


WEIGHT  PER  SQUARE  FOOT  OF  SHEETS  OF  WROUGHT 
IRON,  STEEL,  COPPER,  AND  BRASS. 

(Thickness  by  American  (B.  &  S.)  Gauge.) 


No.  of 
Gauge. 

Thickness 
in  Inches. 

Iron. 

Steel. 

Copper. 

Brass. 

0000 

.46 

18.46 

18.70 

20.84 

19.69 

000 

.4096 

16.44 

16.66 

18.56 

17.53 

00 

.3648 

14.64 

14.83 

16.53 

15.61 

0 

.3249 

13.04 

13.21 

14.72 

13.90 

1 

.2893 

11.61 

11.76 

13.11 

12.38 

2 

.2576 

10.34 

10.48 

11.67 

11.03 

3 

.2294 

9.21 

9.83 

10.39 

9.82 

4 

.2043 

8.20 

8.31 

9.26 

8.74 

5 

.1819 

7.30 

7.40 

8.24 

7.79 

6 

.1620 

6.50 

6.59 

7.34 

6.93 

7 

.  1443 

5.79 

5.87 

6.54 

6.18 

8 

.1285 

5.16 

5.22 

5.82 

5.50 

9 

.1144 

4.59 

4.65 

5.18 

4.90 

10 

.1019 

4.09 

4.14 

4.62 

4.36 

11 

.0907 

3.64 

3.69 

4.11 

3.88 

12 

.0808 

3.24 

3.29 

3.66 

3.46 

13 

.0720 

2.89 

2.93 

3.26 

3.08 

14 

.0641 

2.57 

2.61 

2.90 

2.74 

15 

.0571 

2.29 

2.32 

2.59 

2.44 

16 

.0508 

2.04 

2.07 

2.30 

2.18 

17 

.0453 

1.82 

1.84 

2.05 

1.94 

18 

.0403 

1.62 

1.64 

1.83 

1.73 

19 

.0359 

1.44 

1.46 

1.63 

1.54 

20 

.0320 

1.28 

1.30 

1.45 

1.37 

21 

.0285 

1.14 

1.16 

1.29 

1.22 

22 

.0253 

1.02 

1.03 

1.15 

1.08 

23 

.0226 

.906 

.918 

1.02 

.966 

24 

.0201 

.807 

.817 

.911 

.860 

25 

.0179 

.718 

.728 

.811 

.766 

26 

.0159 

.640 

.648 

.722 

.682 

27 

.0142 

.570 

.577 

.643 

.608 

28 

.0126 

.507 

.514 

.573 

.541 

29 

.0113 

.452 

.458 

.510 

.482 

30 

.0100 

.402 

.408 

.454 

.429 

31 

.0089 

.358 

.363 

.404 

.382 

32 

.0080 

.319 

.323 

.360 

.340 

33 

.0071 

.284 

.288 

.321 

.303 

34 

.0063 

.253 

.256 

.286 

.270 

35 

.0056 

.225 

.228 

.254 

.240 

Specific  gn 
Weight,  cu 
Weight,  cu 

ivity  

7.704 
481.25 

.2787 

7.806 

487.75 
.2823 

8.698 
543.6 
.3146 

8.218 
513.6 
.2972 

bic  feet.  .  . 
bic  ins.  .  .  . 

1348    WEIGHT  OF  LEAD,  COPPER,  AND   BRASS. 


WEIGHT  OF  SHEETS  AND  BARS  OF  LEAD,  COPPER,  AND  BRASS. 

|S|J 

els  3 

(CO      CO 
<MCO<M         (NCO(N         CO         CO         CO         TH         rH 

CO 

03 
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[Round  Bars 
1  Foot  Long. 

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&*) 

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KO 

11 

02  TH 

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OOOOOOOOOOOOrH.   ^(M(M(NCOCO-t^COCi005rHcq^ 

Sheets,  per 
Square  Foot. 

cOr-  icO<M»OCOOOOOOOOOOOOC 

5OOOOOOOOOO 

rs.co  co  t-  <N  co  o  •*  a>  co  b- 

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COPPER. 

Round  Bars 
1  Foot  Long. 

y,  c5  T-I  <N  rt*  i-^  o  "*  oc  65  cu^  >o  >o  oo  co  o  o  >- 

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IfMCOCOtiOCOt-OiOfN 

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Round  Bars 
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SMOOTH  STEEL  WIRE. 


1349 


SIZE  AND  WEIGHT  OF  SMOOTH  STEEL 
WIRE. 

(As  Made  by  the  American  Steel  and  Wire  Company). 


A.  S.  & 
W.  Co. 

Gauge. 

Diam- 
eter 
in 
Decimal 
of  an 
Inch. 

Sectional 
Area, 
Sq.  Ins. 

Approxi- 
mate 
Weight 
of 
100    Feet 
(Lbs.). 

A.S.  & 
W.  Co. 
Gauge. 

Diam- 
eter 
in 
Decimal 
of  an 
Inch. 

Sectional 
Area, 
Sq.  Ins. 

Approxi- 
mate 
Weight 
of 
100    Feet 
(Lbs.). 

000 

.3625 

.1029 

35.05 

16 

.0625 

.00311 

1.042 

00 

.3310 

.0360 

29.22 

17 

.0540 

.00229 

.7778 

0 

.3065 

.0740 

25.06 

18 

.0475 

.00173 

.6018 

1 

.  2830 

.0629 

21.36 

19 

.0410 

.00132 

.4484 

2 

.2625 

.0543 

18.38 

20 

.0348 

.00096 

.3230 

3 

.2437 

.0467 

15.84 

21 

.0317 

.00080 

.2680 

4 

.2253 

.0398 

13.54 

22 

.0286 

.00061 

.2182 

5 

.2070 

.0338 

11.43 

23 

.0258 

.00049 

.1775 

6 

.1920 

.0289 

9.832 

24 

.0230 

.00041 

.1411 

7 

.1770 

.0246 

8.356 

25 

.0204 

.00031 

.1110 

8 

.1620 

.0206 

7.000 

26 

.0181 

.00025 

.08738 

9 

.  14^3 

.0172 

5.866 

27 

.0173 

.00022 

.07983 

10 

.1350 

.0143 

4.861 

28 

.0162 

.00020 

.07 

11 

.1205 

.0113 

3.873 

29 

.0150 

.00017 

.06001 

12 

.1055 

.0086 

2.969 

30 

.0140 

.00015 

.  05228 

13 

.0915 

.0066 

2.233 

31 

.0132 

.00014 

.04647 

14 

.0800 

.0050 

1.707 

32 

.0128 

.00013 

.04370 

15 

.0720 

.0041 

1.383 

33 

.0118 

.00009 

.03714 

Kinds    of  Wire   Manufactured   by  the  American 
Steel  and  Wire  Company. 

Market  wire,  Nos.  40  to  18. 

Annealed  stone  or  weaving  wire,  Nos.  16  to  47. 

Tinned  wire,  Nos.  0  to  18. 

Tinned  stone  wire,  Nos.  18  to  36. 

Gun  screw  wire,  finished  with  great  care  as  regards  round- 
ness and  exactness  to  gauge,  Nos.  50  to  18. 

Machinery  wire,  Nos.  00000  to  18. 

Cast-steel  wire,  J-inch  diameter,  down  to  No.  20. 

Drill  and  needle  steel  wire,  Nos.  12  to  25. 

The  term  " market  wire"  applies  to  the  ordinary  and  most 
used  forms  of  Bessemer  annealed,  bright,  galvanized,  tinned,  and 
coppered  wires. 

Sectional  area,  weight,  and  strength  of  iron  wire  measured  by 
the  Trenton  Iron  Company's  gauge  is  given  on  page  351. 


1350 


WEIGHTS,  AREAS,  ETC.,  OF  BARS. 


WEIGHTS  AND  AREAS  OF  SQUARE  AND  ROUND  BARS 
AND  CIRCUMFERENCES  OF  ROUND  BARS. 

(Weights  are  for  steel,  at  489.6  Ibs.  per  cu.  ft.) 


Thickness 
or 
Diameter 
in  Inches. 

Weight  of 
D  Bar 
1  Foot 
Long. 

Weight  of 
QBar 
1  Foot 
Long. 

Area  of 
DBar 
in  Square 
Inches. 

Area  of 
O  Bar 
in  Square 
Inches. 

Circumfer- 
ence 
of  O  Bar 
in  Inches. 

X 

.013 

.010 

.0039 

.0031 

.1963 

%4 

.021 

.016 

.0061 

.0048 

.2454 

%2 

.030 

.023 

.0088 

.0069 

.2945 

%4 

.041 

.032 

.0120 

.0094 

.3436 

| 

.053 

.042 

.0156 

.0123 

.3927 

%* 

.067 

.053 

.0198 

.0155 

.4418 

%3 

.083 

.065 

.0244 

.0192 

.4909 

l%4 

.100 

.079 

.0295 

.0232 

.  5400 

% 

.120 

.094 

.0352 

.0276 

.5S90 

1%4 

.140 

.110 

.0413 

.0324 

.6381 

%2 

.163 

.128 

.0479 

.0376 

.6872 

1%4 

.187 

.147 

.0549 

.0431 

.7363 

1 

4 

.213 

.167 

.0625 

.0491 

.7854 

17/64 

.240 

.188 

.0706 

.0554 

.8345 

%2 

.269 

.211 

.0791 

.0621 

.8836 

19/64 

.300 

.235 

.0881 

.0692 

.9327 

% 

.332 

.261 

.0977 

.0767 

.9817 

% 

.402 

.316 

.1182 

.0928 

1.0799 

f 

.478 

.376 

.1406 

.1104 

1.1781 

1%3 

.561 

.441 

.1650 

.1296 

1.2763 

% 

.651 

.511 

.1914 

.1503 

1.3744 

1%2 

.747 

.587 

.2197 

.1726 

1.4726 

i 

.850 

.668 

.2500 

.1963 

1.5708 

17/32 

.960 

.754 

.2822  ' 

.2217 

1.6690 

% 

1.076 

.845 

.3164 

.2485 

1.7671 

19/82 

1.199 

941 

.3525 

.2769 

1.8653 

f 

1.328 

1.043 

.3906 

.3068 

1.9635 

% 

1.607 

1.262 

.4727 

.3712 

2.1598 

f 

1.913 

1.502 

.  5625* 

.4418 

2.3562 

% 

2.245 

1.763 

.6602 

.5185 

2.5525 

| 

2.603 

2.044 

.7656 

.6013 

2.74  9 

% 

2.989 

2.347 

.8789 

.  6903 

2.9452 

WEIGHTS,  AREAS,  ETC.,  OF   BARS. 


1351 


WEIGHTS  AND  AREAS  OF  SQUARE  AND  ROUND 
STEEL  BARS. 

(Weights  are  for  steel,  at  489.6  Ibs.  per  eu.  ft.) 


Thickness,  Ins. 

D 

G 

Thickness,  Ins. 

D 

O 

Area. 

Weight 
per 
Foot. 

Area. 

Weight 
per 
Foot. 

Area. 

Weight 
per 
Foot. 

Area. 

Wgt. 
per 
Foot. 

1 

1.000 

3.400 

.785 

2.670! 

3 

9.000 

30.60 

7.069 

24.03 

>JB 

1.129 

3.838 

.887 

3.014! 

1A\  9.379 

31.89    7.366 

25.04 

1.266 

4.303 

.994 

3.379 

i 

9.766 

33.20    7.670 

26.08 

\ 

1.410 

4.795 

1.103 

3.766 

% 

10.16 

34.55 

7.980 

27.13 

i 

1.563 

5.312 

1.227 

4.173 

i 

10.56 

35.92 

8.296 

28.20 

% 

1.723 

5.857 

1.353 

4.600 

% 

10.97 

37.31 

8.618 

29.30 

f 

1.891 

6.423 

1.4^5 

5.049| 

f 

11.39 

38.73 

8.946 

30.42 

JT6 

2.066 

7.026 

1.623 

5.518 

^6 

11.82 

40.18 

9.281 

31.56 

i 

2.250 

7.650 

1.767 

6.008 

\ 

12.25 

41.65 

9.621 

32.71 

%2.441 

8.301 

1.918 

6.520 

%> 

12.69 

43.14    9.968 

33.90 

f  12.641 

8.978 

2.074 

7.051 

f 

13.14 

44.6810.32 

35.09 

% 

2.848 

9.632 

2.237 

7.604 

% 

13.60 

46.24 

10.63 

36.31 

i 

3.063 

10.41 

2.405 

8.178 

i 

14.06 

47.82 

11.05 

37.56 

% 

3.285 

11.17 

2.  580 

8.773 

% 

14.54 

49.4211.42 

38.81 

I 

3.516 

11.95 

2.761 

9.388 

1 

15.02 

51.0511.79 

40.10 

% 

3.754 

12.76 

2.948 

10.02 

% 

15.50 

52.71 

12.18 

41.40 

9 

4.000 

13.60 

3.142 

10.68 

4 

16.00 

54.40 

12.57 

42.73 

# 

4.254 

14.46 

3.341 

11.36 

1A 

16.50 

56.11  12.96 

44.07 

i 

4.516 

15.35 

3.547 

12.06 

i 

17.02 

57.8513.36 

45.44 

% 

4.785 

16.27 

3.75S 

12.78 

% 

17.54 

59.62 

13.77 

46.83 

i 

5.063 

17.22 

3.976 

13.52 

i 

18.06 

61.41 

14.19 

48.24 

% 

5.348 

18.19 

4.200 

14.28 

» 

18.60 

63.2314.61 

49.66 

I 

5.641 

19.18 

4.430 

15.07 

19.14 

65.08 

15.03 

51.11 

% 

5.941 

20.20 

4.666 

15.86 

k 

19.69 

66.95 

15.47 

52.58 

% 
f 

6.250 
6.566 
6.891 

21.25 

22.33 
123.43 

4.909 
5.157 
5.412 

16.69 
17.53 
18.40 

% 

t 

20.25 
20.82 
21.39 

68.85 
70.78 
72.73 

15.90 
16.35 
16.80 

54.07 
55.59 
57.12 

% 

,7.223 

24.56 

5.673 

19.29 

% 

21.97 

74.70 

17.26 

58.67 

I 

7.563 

25.71 

5.940 

20.20 

i 

22.56 

76.71 

17.72 

60.25 

% 

,7.910 

26.90 

6.213 

21.12 

% 

23.16 

78.74 

18.19 

61.84 

7 
'8 

8.266 

28.10 

6.492 

22.07 

i 

23.77 

80.81 

18.67 

63.46 

* 

}8.62S 

29.34 

6.777 

23.04 

% 

24.38 

82.89 

19.15 

65.10 

1352 


WEIGHTS,  AREAS,  ETC.,  OF  BARS. 


WEIGHTS  AND  AREAS  OF  SQUARE  AND  ROUND 
STEEL  "BARS— Continued. 

(Weights  are  for  steel,  at  489.6  Ibs.  per  cu.  ft.) 


s 

1—  I 

b 

0 

§ 
i—  i 

D 

O 

i 
n 

Weight 

Weight 

ff 

§ 

Weight 

Wgt. 

M 

o 
3 

Area. 

Foot. 

Area. 

per 
Foot 

^ 

0 

'£ 

Area. 

per 
Foot. 

Area. 

per 
Foot. 

H 

H 

5 

25.00 

85.00 

19.64 

66.76 

7 

49.00 

166.6 

38.49 

130.9 

« 

25.63 

87.14 

20.13 

68.44 

i 

52.56 

178.7 

41.28 

140.4 

i 

26.27 

89.30 

20.63 

70.14 

) 

56.25 

191.3 

44.18 

150.2 

K 

26.91 

91.49 

21.14 

71.86 

i 

60.06 

204.2 

47.17 

160.3 

i 

27.56 

93.72 

21.65 

73.60 

8 

64.00 

217.6 

50.27 

171.0 

% 

2S.22 

95.96 

22.17 

75.37 

1 

68.06 

231.4 

53.46 

181.8 

28.89 

98.23 

22.69 

77.15 

i 

72.25 

245.6 

56.75 

193.0 

!t 

29.57 

100.5 

23.22 

78.95 

i 

76.56 

260.3 

60.13 

204.4 

i 

30.25 

102.8 

23.76 

80.77 

9 

81.00 

275.4 

63.62 

216.3 

% 

30.94 

105.2 

24.30 

82.62 

1 

85.56 

290.9 

67.20228.5 

§ 

31.64 

107.6 

24.85 

84.49 

\ 

90.25 

306.8 

70.88241.0 

% 

32.35 

110.0 

25.41 

86.38 

1 

95.06 

323.2 

74.66 

253.9 

l 

33.06 

112.4 

25.97 

88.29 

10 

100.0 

340.0 

78.54 

267.0 

% 

33.79 

114.9 

26.54 

90.22 

1 

105.1 

157.2 

82.  52  2.-  0  0 

i 

34.52 

117.4 

27.11 

92.17 

\ 

110.3 

374.9 

86.59294.4 

% 

35.25 

119.9 

27.69 

94.14 

i 

115.6 

392.9 

90.76 

308.6 

6 

36.00 

122.4 

28.27 

96.14 

11 

121.0 

411.4 

95.03 

323.1 

i 

37.52 

127.6 

29.47 

100.2 

i 

126.6 

430.3 

99.40337.9 

39.06 

132  8 

30.68 

104.3 

i 

132.3 

449.6 

103.9 

353  .  1 

I 

40.64 

138.2 

31.92 

108.5 

138.1 

469.4 

108.4 

368.6 

1 

42.25 

143.6 

33.18 

112.8 

12 

144.0 

489.6 

113.1 

384.5 

1 

43.89 

149.2 

34.47 

117.2 

I 

45.56 

154.9 

35.79 

121.7 

i 

47.27 

160.8 

37.12 

126.2 

Stock  sizes  of  round  and  square  bars  vary  by  thirty  sec- 
onds of  an  inch  from  %  in.  to  %  in.  diameter,  by  sixteenths 
from  f  to  2  ins.  diameter,  by  eighths  from  2  to  3  ins.  diameter, 
and  by  quarters  of  an  inch  from  3  ins.  diameter  and  upwards. 
Round  bars  are  also  rolled  by  a  few  companies  in  sixty-fourths 
of  an  inch  up  to  1  in.  diameter.  Below  %  in.  rounds  are  com- 
monly designated  by  wire-gauge  numbers. 


WEIGHTS   OF  FLAT  ROLLED   STEEL  BARS.   1353 


WEIGHTS  OF  FLAT  ROLLED  STEEL  BARS. 

PER    LINEAL    FOOT. 

(One  cubic  foot  of  steel  weighs  489.6  Ibs.) 
For  thicknesses  from  He  inch  to  %&  inch  and  widths  from  }/i  inch  to  M  inch. 


Thick- 
ness, 
in 
Inches. 

Width  in  Inches. 

H" 

He" 

w 

%." 

Y2" 

W 

H" 

Hie" 

g 

He 

.053 

.066 

.080 

.093 

.106 

.120 

.133 

.146 

.159 

5/G4 

.066 

.033 

.100 

.116 

.133 

.149 

.166 

.183 

.199 

'       %2 

.080 

.100 

.120 

.139 

.159 

.179 

.199 

.219 

.239 

%4 

.093 

.116 

.139 

.163 

.186 

.209 

.232 

.256 

.279 

Y% 

.106 

.133 

.159 

.186 

.212 

.239 

.266 

.292 

.319 

9/64 

.120 

.149 

.179 

.209 

.239 

.269 

.299 

.329 

.359 

%2 

.133 

.166 

.199 

.232 

.266 

.299 

.332 

.365 

.398 

11/64 

.146 

.183 

.219 

.256 

.292 

.329 

.365 

.402 

.438 

%e 

.159 

.199 

.239 

.279 

.319 

.359 

.398 

.438 

.478 

13/64 

.173 

.216 

.259 

.302 

.345 

.388 

.432 

.475 

.518 

T/32 

.186 

.232 

.279 

.325 

.372 

.418 

.465 

.511 

.553 

15/64 

.199 

.249 

.299 

.349 

.398 

.448 

.498 

.548 

.598 

K 

.213 

.266 

.319 

.372 

.425 

.478 

.531 

.584 

.638 

17/64 

.226 

.232 

.339 

.395 

.452 

.503 

.564 

.621 

.677 

%2 

.239 

.299 

.359 

.418 

.478 

.538 

.598 

.657 

.717 

1%4 

.252 

.315 

.379 

.442 

.505 

.568 

.631 

.694 

.757 

5/16 

.266 

.332 

.398 

.465 

.531 

.598 

.664 

.730 

.797 

sy64 

.279     .349 

.418 

.488 

.558 

.628 

.697 

.767 

.827 

ii/32 

.292 

.365 

.438 

.511 

.584 

.657 

.730 

.804 

.877 

2%4 

.305 

.382 

.458 

.535 

.611 

.687 

.764 

.840 

.916 

N 

.319 

.398 

.478 

.553 

.638 

.717 

.797 

.877 

.956 

2%4 

.332 

.415 

.498 

.581 

.664 

.747 

.830 

.913 

.996 

13/32 

.345 

.432 

.518 

.604 

.691 

.777 

.863 

.950 

1.04 

2%4 

.359 

.448 

.538 

.628 

.717 

.807 

.896 

.986 

1.03 

7/16 

.372 

.465 

.558 

.651 

.744 

.837 

.930 

1.02 

1.12 

2%4 

.385 

.481 

.578 

.674 

.770 

.867 

.963 

1.06 

1.16 

15/32 

.398 

.498 

.598 

.697 

.797 

.896 

.996 

1.10 

1.20 

Hk 

.412 

.515 

.618 

.721 

.823 

.926 

1.03 

1.13 

1.24 

Y* 

.425 

.531 

.638 

.744 

.850 

.956 

1.06 

1.17 

1.28 

33/64 

.438 

.548 

.657 

.767 

.877 

.986 

1.10 

1.21 

1.31 

17/o.3 

.452 

.564 

.677 

.790 

.903 

1.02 

1.13 

1.24 

1.35 

85/64 

.465 

.581 

.697 

.813 

.930 

1.05 

1.16 

1.28 

1.39 

9/16 

.478 

.598 

.717 

.837 

.956 

1.08 

1.20 

1.31 

1.43 

1354  WEIGHTS  OF  FLAT  ROLLED  STEEL  BARS. 


WEIGHTS  OF  FLAT  ROLLED   STEEL  BARS.— Continued. 

PER    LINEAL    FOOT. 
(Vie"  to  2"  in  thickness,  1"  to  12"  in  width.) 


Thick- 
ness, 
in 
Inches. 

1A 

.21 

.26 

.32 

.37 

.43 

.48 

.53 

.58 

.63 

1 

.42 

.53 

.64 

.75 

.85 

.96 

1.06 

1.17 

1.28 

.63 

.79 

.96 

1.11 

1  2S 

1.44 

1.59 

1.75 

1.91 

J 

.85 

1.06 

1.28 

1.49 

1.70 

1.91 

2.12 

2.34 

2.55 

%> 

1.06 

1.33 

1.59 

1.86 

2.12 

2  39 

2.65 

2.92 

3.19 

I 

1.28 

1.59 

1.92 

2.23 

2.55 

2.87 

3.19 

3.51 

3.83 

1.49 

1.86 

2.23 

2.60 

2.98 

3.35 

3.72 

4.09 

4.46 

1 

1.70 

2.12 

2.55 

2.98 

3.40 

3.83 

4.25 

4.67 

5.10 

% 

1.92 

2.39 

2.87 

3.35 

3.83 

4.30 

4.78 

5.26 

5.74 

§ 

2.12 

2.65 

3.19 

3.72 

4.25 

4.78 

5.31 

5.84 

6.38 

% 

2.34 

2.92 

3.51 

4.09 

4.67 

5.26 

5.84 

6.43 

7.02 

i 

2.55 

3.19 

3.83 

4.47 

5.10 

5.75 

6.38 

7.02 

7.65 

% 

2.76 

3.45 

4.14 

4.84 

5.53 

6.21 

6.90 

7.60 

8.29 

i 

2.98 

3.72 

4.47 

5.20 

5.95 

6.69 

7.44 

8.18 

8.93 

3.19 

3.99 

4.78 

5.58 

6.38 

7.18 

7.97 

8.77 

9.57 

i/l0 

3.40 

4.25 

5.10 

5.95 

6.80 

7.65 

8.50 

9.35 

10.20 

1/16 

3.61 

4.52 

5.42 

6.32 

7.22 

8.13 

9.03 

9.93 

10.84 

H 

3.83 

4.78 

5.74 

6.70 

7.65 

8.61 

9.57 

10.52 

11.48 

4.04 

5.05 

6.06 

7.07 

8.08 

9.09 

10.10 

11.11 

12.12 

H6 

4.25 

5.31 

6:38 

7.44 

8.50 

9.57 

10.63 

11.69 

12.75 

1516 

4.46 

5.5S 

6.69 

7.81 

8.93 

10.04 

11.16 

12.27 

13.39 

1| 

4.67 

5.84 

7.02 

8.18 

9.35 

10.52 

11.69 

12.85 

14.03 

4.89 

6.11 

7.34 

8.56 

9.78 

11.00 

12.22 

13.44 

14.66 

li6 

5.10 

6.38 

7.65 

8.93 

10.20 

11.48 

12.75 

14.03 

15.30 

1% 

5.32 

6.64 

7.97 

9.30 

10.63 

11.95 

13.28 

14.61 

15.94 

If 

5.52 

6.90 

8.29 

9.67 

11.05 

12.43[13.81 

15.19 

16.58 

1% 

5.74 

7.17 

8.61 

10.04 

11.47 

12.91 

14.34 

15  .  78 

17.22 

5.95 

7.44 

8.93 

10.42 

11.90 

13.40 

14.88 

16.37 

17.85 

1% 

6.16 

7.70 

9.24 

10.79 

12.33 

13.86 

15.40 

16.95 

18.49 

if 

6.38 

7.97 

9.57 

11.15 

12.75 

14.34 

15.94 

17.53 

19.13 

6.59 

8.24 

9.88 

11.53 

13.18 

14.83 

16.47 

18.12 

19.77 

2  16 

6.80 

8.50 

10.20 

11.90 

13.60 

15.30 

17.00 

18.70 

20.40 

WEIGHTS  OF  FLAT   ROLLED   STEEL   BARS.   1355 


WEIGHTS  OF  FLAT   ROLLED  STEEL    BARS.—  Continued. 

PER    LINEAL    FOOT. 
(Vie"  to  2"  in  thickness,  1"  to  12"  in  width.) 


Thick- 

in 
Inches. 

*4 

4" 

2 

><6 

.75 

.85 

.96 

1.06 

1.17 

1.28 

1.39 

1.49 

1.60 

i16 

1.49 

1.70 

1.92 

2.13 

2.34 

2.55 

2.77 

2.98 

3.19 

2.23 

2.55 

2.87 

3.19 

3.51 

3.83 

4.14 

4.46 

4.78 

i6 

2.98 

3.40 

3.83 

4.25 

4.67 

5.10 

5.53 

5.95 

6.36 

Y 

3.72 

4.25 

4.78 

5.31 

5.84 

6.  38 

6.90 

7.44 

7.97 

j1 

4.47 

5.10 

5.74 

6.38 

7.02 

7.65 

8.29    8.93 

9.57 

7/ 

5.20 

5.95 

6.70 

7.44 

8.18 

8.93 

9.6710.41 

11.16 

i 

5.95 

6.80 

7.65 

8.50 

9.35 

10.20 

11.0511.90 

12.75 

V 

6.70 

7.65 

8.61 

9.57 

10.52 

11.48 

12.43 

13.39 

14.34 

r 

7.44 

8.50 

9.57 

10.63 

11.69 

12.75 

13.8lll4.87 

15.94 

8.18|  9.35 

10.52 

11.69 

12.85 

14.03 

15.2016.36 

17.53 

i 

8.93 

10.20 

11.48 

12.75 

14.03 

15.30 

16.58 

17.85 

19.13 

% 

9.67 

11.0512.43 

13.81 

15.19 

16.58 

17.9519.34 

20.72 

r 

10.41 

11.9013.39 

14.87 

16.36 

17.8519.3420.83 

22.32 

11.16 

12.7514.34 

15.94 

17.53 

19.1320.7222.32 

23.91 

i 

11.90 

13.6015.30 

17.00 

18.70 

20.4022.1023.80 

25.50 

1rx 

12.65 

14.45 

16.26 

18.06 

19.87 

21.68 

23.4825.29 

27.10 

H6 

13.39 

15.30 

17.22 

19.13 

21.04 

22.9524.8726.78 

28.68 

14.13 

16.15 

18.17 

20.19 

22.21 

24.231  26.  24  28.  26 

30.28 

H° 

14.87 

17.00 

19.13 

21.25 

23.38 

25.50 

27.6229.75 

31.88 

1% 

15.62 

17.85 

20.08 

22.32 

24.54 

26.78 

29.01  31.23 

33.48 

if6 

16.36 

18.70 

21.04 

23.38 

25.71 

28.0530.3932.72 

35.06 

l/ie 

17.10 

19.85 

21.99 

24.44 

26.88 

29.  33  31.  77134.21 

36.66 

1J 

17.8520.40 

22.95 

25.50 

28.05 

30.60 

33.1535.70 

38.26 

1% 

18.6021.25 

23.91 

26.57 

29.22 

31.8834.53 

37.19 

39.84 

If 

19.3422.10 

24.87 

27.63 

30.39 

33.1535.9138.67 

41.44 

1/16 

20.0822.95 

25.82 

28.69 

31.55 

34.4337.3040.16 

43.03 

If 

20.83 

23.80 

26.78 

29.75 

32.73 

35.70 

38.6841.65 

44.63 

liax 

21.57 

24.65 

27.73 

30.81 

33.89 

36.98 

40.05 

43.14 

46.22 

If 

22.31 

25.50 

2S.69 

31.87 

35.06 

38.2541.4444.63 

47.82 

23.0626.35 

29.64 

32.94 

36.23 

39.5342.8246.12 

49.41 

2   ° 

23.80 

27.20 

30.60 

34.00 

37.40 

40.80 

44.20 

47.60 

51.00 

1353  WEIGHTS  OF  FLAT  ROLLED  STEEL   BARS. 


WEIGHTS  OF  FLAT  ROLLED   STEEL   BARS.— Continued. 

PER    LINEAL    FOOT. 
(Vie"  to  2"  in  thickness,  I"  to  12"  in  width.) 


Thick- 
ness, 
in 
Inches. 

8" 

w 

9" 

UH 

11" 

IIH 

12" 

k 

1.70 
3.40 
5.10 
6.80 

1.81 
3.61 
5.42 

7.22 

1.91 
3.82 
5.74 
7.65 

2.02 
4.04 
6.06 

8.08 

2.13 
4.25 
6.38 
8.50 

2.23 
4.46 
6.70 

8.92 

2.34 
4.68 
7.02 
9.34 

2.45 
4.89 
7.32 

9.78 

2.55 
5.10 
7.65 
10.20 

i6 

8.50 
10.20 
11.90 
13.60 

9.03 
10.84 
12.64 
14.44 

9.56 
11.48 
13.40 
15.30 

10.10 
12.12 
14.14 
16.16 

10.62 
12.75 

14.88 
17.00 

11.16 
13.39 
15.62 

17.85 

11.68 
14.03 
16.36 
18.70 

12.22 
14.68 
17.12 
19.55 

12.75 
15.30 

17.85 
20.40 

i6 

r 

15.30 
17.00 
18.70 
20.40 

16.26 
18.06 
19.86 
21.68 

17.22 
19.13 
21.04 
22.96 

18.18 
20.19 
22.21 
24.23 

19.14 
21.25 
23.38 
25.50 

20.08 
22.32 
24.54 
26.78 

21.02 
23.38 
25.70 
28.05 

22.00 
24.44 

26.88 
29.33 

22.95 
25.50 
28.05 
30.60 

1 

22.10 
23.80 
25.50 
27.20 

23.48 
25.30 
27.10 
28.90 

24.86 
26.78 
28.69 
30.60 

26.24 
28.26 
30.28 
32.30 

27.62 
29.75 
31.88 
34.00 

29.00 
31.24 
33.48 
35.70 

30.40 
32.72 
35.06 
37.40 

31.76 
34.21 
36.66 
39  .  10 

33.15 
35.70 
38.25 

40.80 

1J1 

28.90 
30.60 
32.30 
34.00 

30.70 
32.52 
34.32 
36.12 

32.52 
34.43 
36.34 
38.26 

34.32 
36.34 

38.36 
40.37 

36.12 
38.25 
40.38 
42.50 

37.92 
40.17 
42.40 
44.63 

39.74 
42.08 
44.42 
46.76 

41.54 
44.00 
46.44 

48.88 

43.35 
45.90 

48.45 
51.00 

If6 
H6 

35.70 
37.40 
39.10 
40.80 

37.93 
39.74 
41.54 
43.35 

40.16 
42.08 
44.00 
45.90 

42.40 
44.41 
46.44 

48.45 

44.64 
46.75 

48.88 
51.00 

46.86 
49.08 
51.32 
53.55 

49.08 
51.42 
53.76 
56.10 

51.32 
53.76 
56.21 
58.65 

53.55 
56.10 
58.65 
61.20 

If" 

42.50 
44.20 
45.90 
47.60 

45.16 
46.96 

48.76 
50.58 

47.82 
49.73 
51.64 
53.56 

50.48 
52.49 
54.51 
56.53 

53.14 
55.25 

57.38 
59.50 

55.78 
58.02 
60.24 
62.48 

58.42 
60.78 
63.10 
65.45 

61.10 
63.54 
65.98 
68.43 

63.75 
66.30 

68.85 
71.40 

}f 
2  16 

49.30 
51.00 
52.70 
54.40 

52.38 
54.20 
56.00 
57.80 

55.46 

57.38 
59.29 
61.20 

58.54 
60.56 
62.58 
64.60 

61.62 
63.75 

65.88 
68.00 

64.70 
66.94 
69.18 
71.40 

67.80 
70.12 
72.46 
74.80 

70.86 
73.31 
75.76 
78.20 

73.95 
76.50 
79.05 
81.60 

ESTIMATING  WEIGHT  OF  WROUGHT  IRON,  ETC.    1357 

Rules  for  Estimating  the  Weight  of  any  Piece  of 
Wrought  Iron,  Steel,  or  Cast  Iron. 

Wrought  iron: 

One  cubic  foot  of  wrought  iron  weighs .  .  .   480  Ibs. 
One  square  foot,  one  inch  thick,  weighs.  .     40    tl 
One  square  inch,  one  foot  long,  weighs..  .        3J  " 
To  find  the  weight  per  square  foot  of  sheet  iron,  multiply 
the  thickness  in  inches  by  40. 

To   find  the  weight  per  lineal  foot  of  bars  of  any  section, 
multiply  the  cross-sectional  area  in  square  inches  by  3J. 
Steel  : 

One  cubic  foot  of  steel  weighs 489 . 6  Ibs. 

(Or  just  2  per  cent,  more  than  wrought  iron.) 
One  square  foot,  one  inch  thick,  weighs.  .40.8     ' 
One  square  inch,  one  foot  long,  weighs.  .      3.4     " 
To  find  the  weight  per  lineal  foot,  of  bars  of  any  section, 
multiply  the  cross-sectional  area  in  square  inches  by  3.4;    or, 
if  the  weight  is  known,  the  exact  sectional  area  may  be  obtained 
by  dividing  by  3.4. 
Cast  iron : 

One  cubic  foot  of  cast  iron  weighs 450  Ibs. 

One  square  foot,  one  inch  thick,  weighs.  .      37J  " 
One  square  inch,  one  foot  long,  weighs.  .  .        3J  tl 

One  cubic  inch  weighs .  26  ' ' 

The  weight  of  irregular  castings  must  be  estimated  by  the 
cubic  inch. 

Rules  for  Weights  of  Castings. 

Multiply  the  weight  of  the  pattern  by  18  for  cast  iron,  13  for 
brass,  19  for  lead,  12. 2  for  tin,  11.4  for  zinc,  and  the  product  is 
the  weight  of  the  casting. 

Reduction  for  Round  Cores  and  Core  Prints. 
RULE. — Multiply  the  square  of  the  diameter  by  the  length  of 
the  core  in  inches,  and  the  product  multiplied  by  0.017  is  the 
weight  of  the  pine  core  to  be  deducted  from  the  weight  of  the 
pattern. 

Shrinkage  in  Castings. 

Cast  iron,    J  1 

Brass  .  .  .  .%  \  of  an  inch   longer    per 

Pattern-makers'  Rule,  i  Lead J    j-      lineal  foot 

Tin y 

Zinc  .  .        « 


1358  WEIGHT  OF   SQUARE  CAST-IRON   COLUMNS, 


WEIGHT  OF  SQUARE  CAST-IRON  COLUMNS  IN  POUNDS 
PER  LINEAL  FOOT. 

(Birkmire.) 


•9 

2a  +  2b 

Thickness  of  Metal  in  Inches. 

H 

X 

7A 

1 

l.'-S 

in 

1H 

w 

2 

# 

12 

18.6 

21.1 

23.3 

25.0 

26.4 

27.3 

28.1 

14 

22.5 

25.8 

28.7 

31.3 

33.4 

35.1 

37.5 

16 

26.4 

30.5 

34.2 

37.5 

40.4 

43.0 

46.9 

49.2 

50.0 

18 

30.3 

35.2 

39.7 

43.8 

47.4 

50.8 

56.3 

60.2 

62.5 

20 

34.2 

39.8 

45.1 

50.0 

54.5 

58.6 

65.6 

71.1 

75.0 

22 

38.1 

44.5 

50.6 

56.3 

61.5 

66.4 

75.0 

82.0 

87.5 

24 

42.0 

49.2 

56.1 

62.5 

68.5 

74.2 

84.4 

93.0 

100.0 

26 

45.9 

53.9 

61.5 

68.8 

75.6 

82.0 

93.8 

103  .  9 

112.5 

28 

49.8 

58.6 

67.0 

75.0 

82.6 

89.8 

103.1 

114.8 

125.0 

30 

53.7 

63.3 

72.5 

81.3 

89.6 

97.7 

112.5 

125.8 

137.5 

32 

57.6 

68.0 

77.9 

87.5 

96.7 

105.5 

121.9 

136.7 

150.0 

34 

61.5 

72.7 

83.4 

93.8 

103.7 

113.3 

131.3 

147.7 

162.5 

36 

65.4 

77.3 

88.9 

100.0 

110.7 

121.1 

140.6 

158.6 

175.0 

38 

69.3 

82.0 

94.3 

106.3 

117.8 

128.9 

150.0 

169.5 

187.5 

40 

73.2 

86.7 

99.8 

112.5 

124.8 

136.7 

159.4 

180  .  5 

200.0 

42 

77.1 

91.4 

105.3 

118.8 

131.8 

144.5 

168.8 

191.4 

212.5 

44 

81.0 

96.1 

110.8 

125.0 

138.8 

152  .  3 

178.1 

202.3 

225.0 

46 

84.9 

100.8 

116.2 

131.3 

145.9 

160.2 

187.5 

213.3 

237.5 

48 

88.8 

105.5 

121.7 

137.5 

152.9 

168.0 

196.9 

224.2 

250.0 

50 

92.8 

110.2 

127.2 

143.8 

159.9 

175.8 

206.3 

235.2 

262  .  5 

52 

96.7 

114.3 

132.6 

150.0 

167.0 

183.6 

215.6 

246.1 

275.0 

54 

100.6 

11  -.5 

138.1 

156.3 

174.0 

191.4 

225.0 

257.0 

287  .  5 

56 

104.5 

124.2 

143.6 

162.5 

181.0 

199.2 

234.4 

268.0 

300.0 

58 

108.4 

128.9 

149.0 

168.8 

188.1 

207.0 

243.8 

278.9 

312.5 

60 

112.3 

133.6 

154.5 

175.0 

195.1 

214.9 

253.2 

289.8 

325.0 

62 

116.2 

138.3 

160.0 

181.3 

202.1 

222.7 

262.5 

300.8 

337.5 

64 

120.1 

143.0 

165.4 

187.5 

209.2 

230.5 

271.9 

311.7 

350.0 

66 

124.0 

147.7 

170.9 

193.8 

216.2 

238.3 

281.3 

322.7 

362  .  5 

68 

127.9 

152.3 

176.4 

200.0 

223.2 

246.1 

290.6i  333.6 

375.0 

70 

131.8 

157.0 

181.8 

206.3 

230.3 

253.9 

300.0 

344.5 

387.5 

72 

135.7 

161.7 

187.3 

212.5 

237  .  3 

261.7 

309.4 

355.5 

400.0 

74 

139.6 

166.4 

192.8 

218.8 

244  .  3 

269.5 

318.8 

366.4 

412.5 

76 

143.5 

171.1 

198.3 

225.0 

251.3 

277.3 

328.1 

377.3 

425.0 

78 

147.4 

175.8 

203.7 

231.3 

258.4 

285.2 

337.5 

388.3 

437  .  5 

80 

151.3 

180.5 

207.2 

237.5 

265.4 

293.0 

346.9 

309.2 

450.0 

1 

*a  and  &  =  either  side  (outside  measurement).      2a-f2fr  =  number. 
Allowance  has  been  made  in  this  table  for  corners  counted  twice. 

EXAMPLE. — What  is  the  weight  per  lineal  foot  of  a  12"X16" 
X  1"  thick  column? 

Ans. — 2a  4- 26=  24 +  32=  56.  Opposite  this  number,  under 
1-inch  thick  metal,  we  find  162.5,  or  weight  per  lineal  foot  of  a 
12//X16//X1//  thick  column. 

NOTE. — For  flanges,  brackets,  etc.,  calculate  the  cubical  con- 
tents of  same  and  multiply  by  .26;  cast  iron  averaging  450  pounds 
per  cubic  foot. 


WEIGHT  OF  CIRCULAR  CAST-IRON  COLUMNS.  1359 


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1360 


WEIGHT  OF  CAST-IRON  PLATES. 


WEIGHT    OF    CAST-IRON    PLATES. 

WEIGHT,    IN    POUNDS,    OF   CAST-IRON    PLATES    ONE 
INCH  THICK. 

(Calculated  at  450  Ibs.  per  cubic  foot.) 

_-  «    I  Width,  in  Inches. 


^<r" 

1  6 

8 

10 

12 

14 

16 

18 

20 

24 

30 

4  j  6.25 

8.3 

10.4 

12.5 

14.6 

16.6 

18.7 

20.8 

25 

31 

6 

9.37 

12.5 

15.6 

18.7 

21.8 

25.0 

28.1 

31.2 

3<S 

47 

8 

12.50 

16.6 

20.8 

25.0 

29.1 

33.3 

37.4 

41.6 

50 

62 

10 

15.60 

20.8 

26.0 

31.2 

36.4 

41.6 

46.8 

52.0 

63 

78 

12 

18.70 

25.0 

31.2 

37.5 

43.7 

49.9 

56.2 

62.4 

75 

94 

14 

21.80 

29.2 

36.4 

43.7 

51.0 

58.2 

65.5 

72.81  88 

109 

16 

24.90 

33.3 

41.6 

50.0 

58.2 

66.6 

74.9 

83.2 

100 

125 

18 

28.10 

37.5 

46.8 

56.2 

65.5 

74.9 

84.2 

93.6 

113 

140 

20 

31.20 

41.6 

52.0 

62.3 

72.8 

83.2 

93.6 

104.0 

125 

156 

22   34.30 

45.8 

57.2 

68.6 

80.1 

91.5 

103.0 

114.4 

138 

172 

24 

37.50 

50.0 

62.4 

75.0 

87.4 

99.8 

112.3 

124.8 

150 

187 

26 

40.60 

54.0 

67.6 

81.2 

94.6 

108.2 

121.7 

135.2 

163 

203 

28 

43.60 

58.2 

72.8 

87.5 

101.9 

116.5 

131.0 

145.6 

175 

218 

30 

46.80 

62.4 

78.0 

93.7 

109.2 

124.8 

140/4 

156.0 

188 

234 

32 

49.80 

66.6 

83.2 

100.0 

116.5 

133.1 

150.3 

166.4 

200 

250 

36 

56.10 

75.0 

93.6 

112.5 

131.0 

150.0 

168.4 

187.2 

225 

281 

For  larger  plates  take  size  of  plate  one  half  smaller  and  mul- 
tiply by  2.  Thus  a  plate  28"X32"  will  weigh  twice  as  much 
as  one  14//X32//.  For  plates  more  or  less  than  one  inch  in 
thickness  multiply  weight  of  plate  by  thickness  in  inches. 


APPROXIMATE    WEIGHT    OF   SQUARE-RIBBED    CAST- 
IRON  COLUMN  BASES. 

The  following  table,  giving  the  weight  of  cast-iron  column 
bases,  is  new  and  will  be  useful  when  estimating  the  steel  and 
iron  in  tall  buildings :  * 


Size 

of  Square 
Base. 


Weight 

in 
Pounds. 


of  Square 
Base. 


Weight 

in 
Pounds. 


22X22 600 

24X24 750 

26X26 880 

28X28 1,020 

30X30 1,180 


32X32 1,340 

34X34 1,450 

36X36 1,600 

38X38 1,720 

40X40..  .  1,850 


*H..G.  Tyrrell,  C.E.,  in  Architects  and  Builders  Magazine,  Jan.,  1903. 


SCREW-THREADS,  NUTS,  AND  BOLT-HEADS.   1361 


SCREW-THREADS,  NUTS,  AND  BOLT-HEADS. 

STANDARD  SCREW-THREADS. 

Recommended  by  Franklin  Institute,  Dec.  15,  1864,  and  adopted  by 
Navy  Dept  of  the  United  States:  by  the  R.  R.  Master  Mechanics'  and 
Master  Car-builders'  Associations;  by  Messrs.  Jones  &  Laughlins,  Limited; 
and  by  many  other  of  the  prominent  engineering  and  mechanical  estab- 
lishments xxf  the  country. 


Angle  of  thread  60°      Flat  at  top  and  bottom  H  of  pitch. 


Diam. 
of 
Screw. 

Threads 
per  Inch. 

Diam.  at 
Root  of 
Thread. 

Area  at 
Root  of 
Thread. 

Diam. 
of 
Screw. 

Threads 
per  Inch. 

Diam.  at 
Root  of 
Thread. 

Area  at 
Root  of 
Thread. 

sq.  in. 

sq.  in. 

# 

20 

.185 

.027 

2 

4^ 

1.712 

2.302 

5/16 

18 

.240 

.045 

2X 

4^ 

1.962 

3.023 

it 

16 

.294 

.068 

21A 

4 

2.176 

3.719 

7/ie 

14 

.344 

.093 

2M 

4 

2.426 

4.620 

% 

13 

.400 

.126 

3 

3^ 

2.629 

5.428 

8/16 

12 

.454 

.162 

3K 

3^ 

2.879 

6.510 

H 

11 

.507 

.202 

&A 

3 

3.100 

7.548 

H 

10 

.620 

.302 

3% 

a 

3.317 

8.641 

H 

9 

.731 

.420 

4 

3 

3.567 

9.963 

i 

8 

.837 

.550 

4K 

2 

3.798 

11.329 

IK 

7 

.940 

.694 

4H 

2 

4.028 

12.753 

iM 

7 

1.065 

.893 

4% 

2 

4.256 

14.226 

IH 

6 

1.160 

1.057 

5 

2 

4.480 

15.763 

W 

6 

1.284 

1.295 

5M 

2 

4.730 

17.572 

1^8 

5^ 

1  .  389 

1.515 

2 

4.953 

19.267 

1-M 

5 

1.491 

1.746 

5M 

2 

5.203 

21.262 

in 

5 

1.616 

2.051 

6 

2 

5.423 

23.098 

Nuts  and  Bolt-heads  are  determined  by  the  following  rules,  which  apply 
to  both  square  and  hexagon  nuts: 

Short  diameter  of  rough  nut  =  13^Xdiam.  of  bolt  +  H  in. 

Short  diameter  of  finished  nut  =  1>£X  diam.  of  bolt  +  Vie  in. 

Thickness  of  rough  nut  =  diam.  of  bolt. 

Thickness  of  finished  nut  =  diam.  of  bolt  —  ^{Q  in. 

Short  diameter  of  rough  head  =  l^Xdiam.  of  bolt  +  K  in. 

Short  diameter  of  finished  head  =  1^  X  diam.  of  bolt  +  ^ie  in. 

Thickness  of  rough  head  =  ^  short  diam.  of  head. 

Thickness  of  finished  head  =  diam.  of  bolt  — Me  in. 

The  long  diameter  of  a  hexagon  nut  may  be  obtained  by  multiplying 
the  short  diameter  by  1.155,  and  the  long  diameter  of  a  square  nut  by 
multiplying  the  short  diameter  by  1.414. 


1362 


STANDARD   NUTS  AND   BOLT-HEADS. 


STANDARD  DIMENSIONS  OF  NUTS  AND 
BOLT-HEADS. 


Dia. 

of 

Short 
Diam. 
Rough. 

Sho-t 
Diam. 
Finish. 

Long 
Diam. 
Rough. 

Long 
Diam. 
Rough. 

Thick- 
ness, 
Rough, 

Nut. 

Thick- 
ness. 
Finish. 
Both. 

Thic 
nesfc 
Roup 
Hea 

Bolt. 

^\ 

.XX. 

/-, 

y. 

rm 

cc 

t@3 

s§? 

® 

^ 

niD 

UI 

t: 

1 

i 

% 

87/fl4 

7/io 

i 

% 

* 

¥ 

19/32 

i 

51^ 

«%I 

f6 

Ire 

/( 

m 

%> 

2%2 

9/10 

l-/64 

i1 

25/t 

i 

f 

%6 

1 

ll5/64 

i 

Jie 

8y32 

2%2 

it 

12%4 

/ie 

J 

8ye 

§ 

1 

11 

J 

%b 

17/a 

j 

ii6 

1/ie 

IJie 

l49/64 

1 

% 

f 

i 

If 

1-^32 

2%, 

i 

% 

i 

if 

1% 

1} 

219/64 

1 

% 

% 

« 

1! 

2%2 

2% 

1) 

l/^ 

2% 

11 

2  16 

1% 

2^ 

253/64 

11 

1% 

1 

2/le 

aj 

3%2 

If 

IM 

l%o 

4 

2| 

2% 

2!C2 

323/64 

li 

1/ie 

1/S 

if 

2% 

2J 

3| 

If 

1/ie 

l%o 

it 

2% 

2% 

2J 

3%2 

3l3/32 

3r>7/04 

:! 

1% 

11 

2 

3^ 

3^6 

3| 

427/64 

2 

2% 

1^ 

21 

31 

3% 

4>/6 

21 

2% 

If 

2| 

3| 

3% 

4i 

53^64 

2J 

2% 

41 

4,¥6 

42%o 

6 

2J 

2% 

2i16 

3 

4| 

4% 

5| 

617/82 

3 

2% 

2^6 

31 

5 

4% 

5% 

7/ie 

31 

3% 

21 

3} 

5  1 

5%    . 

6y64 

73%4 

3i 

3/1(5 

2% 

3f 

5| 

5% 

621/33 

8i 

3J 

3% 

4 

6i 

6Ji 

73/S2 

8*Ve4 

4 

3% 

3  He 

41 

6? 

6J^ 

7X 

9^6 

41 

4% 

31 

4i 

6J 

6l^6 

731/32 

9f 

4J 

4% 

4J 

71 

813/33 

101 

4| 

4% 

3} 

5 

7| 

7% 

827/32 

104%4 

5 

4% 

3% 

51 

8 

7!%6 

9%o 

Il2%4 

5} 

5% 

4 

g| 

8^6 

92%, 

5i 

5% 

4% 

5f 

8^ 

8% 

10%, 

121 

5} 

5% 

4| 

6 

9^ 

9;rG 

10l%2 

12% 

6 

5% 

4% 

WEIGHT  OF  BOLTS,  NUTS,  AND  BOLT-HEADS.  1363 


WEIGHT   OF   ONE   HUNDRED   BOLTS   WITH   SQUARE 
HEADS  AND  NUTS. 

INCLUDES   WEIGHT   OF   NUT. 
(Hoopes  &  Townsend's  List.) 


Length 
under 
Head 

Diameter  of  Bolts,  Inches. 

to  Point. 

H 

5/16 

y8 

Vl6 

H 

K 

H 

H 

1 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

VA 

4.00 

7.00 

10.50 

15.20 

22.50 

39.50 

63.00 

— 

— 

1M 

4.35 

7.50 

1  1  .  25 

16.30 

23.82 

41.62 

66.00 

— 

— 

2 

4.75 

8.00 

12.00 

17.40 

25.15 

43.75 

69.00 

109.00 

163 

2K 

5.15 

8.50 

12.75 

18.50 

26.47 

45.88 

72.00 

113.25 

169 

%1A 

5.50 

9.00 

13.50 

19.60 

27.80 

48.00 

75.00 

117.50 

174 

2M 

5.75 

9.50 

14.25 

20.70 

29.12 

50.12 

78.00 

121.75 

180 

3 

6.25 

10.00 

15.00 

21.80 

30.45 

52.25 

81.00 

126.00 

185 

3^ 

7.00    11.00 

16.50 

24.00 

33.10 

56.50 

87.00 

134.25 

196 

4 

7.75    12.00 

18.00 

26.20 

35.75 

60.75 

93.10 

142  .  50 

207 

4^ 

8.50!    13.00 

19.50 

28.40 

38.40 

65.00 

99.05 

151.00 

218 

5 

9.25'    14.00 

21.00 

30.60 

41.05 

69.25 

105.20 

159.55 

229 

&A 

10.001    15.00 

22.50 

32.80 

43.70 

73.50 

111.25 

168.00 

240 

6 

10.75    16.00 

24.00 

35.00 

46.35 

77.75 

117.30 

176.60 

251 

6^ 

—  • 

— 

25.50 

37.20 

49.00 

82.00 

123.35 

185.00 

262 

—  . 

— 

27.00 

39.40 

51.65 

86.25 

129.40 

193.65 

273 

IX 

— 

.  —  . 

28.50 

41.60 

54.30 

90.50 

135.00 

202.00 

284 

8 

— 

— 

30.00 

43.80 

59.60 

94.75 

141.50 

210.70 

295 

9 

— 

— 

— 

46.00 

64.90 

103.25 

153.60 

227.75 

317 

10 

—  • 

— 

— 

48.20 

70.20  111.75 

165.70 

224.80 

339 

11 

— 

— 

— 

50.40 

75.50  120.25 

177.80 

261.85 

360 

12 

— 

— 

— 

52.60 

80.  80'  128.  75 

189.90 

278.90 

382 

13 

— 

— 

— 

— 

86.10  137.25 

202.00 

295.95 

404 

14 

— 

— 

— 

!- 

91.40  145.75 

214.10 

313.00 

426 

15 

— 

— 

— 



96.70:154.25 

226  .  20 

330.05 

448 

16 

— 

— 

— 



102.00  162.75 

238  .  30 

347.10 

470 

17 

—  . 

— 

— 



107.30  171.00 

250.40 

364.15 

492 

18 

— 

— 

—  . 



112.60  179.50 

262  .  60 

381.20 

514 

19 

— 

— 

— 

- 

117.90  188.00 

274.70 

398  .  25 

536 

20 

.  — 

— 

— 



123.20  206.50 

286.80 

415.30 

558 

Per  inch 
addit'l 

j-  1.37 

2.13 

3.07 

4.18 

5.45 

8.52 

12.27 

16.70 

21.82 

WEIGHTS   OF   NUTS   AND    BOLT-HEADS,    IN    POUNDS. 

(For  calculating  the  weight  of  longer  bolts.) 


Diameter  of  Bolt,  in  Inches. 

H 

H 

H 

N 

H 

0.43 
0.55 

% 

0.73 

0.88 

Weight  of  hexagon  nut  and 
head.  .  . 

— 

0.017 
0.021 

0.057 
0.069 

0.128j0.267 
0.1640.320 

Weight  of  square  nut  and 
head.  ...  .  . 

Diameter  of  Bolt,  in  Inches. 

1 

m 

m 

1% 

2 

2y2 

3 

Weight    of   hexagon    nut   and 
head  
Weight    of    square    nut    and 
head  

1.10 
1.31 

2.14 
2.56 

3.78 
4.42 

5.6 
7.0 

8.75 
10.50 

17 
21 

28.8 
36.4 

1364 


WEIGHT  OF  RIVETS. 


WEIGHT    OF    RIVETS    AND    ROUND-HEADED 
WITHOUT  NUTS— STEEL. 

POUNDS    PER    HUNDRED. 


Length, 
Inches. 

NIn. 

Diam. 

^2  In. 
Diam. 

MIn. 
Diam. 

MIn. 
Diam. 

Kin. 
Diam. 

llri. 

Diam. 

I1  8  In. 
Diam. 

\M  In. 
Diam. 

li 

5.5 

12.8 

22.0 

29.3 

43.9 

66.6 

93.3 

127. 

li 

6.3 

14.2 

24.1 

32.4 

4S.2 

72.1 

100. 

136. 

If 

7.0 

15.5 

26.3 

35.5 

52.5 

77.7 

107. 

145. 

2 

7:9 

16.9 

28.5 

38.7 

56.7 

83.3 

114. 

153. 

21 

8.7 

18.3 

30.7 

41.8 

61.0 

88.8 

121. 

162. 

2* 

9.4 

19.7 

32.8 

44.9 

'65.2 

94.4 

128. 

171. 

2i 

10.2 

21.1 

35.0 

48.0 

69.5 

100. 

136. 

179. 

3 

11.0 

22.5 

37.2 

51.1 

73.7 

105. 

143. 

188- 

31 

11.7 

23.9 

39.3 

54.3 

78.0 

111. 

150. 

197. 

3i 

12.6 

25.3 

41.5 

57.4 

82.3 

116. 

157. 

205. 

3f 

13.4 

26.7 

43.7 

60.5 

86.5 

122. 

164. 

214. 

4 

14.1 

23.1 

45.9 

63.6 

90.8 

128. 

170. 

223. 

41 

14.9 

29.4 

48.0 

66.7 

95.0 

134. 

177. 

231. 

4i 

15.7 

30.8 

50.2 

69.9 

99.3 

139. 

185. 

240. 

4| 

16.5 

32.2 

52.4 

73.0 

104. 

145. 

192. 

249. 

5 

17.2 

33.6 

54.5 

76.1 

108. 

150. 

199. 

258. 

51 

18.1 

35.0 

56.7 

79.2 

112. 

156. 

206. 

266. 

5£ 

18.8 

36.4 

58.9 

82.3 

116. 

161. 

213. 

275. 

6} 

19.6 

37.8 

61.1 

85.5 

120. 

166. 

220. 

284. 

6 

20.4 

39.2 

63.2 

88.6 

124. 

172. 

227. 

292. 

6i 

21.9 

42.0 

67.6 

95.1 

133. 

184. 

241. 

310. 

7 

23.5 

44.7 

71.9 

101. 

142. 

195. 

255. 

327. 

7i 

25.1 

47.5 

76.1 

108. 

150. 

206. 

269. 

345. 

8 

26.6 

50.3 

80.6 

114. 

159. 

217. 

284. 

362. 

8* 

2S.2 

53.1 

85.0 

120. 

167. 

227 

298. 

379. 

9 

29.8 

55.9 

89.3' 

126. 

176. 

239! 

312. 

397. 

9i 

31.3 

5S.7 

93.7 

133. 

185. 

250. 

325. 

414. 

10 

32.8 

61.4 

98.0 

139. 

193. 

261. 

340. 

431. 

10J 

34.5 

64.2 

103. 

145. 

202. 

272. 

354. 

449. 

11 

36.0 

67.0 

107. 

151. 

210. 

284. 

368. 

466. 

UJ 

37.6 

69.8 

111. 

153, 

218. 

295. 

382. 

484. 

12 

39.2 

72.5 

115. 

164. 

227. 

306. 

396. 

501. 

Heads. 

1.8 

5.8 

11.1 

13.6 

22.6 

39.0 

58.0 

83.5 

For  length  of  shaft  required  to  form  rivet-head,  see  p.  374. 


NAILS.  1365 

NAILS. 
Kinds. — The  different  kinds  of  nails  may  be  classified  as 

follows : 

Wrought  nails,  which  are  forged  either  by  hand  labor  or 
machine  power-  sometimes  designated  as  clinch  naUsj  on  ac- 
count of  their  property  of  bending  without  breaking.  Seldom 
used  in  connection  with  wood- work,  although  they  are  the  best 
clinch  nail  that  can  be  had. 

Cut  nails,  which  are  cut  from  a  strip  of  rolled  iron  or  steel  of 
the  thickness  that  the  nail  is  to  be  and  a  little  wider  than  the 
length  of  the  nail.  Cut  nails  are  now  commonly  made  of  steel. 

Wire  nails,  which  are  made  from  steel  wire  of  the  same  size 
as  the  shank  of  the  nail  is  to  be. 

Copper  and  brass  nails — are  manufactured,  and  are  sometimes 
used  in  connection  with  marine  and  refrigerator  work,  and  about 
physical  laboratories,  to  avoid  the  magnetic  effects  of  iron  or  steel. 

Composition  nails — are  made  of  different  alloys  to  avoid  cor- 
rosion, or  to  prevent  galvanic  action  set  up  by  iron  when  in 
contact  with  zinc  or  other  metals. 

Varieties. — Nails  are  also  made'  in  a  variety  of  shapes  and 
sizes  to  adapt  them  to  different  classes  of  work;  the  principal 
varieties  are  indicated  by  the  tables  on  following  pages. 

Galvanized-wire  nails — may  be  obtained  if  desired.  Wherever 
exposed  to  constant  or  frequent  moisture  they  are  more  durable 
and  satisfactory  than  uncoated  nails,  and  are  to  be  preferred  for 
securing  shingles,  slates,  and  all  kinds  of  roofing. 

Cement-coated  Nails. — J.  C.  Pearson  Company,  of  Boston, 
Mass.,  have  obtained  a  patent  on  coating  wire  nails  with  an 
asphaltum  cement  which  greatly  increases  their  holding  power. 
Most  varieties  are  carried  in  stock  in  the  larger  cities.  With  this 
coating  slightly  smaller  nails  may  be  used,  with  equal  or  greater 
holding  power.  It  is  claimed  that  it  is  cheaper  for  contractors 
to  use  cement-coated  nails  than  ordinary  wire  nails.  Most  of 
the  wooden-box  factories  use  these  nails,  and  they  are  especially 
desirable  for  nailing  flooring,  siding,  etc. 

Holding"  Power  of  Nails. — A  committee  appointed  by 
the  Wheeling  nail  manufacturers,  a  number  of  years  ago,  to  test 
the  comparative  holding  power  of  cut  and  wire  nails,  published 
the  following  data,  although  the  kind  of  wood  is  not  named. 
POUNDS  REQUIRED  TO  PULL  NAILS  OUT. 

Cut.  Wire.  Cut.  Wire. 

Twenty-penny 1593  703         Sixpenny 383  200 

Ten  penny.  .     908       315         Fourpenny 286       123 

Eight  penny 597       227 


1366 


NAILS. 


The  following  table  shows  the  result  of  tests  made  at  the  U.  S. 
Arsenal,  Watertown,  Mass.,  In  1902,  the  wood  being  pine: 

COMPARATIVE   ADHESIVE   RESISTANCE   OF   COMMON 
SMOOTH  WIRE  NAILS  AND  CEMENT-COATED  NAILS. 

All  nails  driven  into  the  same  piece  perpendicular  to  the  grain. 


Size  and  Name. 

Diameter 
in 
Inches. 

Length 
Driven,* 
Inches. 

Adhesive 
Resistance,  f 
Pounds. 

Tenpenny,  common,  smooth.  .  .  . 

.145 
.117 
.132 
.114 
.132 
.112 
.097 
.092 

\N\N\-)lVJ(  \03\00 

r-l\,4\,-H\r-4\  US\lrf\ 

<N<MC^<N<N03i-iT-i 

167 
418 
182 
327 
189 
316 
106 
226 

coated  

Ninepenny  common,  smooth. 

coated  

Eightpenny,  common,  smooth.  . 

coated 

Sixpenny,  common,  smooth.  .  . 

coated. 

*  All  of  the  nails  were  left  with  their  heads  projecting  from  %  to  ^  inch, 
t  Average  of  three  trials. 

The  holding  power  of  nails  varies  with  the  kind  of  wood  into 
which  they  are  driven.  Austin  T.  Byrne  gives  the  relative 
holding  power  of  woods  about  as  follows:  White  pine,  1;  yellow 
pine,  1.5;  white  oak,  3;  chestnut,  1.6;  beech,  3.2;  sycamore, 
2;  elm,  2;  basswood,  1.2. 

COMPARATIVE  HOLDING  POWER  OF  CUT  AND 
WIRE  NAILS. 

Very  thorough  tests  of  the  comparative  holding  power  of  wire 
nails  and  cut  nails  of  equal  lengths  and  weights  were  made  at  the 
U.  S.  Arsenal  in  1892  and  1893.  From  forty  series,  comprising 
forty  sizes  of  nails  driven  in  spruce  wood,  it  was  found  that  the 
cut  nails  showed  an  average  superiority  of  60.50  per  cent.,  the 
common  nails  showing  an  average  superiority  of  47.51  per  cent, 
and  the  finishing  nails  an  average  of  72.22  per  cent. 

In  eighteen  series,  comprising  six  sizes  of  box  nails  driven  into 
pine  wood,  in  three  ways  the  cut  nails  showed  an  average  supe- 
riority of  99.93  per  cent.  In  no  series  of  tests  did  the  wiro  nails 
hold  as  much  as  the  cut  nails. 

QUANTITY   OF    NAILS    REQUIRED    FOR    DIFFERENT 
KINDS   OF   WORK. 

For  1,000  shingles  allow  5  Ibs.  fourpenny  nails  or  3J^  Ibs.  threepenny. 

1,000  laths,  7  Ibs.  threepenny  fine,  or  for  100  square  yards  of  lathing, 

10  Ibs.  threepenny  fine. 
1,000  square  feet  of  beveled  siding,  18  Ibs.  sixpenny. 


1,000 
1,000 
1,000 
1,000 

1,000 


"  sheathing,  20  Ibs.  eightpenny  or  25  Ibs.  tenpenny. 
"  flooring,  30  Ibs.  eightpenny  or  40  Ibs.  tenpenny. 
"  studding,  15  Ibs.  tenpenny  and  5  Ibs.  twenty-penny. 
"  1"  X2W  furring,  12"  centres,  9  Ibs.  eightpenny  or 

14  Ibs.  tenpenny. 
*'  l"X2}/2//  furring,  16"  centres,  7  Ibs.  eightpenny  or 

10  Ibs.  tenpenny. 


CUT  NAILS  AND  SPIKES. 


1367 


CUT  STEEL  NAILS  AND  SPIKES. 
SIZE,  LENGTH,  AND  NUMBER  TO  THE  POUND. 


ORDINARY. 

CLINCH. 

FINISHING. 

Size. 

Length, 
in  Ins. 

No.  to 
Pound. 

71G 

5S8 
44S 
336 
216 
166 
118 
94 
72 
50 
32 
20 
17 
14 
10 

Length, 
in  Ins. 

No.  to 
Pound. 

Size. 

Length, 
in  Ins. 

No.  to 
Pound. 

2d 
3d  fine 

3d 

4d 
5d 
6d 
7d 
8d 
Wd 
12d 
20d 
30d 
40d 
50d 
GOd 

,fc 

H 
14 
l| 

2 
21 
24 
3 
3i 
4 
41 
4f 
5 

si- 

2 

21 
2i 
2| 
3 
3i 

152 
133 
92 

72 
60 
43 

4d 
5d 
6d 
8d 
Wd 
I2d 
2Qd 

If 
If 
2 

2i 

3 
3f 
3J 

3S4 
256 
204 
102 
80 
65 
46 

FENCE. 

CORE. 

2 
2J 
24 
21 
3 

96 
66 
56 
50 
40 

6^ 
Sd 
Wd 
I2d 
20d 
30d 
40d 

WH 
WHL 

2 
2i 
2i 
3i 
3J 
4i 
41 

2i 
21 

143 
68 
60 
42 
25 
18 
14 

69 

72 

LIGHT. 

SPIKES. 

4d 
5d 
Qd 

if 

If 

2 

373 

272 
196 

3i 
4 
4i 
5 
5§ 
6 

19 
15 
13 
10 
9 
7 

SLATE. 

BRADS. 

6d 
8d 
Wd 
I2d 

2 

2J 
2f 

34 

163 
96 
74 
50 

BOAT. 

3^ 
4d 

5d 
6d 

1% 
1« 
If 
2 

288 
244 
187 
146 

H 

206 

TACKS. 


Number 

J 

Number 

Number 

Size. 

Length. 

to 

Size. 

^ 

to 

Size. 

Length. 

to 

Pound. 

A 

Pound. 

Pound. 

1     oz. 

* 

16,000 

4  oz. 

% 

4,000 

14  oz. 

!¥e 

1,143 

H  " 

% 

10,066 

6  " 

% 

2,666 

16  " 

I 

1,000 

2     " 

i 

8,000 

8  " 

I 

2,000 

18  " 

% 

888 

2*  " 

5/l6 

6,400 

10  " 

% 

1,600 

20  " 

soo 

3     " 

1 

5,333 

12  " 

J 

1,333 

22  " 

IJtfi 

727 

1368         WIRE  NAILS,  SPIKES,  AND  TACKS. 


STEEL-WIRE  NAILS,  SPIKES,  AND  TACKS. 

SIZE,  LENGTH,  GAUGE,  AND  APPROXIMATE  NUMBER 

TO  THE  POUND. 

Compiled  from  Catalogue  of  American  Steel  and  Wire  Company,  1903. 
Gauge  is  the  A.  S.  and  W.  Co.'s  Gauge,  p.  1349. 


Common  Nails  and  Brads.* 

Casing  Nails,  t 

Finishing  Nails.f 

Size. 

Length, 
Inches. 

Gauge. 

No.  to 
Pound. 

Gauge.       No.  to 
Pound. 

Gauge. 

No.  to 

Pound. 

2d 

1 

15 

876 

151     I  1,010 

16J 

1,351 

3d 

li 

14 

568 

141 

635 

15^ 

807 

4d 

11 

12| 

316 

14 

473 

15" 

5S4 

5d 

If 

121 

271 

14 

406 

15 

500 

Qd 

2 

HI 

181 

121 

236 

131 

309 

7d 

2i 

1H 

161 

121 

210 

13 

238 

8d 

2| 

104 

106 

111 

145 

121 

1S9 

Qd 

96 

111 

132 

172 

Wd 

3* 

94 

69 

94 

Hi 

121 

I2d 

9 

63 

101 

87 

111 

113 

Wd 

8 

49 

10 

71 

11 

90 

20d 

4 

6 

31 

9 

52 

10 

62 

30d 

41 

5 

24 

9 

46 

40d 

5 

4 

18 

8 

35 

60d 

51 
6 

3 

2 

14 
11 

Shingle  Nails. 

Size. 

Length, 
Inches. 

Gauge. 

No.  to 
Pound. 

Spikes.* 

3d 

1-1 

13 

429 

Size. 

Length, 
Inches. 

Gauge. 

No.  to 
Pound. 

fd 

If 

12 
12 

274 
235 

Wd 

3 

6 

41 

Id 

2 
21 

12 
11 

204 
131 

I2d 

3i 

6 

38 

8d 

11 

125 

Wd 

31 

5 

30 

2} 

11 

114 

20d 

4 

A  1 

4 

23 

Wd 

3 

10 

83 

3Qd 

41 

40d 

5 

2 

13 

Fine  Nails. 

5Qd 

51 

1 

10 

QOd 

6 

1 

8 

2d 

1 

161 

1,351 

7" 

7 

0 

7 

3d 

1J 

15 

778 

8" 

8 

00 

6 

4-d 

11 

14 

473 

9" 

9 

00 

5 

3d] 

10" 

10 

V 

4 

extra  > 

H 

16 

1,015 

12" 

12 

i" 

3 

fine    ) 

*  Common  brads  differ  from  common  nails  only  in  the  head  and  point. 
t  Lengths  are  the  same  as  common  nails  for  corresponding  size. 
j  Spikes  are  made  with  chisel   points   and  diamond  points ;  also  with 
convex  heads  and  flat  heads. 


WIRE  NAILS,  SPIKES,  AND  TACKS.  1369 

STEEL-WIRE  NAILS.— Continued. 


Clinch  Nails. 

Fence  Nails.* 

Slating  Nails.* 

Size. 

Length, 
Inches. 

Gauge. 

No.  to 
Pound. 

Gauge. 

No.  to 
Pound. 

Gauge. 

No.  to 
Pound. 

2d 
3d 
4d 
5d 
Qd 
Id 
8d 
9d 
lOd 
I2d 
Wd 
2Qd 

1 
H 
lj 

if 

2 
21 
$ 

2i 
3 
3i 

3^ 
4 

14 
13 
12 
12 
11 
11 
10 
10 
9 
9 
8 
7 

710 
429 
274 
235 
157 
139 
99 
90 
69 
62 
49 
37 

No.  5  s 
si 
10 
10 
9 
9 
8 
7 
6 
5 
4 

mallest 
ze 
142 
124 
92 
82 
62 
50 
40 
30 
23 

12 
10J 
10J 
10 
9 

411 
225 
187 
142 
103 

Barbed  Roofing  Nails.  f 

?"XNo.  13 
f'XNo.  12 
l"XNo.  12 
li"XNo.,!2 
H"XNo.  11 

714 
469 
411 
365 
251 

*  Length  same  as  clinch  nails  of  corresponding  size, 
t  Roofing  nails  are  designated  by  the  length,  not  by  "penny."     These 
nails  are  made  up  to  2  ins.  long. 


WIRE  TACKS. 


oJ 
§ 

jj 

j| 

0)         S 

jj 

U| 

o>      d 

g 

iST- 

6  ^ 

»§ 

S  <3  O 

oT3 

wj  2 

'd    fe    O 

a?  d 

M§ 

^  ^  O 

gU 

1** 

53O 

H 

S^ 

1^ 

H 

r 

la^ 

1 

i 

16,000 

4 

% 

4,000 

14 

^ 

1  143 

H 

10,666 

6 

/l6 

2,666 

16 

i 

1,000 

2 

i 

8,000 

8 

1 

2,000 

18 

888 

2* 

6,400 

10 

1,600 

20 

i 

800 

3 

1 

5,333 

12 

i 

1,333 

22 

i^ 

727 

24 

H 

666 

Wire  carpet  tacks  are  made  polished,  blued,  tinned,  or  cop- 
jred;   there  are  also  upholsterers'  and  bill-posters'  or  railroad 

nlrs 


pered 
tacks 


370  SCREWS  AND   EXPANSION  BOLTS. 

Expansion  Bolts. — These  are  commonly  used  for  bolting 
wood  or  iron  to  masonry  that  is  already  built.  A 
hole  is  drilled  in  the  masonry  of  such  size  that  the 
expansion  nut  will  fit  closely,  and  when  the  bolt  is 
screwed  up  the  nut  expands  and  binds  firmly  in  the 
masonry.  The  illustration  shows  the  Evans  expan- 
sion bolt,  which  is  also  furnished  with  screw-head 
bolts.  There  are  two  other  forms  of  expansion  bolts 
on  the  market. 

Screws. — Screws  are  made  of  iron,  steel,  brass, 
copper,  bronze,  and   phosphor-bronze,  the  ordinary 
XBoltJ10n  screw  being  of  iron.     Iron  screws   are  finished  with 
either   a   bright,  blue,  bronze,  lacquered,  tinned,  or 
galvanized  surface,  and  are  also  plated  in  nickel,  brass,  bronze, 
copper,  and  silver. 

The  size  of  screws  is  designated  by  the  length  in  inches  and 
the  number  of  gauge — which  denotes  the  diameter  of  the  body 
of  the  screw.  Thus  a  1-in.  No.  12  screw  denotes  a  screw 
1  in.  long  and  .2158  of  an  inch  in  diameter. 

The  gauge  numbers  range  from  No.  0  to  No.  30,  and  the 
length  from  J  in.  to  6  ins.  Lengths  vary  by  eighths  of  an 
inch  up  to  1  in.,  by  quarters  of  an  inch  up  to  3  ins.,  by  halves 
up  to  5  ins. 

Screws  from  f  in.  to  4J  ins.  long  are  made  in  about  sixteen 
different  gauge  numbers. 

The  table  on"  page  1346  shows  the  diameter  to  four  places  of 
decimals  of  the  American  Screw  Gauge. 

It  should  be  noticed  that  unlike  the  ordinary  wire  gauges, 
the  0  of  the  screw  gauge  is  the  smallest,  and  the  diameter 
increases  with  the  number  of  the  gauge. 

Wood-screws  are  made  with  twenty-five  different  shapes  of 
heads  for  different  purposes.  The  most  common  shapes, 
however,  are  the  ordinary  flat  head,  round  head,  and  oval 
head.  The  latter  is  tapered  for 
counter-sinking,  but  is  slightly 
rounded  on  top. 

Patent  diamond  -  point  steel 
screws  are  made  especially  for 
driving  with  a  hammer.  "^g- and  Cbach-screws. 

Screws  for  metal  have  the  same 
diameter  throughout  and  the  threads  are  V  shaped. 

Lag-  or  coach-screws  are  large  heavy  screws  used  where  great 


DATA  ON   EXCAVATING. 


1371 


strength  is  required,  as  in  heavy  framing,  and  for  fixing  iron- 
work to  timber.  Lag-screws  with  conical  point  are  made  with 
diameters  of  %,  f ,  %,  J,  %,  f,  f,  and  1  in.,  and  in  lengths  from 
1 J  to  12  ins. ;  coach-screws  in  diameters  from  %  to  }  in.  and  in 
lengths  from  1J  to  12  ins. 

HOLDING  POWER  OF  LAG-SCREWS. 

(Tests  made  by  A.  J.  Cox,  University  of  Iowa,  1891,  quoted 
by  Kent,  page  290.) 


Max- 

Kind of  Wood. 

Size 
Screw. 

Size 
Hole 
Bored. 

Length 
in 
Wood. 

imum 
Resist- 
ance, 

No. 
Tests. 

Lbs. 

Inch. 

Inch. 

Inches. 

Seasoned  white  oak 

£ 

1 

44 

8  037 

3 

U                       11               U 

% 

% 

3 

6,480 

1 

({                 <(           11 

1 

4§ 

8,780 

2 

Vellow-pine  stick 

5 

\ 

4 

3800 

2 

White  cedar,  unseasoned.  . 

1- 

i 

4 

3,405 

2 

(Hoopes   &   Townsend   give   the   force   at   which   screws   were 
.drawn  out  of  yellow  pine  as  follows:) 


Screw.  .  .  . 

y*  in. 

%  in. 

H  in. 

Kin. 

1  in. 

Wood,  depth  . 

3i  ins 

4  ins 

4  ins 

5  ins 

6  ins 

Force,  pounds  

4,960 

6,000 

7,685 

11,500 

12,620 

Wood-screws  are  sold  by  the  gross,  lag-  and  coach-screws  by 
the  pound. 

DATA  ON  EXCAVATING. 

Excavating  is  almost  invariably  measured  by  the  cubic  yard 
of  27  cu.  ft. 

For  measuring  excavations  of  irregular  depth  see  p.  69. 

For  computing  the  contents  of  wells  and  cesspools,  the  circu- 
lar area  in  square  feet  may  be  obtained  from  the  table  on 
p.  53,  and  this  multiplied  by  the  depth  in  fes'c  will  give  contents 
in  cubic  feet. 

The  cost  of  excavating  and  removing  earth  is  ordinarily  made 
up  of  the  following  items: 

a.  Loosening  the  earth  for  the  shovellers. 


1372  DATA  ON  EXCAVATING. 

b.  Loading  by  shovels  into  carts  or  barrows. 

c.  Hauling   or   wheeling   it    away,    including    emptying   and 
returning. 

d.  Spreading  it  out  on  the  dump. 

For  every  large  job,  such  as  railroad  work,  it  is  also  neces- 
sary to  make  an  allowance  for  keeping  the  hauling  road  in 
repair,  sharpening  and  repair  of  tools,  carts,  harness,  super- 
intendence, and  water-carriers. 

Where  the  dirt  excavated  can  be  spread  over  the  ground 
immediately  surrounding  the  excavation  the  loosened  dirt 
may  be  removed  by  scrapers  without  shovelling. 

Data  for  Estimating  Cost. — For  loosening:  Two  men  with  a 
plough  and  team  of  horses  will  loosen  from  20  to  30  cu.  yds.  of 
strong,  heavy  soils  per  hour  or  from  40  to  60  cu.  yds  of  ordinary 
loam.  One  man  with  a  pick  will  loosen  1J  yds.  per  hour  of 
stiff  clay  or  cemented  gravel,  4  yds.  of  common  loam,  or  6  yds. 
of  light  sand. 

The  average  quantity  of  loosened  earth  which  a  man  can 
shovel  into  a  cart  per  hour  is: 

Loam  or  sand 2.0  cu.  yds. 

Clay  and  heavy  soils 1.7        " 

Rock 1.0  cu  yd. 

Average  earth  loosened  swells  to  from  1J  to  1J  times  its 
original  bulk  in  place. 

The  capacity  of  vehicles  used  for  moving  excavated  materials 
is  about  as  follows: 

Wheelbarrows 3  to    4  cu.  ft. 

1-horse  dump-carts , 18  "  22       " 

2-horse  dump-wagons. 27  "  45       "    * 

Drag  scrapers 3  "    7       " 

Wheel  scrapers 10  "  17       " 

Dump-cars  on  rails 27  "  80       " 

The  economical  length  of  haul  with  drag  scrapers  is  about 
150  ft.;  with  wheeled  scrapers,  500  ft.;  with  wheelbarrows, 
250  ft.;  with  1-horse  dump-carts,  600  ft.f 

The  average  speed  of  horses  is  given  as  about  200  ft.  per 
minute. 

*  The   ordinary   load   for   2-horse   wagons    such  as  are  commonly  used 
for  hauling  dirt,  sand,  and  gravel   is  from  1J4  to  1H  cu.  yds. 
t  Inspectors'  Pocket-book,  A.  T.  Byrne,  C  E. 


DATA  ON  STONEWORK.  1373 

Much  valuable  data  for  estimating  the  cost  of  excavating 
may  be  found  in  Trautwine's  Engineer's  Pocket-book,  p.  800- 
810. 

Weight  of  Earth,  Sand,  and  Gravel. — For  general  calculations 
the  following  average  values  may  be  taken: 


19  cu.  ft.  of  gravel  weigh  1  ton 
22       "      "    sand         "      1    " 


1-1  cu.  ft.  of  chalk  weigh  1  ton 
18       "      "    clay        "       1     " 
21       "      "    earth     "       1     " 

Rock  Excavation. — A  cubic  yard  of  rock,  in  place,  when 
broken  up  by  blasting  for  removal  by  wheelbarrows  or  carts, 
will  occupy  a  space  of  about  1|  cu.  yds.;  consequently  the 
cost  of  hauling  or  removal  is  about  50  per  cent,  more  than 
for  dirt. 

With  labor  at  $1  per  day,  the  actual  cost  for  loosening  hard 
rock,  including  tools,  drilling,  powder,  etc.,  will  average  about 
45  cts.  per  cubic  yard,  in  place,  under  all  ordinary  circumstances. 
In  practice  it  will  generally  range  between  30  and  60  cts., 
depending  on  the  position  of  the  strata,  hardness,  toughness, 
water,  and  other  considerations.  Soft  shales  and  other  allied 
rocks  may  frequently  be  loosened  by  pick  and  plough  as  low 
as  15  to  20  cts.,  while  on  the  other  hand  shallow  cuttings  of 
very  tough  rock  with  an  unfavorable  position  of  strata, 
especially  in  the  bottoms  of  excavations,  may  cost  $1  per  cubic 
yard,  or  even  considerably  more.  The  quarrying  of  average 
hard  rock  requires  about  i  to  J  Ib.  of  powder  per  cubic  yard, 
in  place,  but  the  nature  of  the  rock,  the  position  of  the  strata, 
etc.,  may  increase  it  to-  §•  Ib.  or  more.  Soft  rock  frequently 
requires  more  powder  than  hard.  A  good  churn-driller  will 
drill  8  to  10  ft.  in  depth  of  holes  about  2J  ft.  deep  and  2  ins. 
diameter  per  day  in  average  hard  rock,  at  from  12  to  18  cts. 
per  foot.* 

DATA  ON  STONEWORK. 

(For  description  of  various  kinds  of  stonework,  see  Building 
Construction  and  Superintendence,  Part  I  Chapter  VI.) 

The  commonest  kind  of  stonework,  i.e.  for  walls,  is  called 
rubblework.  No  work  whatever  Is  done  on  the  stones  except 
to  break  them  up  with  a  hammer. 

If  the  wall  is  built  in  courses  it  is  designated  as  coursed 
rubble. 

*  Trautwine,  p.  8 10. 


1374  DATA  ON  STONEWORK. 

When  the  stones  showing  on  the  outside  face  of  the  wall  are 
squared,  the  work  is  designated  as  ashlar.  Ashlar  is  of  two 
kinds:  coursed  ashlar,  in  which  the  stones  are  laid  to  form 
courses  around  the  building,  all  of  the  stones  in  any  course 
being  of  the  same  height,  and  broken  ashlar,  in  which  stones 
of  different  heights  are  used.  Hammer-dressed  ashlar  desig- 
nates work  where  the  stones  are  roughly  squared  with  a  hammer. 
This  is  a  very  cheap  class  of  work.  Good  ashlar  work  should 
be  squared  on  the  bench  with  chisels,  and  with  beds  and  end 
joints  cut  square  to  the  face. 

Stonework  which  requires  a  chisel  or  any  other  tool  except 
a  hammer  for  dressing  is  called  "cut- work."  Cut-work  costs 
considerably  more  than  hammer-dressed  work. 

Measurement  of  Stonework. — Rough  stone  from  the  quarry 
is  usually  sold  under  two  classifications:  rubble-  and  dimension- 
stone.  Rubble  includes  the  pieces  of  irregular  size  most  easily 
obtained  from  the  quarry,  and  suitable  for  cutting  into  ashlar 
12  ins.  or  less  in  height  and  about  2  ft.  long.  Stone  ordered  of 
a  certain  size,  or  to  square  over  24  ins.  each  way,  and  of  a  par- 
ticular thickness,  is  called  dimension-stone.  The  price  of  the 
latter  varies  from  two  to  four  times  the  price  of  rubble. 

Rubble  is  generally  sold  by  the  ton  or  car-load.  Footings 
and  flagging  are  usually  sold  by  the  square  foot;  dimension- 
stone  by  the  cubic  foot.  In  Boston  granite  blocks  for  founda- 
tions are  usually  sold  by  the  ton. 

In  estimating  on  the  cost  of  stonework  put  into  a  building, 
the  custom  varies  with  different  localities,  and  even  among 
contractors  in  the  same  city. 

Dimension-stone  footings  (that  is,  squared  stone  2  ft.  or  more 
in  width)  are  usually  measured  by  the  square  foot.  If  built 
of  large  rubble  or  irregular  stones  the  footings  are  measured  in 
with  the  wall,  allowance  being  made  for  the  projections  of  the 
footings. 

Rubblework  is  almost  universally  measured  by  the  perch 
of  16 J  cu.  ft.  The  author  has  been  unable  to  find  any  locality 
where  the  legal  perch  of  24f  cu.  ft.  is  used  by  stone-masons. 
In  Philadelphia,  St.  Louis,  and  some  portions  of  Illinois,  22  cu.  ft. 
are  called  a  perch. 

Railroad  work  is  usually  measured  by  the  cubic  yard. 

When  stonework  is  let  by  the  perch,  the  number  of  cubic 
feet  to  the  perch  should  be  stated  in  the  contract,  and  also 
whether  or  not  openings  are  to  be  deducted.  As  a  rule  no 


DATA  ON  STONEWORK.  1375 

deductions  are  made  for  openings  of  less  than  70  superficial 
feet. 

Data  for  Estimating  Cost. — The  price  of  common  rubble 
as  it  comes  from  the  quarry  will  vary  from  50  cts.  to  $1.50  per 
ton,  f  .o.b.  at  point  of  delivery,  according  to  the  cost  of  quarrying, 
transportation,  etc.  $1.25  a  perch  is  probably  a  fair  average. 

A  ton  of  most  stones  will  make  from  1  to  1J  perch. 

The  cost  of  laying  one  perch  of  stone  may  be  estimated  by 
the  following  items: 

Labor:  mason  2|  hrs.,  helper  If  hrs.  (based  on  2  helpers 
to  3  masons);  sand  J  load;  lime  f  bu.,  or  if  laid  in  all  cement 
mortar,  one  perch  will  require  from  J  to  ^  bbl.  cement. 

At  average  wages,  rubble  cellar  walls,  18  ins.  to  2  ft.  thick, 
laid  in  lime  mortar,  vary  in  cost  from  $2.75  to  $4  per  perch, 
$3.25  a  perch  being  a  fair  average;  in  all  cement  mortar 
from  $3.25  to  $4.25  per  perch. 

The  cost  of  ashlar  depends  very  largely  upon  the  kind  of 
stone  used  and  the  distance  it  has  to  be  brought.  The  price 
of  the  rough  stock  on  the  cars  at  point  of  delivery  may  vary 
from  70  cts.  to  $1.25  per  cubic  foot  for  granite  and  55  cts.  to  $1 
for  sandstones  and  limestones,  depending  largely  upon  cost  of 
transportation.  1  cu.  ft.  of  stone  should  make  2  sq.  ft.  of 
ashlar,  at  least.  Some  quarries  get  out  stone  especially  suit- 
able for  ashlar  and  sell  it  at  about  25  cts.  per  lineal  foot  for 
courses  12  ins.  high. 

The  cost  of  cutting  ashlar,  with  stone-cutters'  wages  at  $4 
per  day,  will  average  about  15  cts.  per  square  foot  for  soft 
stones,  15  to  20  cts.  per  square  foot  for  hard  sandstones  and  lime- 
stones, and  25  to  30  cts.  for  granite.  The  cost  of  setting  ashlar 
will  vary  from  10  cts.  per  square  foot  to  25  cts.  for  soft  stones 
or  30  cts.  for  granite,  15  cts.  being  an  average  price  for  sand- 
stones and  limestones. 

The  cost  of  cut-stone  trimmings  depends  so  largely  upon  the 
kind  of  stone,  that  it  is  quite  impossible  to  give  prices  that 
would  be  of  any  service. 

The  following  figures,  however,  quoted  from  The  Building 
Trades  Pocket-book,  may  be  of  some  guide  in  forming  a 
rough  estimate,  the  prices  if  anything  being  probably  a  little 
above  the  cost  of  the  local  stone  in  most  localities. 

Flagstones  for  sidewalks,  ordinary  stock,  natural  surface, 
3  ins.  thick,  with  joints  pitched  to  line,  in  lengths  (along  walk) 
from  3  to  5  ft.,  will  cost,  for  3-ft,  y^lk,  about  8  cts.  per  square 


1376        DATA  ON  BRICKS  AND   BRICKWORK. 

foot  (if  2  ins.  thick,  6  cts.);  for  4-ft.  walk,  9  cts.;  and  for  5-ft. 
walk,  10  cts.  per  square  foot.  The  cost  of  laying  all  sizes 
will  average  about  3  cts.  per  square  foot.  The  above  figures 
do  not  include  cost  of  hauling. 

Curbing  (4-in.X24-in.  granite)  will  cost  at  quarry  from  25 
to  30  cts.  per  lineal  foot;  digging  and  setting  will  cost  from 
10  to  12  cts.  additional;  and  the  cost  of  freight  and  hauling 
.must  also  be  added. 

The  following  figures  show  the  approximate  cost  of  cut  blue- 
stone  for  various  uses: 

Flagstone,  5  ins.,  size  8  ft.XlO  ft.,  edges  and  top  bush- 
hammered,  per  square  foot  face  measure $0 . 65 

Flagstone,  4  ins.,  size  5  ft.  X5  ft.,  select  stock,  edges  clean- 
cut,  natural  top,  per  square  foot 30 

Door-sills,  8  in.  X 12  in.,  clean  cut,  per  lineal  foot 1 . 25 

Window-sills,  5  in.  X 12  in.,  clean-cut,  per  lineal  foot 80 

Window-sills,  4  in.  X8  in.,  clean-cut,  per  lineal  foot 45 

Window-sills,  5  in.  X8  in.,  clean-cut,  per  lineal  foot 60 

Lintels,  4  in.  X 10  in.,  clean-cut,  per  lineal  foot .60 

Lintels,  8  in.  X 12  in.,  clean-cut,  per  lineal  foot 1.10 

Water-table,  8  in.  X 12  in.,  clean-cut,  per  lineal  foot 1 . 25 

Coping,  4  in.  X 21  in.,  clean  cut,  per  lineal  foot 1 . 10 

Coping,  4  in.  X 21  in.,  rock-face  edges  and  top,  per  lineal  foot  . 45 
Coping,  3  in.  X 15  in.,  rock-face  edges  and  top,  per  lineal  foot  .  25 
Coping,  3  in.  X 18  in.,  rock-face  edges  and  top,  per  lineal  foot  .  30 

Steps,  sawed  stock,  7  in.  X 14  in.,  per  lineal  foot 90 

Platform,  6  in.  thick,  per  square  foot 45 

To  the  prices  of  cut  stone  above  given  must  be  added  the 
cost  of  setting,  which,  for  water-tables,  steps,  etc.,  will  be 
about  10  cts.  per  lineal  foot,  and  for  window-sills,  etc.,  about 
5  cts.  per  lineal  foot. 

DATA  ON  BRICKS  AND  BRICKWORK. 

[For  a  complete  description  of  clay  bricks,  their  process  of 
manufacture,  etc.,  also  of  all  kinds  of  brickwork,  see  Chapter 
VII,  Part  I,  of  Building  Construction  and  Superintendence.] 

The  word  brick  as  commonly  used  refers  to  blocks  made 
Irom  clay  that  have  been  moulded  into  the  required  shape 
and  burned  in  a  kiln,  and  until  quite  recently  practically  all 
bricks  were  made  from  clay;  at  the  present  time,  however, 
bricks  are  also  made  from  sand  and  lime. 

Clay  Bricks. — These  may  be  broadly  classified  as  common 
brick,  face-brick,  fire-brick,  and  paving-brick. 

As  to   the  process  of  i^ianufacture,   bricks  are   classified  as 


DATA  ON  BRICKS  AND  BRICKWORK.        1377 

soft-mud  bricks,  stiff-mud  bricks,  dry-pressed  bricks,  and 
re-pressed  bricks. 

Soft-mud  bricks  are  made  by  tempering  the  clay  with  water 
until  it  becomes  soft  and  plastic,  when  it  is  pressed  into  the 
moulds  either  by  hand  or  by  a  machine.  Practically  all  hand- 
made bricks  are  soft-mud  bricks. 

Stiff-mud  bricks  are  machine-made.  The  clay  is  first  ground 
and  only  enough  water  is  added  to  make  a  stiff  mud.  The 
stiff  clay  is  forced  through  a  die  or  dies  in  the  machine  in  a 
continuous  stream,  which  is  cut  up  automatically  into  pieces 
the  size  either  of  the  end  or  side  of  the  brick.  If  the  opening 
is  the  size  of  the  end  of  the  brick,  the  bricks  are  end-cut;  if 
of  the  size  of  the  side  of  the  brick,  they  are  side-cut.  Stiff- 
mud  bricks  can  readily  be  distinguished  from  soft-mud  bricks  by 
their  appearance.  As  good  if  not  better  bricks  can  be  made  by 
the  soft-mud  process  as  by  the  stiff-mud  process,  and  in  the 
Eastern  States  the  soft-mud  bricks  are  probably  the  strongest. 
As  far  as  the  author's  observation  has  extended  in  the  Western 
States,  the  stiff-mud  bricks  are  as  a  rule  preferable  to  those 
made  by  the  soft-mud  process. 

Stiff-mud  bricks  are  usually  heavier  than  soft-mud  or  hand- 
made bricks. 

Soft-mud  bricks  are  often  re-pressed  to  make  face-bricks. 

Dry-pressed  bricks  are  made  almost  entirely  for  face- work, 
although  in  some  localities  dry-pressed  bricks  are  also  used  for 
common  bricks.  Hydraulic-pressed  bricks  are  dry-pressed. 
Moulded  bricks  are  always  dry-pressed.  Very  fine  bricks  are 
made  by  this  process. 

Bricks  made  by  any  of  the  above  processes  require  to  be  burned 
in  a  kiln.  According  to  their  position  in  the  kiln,  common 
brick  are  designated  as  arch  or  hard-burned  brick,  red  or  well- 
burned  brick,  and  salmon  or  soft  brick.  As  a  rule,  salmon 
brick  are  not  fit  to  use  in  an  exterior  or  bearing  wall. 

Color. — The  color  of  brick  depends  principally  upon  the 
presence  of  iron,  lime,  and  magnesia  in  the  clay.  A  large 
proportion  of  oxide  of  iron  gives  a  clear  bright  red.  Magnesia 
produces  a  brown  color,  and  when  in  the  presence  of  iron  gives 
&  light  drab  color. 

Dryoressed  bricks  are  often  colored  artificially  either  by 
mixing  clays  of  different  composition,  or  by  mixing  mineral 
colors  *vith  the  finely  ground  clay. 

Fi>*o-brick.s   are   ordinarily  made  from  a  mixture  of  flint 


1378        DATA  ON  BRICKS  AND  BRICKWORK. 

clay  and  plastic  clay.  They  are  usually  white  or  white  mixed 
with  brown  in  color  and  are  used  for  the  lining  of  furnacesi 
fireplaces,  and  tall  chimneys. 

Paving-bricks  are  a  very  hard  brick,  usually  vitrified  or 
annealed.  They  are  much  more  expensive  than  common 
brick  and  are  seldom  used  in  buildings. 

Size  and  Weight  of  Clay  Bricks. —  In  this  country 
there  is  no  legal  standard  for  the  size  of  bricks,  and  the  dimen- 
sions vary  with  the  maker  and  also  with  the  locality.  In  the 
New  England  States  the  common  brick  averages  about 
7f  X  3f  X  2|  ins.  In  most  of  the  Western  States  common  bricks 
measure  about  8JX4J  X2J  ins.,  and  the  thickness  of  the  walls 
measures  about  9,  13,  18,  and  22  inches  for  thickness  of  1,  1J, 
2,  and  2J  bricks.  The  size  of  all  common  bricks  varies  con- 
siderably in  each  lot,  according  to  the  degree  to  which  they 
are  burnt;  the  hard  bricks  being  from  %  to  %>  of  an  inch 
smaller  than  the  salmon  bricks. 

Pressed  bricks  or  face-bricks  are  more  uniform  in  size,  as  most 
of  the  manufacturers  use  the  same  size  of  mould.  The  pre- 
vailing size  for  pressed  bricks  is  8f  X4-|X2f  ins.  Pressed  bricks 
are  also  made  \\  ins.  thick  and  12x4Xli  ins.,  the  latter  size 
being  generally  termed  Roman  brick,  or  tile. 

The  weight  of  bricks  varies  considerably  with  the  quality 
of  the  clay  from  which  they  are  made,  and  also,  of  course,  with 
their  size.  Common  bricks  average  about  4J  Ibs.  each,  and 
pressed  bricks  vary  from  5  to  5J  Ibs.  each. 

For  strength  of  bricks  and  brickwork,  see  pp.  213,  218,  229. 

Fire-bricks  are  made  in  various  forms  to  suit  the  required 
work.  A  straight  brick  measures  9X4JX2J  ins.  and  weighs 
about  7  Ibs. 

To  secure  the  best  results  fire-bricks  should  be  laid  in  the  same 
clay  from  which  they  are  manufactured,  this  being  mixed  with 
water  into  a  thin  paste.  The  thinner  the  joint,  the  better  the 
wall  will  stand  heat. 

Paving-bricks  vary  in  size  and  wreight  according  to  the  locality 
and  the  requirements  of  the  specifications. 

The  "standard"  bricks  are  2JX4X8  ins.,  requiring  61  bricks 
to  the  square  yard  (on  edge),  and  weigh  7  Ibs.  each.  " Re- 
pressed" bricks  are  2JX4X8J  ins.,  requiring  58  to  the  square 
yard  and  weigh  6J  Ibs.  each.  " Metropolitan"  are  3X4X9  ins., 
requiring  45  to  the  square  yard,  and  weigh  9J  Ibs.  each.* 

*  Building  Inspectors'  Pocket-book. 


DATA  ON  BRICKS  AND  BRICKWORK.        1379 

Saiid-lime  Brick. — Bricks  made  of  sand  and  lime  have 
been  made  in  Germany  for  fifty  years  or  more  and  the  industry 
appears  to  be  established  on  a  successful  basis.  During  the 
past  three  or  four  years  a  number  of  plants  have  been  equipped 
in  this  country  for  the  manufacture  of  these  bricks.  There 
are  three  or  four  different  processes  of  manufacture,  the  prin- 
cipal ones  being  the  "Huennekes"  and  "Schwarz"  systems. 
Parties  who  have  personally  inspected  plants  operated  by  each 
system  appear  to  be  divided  in  their  opinion  as  to  which  pro- 
cess produces  the  best  brick.  The  hardening  process,  by  steam, 
is  common  to  all  systems,  as  the  practicability  of  sand-lime 
bricks  is  due  to  the  formation  of  silicate  of  lime,  brought  about 
by  the  heat  and  moisture. 

Under  the  "  Huennekes  System"  the  process  is  briefly  as 
follows  :*  The  sand  is  put  through  a  dryer,  and  then  passes  to 
a  measuring-machine.  The  lime,  previously  burnt  in  a  kiln,  is 
crushed  very  fine,  and  then  passes  to  the  measuring-machine, 
and  is  mixed  with  the  sand  just  after  leaving  it.  The  mixture 
is  measured  to  contain  94  per  cent,  of  sand  and  G  per  cent,  of 
lime.  This  mixture  is  then  conveyed  to  a  tube-mill,  where 
it  is  ground  very  fine,  and  then  drops  into  the  wet  mixer,  where 
enough  water  is  added  so  that  the  mixture  will  ball  easily  in 
the  hand.  It  is  then  conveyed  to  a  large  bin,  where  it  is  kept 
about  twelve  hours  to  permit  the  lime  to  slake.  From  this 
bin  it  goes  to  the  press  in  which  the  bricks  are  formed  under  a 
pressure  of  about  175  tons  to  the  brick.  They  are  then  piled 
on  cars  holding  from  850  to  1000  bricks,  and  the  cars  are  run 
into  a  steel  cylinder  62  ft.  long  and  6  ft.  in  diameter,  fitted  with 
a  track  and  a  tank  for  holding  chemicals.  As  soon  as  the  cylin- 
der is  filled,  the  head  is  bolted  on  and  steam  is  introduced.  The 
steam  on  entering  goes  through  the  chemical  tank  and  becomes 
supercharged  with  the  chemical.  Steam  is  kept  at  120  Ibs. 
pressure  for  eleven  hours,  when  it  is  blown  off,  the  head  taken 
off,  and  the  bricks  are  taken  out  ready  for  the  market. 

The  chemical  combination  is  controlled  exclusively  by  II. 
Huennekes  Company  of  New  York  City,  who  license  and  equip 
factories  for  the  manufacture  of  bricks  under  their  process. 

The  Schwarz  system  f  differs  from  the  above  in  the  prepara- 
tion of  the  sand  and  lime  for  the  press,  which  is  done  in  a  prepar- 

*  This  information  was  furnished  the  author  by  Mr.  D.  P.  De  Long,  Prest. 
Granite  Brick  Company  of  Glens  Falls,  N.  Y. 

t  Schwarz  System  Brick  Co.,  8  Bridge  Street,  New  York, 


1380        DATA  ON  BRICKS  AND  BRICKWORK. 

ing-machine  invented  by  Dr.  Schwarz  of  Zurich,  Switzerland; 
also  no  chemicals  are  used  with  this  system — nothing  but  lime 
and  sand.  [It  is  claimed  that  not  a  single  sand-lime  brick 
factory  in  Europe  applies  any  kind  of  chemicals  whatsoever.] 
In  the  Schwarz  preparing-machine  all  the  moisture  of  the 
sand  is  first  removed  by  drying  the  same  under  vacuum;  the 
lime  is  then  added  and  the  materials  thoroughly  mixed  by  two 
wing-shaped  agitators  revolving  in  the  cylinder  in  opposite 
directions.  Then  follows  a  carefully  measured  and  always  con- 
stant amount  of  water  to  slaken  the  lime,  and  the  heat  evolved 
upon  this  reaction  is  immediately  utilized  for  a  second  reaction, 
i.e.,  the  opening  up  of  the  silica  of  the  sand  and  the  formation 
of  silicate  of  lime,  by  which  process  the  mass  is  rendered  soft 
and  plastic,  easy  to  mold,  and  causing  little  wear  and  tear  to  the 
press.  Finally,  the  mixing  going  on  continually,  again  a 
definite  amount  of  water  is  added  to  moisten  the  mass  for  the 
press,  whereupon  the  apparatus  is  emptied  and  recharged. 

The  advocates  of  the  Schwarz  system  claim  that  their  pro- 
cess produces  a  more  uniform  mixture,  and  consequently  a 
brick  of  more  uniform  quality. 

The  sand  used  should  be  a  sharp  silica  sand  free  from  clay  * 
and  nearly  free  from  loam.  The  lime  should  be  a  fat,  quick- 
slaking  lime  free  from  magnesia. 

Qualities. — The  natural  color  of  sand-lime  brick  is  white  or 
a  light  gray;  the  bricks  are  said  to  present  a  fine  appearance. 
They  are  very  dense,  and  show  a  very  small  absorption  of 
moisture,  usually  under  10  per  cent. 

The  average  crushing  strength  seems  to  be  about  3,000  Ibs. 
per  square  inch,  although  tests  have  shown  an  ultimate  strength 
of  6,700  Ibs.  per  square  inch. 

The  bricks  made  by  the  Granite  Brick  Company  of  Glens 
Falls,  N.  Y.,  measure  8^X4  X2|  ins.,  and  weigh  5  Ibs.  each. 
This  company  is  selling  its  face  brick  at  $10  per  M.,  f.o.b.  at 
factory. 

The  author  understands  that  sand-lime  bricks  are  being  used 
to  a  considerable  extent  in  different  portions  of  the  country. 

Glazed  and  Enamelled  Brick. f — The  terms  " enam- 
elled brick"  and  " glazed  brick/7  as  commonly  used,  refer  practi- 

*  The  presence  of  clay  in  the  sand  tends  to  prevent  its  standing  freezing 
weather. 

t  For  description  of  process  of  manufacture,  see  p.  197  Building  Con- 
struction and  Superintendence,  Part  I. 


DATA  ON  BRICKS  AND   BRICKWORK.        1381 

cally  to  the  same  article,  and  neither  include  what  is* known 
as  a  "salt-glazed"  brick.  The  enamelled  or  glazed  brick  are 
generally  dipped  or  sprayed  and  then  burned,  whereas  the  "  salt- 
glaze  "  is  obtained  by  the  introduction  of  salt  into  the  fire- 
boxes of  kilns  while  the  bricks  are  being  burned.  Glazed  or 
enamelled  brick  are  generally  divided  into  two  classes:  true 
enamelled  brick,  which  has  a  glaze  containing  the  coloring  mat- 
ter applied  to  it  without  any  intermediate  slip;  the  other  has  a 
transparent  glaze  placed  over  a  white  or  colored  slip,  the  slip  com- 
ing between  the  glaze  and  the  material^to  be  glazed.  The  latter 
is  the  process  most  used  in  this  country.  Manufacturers  differ 
as  to  which  process  produces  the  best  brick,  although  it  would 
seem  as  though  the  true  enamel  would  not  chip  or  "peel"  as 
readily.  These  bricks  can  be  made  in  a  variety  of  colors,  from 
white  to  dark  green  or  chocolate,  and  either  in  a  highlg  glazed 
or  satin  (dull  finish),  the  latter  finish  being  quite  desirable  in 
many  instances  on  account  of  its  doing  away  with  the  glare  of 
the  more  highly  glazed  bricks  or  tile. 

An  enamelled  surface  may  be  distinguished  from  a  glazed 
surface  by  chipping  off  a  piece  of  the  brick.  The  glazed  brick 
will  show  the  layer  of  slip  between  the  glaze  and  the  brick;  the 
enamelled  brick  will  show  no  line  of  demarcation  between  the 
body  of  the  brick  and  the  enamel. 

Enamelled  bricks  are  made  in  two  regular  sizes,  English  size 
(9"X3"  enamelled  surface,  4%'  bed)  and  American  size 
(8f//X2i"  enamelled  surface,  4J"  bed). 

The  English  size  costs  about  $10  per  M.  more  than  the  Ameri- 
can, but  on  account  of  the  saving  in  the  number  of  bricks, 
labor  of  laying,  and  mortar  in  joints,  they  really  effect  a  saving 
of  about  7  cts.  per  square  foot. 

The  Tiffany  Enamelled  Brick  Company  also  make  a  ' '  Norman 
flat"  (12"X4J"  enamelled  surface,  2i"  bed). 

The  selling  price  of  enamelled  brick  in  Chicago  at  the  present 
time  (June,  1904),  is  as  follows: 

American  size    .  .   $75  per  M.       English   size $85  per  M. 

Norman  flat  ....   $100 

At  these  prices  the  cost  of  the  bricks  per  square  foot  will  be: 

American  size,  7  bricks  to  the  foot 52  J  cts. 

English  size,  5|  bricks  to  the  foot 45 £  " 

English  flat,  3|  bricks  to  the  foot 36  " 

Norman  flat,  3  bricks  to  the  foot 30  " 


1382        DATA  ON  BRICKS  AND  BRICKWORK. 

The -standard  colors  carried  in  stock  are  white,  cream,  and 
buff;  other  colors  are  made  to  order. 

American  enamelled  and  glazed  bricks  are  now  extensively 
used  for  the  exterior  surfaces  of  buildings,  particularly  for  street 
fronts,  light  courts,  and  for  interior  side  walls  and  partitions  of 
rooms  or  buildings  used  for  a  great  variety  of  purposes. 

The  principal  manufacturers  are  the  Tiffany  Enamelled  Brick 
Company,  Chicago;  Blue  Ridge  Enamelled  Brick  Company, 
Newark,  N.  J. ;  Pennsylvania  Enamelled  Brick  Company,  New 
York  City. 

Estimating  Quantities   and  Cost   of  Brickwork. 

The  almost  universal  method  of  figuring  the  cost  of  brick- 
work is  by  estimating  the  number  of  thousands  of  bricks,  wall 
measure,  arid  then  multiplying  by  a  certain  price  per  thousand, 
which  is  usually  determined  by  experience  and  which  is  in- 
tended to  include  every  item  affecting  the  cost,  and  very  often 
the  profit.  All  of  the  common  brickwork  in  any  given  building 
is  usually  figured  at  the  same  price  per  thousand,  the  adjust- 
ment for  the  more  expensive  portions  of  the  work  being  made 
in  the  manner  of  measuring. 

The  principle  underlying  this  system  is  explained  as  follows: 

"The  plain  dead  wall  of  brickwork  is  taken  as  the  standard, 
and  the  more  difficult,  complicated,  ornamental,  or  hazardous 
kinds  of  work  are  measured  up  to  it  so  as  to  make  the  compensa- 
tion equal. 

"To  illustrate:  If,  in  one  day,  a  man  can  lay  two  thousand 
bricks  in  a  plain  dead  wall,  and  can  lay  only  five  hundred  in  a 
pier,  arch,  or  chimney-top  in  the  same  time,  the  cost  of  labor 
per  thousand  in  such  work  is  four  times  as  much  as  in  the  dead 
wall,  and  he  is  entitled  to  extra  compensation;  but  instead  of 
varying  the  price,  the  custom  is  to  vary  the  measurement  to 
compensate  for  the  difference  in  the  time,  and  thus  endeavor 
to  secure  a  uniform  price  per  thousand  for  all  descriptions  of 
ordinary  brickwork,  instead  of  a  different  price  for  the  execu- 
tion of  the  various  kinds  of  work.77* 

Wall  Measure,  How  Figured. — Plain  walls  are  quite 
universally  figured  at  15  bricks  to  the  square  foot  of  8-  or  9-in. 
wall,  22£  bricks  per  square  foot  of  12-  or  13-in.  wall,  30  bricks 
per  square  foot  of  16-  or  17-in.  wall,  and  7J  bricks  for  each 
additional  4  or  4^  ins.  in  thickness  of  the  wall.  These  figures 

*  From  Rules  of  Measurement  adopted  by  the  Brick  Contractors'  Ex- 
change of  Denver,  Col. 


MEASUREMENT  OF  BRICKWORK  1383 

are  used  without  regard  to  the  size  of  the  bricks,  the  effect  of 
the  latter  being  taken  into  account  in  fixing  the  price  per 
thousand.  No  deduction  is  made  for  openings  of  less  than 
80  superficial  feet,  and  when  deductions  are  made  for  larger 
openings  the  width  is  measured  2  ft.  less  than  the  actual  width. 
Hollow  walls  are  also  measured  as  if  solid.  To  the  number 
of  bricks  thus  obtained  is  added  the  measurement  for  piers, 
chimneys,  arches,  etc. 

Footings  are  generally  measured  in  with  the  wall  by  adding 
the  width  of  the  projection  to  the  height  of  the  wall.  Thus 
if  the  footings  project  6  ins.  on  each  side  of  the  wall,  1  ft.  is 
added  to  the  actual  height  of  the  wall. 

Chimney-breasts  and  pilasters  are  measured  by  multiplying 
the  girth  of  the  breast  or  pilaster  from  the  intersections  with 
the  wall  by  the  height,  and  then  by  the  number  of  bricks  corre- 
sponding with  the  thickness  of  the  projection.  Flues  in  chimneys 
are  always  measured  solid. 

Detached  chimneys  and  chimney-tops  are  measured  as  a 
wall  having  a  length  equal  to  the  sum  of  the  side  and  two  ends 
of  the  chimney,  and  a  thickness  equal  to  the  width  of  the 
chimney.  Thus  a  chimney  measuring  3  ft.  by  1  ft  4  ins.  would 
be  measured  as  a  16-  or  17-in.  wall,  5  ft.  8  ins.  long. 

The  rule  for  independent  piers  is  to  multiply  the  height  of 
the  pier  by  the  distance  around  it  in  feet,  and  consider  the 
product  as  the  superficial  area  of  a  wrall  whose  thickness  is 
equal  to  the  width  of  the  pier.  In  practice,  many  masons 
measure  only  one  side  and  one  end  of  a  pier  or  chimney. 

Arches  of  common  bricks  over  openings  of  less  than  80  super- 
ficial feet  are  usually  disregarded  in  estimating.  If  the  arch  is 
over  an  opening  larger  than  80  sq.  ft.,  the  height  of  the  wall  is 
measured  from  the  springing  line  of  the  arch.  No  deduction 
is  made  in  the  wall  measurement  for  stone  sills,  caps,  or  belt 
courses,  nor  for  stone  ashlar,  if  the  same  is  set  by  the  brick- 
mason.  If  the  ashlar  is  set  by  the  stone-mason,  the  thickness 
of  the  ashlar  is  deducted  from  the  thickness  of  the  wall. 

The  sum  of  all  of  these  measurements  represents  a  certain 
number  of  thousands  of  bricks,  and  the  whole  is  then  multiplied 
by  a  common  price  per  thousand,  as  $6,  $8,  $12,  or  $16,  accord- 
ing to  whatever  the  cost  of  plain  brickwork  may  be.  If  the 
building  is  to  be  faced  with  pressed  brick,  the  actual  cost  of 
the  pressed  brick,  as  nearly  as  it  can  be  computed,  is  added 
to  the  estimated  price  of  the  common  brick  work,  nothing 


1334        DATA   ON   BRICKS   AXD   BRICKWORK. 

being  added  for  laying  the  pressed  brick,  nor  anything  deducted 
from  the  common-brick  measurement,  the  measurement  of  the 
common  work  displaced  by  the  pressed  brick  being  assumed  to 
offset  the  difference  in  the  cost  of  laying  the  pressed  and 
common  brickwork. 

In  arriving  at  the  cost  of  the  pressed  brick,  the  external  super- 
ficial area  of  the  walls  faced  with  such  brick  is  computed,  and 
all  openings,  belt  courses,  stone  caps,  etc.,  deducted.  5-in  stone 
sills  are  not  usually  deducted.  If  a  portion  of  the  wall  is  covered 
by  a  porch,  so  that  common  brick  may  be  used  back  of  it,  this 
space  is  also  deducted.  The  net  pressed-brick  surface  is  then 
multiplied  by  6,  6J,  or  7  to  obtain  the  number  of  bricks  required, 
6J  giving  about  the  number  of  pressed  bricks  required  to  the 
square  foot  of  the  standard  size. 

The  topping  out  of  the  chimneys,  if  of  face-brick,  is  measured 
by  girting  the  chimney  and  multiplying  by  the  height,  and 
adding  the  sum  to  the  wall  area. 

EXAMPLE. — As  a  simple  example  of  this  system  of  estimating 
we  will  take  a  small  brick  house  28  by  32  ft.  without  cross- 
walls,  the  basement  walls  to  be  13  ins.  thick,  with  footings 
2  ft.  6  ins.  wide;  first-story  walls,  13  ins.  thick;  second-story 
walls,  9  ins.  thick;  height  of  basement  walls  from  trench  to 
top  of  first-floor  joists,  8  ft.  6  ins.;  from  first-floor  joists  to 
top  of  second-floor  joists,  10  ft.  6  ins.;  from  second-floor  joists 
to  plate,  9  ft. 

Wall  Measurement. — Basement  walls,  equal  120  ft.  (girth  of 
building)  X9  ft.  10  ins.  (height  and  projection  of  footing) 
X22|;  equals  26,550  bricks. 

First-story  walls,  120  ft.XlO  ft.  6  iiis.X22J;  equals  28,360 
bricks. 

Second-story  walls,  120  ft.X9  ft.Xl5;  equals  16,200 
bricks. 

Topping  out  two  chimneys,  each  1  ft.  9  iiis.Xl  ft.  5  ins.,  14 
ft.  high  above  roof,  equals  2X14  ft.X(l  ft.  5  ins.  +  l  ft.  9  ins. 
+  1  ft.  5  ins.)X30;  equals  3,600  bricks. 

Total  brickwork  equals  74,710  bricks;  at  $9  per  M.  (present 
price  in  Denver),  equals  $672.39. 

Pressed  Brick. — From  grade  to  the  under  side  of  plate  the 
wall  measures  22  ft.  6  ins.;    to  be  faced  with  $15  pressed  brick  f 
of  the  standard  size. 

The  door  and  window  openings  measure  384  superficial 
feet. 


ESTIMATING  COST  OF  BRICKWORK          1385 

Surf  ace  of  pressed  brick  equals  1 20  X  22  J,  equals.  .    2,700  sq.  ft. 
Deduct  for  openings 384        " 

2,316        " 
Add  for  two  chimneys,  2 X 14 X 6  ft.  4  ins.,  equals. .  .       177        " 

2,493        " 

2,493  X6J  equals  16,204  pressed  bricks,  at  $15  per  M.,  equals 
$243. 

Total  amount  of  bid,  $672.39 +  $243,   equals  $915.39. 

The  above  figures  are  supposed  to  include  the  necessary 
lime,  sand,  water,  scaffolding,  etc.,  required  to  make  the  mortar 
and  put  up  the  walls,  and  also  a  profit  for  the  contractor,  but 
anything  in  the  way  of  ironwork,  as  ties,  thimbles,  ash  doors, 
etc.,  are  figured  additional  to  the  above. 

Detailed  Estimates.  —  In  estimating  by  the  above 
method,  the  price  per  thousand  is  to  some  extent  a  matter  of 
guesswork,  and  while  an  experienced  contractor  may  perhaps 
make  as  accurate  an  estimate  by  this  method  as  is  possible  by 
any,  yet  it  is  often  necessary  to  estimate  the  work  in  detail,  and 
even  Avhen  the  work  has  been  estimated  as  above,  it  is  necessary 
for  the  contractor  to  know  how  many  bricks  and  how  much 
sand  and  lime  will  be  required  to  do  the  work.  The  following 
data  will  assist  in  making  such  detailed  estimates: 

With  the  size  of  bricks  used  in  the  Western  States,  from 
16|  to  17§  common  bricks  are  required  to  the  cubic  foot  after 
deducting  openings,  and  figuring  the  thickness  of  walls  at 
8,  12,  16,  20  ins.,  etc.,  or  the  actual  number  of  bricks  required 
will  run  about  two-thirds  of  the  "  wall  measure  "  when  the  open- 
ings are  of  about  the  average  number  and  size.  , 

The  number  of  pressed  bricks  will  be  about  6  or  6|  bricks 
to  the  foot  after  deducting  openings. 

To  lay  1,000  common  bricks,  kiln  count,  requires  2J  bushels 
or  200  Ibs.  of  white  lime  and  f  yd.  of  sand.  For  a  good  lime 
and  cement  mortar  allow  2  bushels  lime,  1  bbl.  cement,  and 
f  yd.  sand.  For  1  to  3  cement  and  sand  mortar  allow  1J  bbls. 
cement  and  f  yd.  sand,  or  one  half  load. 

To  lay  1,000  pressed  bricks  with  buttered  joints  will  require 
2  bushels  of  lime  (160  Ibs.)  and  J  yd.  of  sand;  with  spread  joints 
2  to  2i  bushels  of  lime  and  f  to  £  yd.  of  sand. 

If  colored  mortar  is  used,  about  $1  per  1,000  bricks  should  be 
added  for  the  mortar  color. 


1386        DATA  *ON  BRICKS  AND  BRICKWORK. 

A  brick-mason,  working  on  a  city  job  under  a  good  foreman, 
will  lay  60  pressed  (face)  bricks  per  hour,  on  an  average,  and 
from  150  to  175  common  bricks  per  hour,  160  being  a  fair 
average.  In  country  towns  the  average  is  nearer  120  an  hour. 

With  wages  at  62  J  cts.  per  hour  for  masons,  31  i  cts.  for  hod- 
carriers,  and  34f  cts.  for  mortar-mixers  and  carriers,  sand  at 
60  cts.  a  yard,  and  lime  at  40  cts.  per  bushel  of  80  Ibs.,  brick' 
masons  in  Denver  find  that  the  average  cost  for  laying  common 
brick  in  12-in.  walls  is  about  $6  per  M.,  kiln  count,  and  for 
laying  pressed  brick,  about  $10  per  M. 

For  common  brickwork,  one  helper  will  be  required  for  every 
mason,  and  on  9-in.  walls  faced  with  pressed  brick,  one  helper 
to  every  two  masons. 

In  building  common-brick  fireplaces  and  chimneys  one  mason 
and  helper  will  lay  about  600  bricks  in  a  day  of  nine  hours. 

As  a  rule,  chimneys  of  common  brick  with  4-in.  walls  cost 
about  50  cts.  per  running  foot,  in  height,  for  single  flues,  and 
90  cts.  for  double  flues. 

Space  Required  for  Piling  Bricks. — One  thousand  bricks 
closely  stacked  occupy  about  56  cu.  ft. 

One  thousand  old  bricks,  cleaned  and  loosely  stacked,  occupy 
about  72  cu.  ft. 

A  brick-layer's  hod  measures  21  ins.X7  ins.  X7  ins.,  and  will 
hold  18  bricks. 

A  mortar  hod  measures  24  ins.  X  12  ins. X 12  ins.  X  12  ins.  across 
the  top. 

Mortar  colors  are  usually  in  the  form  of  a  dry  powder,  put 
up  in  barrels,  the  number  of  pounds  to  the  barrel  and  price  per 
pound  averaging  about  as  follows: 

Red,  in  500-lb.  barrels,  dry 2    cts.  per  pound 

Brown,  in  450-lb.  barrels,  dry 2J   "      "         "  . 

Buff,  in  400-lb.  barrels,  dry 2J   "      " 

Black,  in  1,000-lb.  barrels,  dry .   3}  "      " 

Red,  brown,  buff,  or  black,  in  pulp,  \  ct.  per  pound  extra. 
For  lots  of  less  than  full  barrels  an  extra  charge  is  made  for 
packing  and  dray  age.* 

To  color  the  mortar  for  laying  1,000  bricks  with  spread 
joints  will  require  about  50  Ibs.  of  red,  brown,  or  buff,  and  from 
40  to  45  Ibs.  of  black;  with  buttered  joints,  40  Ibs.  of  red, 
brown,  or  buff,  or  from  25  to  35  Ibs.  of  black. 

The  colors .  should  first  be  mixed  with  dry  sand,  then  the 
*  These  figures  are  for  Ricketson's  mortar  colors. 


LIME.  1387 

cold  slaked  lime  added  and  again  mixed  thoroughly.  It  is  very 
important  that  the  color  be  uniformly  mixed.  If  it  is  not  added 
at  first,  but  is  left  until  the  mortar  is  made,  the  labor  of  mixing 
is  doubled.  The  more  thorough  the  mixing  the  less  color  is 
required.  Mortar  colors  should  never  be  mixed  with  hot  lime. 

LIME. 

Definitions  and  Useful  Data. — Pure  lime  is  a  prot- 
oxide of  calcium,  or,  in  other  words,  a  metallic  oxide.  It  has  a 
specific  gravity  of  2.3,  is  amorphous,  somewhat  spongy,  highly 
caustic,  quite  infusible,  possesses  great  affinity  for  water,  and  if 
brought  in  contact  with  it  will  rapidly  absorb  22  to  23  per  cent, 
of  its  weight,  passing  into  the  condition  of  hydrate  01  lime. 

Slaked  lime  is  hydrate  of  lime. 

Quicklime,  or  caustic  lime,  is  the  resulting  lime  left  from  the 
calcination  of  limestone.  It  is  chemically  known  as  calcium 
oxide. 

Limestone,  carbonate  of  lime.  Crystallized  lime,  marble. 
Fossil  lime,  chalk.  Sulphate  of  lime,  gypsum.  Calcination  is 
heating  to  redness  in  air. 

Slaking  is  the  process  of  chemical  combination  of  quicklime 
with  water. 

Air-slaking. — Hydration  by  the  absorption  of  moisture  from 
the  atmosphere. 

Lime  is  shipped  either  in  barrels  or  bulk.  In  dry  climates 
it  will  keep  for  a  long  time  in  bulk,  but  in  damp  climates  and 
along  the  coast  it  soon  slakes  unless  enclosed  in  barrels. 

In  most  of  the  Eastern  cities  it  is  sold  by  the  barrel,  weighing 
for  Rockland  (Me.)  lime  220  Ibs.  net.  When  shipped  in  bulk 
it  is  generally  sold  by  the  bushel  of  8.0  Ibs.,  2^  bushels,  or  200  Ibs., 
of  lime  being  considered  as  equivalent  to  a  barrel. 

The  average  yield  of  lime  paste  from  the  best  Eastern  limes 
has  been  found  to  be  2.62  times  the  bulk  of  unslaked  lime.  A 
barrel  of  good  quality  well-burnt  lime  should  make  8  cu.  ft., 
or  20  pails,  of  lime  paste  or  putty. 

Careful  experiments  conducted  by  U.  S.  engineers  have 
demonstrated  that  the  best  mortar  is  obtained  by  mixing 
one  part  lime  paste  to  two  of  sand. 

" Popping"  of  Lime. — The  best  qualities  of  lime  should  com- 
pletely slake  in  forty-eight  hours,  but  there  are  some  limes  in 
which  some  of  the  particles  will  not  slake  with  the  bulk  of  the 
lime,  but  continue  to  absorb  moisture,  and  finally,  after  a  long 


1388  SAND  AND  GRAVEL. 

period  extending  sometimes   over  two   years,   they  will   slake 
or  "pop,"  and  if  on  a  wall  or  ceiling  will  cause  a  speck  of  plaster 
to  fall  off.     Such  limes  should  not  be  used  for  plastering. 
Cements. — For  data  on  cements,  see  pp.  192-204. 

SAND  AND  GRAVEL. 

Sand  is  obtained  from  banks  or  pits,  from  river-beds,  and 
from  the  seashore.  Pit-  or  bank-sand,  free  from  clay  or  earth 
materials,  is  generally  considered  the  best  for  mortar,  although 
excellent  sand  is  often  obtained  from  river-beds.  Sea-sand 
contains  alkaline  salts  which  attract  and  retain  moisture  and 
cause  efflorescence  when  used  in  brickwork,  unless  thoroughly 
washed. 

Both  sea-  and  river-sand  have  more  or  less  rounded  grains, 
to  which  lime  or  cement  will  not  adhere  as  well  as  to  sharp, 
angular  grains.  Both  are  extensively  used,  however,  for  lack 
of  better  materials. 

The  use  of  sand  in  mortar  is  to  prevent  excessive  shrinkage, 
and  to  save  the  cost  of  lime  or  cement.  Sand  when  used  in  the 
proportion  of  1  to  2  strengthens  lime  mortar,  but  any  addition 
of  sand  to  cement  weakens  it. 

Screening. — Sand  for  mortar  must  ordinarily  be  screened. 

Sand  for  brown  mortar  for  plastering  or  common  brickwork 
is  ordinarily  run  through  a  No.  4  screen  having  4X4  meshes 
to  the  inch.  For  sand  finish  and  mortar  for  pressed  brickwork 
either  a  No.  10  or  No.  12  screen  with  10X10  or  12X12  meshes 
to  the  inch  is  commonly  used. 

For  rubble  stonework  the  sand  is  not  ordinarily  screened, 
unless  it  contains  much  gravel,  in  which  case  it  should  be  screened 
through  a  f-in.  mesh. 

Weight. — Dry  sand  weighs  from  80  to  115  Ibs.  per  cubic  foot. 
The  average  weight  of  damp  (not  wet)  sand  is  about  96  Ibs. 
per  cubic  foot,  or  2,600  Ibs.  per  yard. 

The  voids  for  ordinary  sand  range  from  .3  to  .5  of  the  volume, 
the  average  for  screened  sand  suitable  for  mortar  being  .35. 
The  more  uneven  the  grains  in  size  the  smaller  the  percentage 
of  the  voids. 

A  one-horse  load  of  sand  contains  about  22  cu.  ft.  Two- 
horse  loads  vary  from  1J  to  2  yds.  The  amount  hauled  per 
load  in  the  larger  cities  is  generally  fixed  by  the  Team  Owners' 
Association.  1J  yds.  is  a  fair  load,  1J  yds.  a  good  load,  and 
2  yds.  a  large  load. 


LATHING  AND   PLASTERING.  1389 


LATHING  AND  PLASTERING. 

(For  more  complete  description  of  materials  and  processes 
see  Chapter  ^XI,  Building  Construction  and  Superintendence, 
Part  I.) 

Wooden  JLaths  should  be  well  seasoned,  free  from  sap, 
bark,  and  dead  knots.  Bark  on  laths  is  quite  sure  to  stain 
the  plaster.  White  pine  is  generally  considered  as  the  best 
wood  for  laths,  although  spruce  and  hemlock  laths  are  much 
used.  Hard  pine  is  not  a  good  material,  as  it  contains  too 
much  pitch. 

The  regular  size  of  laths  is  J  in.  XI}  in.  X4  ft.;  the  width  and 
thickness  vary  somewhat  in  different  mills  but  the  length  is 
always  the  same.  Laths  are  sold  by  the  1,000  in  bunches 
containing  100  laths,  $2.75  being  about  an  average  price. 

For  Metal  lathing  see  pp.  825-831. 

Plastering'  on  laths  is  generally  done  in  three  coats.* 

The  first  coat  is  called  the  scratch  coat;  the  second,  the 
brown  coat,  and  the  third,  the  white  coat,  skim  coat,  or  finish. 

On  brick  or  stonework  the  scratch  coat  is  generally  emitted. 
For  first-class  work  each  coat  should  be  permitted  to  dry 
thoroughly  before  the  next  coat  is  applied,  and  under  no  cir- 
cumstances should  the  finish  coat,  be  applied  before  the  "brown 
coat  is  thoroughly  dry. 

"Drawn  work"  is  where  the  brown  coat  is  applied  to  the 
scratch  coat  from  the  same  staging,  immediately  after  the 
latter  is  applied.  It  is  a  little  cheaper  than  "dry  scratch,"  and 
much  of  this  work  is  done  in  the  Western  States. 

The  scratch  coat  should  always  be  made  rich  in  lime,  and 
should  contain  1J  bu.  of  hair  (or  an  equivalent  quantity  of 
fibre)  to  each  cask  of  lime,  or  1  bu.  of  hair  to  2  of  lime. 

A  proportion  of  1  part  lime  paste  to  2  of  sand  will  require 
1  cask  (2J  bu.)  of  lime  to  5i  bbls.  of  screened  sand. 

The  brown  coat  should  contain  1  cask  (2J  bu.)  of  lime  to 
7  bbls.  of  screened  sand,  and  1  bu.  of  hair  to  5  of  lime. 

Very  little  plaster  is  mixed  by  measure,  however,  the  usual 
custom  being  to  mix  as  much  sand  with  the  slaked  lime  as  the 
mortar-mixer  thinks  it  will  stand  and  give  satisfaction,  the 
tendency  being  always  to  make  the  lime  go  as  far  as  possible. 

*  In  the  Eastern  States,  dwellings  of  moderate  cost  are  generally  plas- 
tered with  two-coat  work,  the  first  or  scratch  coat  being  brought  nearly 
to  the  grounds,  and  carefully  straightened  to  receive  the  skim  coat. 


1390  LATHING  AND  PLASTERING. 

The  third  or  finishing  coat  is  designated  by  various  terms, 
such  as  skim  coat,  white  coat,  putty  coat,  sand-finish,  etc.  The 
skim  coat  as  used  in  the  Eastern  States  is  generally  composed 
of  lime  putty  and  washed  beach-sand  in  equal  proportions. 
Sand-finish,  which  has  a  rough  surface  resembling  coarse  sand- 
paper, is  mixed  in  the  same  way,  only  that  coarser  sand  and 
more  of  it  is  used,  and  it  is  finished  with  a  wooden  or  cork-faced 
float. 

White  coating  or  hard  finish  generally  means  a  composition 
of  lime  putty  and  plaster  of  Paris,  to  which  marble-dust  is 
sometimes  added.  Plaster  of  Paris  and  marble-dust  when 
used  should  not  be  mixed  with  the  lime  putty  until  a  few 
moments  before  using,  and  no  more  should  be  prepared  at 
one  time  than  can  be  used  up  at  once,  as  it  soon  "sets,"  after 
which  it  should  not  be  used.  The  skim  coat  or  hard  finish 
should  be  finished  with  a  steel  trowel  and  wet  brush.  The 
more  the  work  is  trowelled  the  harder  it  becomes. 

A  superior  hard  finish  is  obtained  by  mixing  4  parts  Best's 
Keene's  cement  to  1  part  lime  putty. 

To  make  sure  that  the  lime  is  well  slaked,  it  is  customary 
to  require  that  the  mortar  for  plastering  shall  be  mixed  at 
least  seven  days  before  it  is  used. 

Hair  such  as  is  used  by  plasterers  is  obtained  from  the  hides 
of  cattle,  and  after  being  washed  and  dried  is  put  up  in  paper 
bags,  each  bag  being  supposed  to  contain  one  bushel  of  hair 
when  beaten  up.  Each  package  is  supposed  to  weigh  from 
seven  to  eight  pounds,  but  the  weight  often  falls  short. 

Asbestos  and  manilla  fibre  are  both  used  in  place  of  hair; 
they  are  cleaner  than  hair  and  are  said  to  be  less  injured  by 
the  lime. 

It  is  much  better  to  add  the  hair  to  the  lime  paste  after  it 
is  cold  and  before  mixing  in  the  sand,  as  hot  lime,  and  the 
steam  caused  by  the  slaking,  burn  or  rot  the  hair  so  as  to 
greatly  weaken  it.  The  common  practice  is  to  put  the  hair 
in  the  mortar  box,  then  run  off  the  hot  lime  as  soon  as  it  is 
slaked,  and  then  to  throw  in  the  sand  and  mix  the  whole 
together,  when  it  is  thrown  out  of  the  box  into  a  pile  and  a 
new  batch  mixed  up. 

Machine-made  Mortar. — In  several  of  the  larger  cities 
plants  have  been  equipped  for  the  mixing  of  mortar  by  machinery. 
Machine-mixed  mortar  should  be  much  better  than  the  ordinary 
hand-mixed  mortar,  for  the  reason  that  time  can  be  given 


HARD  WALL  PLASTERS.  1391 

for  the  lime  to  slake,  the  lime  and  sand  can  be  accurately 
measured,  and  the  hair  and  lime  are  not  mixed  with  the  lime 
until  just  before  delivery.  The  mixing  may  also  be  more 
thoroughly  and  evenly  done  by  machinery  than  is  possible  by 
hand. 

Improved  Wall  Plasters. — Owing  to  the  difficulty  of 
obtaining  an  economical  and  satisfactory  quality  of  walls 
and  ceilings  by  the  use  of  the  ordinary  hand-mixed  lime  mortar, 
other  and  more  reliable  plastering  materials  have  been  invented, 
and  are  now  being  extensively  employed,  especially  on  the 
largest  and  most  costly  structures,  and  are  giving  general 
satisfaction. 

Among  the  best-known  of  these  improved  plasters  are  the 
Acme,  Agatite,  and  Royal  cement  plasters,  Adamant,  Windsor 
cement  dry  plaster,  Rock  wall  plaster,  and  Best's  Keene's 
cement.  The  first  three  are  natural  products  found  in  certain 
parts  of  Kansas  and  Texas  and  simply  calcined.  Many  other 
brands  of  these  cement  plasters  are  made  in  the  Western  States 
to  supply  the  local  markets.  The  other  four  plasters  named 
above  are  composed  principally  of  plaster  of  Paris  with  certain 
chemicals  added.  All  appear  to  produce  about  the  same 
results.  The  Windsor  dry  plaster,  Adamant,  and  Rock  plaster 
are  mixed  with  the  proper  proportion  of  sand  by  the  manu- 
facturers, and  only  require  being  "wet  up"  before  using.  All 
of  these  materials  are  sold  by  weight.  They  should  be  used 
strictly  in  accordance  with  the  directions  furnished  by  the 
manufacturers . 

Among  the  advantages  gained  by  the  use  of  these  plasters 
are  uniformity  in  strength  and  quality,  extra  hardness  arid 
toughness,  freedom  from  pitting,  saving  in  time  required  in 
making  and  drying  the  plaster,  minimum  danger  from  frost, 
less  weight  and  moisture  in  the  building,  and  greater  resistance 
to  the  action  of  fire  and  water. 

Measuring  Plasterers'  Work. — Lathing  is  always 
figured  by  the  square  yard  and  is  generally  included  with  the 
plastering,  although  in  small  country  towns  the  carpenter  often 
puts  on  the  laths. 

Plastering  on  plain  surfaces,  as  walls  and  ceilings,  is  always 
measured  by  the  square  yard,  whether  it  be  one,  two,  or  three- 
coat  work,  or  lime  or  hard  plaster. 

In  regard  to  deducting  for  openings,  custom  varies  some- 
what in  different  portions  of  the  country  and  also  with  different 


1392  LATHING  AND  PLASTERING. 

contractors.  Some  plasterers  allow  one  half  the  area  of  open- 
ings for  ordinary  doors  and  windows,  while  others  make  no 
allowance  for  openings  less  than  7  sq.  yds. 

Returns  of  chimney-breasts,  pilasters,  and  all  strips  less 
than  12  ins.  in  width  should  be  measured  as  12  ins.  wide. 
Closets,  soffits  of  stairs,  etc.,  are  generally  figured  at  a  higher 
rate  than  plain  walls  or  ceilings,  as  it  is  not  as  easy  to  get  at 
them.  For  circular  or  elliptical  work,  domes,  or  groined  ceilings, 
an  additional  price  is  also  made.  If  the  plastering  cannot 
be  done  from  trestles  an  additional  charge  must  be  made  for 
staging. 

Stucco  cornices  and  moulded  work  are  generally  measured 
by  the  superficial  foot,  measuring  on  the  profile  of  the  mould- 
ing. When  less  than  12  iris,  in  girth  they  are  usually  rated  as 
1  ft.  For  each  internal  angle  1  lin.  ft.  should  be  added,  and  for 
external  angles,  2  ft. 

For  cornices  on  circular  or  elliptical  work  an  additional  price 
should  be  charged. 

Enriched  mouldings  are  generally  figured  by  the  lineal  foot, 
the  price  depending  upon  the  design  and  size  of  the  mould. 

Whenever  plastering  is  done  by  measurement  the  contract 
should  definitely  state  whether  or  not  openings  are  to  be  de- 
ducted, and  a  special  price  should  be  made  for  the  stucco-work, 
based  on  the  full-size  details. 

Quantities  of  Materials  Required  for  Lathing 
and  Plastering1. 

To  cover  100  sq.  yds.  requires  from  1,400  to  1,500  laths, 
or  say  1,450  for  an  average  job,  and  10  Ibs.  of  3d.  nails. 

Three-coat  plastering  on  wood  laths,  plaster-of-Paris  finish, 
will  require  from  8  to  10  bu.  of  lime,  1J  yds.  of  sand,  2  bu.  of 
hair,  and  100  Ibs.  of  plaster  of  Paris  per  100  sq.  yds. 

If  finish  coat  is  omitted,  deduct  2  bu.  of  lime,  and  all  of  the 
plaster  of  Paris. 

If  sand-finished,  omit  the  plaster  of  Paris  and  add  J  yd.  of 
sand. 

Two  coats  on  brick  or  stone  walls  (brown  coat  and  finishing 
coat)  will  require  6  to  8  bu.  of  lime,  1|  yds.  of  sand,  and  100  Ibs. 
of  plaster  of  Paris,  to  100  sq.  yds. 

Using  Best's  Keene's  cement  for  brown  mortar  and  Keene's 
finish  on  expanded  metal  lath  will  require,  for  brown  mortar, 


COST  OF  PLASTERING.  1393 


550  Ibs.  cement,  5J  bu.  lime,  2  yds.  sand,  2  bu.  hair;  for  the 
finish,  300  Ibs.  cement  and  1  bu.  of  lime  per  100  yds. 

Hard  plasters  on  expanded  rnetal  lath,  plaster-of-Paris  finish, 
require  for  brown  mortar  2,000  Ibs.  plaster  and  2  yds.  sand; 
for  the  finish,  1  bu.  lime  and  100  Ibs.  plaster  of  Paris  per  100  yds. 
Cost. — The  standard  price  for  putting  on  wood  laths  (labor 
only)  in  Denver  (1904)  is  3J  cts.  per  yard.  For  expanded  or 
sheet-metal  laths  on  wood  studding,  5  cts.;  on  steel  studding, 
wired,  8  cts. 

The  cost  of  putting  three  coats  on  laths,  plaster-of-Paris  finish 
(labor  only),  runs  about  15  cts.  per  yard  for  drawn  work  and 
16  cts.  for  dry  scratch. 

With  sand  finish  the  cost  is  about  the  same  as  for  white  finish. 

These  figures  are  based  on  plasterers'  wages  at  62  J  cts.  per 

hour,  and  37^  cts.  per  hour  for  hod-carriers  and  mortar-mixers. 

The  following  table  gives  the  average  cost  of  different  kinds 

of  plastering  in   Denver  in   1904,   based  on  Missouri  lime  at 

40  cts.  per  bushel,  sand  at  75  cts.  per  load  of  1|  yds.,  hair  at 

40  cts.  per  bushel,  and  plaster  of  Paris  at  50  cts.  per  100  Ibs., 

and  wages  as  given  above. 

Scratch  and  brown  coat  (lime)  on  wood  laths 25  cts.  per  yd. 

3  coats   (lime)    on    wood    laths,    plaster-of-Paris 

finish 30   "      "     " 

3  coats  (lime)  on  wood  laths,  sand  finish 30   " '    "     " 

Brown  coat  and  finish  on  brick  walls 23    "      "     " 

For  hard  wall  plaster  instead  of  lime,  add 3   "      "     " 

3  coats  (lime),  plaster-of-Paris  finish,  metal  lath 

on  wood  studding 65   "      "     " 

3  coats  (lime)  plaster-of-Paris  finish,  metal  lath 

on  steel  studding 68   "      "     " 

For  Keene's  cement  finish,  add 10   "      "     " 

For  blocking  in  imitation  of  tile,  add 50   "      "     " 

2  coats  hard  wall  plaster,  plaster-of-Paris  finish, 

metal  lath,  wood  studding 70   "      "     " 

2  coats  hard  wall  plaster,  plaster-of-Paris  finish, 

metal  lath  on  steel  studs 73    "      "  " 

For  Keene's  cement  finish,  add 10   "      "     " 

Portland    cement,     brown    coat,    finished    with 
Keene's  cement  blocked  in  imitation  of  tile, 

3"X  6" : $2.80  per  yd. 

For  running  base,  9"  high,  in  Best's  Keene's  ce- 
ment     10  cts.  per  ft. 


1394  DATA  ON  LUMBER. 

For  running  plain  mouldings  in  plaster  of  Paris,  3  to  5  cts.  per 

inch  of  girth. 

For  finishing  shafts  of  columns,  16  to  24  ins.  diam.,  12  to  14  ft. 
high,  $3  per  column  (labor  only). 

These  prices  are  believed  to  be  pretty  near  an  average  for 
the  entire  country.  In  some  localities  prices  for  materials  or 
labor  are  less,  in  others  higher. 

Staff  is  a  composition  of  plaster  of  Paris  and  hemp  fibre,  cast 
in  moulds,  and  nailed  or  wired  in  place.  All  of  the  buildings 
of  the  Columbian  Exposition  at  Chicago  (1893)  were  covered 
with  this  material  and  all  of  the  temporary  buildings  of  the 
St.  Louis  Exposition  of  1904.* 

It  is  not  sufficiently  durable  for  permanent  work  unless 
kept  well  painted. 

The  cost  of  " staff"  as  used  on  the  buildings  at  Chicago  in 
1893  varied  from  $2  to  $2.25  per  square  yard. 

DATA   ON   LUMBER   AND   CARPENTERS'   WORK.f 

Framing  Lumber  may  commonly  be  purchased  in  any 
of  the  following  sizes,  except  that  common  pine,  spruce,  and 
hemlock  cannot  usually  be  obtained  in  larger  sizes  than  12x12 
ins. 

2   X4  3X6  4X12  •  8X12 

2   X6  3X8  4X14  8X14 

2   X8  3X10  6X6  10X10 

2   X10  3X12  6X8  10X12 

2   X12  3X14         .         6X10  10X14 

2   X14  3X16  6X12  10X16 

2   X16  4X  4  6X14  12X12 

2JX12  4X   6  6X16  12X14 

2iXl4  4X   8  8X   8  12X16 

2JX16  4X10  8X10  14X14 

14X16 

In  some  of  the  New  England  mills,  the  following  sizes  are 
also  sawn:  2X3,  2X5,  2X7,  2X9,  3X4,  and  3X5. 

These  sizes  are  not  commonly  carried  in  stock,  and  in  most 
localities  would  have  to  be  obtained  by  ripping  larger  sizes. 

*  A  description  of  the  process  of  manufacture  is  given  in  Part  I,  Build- 
ing Construction  and  Superintendence,  p.  347. 

t  A  comprehensive  booklet  giving  the  rules  for  the  grading  and  classi- 
fication of  yellow-pine  lumber  and  dressed  stock  may  be  obtained  from  the 
Southern  Lumber  Manufacturers  Association,  Equitable  Building,  St. 
Louis,  Mo, 


DATA  ON  LUMBER.  1395 

Most  of  the  Southern  yellow  pine,  Oregon  pine,  or  Washing- 
ton fir  is  shipped  surfaced  one  side  and  edge  —  the  actual  di- 
mensions being  from  J  in.  to  f  in.  scant  of  the  nominal  dimen- 
sions, and  sometimes  J  in.  When  framing  lumber  is  required 
to  be  full  to  dimensions  it  should  be  ordered  "in  the  rough,"  and 
a  special  contract  made  on  that  understanding. 

Length.  —  All  timber  is  cut  and  sold  in  even  lengths,  as  10, 
12,  14,  and  16  ft.  Odd  and  fractional  lengths  are  counted  as 
the  next  higher  even  length;  consequently  it  is  economical  to 
plan  buildings  so  that  timbers  of  even  lengths  may  be  used 
without  waste. 

Measurement  of  Rough  Lumber.  —  All  rough  lumber 
is  sold  by  the  foot,  board  measure,  one  foot  being  the  equivalent 
of  a  board  one  foot  wide,  one  foot  long,  and  one  inch  thick. 

To  compute  the  board  measure  in  any  board,  plank,  or  timber, 
divide  the  nominal  sectional  area,  in  inches,  by  12,  and  multiply 
by  the  length  in  feet.  Thus  the  number  of  "feet"  in  a  2X4 

2X4 
scantling  8  ft.  long=  -v^-X8=5j  ft.  b.  in.     A  10  -inch  board, 


12  ft.  long,  contains  X12=10  ft.  b.  m. 

Extensive  tables  are  published  showing  the  feet,  board  measure, 
in  almost  any  commercial  size  of  timber.  The  following  table, 
however,  although  compact,  will  enable  one  to  readily  estimate 
the  number  of  "feet"  in  any  of  the  standard  sizes  of  boards, 
planks,  or  timbers. 

,  To  use  this  table,  multiply  together,  mentally,  the  dimen- 
sions of  the  cross-section,  and  then  in  the  column  having  a 
heading  equal  to  this  product,  and  opposite  the  given  length 
will  be  found  the  feet,  board  measure.  Thus,  for  a  3X4,  2X6, 
or  1X12,  look  in  column  headed  12;  for  a  2X12,  4X6,  or  3X8, 
look  in  column  headed  24. 

For  lengths  not  given  in  the  table,  take  either  twice  the 
length  and  divide  by  2,  or  one  half  the  length  and  multiply  by  2. 

Where  timbers  of  the  same  size  abut  end  to  end,  it  economizes 
labor  in  reducing  to  board  measure  to  take  the  full  length;  for 
this  reason  the  lengths  in  the  table  are  carried  beyond  that 
for  a  single  stick. 


1396 


DATA  ON  LUMBER. 


TABLE  OF  BOARD  MEASURE. 

For  explanation,  see  p.  1395. 


*l 

Sectional  Area  in  Square  Inches. 

tc  fl 

4 

6 

8 

10 

12 

14 

16 

18 

20 

ft.  ins. 

ft.* 

ft.  ins. 

ft.  ins 

ft.* 

ft.  ins. 

ft.  ins. 

ft.* 

ft.  ins. 

6 

2  0 

3 

4  0 

5  0 

6 

7  0 

8  0 

9 

10  0 

8 

2  8 

4 

5  4 

6  8 

8 

9  4 

10  8 

12 

13  4 

10 

3  4 

5 

6  8 

8  4 

10 

11  8 

13  4 

15 

16  8 

12 

4  0 

6 

8  0 

10  0 

12 

14  0 

16  0 

18 

20  0 

14 

4  8 

7 

9  4 

11  8 

14 

16  4 

18  8 

21 

23  4 

16 

5  4 

8 

10  8 

13  4 

16 

18  8 

21  4 

24 

26  8 

18 

6  0 

9 

12  0 

15  0 

18 

21  0 

24  0 

27 

30  0 

20 

6  8 

10 

13  4 

16  8 

20 

23  4 

26  8 

30 

33  4 

22 

7  4 

11 

14  8 

18  4 

22 

25  8 

29  4 

33 

36  8 

24 

8  0 

12 

16  0 

20  0 

24 

28  0 

32  0 

36 

40  0 

26 

8  8 

13 

17  4 

21  8 

26 

30  4 

34  8 

39 

43  4 

28 

9  4 

14 

18  8 

23  4 

28 

32  8 

37  4 

42 

46  8 

30 

10  0 

15 

20  0 

25  0 

30 

35  0 

40  0 

45 

50  0 

32 

10  8 

16 

21  4 

26  8 

32 

37  4 

42  8 

48 

53  4 

34 

11  4 

17 

22  8 

18  4 

34 

39  8 

45  4 

51 

56  8 

36 

12  0 

18 

24  0 

30  0 

36 

42  0 

48  0 

54 

60  0 

38 

12  8 

19 

25  4 

31  8 

38 

44  4 

50  8 

57 

63  4 

40 

13  4 

20 

26  8 

33  4 

40 

46  8 

53  4 

60 

66  8 

42 

14  0 

21 

28  0 

35  0 

42 

49  0 

56  0 

63 

70  0 

Sectional  Area  in  Square  Inches. 

24 

28 

30 

32 

35 

36 

40 

42 

48 

ft.* 

ft.  ins. 

ft,* 

ft.  ins. 

ft.  ins. 

ft.* 

ft,  ins. 

ft.* 

ft.* 

6 

12 

14  0 

15 

16  0 

17  6 

18 

20  0 

21 

24 

8 

16 

18  8 

20 

21  4 

23  4 

24 

26  8 

28 

32 

10 

20 

23  4 

25 

26  8 

29  2 

30 

33  4 

35 

40 

12 

24 

28  0 

30 

32  0 

35  0 

36 

40  0 

42 

48 

14 

28 

32  8 

35 

37  4 

40  10 

42 

46  8 

49 

56 

16 

32 

37  4 

40 

42  8 

46  8 

48 

53  4 

56 

64 

18 

36 

42  0 

45 

48  0 

52  6 

54 

60  0 

63 

72 

20 

40 

46  8 

50 

53  4 

58  4 

60 

66  8 

70 

80 

22 

44 

51  4 

55 

58  8 

64  2 

66 

73  4 

77 

88 

24 

48 

56  0 

60 

64  0 

70  0 

72 

80  0 

84 

96 

26 

52 

60  8 

65 

69  4 

75  10 

78 

86  8 

91 

104 

28 

56 

65  4 

70 

74  8 

81  8 

84 

93  4 

98 

112 

30 

60 

70  0 

75 

80  0 

87  6 

90 

100  0 

105 

120 

32 

64 

74  8 

80 

85  4 

93  4 

96 

106  8 

112 

128 

34 

68 

79  4 

85 

90  8 

99  2 

102 

113  4 

119 

136 

36 

72 

84  0 

90 

96  0 

105  0 

108 

120  0 

126 

144 

38 

76 

88  8 

95 

101  4 

110  10 

114 

126  8 

133 

152 

40 

80 

93  4 

100 

106  8 

116  8 

120 

133  4 

140 

160 

42 

84 

98  0 

105 

112  0 

122  6 

126   140  0 

147 

168 

*  The  measurements  in  these  columns  come  out  in  even  feet. 


TABLE  OF  BOARD  MEASURE. 


1397 


TABLE  OF  BOARD  MEASURE.— Continued. 

For  explanation,  see  p.  1395. 


+3 

Q 

3& 

cS 

O> 

H 

Sectional  Area  in  Square  Inches. 

56 

60 

64 

72 

80 

84 

96 

100 

112 

ft.  ins. 

ft.* 

ft.  ins. 

ft.* 

ft.  ins. 

ft.* 

ft.* 

ft.  iris. 

ft.  ins. 

4 

18  8 

20 

21  4 

24 

26  8 

28 

32 

33  4 

37  4 

6 

28  0 

30 

32  0 

36 

40  0 

42 

48 

50  0 

56  0 

8 

37  4 

40 

42  8 

48 

53  4 

56 

64 

66  8 

74  8 

10 

46  8 

50 

53  4 

60 

66  8 

70 

80 

83  4 

93  4 

12 

56  0 

60 

64  0 

72 

80  0 

84 

96 

100  0 

112  0 

14 

65  4 

70 

74  8 

84 

93  4 

98 

112 

116  8 

130  8 

16 

74  8 

80 

85  4 

96 

106  3 

112 

128 

133  4 

149  4 

18 

84  0 

90 

96  0 

108 

120  0 

126 

144 

150  0 

168  0 

20 

93  4 

100 

106  8 

120 

133  4 

140 

160 

166  8 

186  8 

22 

102  8 

110 

117  4 

132 

146  8 

154 

176 

183  4 

205  4 

24 

112  0 

120 

128  0 

144 

160  0 

168 

192 

200  0 

224  0 

26 

121  4 

130 

138  8 

156 

173  4 

182 

208 

216  8 

242  8 

28 

130  8 

140 

149  4 

168 

186  8 

196 

224 

233  4 

261  4 

30 

140  0 

150 

160  0 

180 

200  0 

210 

240 

250  0 

280  0 

32 

149  4 

160 

170  8 

192 

213  4 

224 

256 

266  8 

298  8 

34 

158  8 

170 

181  4 

204 

226  8 

238 

272 

283  4 

317  4 

36 

168  0 

180 

192  0 

216 

240  0 

252 

288 

300  0 

336  0 

38 

177  4 

190 

202  8 

228 

253  4 

266 

304 

316  8 

354  8 

40 

186  8 

200 

213  4 

240 

266  8 

280 

320 

333  4 

373  4 

42 

196  0 

210 

224  0 

252 

280  0 

294 

336 

350  0 

392  0 

44 

205  4 

220 

234  8 

264 

293  4 

308 

352 

366  8 

410  8 

46 

214  8 

230 

245  4 

276 

306  8 

322 

368 

383  4 

429  4 

48 

224  0 

240 

256  0 

288 

320  0 

336 

384 

400  0 

448  0 

50 

233  4 

250 

266  8 

300 

333  4 

350 

400 

416  8 

466  8 

52 

242  8 

260 

277  4 

312 

346  8 

364 

416 

433  4 

485  4 

54 

252  0 

270 

288  0 

324 

360  0 

378 

432 

450  0 

504  0 

56 

261  4 

280 

298  8 

336 

373  4 

392 

448 

466  8 

522  8 

58 

270  8 

290 

309  4 

348 

386  8 

406 

464 

483  4 

541  4 

60 

280  0 

300 

320  0 

360 

400  0 

420 

480 

500  0 

560  0 

62 

289  4 

310 

330  8 

372 

413  4 

434 

496 

516  8 

578  8 

64 

298  8 

320 

341  4 

384 

426  8 

448 

512 

533  4 

597  4 

66 

308  0 

330 

352  0 

396 

440  0 

462 

528 

550  0 

616  0 

68 

317  4 

340 

362  8 

408 

453  4 

476 

544 

566  8 

634  8 

70 

326  8 

350 

373  4 

420 

466  8 

490 

560 

583  4 

653  4 

72 

336  0 

360 

384  0 

432 

480  0 

504 

576 

600  0 

672  0 

74 

345  4 

370 

394  8 

444 

493  4 

518 

592 

616  8 

690  8 

76 

354  8 

380 

405  4 

456 

506  8 

532 

608 

633  4 

709  4 

78 

364  0 

390 

416  0 

468 

520  0 

546 

624 

650  0 

728  0 

80 

373  4 

400 

426  8 

480 

533  4 

560 

640 

666  8 

746  8 

82 

382  8 

410 

437  4 

492 

546  8 

574 

656 

683  4 

765  4 

84 

392  0 

420 

448  0 

504 

560  0 

588 

672 

700  0 

784  0 

*  The  measurements  in  these  columns  come  out  hi  even  feet. 


1398 


DATA  ON  LUMBER. 


TABLE  OF  BOARD  MEASURE.—  Continued. 

For  explanation,  see  p.  1395. 


J 

Size  and  Sectional  Area  in  Inches. 

t!s 

120 

140 

144 

160 

168 

192 

196 

224 

2 

10X12 

10X14 

12X12 

10X16 

12X14 

12X16 

14X14 

14X16 

ft.* 

ft.  ins. 

ft.* 

ft.  ins. 

ft.* 

ft.* 

ft.  ins. 

ft.  ins. 

4 

40 

46  8 

48 

53  4 

56 

64 

65  4 

74  8 

6 

60 

70  0 

72 

80  0 

84 

96 

98  0 

112  0 

8 

80 

93  4 

96 

106  8 

112 

128 

130  8 

149  4 

10 

100 

116  8 

120 

133  4 

140 

160 

163  4 

186  8 

12 

120 

140  0 

144 

160  0 

168 

192 

196  0 

224  0 

14 

140 

163  4 

168 

186  8 

196 

224 

228  8 

261  4 

16 

160 

186  8 

192 

213  4 

224 

256 

261  4 

298  8 

18 

180 

210  0 

216 

240  0 

252 

288 

294  0 

336  0 

20 

200 

233  4 

240 

266  8 

280 

320 

326  8 

373  4 

22 

220 

256  8 

264 

293  4 

308 

352 

359  4 

410  8 

24 

240 

280  0 

288 

320  0 

336 

384 

392  0 

448  0 

26 

260 

303  4 

312 

346  8 

364 

416 

424  8 

485  4 

28 

280 

326  8 

336 

373  4 

392 

448 

457  4 

522  8 

30 

300 

350  0 

360 

400  0 

420 

480 

490  0 

560  0 

32 

320 

373  4 

384 

426  8 

448 

512 

522  8 

597  4 

34 

340 

396  8 

408 

453  4 

476 

544 

555  4 

634  8 

36 

360 

420  0 

432 

480  0 

504 

576 

588  0 

672  0 

380 

443  4 

456 

506  8 

532 

608 

620  8 

709  4 

40 

400 

466  8 

480 

533  4 

560 

640 

653  4 

746  8 

42 

420 

490  0 

504 

560  0 

588 

672 

686  0 

784  0 

44 

440 

513  4 

528 

586  8 

616 

704 

718  8 

821  4 

46 

460 

536  8 

552 

613  4 

644  j  736 

751  4 

858  8 

48 

480 

560  0 

576 

640  0 

672  !  768 

784  0 

896  0 

50 

500 

583  4 

600 

666  8 

700  !  800 

816  8 

933  4 

52 

520 

606  8 

624 

693  4 

728 

832 

849  4 

970  8 

54 

540 

630  0 

648 

720  0 

756 

864 

882  0 

1,008  0 

56 

560 

653  4 

672 

746  8 

784 

896 

914  8 

1,045  4 

58 

580 

676  8 

696 

773  4 

812 

928 

947  4 

1,082  8 

60 

600 

700  0 

720 

800  0 

840 

960 

980  0 

1,120  0 

62 

620 

723  4 

744 

826  8 

868 

992  1,012  8 

1,157  4 

64 

640 

746  8 

768 

853  4 

896 

1,024  1,045  4 

1,194  8 

66 

660 

770  0 

792 

880  0 

924 

1,056  1,078  0 

1,232  0 

68 

680 

793  4 

816 

906  8 

952 

1,088  1,110  8 

1,269  4 

70 

700 

816  8 

840 

933  4 

980 

1,120 

1,143  4 

1,306  8 

72 

720 

840  0 

864 

960  0 

1,008 

1,152 

1,176  0 

1,344  0 

74 

740 

863  4 

888 

986  8 

1,036 

1,184 

1,208  8 

1,381  4 

76 

760 

886  8 

912 

1,013  4 

1,064 

1,216 

1,241  4 

1,418  8 

78 

780 

910  0 

936 

1,040  0 

1,092 

1,248 

1,274  0 

1,456  0 

80 

800 

933  4 

960 

1,066  8 

1,120 

1,280 

1,306  8 

1,493  4 

82 

820 

956  8 

984 

1,093  4 

1,148 

1,312 

1,339  4 

1,530  8 

84 

840 

980  0 

1,008 

1,120  0 

1,176 

1,344 

1,372  0 

1,568  0 

*  The  measurements  in  these  columns  come  out  in  even  feet. 


MEASUREMENT  OF  FLOORING,  ETC.         1399 


Measurement  of  Finishing1  Lumber,  Flooring, 
Ceiling1,  etc. — Most,  if  not  all,  lumber  for  finishing  is  regular, 
sawn  in  thicknesses  of  1  in.,  1 J  in.,  1J  in.,  and  2  ins.,  and  in  some 
woods,  such  as  white  pine  and  poplar,  is  sawn  2J  ins.  and  3  ins. 
thick. 

When  surfaced  both  sides,  the  thickness  is  reduced  to  %, 
1^6,  I?IXG,  If,  2i,  and  2%  ins. 

All  dressed  stock  is  measured  and  sold  "strip  count,"  i.e., 
full  size  of  rough  material  necessarily  used  in  its  manufacture. 
Thus  1/i^-in.  boards  are  measured  as  though  1J  in.  thick. 
The  number  of  feet,  board  measure,  for  l|-in.  stock  (l}{6  fin- 
ished) is  1^  times  that  in  a  1-in.  board,  and  in  the  same  way 
for  IJ-in.  and  2J-in.  stock.  If-in.  plank  is  always  measured 
2  ins.  thick,  and  2J-m-  stock,  2J  ins.  thick.  Boards  less  than 
1  in.  thick  are  measured  the  same  as  inch  boards,  but  for  f- 
and  f-in.  stock  a  reduced  price  is  generally  made. 

Matched  Flooring.* — The  standard  sizes  are  1X3,  1X4,  and 
1X6,  or  1JX3,  1JX4,  and  liXG.  The  thickness  of  1-in. 
flooring  should  be  %  in.,  and  of  IJ-in.  flooring,  1¥8¥  in.;  3-in- 
flooring  should  show  2^  ins.  on  face,  after  it  is  laid,  4-in.,  3J  ins., 
and  6-in.,  5J  ins. 

Matched  maple  flooring  is  made  in  2-in.,  2J-in.,  and  3^-in.  face, 
and  in  thicknesses  of  J,  1J,  and  If  ins..  There  are  three  grades: 
Clear,  No.  1,  and  Factory. 

Ceiling  (matched  and  beaded  boards)  is  regularly  stuck  in  the 
same  widths  as  flooring.  The  standard  (nominal)  thicknesses 
of  yellow-pine  ceiling  are  f,  J,  },  and  f  in.,  the  actual  thickness 
of  each  being  %>  in.  less.  The  f-in.  ceiling  is  dressed  one  side 
only,  the  other  thicknesses  both  sides. 

Yellow-pine  Drop  Siding,  all  patterns,  measures  f  in.X^i  ms. 
over  all,  and  usually  shows  about  5-in.  face. 

Bevel  Siding  is  resawed  on  a  bevel  from  stock  %  in.XSJ  ins. 
after  surfacing. 

The  New  England  Clapboards  are  4  ft.  long,  6  ins.  wide, 
J  in.  thick  at  the  butt,  and  about  J  in.  thick  at  the  other  edge. 
They  are  put  up  in  bunches  and  sold  by  the  thousand. 

1  till os  for  Estimating-  Quantities  of  Sheathing, 
Flooring,  etc. — For  common  sheathing  laid  horizontally  on 
a  wall  or  roof  without  openings,  add  one  tenth  to  the  actual 
superficial  area  to  allow  for  waste.  On  the  walls  of  dwellings, 

*  Everywhere  except  in  New  England  "flooring"  is  always  understood 
to  be  tongued  and  grooved. 


1400  COST  OF  CARPENTERS'  WORK. 

figure  the  walls  as  though  without  openings  and  allow  nothing 
for  waste.  If  sheathing  is  laid  diagonally,  add  one  sixth  to 
the  actual  superficial  area. 

For  tight  sheathing  laid  horizontally,  add  one  fifth  for  6-in. 
boards,  one  seventh  for  8-in.  boards,  and  one  ninth  for  10-in. 
boards.  If  laid  diagonally  add  one  fourth  for  6-in.  boards, 
one^sixth  for  8-in.  boards,  and  one  eighth  for  10-in.  boards. 

For  3-in.  matched  flooring  add  one  half  to  the  actual  super- 
ficial area  to  be  covered. 

For  4-in.  flooring  add  one  third  and  for  6-in.  flooring  add 
one  fifth.  Ceiling  is  measured  the  same  as  flooring. 

For  drop  siding,  add  one  fifth  to  the  superficial  area. 

For  lap  siding  laid  4  ins.  to  the  weather,  add  one  half  to 
the  actual  superficial  area;  if  4|  ins.  to  the  weather,  add  one 
third. 

Cost  of  Carpenters'  Work. — There  are  so  many  items  and 
conditions  which  enter  into  the  cost  of  carpenters'  work,  and 
the  cost  varies  so  widely  with  the  locality,  that  it  is  quite 
impossible  to  give  figures  which  are  of  general  practical  value, 
although  several  books  have  been  published  on  estimating 
carpenters'  work.  The  best  of  these  that  the  author  has  seen 
is  " Estimating  Frame  and  Brick  Houses,"  by  Fred  T.  Hodgson. 

The  following  figures  of  the  cost  (for  labor  and  nails)  of 
framing  and  putting  on  sheathing  and  siding  and  laying  floor- 
ing are  probably  a  fair  average,  with  carpenters'  wages  at 
$3  a  day  of  eight  hours  (37J  cts.  per  hour).  The  cost  of  fram- 
ing is  almost  always  figured  at  a  certain  price  per  thousand 
feet  of  lumber,  board  measure.  The  cost  of  laying  flooring- 
sheathing,  etc.,  is  always  figured  by  the  square  of  100  sq.  ft. 
(10'XIO'). 

For  setting  up  studding  and  framing  walls  of  wooden  dwellings,  $10 . 00  per  M. 

For  framing  and  setting  floor  joists,   2X8   to  2X12 $9  to  $10    "     " 

Framing  and  setting  heavy  joists  and  girders,  6  X  12  to  10  X  14,   $8 . 50    :i 

Framing  gable  roofs  and  setting  in  place $10.00    " 

Framing  hip  roofs  and  setting  in  place $11  to  $12    " 

For  putting  in  bridging,  after  it  is  cut,  per  100  lin.  ft.  in  the  row,  $1 . 25 
For  covering  the  sides  or  roofs  of  wooden  buildings  with 

dressed  sheathing,  laid  horizontally 0 . 60  per  square 

If  laid  diagonally 0 . 75     " 

The  cost  of  labor  and  nails  for  laying  6"  flooring,  blind 
nailed  to  every  joist  without  dressing  after  laying 

is  about 2 . 00     "          " 

For  4"  flooring,  not  dressed,  allow 2 . 25     ** 

For  3"  flooring,  not  dressed,  allow 2 . 50     "          " 

For  3"  hard-pine  flooring,  hand  smoothed  or  traversed.  ...      3 .  75     "         " 

For  3"  red-oak  flooring,  hand  smoothed  or  traversed 6 . 00     ' 

For  3"  white-oak  flooring,  hand  smoothed  or  traversed.  ...      8 . 00     "          " 
For  3"  maple  flooring,  hand  smoothed  or  traversed.  .$10  to  $12     * 


BUILDING  PAPERS  AND   FELTS.  1401 


BUILDING  PAPERS,  FELTS,   QUILTS,  ETC. 

There  is  a  great  variety  of  papers  and  felts  manufactured 
for  use  on  buildings.  They  may  be  broadly  classified  as  follows : 

Rosiu-sized  Building:  Papers,* — These  are  about  the 
cheapest  grades  of  building  paper;  they  are  not  water-proof, 
and  should  not  be  used  on  roofs,  or  on  walls  in  damp  climates. 
In  dry  places  they  protect  from  dust,  draughts,  and  to  some 
extent  from  heat  and  cold.  They  are  generally  either  a  dull 
red  or  gray  in  color,  have  a  hard  smooth  surface,  and  are  clean 
to  handle.  Always  put  up  in  rolls  36  iris,  wide  and  usually 
containing  500  sq.  ft.  Weight  varies  from  18  to  40  Ibs.  to  the 
roll  of  500  sq.  ft.;  cost,  from  50  cts.  to  $1.50  per  roll.f 

Water-proof  Papers. — Neponset  Black  Sheathing  is 
water-  and  air-proof,  odorless  and  clean  to  handle.  An  excel- 
lent paper  under  siding,  shingles,  slate,  or  tin.  Rolls  36  ins. 
wide,  .containing  250  and  500  sq.  ft.;  cost,  about  $2.00  per  roll 
of  500  sq.  ft. 

Neponset  Red  Rope  Sheathing  and  Roofing. — Made  of  rope  stock ; 
has  great  strength  and  flexibility,  absolutely  water-proof  and 
air-tight.  One  of  the  best  sheathing  papers.  Makes  a  good 
cheap  roofing  for  sheds,  poultry-houses,  etc.  Rolls  36  ins.  wide, 
containing  250  and  500  sq.  ft.  Cost,  about  $5.00  per  500  sq.  ft. 

Parchment  Water-proof  Sheathing. — Semi-transparent,  smooth 
surface,  odorless,  water-,  air-,  and  vermin-proof.  Adapted  for 
general  sheathing  purposes  and  for  use  in  concrete  construction. 
1-ply,  25  Ibs.  to  900  sq.  ft. ;  2-ply,  25  Ibs.  to  500  sq.  ft. ;  3-ply, 
25  Ibs.  to  275  sq.  ft.  All  36  ins.  wide. 

P.  &  B.  Building  Pa  per.— Thoroughly  coated  with  P.  &  B. 
compound  (principally  paraffine),  is  water-,  acid-,  alkali-,  and 
gas-proof ;  claimed  not  to  decay.  An  excellent  sheathing  paper. 
Black  and  glossy,  but  not  sticky.  Rolls  26  ins.  wide,  containing 
1000  sq.  ft.  Made  1-ply  (very  thin),  30  Ibs.;  2-ply,  40  Ibs.; 
3-ply,  65  Ibs. ;  4-ply,  80  Ibs.  Cost,  $3.00,  $4.50,  $6.00,  and  $8.00, 
respectively. 

Dry  Felts. — Common  felts  are  composed  of  waste  vege- 
table fibres  cemented  together  with  rosin.  Better  grades  are 
made  from  wool  stock.  Felts  are  made  in  many  different 
thicknesses,  and  in  32-in.  and  36-in.  widths.  They  should  be 
specified  by  weight  unless  a  particular  brand  is  specified.  Com- 
mon dry  felt  weighs  from  4^  to  5  Ibs.  per  100  sq.  ft. 

Barrett's  Eureka  Brand. — All-wool  stock,  32  ins.  wide,  and 
weighs  1  Ib.  to  the  square  yard. 

*  The  terms  "building"  and  "sheathing"  are  indiscriminately  applied 


are  classed  as  sheathing  papers. 

t  All  prices  are  approximate ;  they  vary  with  locality  and  condition  of 
the  market. 


1402  BUILDING  PAPERS  AND  QUILTS. 

Barrett's  Excelsior  Brand. — All-wool  stock,  32  ins.  wide,  and 
weighs  1J  Ibs.  to  the  square  yard.  This  is  a  very  heavy  felt. 

A  dry  wool  felt  weighing  1  Ib.  to  the  square  yard  will  be 
about  J  in.  thick.  Such  felts  are  used  principally  for  deadening 
between  floors  and  as  carpet  lining.  Commonly  sold  by  the 
pound,  2|  cts.  a  pound  being  perhaps  an  average  price. 

Saturated  Felts. — Common  roofing  felts  are  made  by 
saturating  common  dry  felt  with  coal-tar  pitch.  Roofing  felts 
are  commonly  made  in  weights  of  12,  15,  and  20  Ibs.  to  the 
100  sq.  ft.  Nothing  lighter  than  12  Ibs.  should  be  used  for 
roofing.  Usually  sold  by  weight.  Average  price,  1J  cts.  a 
pound. 

Asphalt  felts  are  commonly  made  in  the  same  weights. 

E>ry  Saturated  Tarred  Felts  are  specially  run  through 
a  tier  of  calenders  to  give  a  hard,  uniform  surface  and  contain 
a  minimum  amount  of  coal-tar.  Are  especially  adapted  for 
slaters'  use,  as  they  will  carry  a  chalk  line  and  are  easy  to  handle. 
Rolls  36  ins.  wide  contain  500  sq.  ft.  and  weigh  about  30  Ibs. 
Cost,  about  80  cts.  per  roll. 

Asbestos  Building'  Felts  are  usually  made  about  6,  10, 
14,  and  16  Ibs.  to  the  100  sq.  ft.,  although  different  manufac- 
turers make  different  weights.  Rolls  36  ins.  wide.  Sold  by 
weight. 

Insulating  and  Deadening  Quilts. 

Cabot's  "Quilt"  consists  of  a  felted  matting  of  eel-grass  held 
in  place  between  two  layers  of  tough  manila  paper  by  "quilt- 
ing." Also  made  with  a  covering  of  asbestos.  Single-ply 
weighs  85  Ibs.  per  bale  of  500  sq.  ft. ,  width  36  ins.  Double-ply 
weighs  125  Ibs.  per  bale  of  500  sq.  ft.,  width  36  ins. 

Keystone  Hair  Insulator. — A  quilt  with  hair  filling.  Four 
brands,  each  packed  in  bales  3  ft.  wide  containing  500  sq.  ft. 
Acme,  plain  paper  both  sides,  weight  per  bale  60  Ibs.  Nep- 
tune, water-proof  paper  one  side,  plain  paper  other  side,  weight 
per  bale  70  Ibs.  Phoenix,  asbestos  paper  one  side,  plain  paper 
other  side,  weight  per  bale  100  Ibs.  Salamander,  asbestos 
paper  both  sides,  weight  per  bale  130  Ibs. 

The  Union  Fibre  Company's  Mineral-wool  Deafener  is  made 
of  rock-fibre  wool,  quilted  between  sheets  of  rosin-sized,  water- 
proof or  fire-proof  paper.  Put  up  in  rolls  36  ins.  wide,  \  in. 
thick,  and  containing  125  sq.  ft. 

The  Union  Fibre  Company's  Flax-fibre  Floor  Deadener  is 
made  of  degummed  flax  fibre,  sewed  between  two  thicknesses 
of  rosin-sized  paper.  Put  up  in  rolls  36  ins.  wide,  J  in.  thick, 
and  containing  200  sq.  ft.  Also  furnished  with  water-proof  or 
asbestos  paper  covering. 

Cost  of  Building-  and  Sheathing  Papers  in  Place. 

The  following,  although  necessarily  restricted  to  a  few  lines, 
will  give  a  general  idea  of  the  cost  of  different  kinds  and  grades 
of  sheathing  papers,  the  price  given  being  a  fair  average  for 
the  material  applied  to  an  outside  wall  or  roof: 


PAINT   AND   VARNISH.  140S 

Price  per  100 
Square  Feet. 

Common  tarred  felts  (15  Ibs.  per  square)* $0  30 

Red  rosin-sized  sheathing,  best  grades 0 . 35 

Manahan's  parchment  sheathing,  single-ply 0 . 26 

double-ply 0 . 40 

"  ship-rigging  tar  sheathing,  2-ply 0.75 

"Neponset"  black  (water-proof)  building  paper 0.45 

red  rope  roofing  fabric 1 . 10 

Sheathing  papers  with  asphalt  centre $0.40  to  0.50 

Johns'  asbestos  building  felt,  10  Ibs.  per  square 0.42 

14  Ibs.  per  square 0 . 55 

Cabot's  sheatning  quilt,  single-ply 1-05 

'•       double-ply 1.25 

Sawyer's  century  sheathing  quilt  (felt  coated  one  side  with  a  water- 

and  vermin-proof  compound) 1 . 35 


Paint  and  Varnish. 

The  solid  ingredient  of  a  paint  is  called  the  pigment,  and  is  a 
fine  powder,  nearly  all  of  which  will  pass  through  a  brass  wire 
sieve  of  100  meshes  to  the  linear  inch;  in  fact,  most  pigments 
are  much  finer  than  that,  and  those  formed  as  precipitates  by 
chemical  processes  are  so  fine  that  there  is  no  way  to  measure 
them. 

The  liquid  part  is  called  the  vehicle;  this  is  usually  linseed 
oil,  sometimes  with  the  addition  of  a  little  turpentine  or  other 
volatile  solvent;  in  the  enamel  paints  it  is  varnish;  in  kalso- 
mine  and  other  cold-water  paints  it  is  a  solution  of  glue,  casein, 
albumen,  or  some  similar  cementing  material.  The  cement- 
ing material  is  sometimes  called  the  binder. 

Ingredients  of  Oil  Paint.— White  lead  and  white  zinc 
are  the  common  white  pigments,  but  there  is  also  a  white 
pigment  called  zinc-lead,  which  is  made  in  a  furnace  from  ores 
containing  lead  and  zinc,  and  is  of  variable  composition;  and 
lithopone,  a  mixture  of  sulphide  of  zinc  and  sulphate  of  barium; 
this  sometimes  darkens  by  exposure  to  light,  and  is  dis- 
colored if  it  comes  in  contact  with  anything  containing  lead. 
Yellow  is  commonly  chromate  of  lead,  or  chrome-yellow; 
green  is  chrome-green,  which  is  a  mixture  of  chrome-yellow  and 
Prussian  blue;  blue  is  ultramarine,  or  sometimes  prussian  blue. 
The  brilliant  reds  are  coal-tar  colors  as  a  rule;  the  dull  reds 
and  browns  are  oxides  of  iron.  Ochres  are  dull  yellow.  Carbon 
forms  the  base  of  all  black  paints,  either  a£  lampblack,  drop- 
black  (boneblack),  or  graphite. 

Linseed  oil  is  either  raw  or  boiled.     Raw  oil  is  the  oil  in  its 

*  A  "square"  is  100  sq,  ft. 


1404  PAINT   AND   VARNISH. 

natural  state  as  it  is  extracted  from  the  seed;  it  should  be  set- 
tled and  filtered  perfectly  clear;  it  is  yellow  or  greenish  yellow 
in  color.  Boiled  oil  is  raw  oil  which  has  been  heated  to  400 
or  500  F.  with  compounds  (usually  oxides)  of  lead  and  man- 
ganese; it  is  darker  in  color  than  raw  oil,  and  dries  more  quickly. 
Raw  oil  exposed  .in  a,  thin  film  to  the  air  is  converted  in 
about  five  days  into  a  tough  leathery  substance;  boiled  oil 
undergoes  this  change  in  ten  to  twenty-four  hours. 

Driers. — These  are  compounds  of  lead  and  manganese, 
dissolved  in  oil,  and  this  solution  thinned  with  turpentine  or 
benzine.  They  act  as  carriers  of  oxygen  between  the  air  and 
the  oil,  and  their  addition  to  a  paint  makes  it  dry  more 
rapidly.  Some  driers  are  also  called  japans.  Not  more  than 
10%  by  volume  of  any  of  these  liquid  driers  should  be  added 
to  oil.  Excess  of  drier  causes  the  paint  to  lack  durability. 

Priming  Coat.  —  This  is  the  first  coat  applied  to  the 
clean  surface;  a  priming  coat  for  wood  is  chiefly  oil,  and  is 
usually  equivalent  to  a  gallon  of  ordinary  paint  thinned  with 
a  gallon  of  raw  linseed  oil.  But  paint  is  not  thinned  to 
make  a  priming  coat  for  structural  metal.  In  all  wood- 
work nail-holes  and  other  defects  are  filled  with  putty  after  the 
priming  coat  has  been  applied;  but  if  the  wood  is  resinous, 
knots  and  resinous  places  must  be  covered  with  shellac  varnish 
before  the  priming  coat  is  put  on. 

Outside  Painting. — The  priming  coat  having  largely 
been  absorbed  by  the  wood,  a  second  and  third  coat  of  paint 
are  to  be  applied.  The  most  common  paint  used  on  houses 
is  white  lead.  This  is  usually  sold  as  paste  white  lead,  con- 
taining 10%  of  oil;  100  Ibs.  of  this  mixed  with  5  gal.  oil  makes 
64  gal.  paint  weighing  about  21J  Ibs.  per  gal.;  a  gal.  of  this 
contains  about  14  Ibs.  dry  white  lead.  White  zinc  is  also  an 
important  paint;  9J  Ibs.  zinc  and  5.7  Ibs.  oil  make  a  gallon  of 
paint. 

The  defect  of  white  lead  is  that  it  "chalks,"  i.e.,  in  time 
its  surface  becomes  a  dry  powder,  which  rubs  off;  the  defect 
of  zinc  is  that  it  becomes  hard  and  shows  a  tendency  to  peel 
off;  the  two  are  mixed  with  good  results,  ^  to  -J  the  mixture 
being  zinc.  Colored  paints  are  made  by  adding  colored  pig- 
ments to  zinc  or  lead;  but  dark  colored  paints  often  contain 
only  iron  oxides,  ochres,  etc.,  as  pigments;  these  weigh  12  to 
14  Ibs.  per  gallon.  In  applying  paint,  allow  a  week  between 
successive  coats.  In  painting  the  outside  of  a  house,  paint  the 


PAINT   AND   VARNISH.  1405 

trim  first,  then  the  body  color  can  be  laid  neatly  against  it. 
It  is  desirable  to  brush  it  on  with  the  grain  of  the  wood. 

A  gallon  of  priming  coat  will  cover  about  300  sq.  ft.,  and  a 
gallon  of  paint  used  in  subsequent  coats  about  600  sq.  ft.  Roof 
paints  should  contain  a  larger  proportion  of  oil,  and  less  drier 
or  none.  Three  coats  are  desirable.  Tin  roofs  and  galvan- 
ized iron  work  should  be  thoroughly  scrubbed  and  then  dried 
before  painting.  Shingles  on  the  wall  of  the  house  (and  some- 
times on  the  roof)  are  sometimes  stained  with  creosote  stain, 
which  consists  of  a  pigment  suspended  in  creosote  or  some 
similar  liquid.  The  creosote  has  some  preservative  effect. 

Inside  Painting.  —  Door  and  window  frames  should 
receive  a  priming  coat  of  paint  in  the  shop;  if  they  are  to  be 
finished  in  varnish  this  paint  will  be  applied  to  the  back  only. 
As  has  already  been  said,  before  any  painting  is  done  any  re- 
sinous knots  are  to  be  varnished  with  shellac.  All  interior 
surfaces  which  are  to  be  painted  should  be  puttied  after 
the  priming  coat;  the  putty  should  be  applied  with  a  wooden 
spatula,  not  a  steel  one,  to  avoid  marring  the  surface.  The 
paint  for  the  second  coat  should  contain  as  much  turpentine 
as  oil.  i.e.,  its  vehicle  should  be  half  oil  and  half  turpentine. 
The  effect  of  this  is  to  make  the  paint  dry  with  a  dull  surface, 
"flat"  is  the  painter's  term;  not  glossy;  to  this  the  next  coat 
will  adhere  well.  If  the  next  is  the  final  coat  this  may  be  an 
ordinary  oil  paint.  When  thoroughly  dry  the  gloss  may  be 
removed  by  lightly  rubbing  it  with  pumice  and  water. 

Enamel  paint  consists  of  pigment  with  varnish  as  a  vehicle, 
and  is  harder  and  makes  a  finer  finish  than  oil  paint.  It  is 
also  more  expensive.  It  is  usual  to  apply  it  over  oil  paint; 
in  this  case  the  last  coat  of  oil  paint  should  be  lightly  sand- 
papered when  quite  hard  and  dry,  then  put  on  a  coat  of  enamel 
paint;  when  this  is  dry  it  should  be  sandpapered  or  rubbed 
with  curled  hair,  and  the  final  coat  of  enamel  is  then  laid  on; 
this  may  be  rubbed  in  a  like  manner  if  a  flat  surface  is  desired, 
or  it  may  be  left  with  the  gloss. 

Varnish.  —  There  are  two  principal  kinds  of  varnish, 
spirit  varnishes,  of  which  shellac  varnish  is  the  most  important, 
and  which  consists  essentially  of  a  resin  dissolved  in  a  volatile 
solvent,  and  oleo-resinous  varnishes,  in  which  the  resinous  in- 
gredient is  combined  with  linseed  oil,  and  this  compound  is 
di'ggdlvetl  in*  turpentine  or  benzine.  The  oleo-resinous  var- 
nishes are  commercially  the  more  important,  and  are  largely 


1406  PAINT  AND  VARNISH. 

used  in  interior  finishing.  A  gallon  of  varnish  covers  500 
sq.  ft.  one  coat.  Surfaces  to  be  varnished  are  treated  in  the 
following  manner:  If  the  wood  is  of  the  open  grained  sort, 
such  as  oak,  chestnut  or  ash,  it  first  receives  a  coat  of  paste 
filler.  Liquid  fillers  are  not  desirable,  as  they  form  a  poor 
base  for  subsequent  work.  A  paste  filler  is  really  a  sort  of 
paint,  the  pigment  being  silex,  or  ground  quartz,  and  the 
vehicle  is  a  quick-drying  varnish  made  thin  with  turpentine 
or  benzine.  This  is  rubbed  strongly  in  on  the  grain  of  the 
wood  with  a  short  stiff  brush,  and  as  soon  as  it  has  set,  usually 
within  half  an  hour,  it  is  rubbed  off  with  a  harsh  cloth  or  a 
handful  of  excelsior,  rubbing  hard  across  the  grain  of  the  wood. 
If  it  is  desired  to  stain  the  wood,  the  oil  stain  may  be  mixed 
with  the  filler;  but  if  a  close-grained  wood  is  used,  which  needs 
no  filler,  the  oil  stain  may  be  thinned  to  the  desired  color  with 
turpentine  or  benzine  and  applied  as  a  wash.  In  cleaning 
the  filler  out  of  mouldings,  corners,  etc.,  a  suitably  shaped  stick 
may  be  used  but  not  a  steel  implement.  If  any  puttying  is 
necessary  it  is  next  done.  After  two  days  the  first  coat  of 
varnish  is  applied;  after  five  days  it  should  be  rubbed  with 
curled  hair  or  fine  sandpaper  to  remove  the  gloss,  so  that  the 
next  coat  will  adhere  well;  then  one,  two  or  three  more  coats 
of  varnish,  five  days  or  more  apart,  each  coat  rubbed  except 
the  last,  which  may  be  rubbed  or  left  with  the  natural  gloss. 
Outside  doors,  window  sills,  jambs,  inside  blinds,  and  all 
surfaces  exposed  to  the  direct  rays  of  the  sun,  are  varnished 
with  spar  varnish  and  left  glossy.  If  shellac  varnish  is  used 
as  the  interior  finish  it  is  applied  in  the  same  way,  but  at  least 
six  coats  should  be  applied.  Floors  which  are  to  be  varnished 
should  be  treated  as  has  been  described;  but  if  they  are  to  be 
waxed  they  should  receive  one  or  two  coats  of  shellac  varnish, 
then  five  or  six  coats  of  wax,  at  intervals  of  a  week,  each  coat 
being  well  polished  with  a  weighted  floor-brush  made  for  the 
purpose.  Floor-wax  is  not  beeswax,  but  is  a  compound 
wax  made  for  the  purpose.  Shellac  is  a  good  floor- varnish; 
it  discolors  the  wood  less  than  any  other  varnish,  and  dries 
rapidly. 

Plastered  walls  which  must  be  painted  are  usually  washed  with 
a  solution  of  soap  and  then  with  a  solution  of  alum.  When 
this  is  dry  it  is  sponged  off,  then  allowed  to  dry,  then  oiled, 
then  painted.  If  the  paint  is  applied  to  the  fresll  plaster  the 
lime  in  the  plaster  will  attack  the  paint. 


PAINT    AND  VARNISH.  1407 

Repainting. — The  exterior  woodwork  of  a  house  needs  re- 
painting once  in  five  to  ten  years,  according  to  climate  and 
similar  conditions,  although  if  not  done  with  proper  material 
or  sufficient  care  it  will  not  last  as  long  as  this;  the  interior 
should,  with  good  care,  stand  fifteen  to  twenty  years,  and  then 
may  not  require  complete  renewal.  Exterior  paint  sometimes 
loses  its  luster,  while  the  body  of  the  paint  is  still  good,  and  in 
such  a  case  it  is  enough  to  wash  the  surface  and  then  give  it 
a  coat  of  oil;  this  will  replace  the  oil  which  has  superficially 
perished  and  will  impart  gloss  and  bring  out  color.  If  the 
paint  is  worn  off  so  as  to  show  the  wood  in  places,  or  is  peeling, 
it  must  be  very  carefully  examined.  In  extreme  cases  it  will 
be  necessary  to  "burn  off"  the  old  paint;  this  is  done  with 
a  painter's  torch,  a  lamp  which  burns  alcohol,  naphtha  or 
kerosene,  and  which  furnishes  a  flaring  blast  of  flame,  which 
is  directed  against  the  painted  surface  just  long  enough  to 
soften  the  paint  which  is  at  once  removed,  while  still  hot, 
with  a  scraper.  The  paint  is  not  actually  burned,  only  softened 
by  the  flame;  but  it  may  thus  be  removed  completely.  Houses 
covered  with  pitchy  wood,  like  southern  pine,  sometimes  re- 
quire this  treatment,  and  the  next  painting  is  found  to  be  more 
lasting.  In  many  cases  it  will  be  sufficient  to  thoroughly 
scrub  the  surface  with  a  stiff  steel  wire  brush.  Interior  sur- 
faces may  be  cleaned  (if  the  removal  of  the  old  paint  and  varnish 
is  necessary)  with  varnish  remover ;  this  is  a  mixture  of  solvent 
liquids,  which  penetrate  the  old  paint  or  varnish  and  softens 
it,  when  it  may  be  removed  with  scrapers  or  brushes.  It  is 
less  dangerous  on  account  of  fire  than  the  burning-ofT  method, 
but  slower  and  more  costly.  It  must  not  be  forgotten  that 
varnish  remover  is  volatile  and  highly  inflammable  and  must 
not  be  used  in  a  room  where  there  is  a  fire.  It  is  especially 
suitable  for  cleaning  out  mouldings  and  all  irregular  surfaces, 
from  which  the  varnish  may  then  be  removed  with  stiff  brushes, 
if  not  convenient  to  use  scrapers.  It  is  especially  desirable 
to  clean  floors  occasionally  in  this  way;  but  if  the  house  has 
been  varnished  originally  with  a  first-class  varnish  it  may  be 
necessary  only  to  wash  it  thoroughly  and  then  apply  another 
coat  of  varnish.  Smoke  and  dirt  may  often  be  removed  per- 
fectly from  ceilings  with  the  crumbs  of  fresh  bread,  where  wash- 
ing would  not  be  desirable.  A  ten  per  cent  solution  of  car- 
bonate of  soda  (sal  soda)  in  hot  water  may  be  used  to  remove 
old  floor-wax, 


1408  PAINT   AND   VARNISH. 

Paint  for  Structural  Steel.  —  Steel  being  usually 
more  perishable  than  wood,  as  well  as  more  expensive,  and 
used  for  service  where  its  strength  is  essential  to  the 
stability  of  the  structure,  its  prevention  from  corrosion  by 
painting  is  of  much  importance.  It  must  first  of  all  be  re- 
cognized that  the  precaution  always  taken  in  painting  wood 
to  secure  a  clean  surface  for  the  paint,  must  not  be  omitted 
with  steel.  Mud  and  dirt  which  have  got  on  it  must  be  first  re- 
moved; then  it  must  be  examined  for  rust,  and  any  rusty  spots 
must  be  cleaned  thoroughly;  loose  scale  may  be  removed  by 
wire  brushes,  but  thick  and  closely-adherent  rust  must  be 
removed  with  steel  scrapers,  or  with  hammer  and  chisel  if 
necessary. 

No  doubt  the  best  way  to  clean  steel  is  with  the  sand-blast, 
but  it  is  not  available  for  much  architectural  work;  but  much 
care  must  be  taken  to  obtain  a  clean  surface.  On  wood  the 
priming  coat  sinks  into  the  wood  and  forms  a  perfect  bond 
between  it  and  the  succeeding  coats;  but  with  metal  no  such 
thing  is  possible;  it  is  a  case  of  simple  adhesion,  and  to  adhere 
well  the  surface  must  be  clean.  The  paint  for  structural 
metal  should  be  tough  and  elastic,  and  to  at,  great  a  degree 
a^  possible  it  should  be  water-proof.  Less  than  two  coats 
should  never  be  applied,  and  three  are  better.  Paint  is  al- 
ways thin  on  edges  and  angles,  also  on  bolt  and  rivets  heads; 
it  is  therefore  good  practice,  after  the  first  full  coat,  to  apply 
a  partial  or  striping  coat,  covering  the  angles  and  edges  for 
at  least  an  inch  back  from  the  edge,  and  covering  all  bolt  and 
rivet  heads.  After  this  striping  coat  has  become  dry,  the 
second  full  coat  it  applied;  it  may  then  be  assumed  that  the 
whole  surface  has  received  two  full  coats.  At  least  a  week 
should  elapse  between  coats. 

In  designing  the  steel- work,  all  cavities  which  may  be  filled 
with  rain  during  erection  should  be  properly  drained;  and 
during  erection  all  small  cavities  should  be  filled  with  cement, 
and  all  contact  surfaces  should  be  thickly  painted. 

Kinds  of  Paint. — One  of  the  most  widely  used  paints 
for  structural  steel,  especially  as  a  first  coat,  is  red  lead;  it  ad- 
heres well,  it  dries,  not  like  an  ordinary  paint  by  oxidation, 
but  by  combining  directly  with  the  oil,  as  a  cement;  it  pro- 
tects the  steel  from  carbonic  acid  to  a  considerable  degree, 
because  the  lead  it  contains  is  easily  acted  on  chemically. 
This  very  fact,  however,  may  make  it  less  permanent,  unless 


PAINT   AND   VARNISH.          1409-1415 

it  is  protected  by  some  other  more  neutral  paint.  In  pure  and 
reasonably  dry  air  red  lead  sometimes  shows  milch  perma- 
nence, but  in  the  air  of  cities  and  near  the  sea  coast  it  is  prob* 
ably  desirable  to  use  it  only  for  undercoat  work.  Red 
lead  should  be  freshly  prepared  from  day  to  day;  30  to  33  Ibs. 
dry  red  lead  to  each  gallon  of  oil  is  about  right;  the  so-called 
" ready-mixed"  red  lead  paints  are  less  valuable. 

Finely  ground  graphite  in  linseed  oil  is  a  favorite  paint  for 
metal;  it  flows  well,  is  easily  applied,  less  expensive  than  red 
lead,  and  if  well  made  gives  exellent  results. 

Graphite  is  sometimes  mixed  with  lamp-black,  probably 
with  advantage.  Boneblack  is  also  an  important  ingredient 
of  " carbon"  paints.  Formerly  oxide  of  iron  in  linseed  oil  was 
used  more  than  all  other  paints  for  this  purpose;  but  while 
many  engineers  still  like  it,  its  use  has  very  greatly  diminished. 
Asphaltum  has  been  used  and  is  still  used,  as  a  varnish  either 
alone  or  in  combination,  and  some  of  these  asphaltic  prepar- 
ations are  fairly  satisfactory.  The  fact  is,  that  a  really  compe- 
tent paint  manufacturer  can  make  a  reasonably  good  paint  out 
of  any  of  these,  and  if  the  application  is  well  and  carefully 
done  the  results  will  be  far  in  advance  of  what  is  commonly 
seen,  and  there  are  great  differences  in  painters. 

As  regards  the  surface  of  structural  steel  covered  by  a  gallon 
of  paint,  there  is  much  difference  of  opinion  among  experts. 
Some  say  300  to  400  sq.  ft.,  others  as  high  as  1000  or  1200. 
The  truth  is  that  any  paint  may  be  by  a  skilled  workman 
brushed  out  into  an  exceedingly  thin  film;  while  ordinary 
usage  gives  one  at  least  twice  as  thick.  The  most  general 
opinion  is  that  it  is  not  wise  to  estimate  more  than  400  sq. 
ft.  to  the  gallon,  one  coat.  Varnish  paints  cover  less  than  oil, 
but  if  well  made  they  are  more  durable. 

GLASS— KINDS  AND  PRICE  LISTS. 

Sheet  Glass  or  Common  Window  Glass. — Com- 
mon window  glass  is  technically  known  as  sheet  or  cylinder 
glass  because  it  is  first  blown  into  the  form  of  a  cylinder,  then 
cut  longitudinally  and  flattened  on  a  stone.  Sheet  glass  can 
readily  be  distinguished  from  plate  glass,  even  at  a  distance, 
because  of  its  wavy  appearance,  which  cannot  be  wholly  avoided. 


1416  GLASS— KINDS  AND   PRICE-LISTS. 

Grades  and  Qualities  of  Sheet  Glass.— All  common  sheet  glass, 
without  regard  to  quality,  is  graded  according  to  thickness, 
as  "single  strength"  or  "double  strength."  The  double- 
strength  glass  is  supposed  to  have  a  nearly  uniform  thickness 
of  J  in.,  while  the  single  strength  may  be  as  thin  as  }{6  in.  The 
thickness  of  single-strength  glass,  however,  is  generally  far 
from  uniform. 

Both  single-  and  double-strength  glass  are  sorted  into  three 
grades  or  qualities,  the  classification  depending  upon  color, 
brilliancy,  and  flaws. 

In  the  common  American  glass  the  best  quality  is  designated 
as  AA,  the  second  as  A,  and  the  third  as  B.  The  A  A  quality 
is  supposed  to  be  as  good  glass  as  can  be  made  by  the  cylinder 
process.  As  even  this  glass,  however,  is  not  entirely  free  from 
defects,  it  is  very  difficult  for  any  one  but  an  expert  to  tell 
exactly  whether  certain  lights  of  glass  are  first  or  second  quality. 
The  A  quality  is  most  used.  The  B  quality  is  only  suitable 
for  cellar  windows,  stables,  factories,  greenhouses,  etc. 

Sizes. — The  regular  stock  sizes  vary  by  inches  from  6  to  16  ins., 
and  above  that  by  even  inches  up  to  60  ins.  in  width  and 
70  ins.  in  height  for  double  strength  and  34  X  50  ins.  for  single 
strength. 

Cost. — The  price  for  sheet  glass,  as  for  all  other  clear  glass, 
varies  with  the  size,  strength,  and  quality.  It  is  determined 
by  a  schedule,  or  price-list,  fixed  from  time  to  time  by  the 
glass  companies,  from  which  a  very  large  discount  is  made, 
fluctuations  in  prices  being  regulated  by  the  discount,  which 
at  present  is  about  90  and  20  off  for  St.  Louis,  the  discount  vary- 
ing with  the  freight  rate.  The  list  on  common  glass  is  changed 
more  frequently  than  that  for  plate  glass ;  the  present  list  hav- 
ing been  adopted  Oct.  1,  1893.  The  only  way  of  ascertaining 
the  price  of  a  light  of  glass  of  a  given  size  is  by  means  of  the 
price-list  and  discount. 

The  price  per  square  foot  increases  rapidly  as  the  size  of 
the  glass  increases,  so  that  it  is  much  cheaper  to  divide  a  large 
window  into  eight  or  twelve  lights  than  into  two  lights. 

The  table  on  page  1417  gives  the  present  list  price  for  single 
lights  of  the  sizes  most  commonly  used.  The  net  price  is 
obtained  by  deducting  the  discounts  as  illustrated  by  the 
example  under  Plate  Glass. 

The  price  by  the  box  is  about  15  per  cent,  less  than  for  single 
lights. 

Polished  Plate  Glass. — Plate  glass  is  the  highest  grade 
of  window  glass,  being  cast  in  large  sheets  on  a  flat  table  and 
then  polished,  while  the  common  sheet  glass  is  blown.  It  is 
manufactured  in  sheets  of  various  sizes,  some  as  large  as  12  ft. 
wide  by  from  15  to  16  ft.  long.  The  average  thickness  is  from 
i  to  %  in. 

The  cost  varies  according  to  the  size  of  the  light.  To  as- 
certain this  cost  a  regular  price-list  is  used,  which  is  subject 
to  a  large  discount.  This  list  is  the  standard  list  for  the  entire 
trade  and  is  maintained  from  year  to  year,  rarely  changing, 
the  present  price-list  having  been  established  in  1894.  The 


GLASS— KINDS  AND  PRICE-LISTS. 


1417 


LIST  PRICE  OF  COMMON  WINDOW  GLASS  IN  1904. 

Prices  are  for  single  lights,  A  quality;  single  strength  up  to  and  includ- 
ing 15"X40",  double  strength  above. 


Size  in 

Price 

Size  in 

Price 

Size  in 

Price 

Size  in 

Price 

Inches. 

per 
Light. 

Inches. 

per 

Light. 

Inches. 

per 
Light. 

Inches. 

per 
Light. 

6X8 

SO.  21 

16X20 

$2.28 

24X32 

$5.98 

32X48 

$14.15 

7X9 

0.27 

16X24 

2.76 

24X34 

6.65 

32X60 

19.55 

8X10 

0.35 

16X28 

3.56 

24X36 

6.65 

32X72 

33.26 

8X12 

0.42 

16X30 

3.80 

24X40 

8.05 

36X36 

11.79 

9X12 

0.46 

16X32 

4.07 

24X44 

9.20 

36X40 

14.15 

9X15 

0.59 

16X36 

4.49 

24X48 

11.79 

36X44 

14.15 

10X12 

0.52 

16X40 

5.44 

24X60 

14.44 

36X48 

18.05 

10X14 

0.59 

16X48 

7.16 

24X72 

23.00 

36X60 

30.67 

10X16 

0.72 

18X24 

3.35 

26X28 

5.98 

36X72 

37.38 

10X18 

0.81 

18X30 

4.07 

26X30 

6.65 

36X84 

48.5-9 

12X14 

0.75 

18X32 

4.38 

26X32 

6.65 

40X40 

14.15 

12X15 

0.81 

18X36 

5.31 

26X34 

8.05 

40X48 

19.20 

12X16 

0.85 

18X40 

5.98 

26X36 

8.05 

40X60 

30.67 

12X18 

0.95 

18X48 

8.05 

28X30 

6.65 

40X72 

41.40 

12X24 

1.38 

18X60 

10.31 

28X32 

8.05 

40X84 

53.77 

12X30 

1.83 

20X22 

3.56 

28X34 

8.05 

44X44 

21.12 

12X32 

1.93 

20X24 

3.80 

28X36 

9.20 

44X48 

28.68 

14X14 

0.88 

20X26 

4.07 

28X40 

9.20 

44X60 

36.59 

14X16 

1.01 

20X28 

4.38 

28X44 

11.79 

44X72 

53.45 

14X18 

1.12 

20X30 

4.75 

28X48 

14.15 

48X48 

33.74 

14X20 

1.24 

20X32 

5.31 

28X60 

19.20 

48X56 

36.59 

14X24 

1.57 

20X36 

5.98 

28X72 

23.00 

48X60 

41.12 

14X28 

1.93 

20X40 

6.65 

30X30 

8.05 

48X72 

53.45 

14X30 

2.15 

20X44 

8.05 

30X32 

9.20 

50X50 

33.74 

14X32 

2.29 

20X48 

8.05 

30X34 

9.20 

50X60 

41.12 

14X36 

2.61 

20X60 

12.03 

30X36 

9.20 

50X72 

59.15 

14X40 

2.90 

22X24 

4.07 

30X40 

10.74 

54X60 

53.45 

15X16 

1.08 

22X28 

4.75 

30X44 

11.79 

54X72 

64.84 

15X18 

1.20 

22X30 

5.31 

30X48 

14.15 

56X60 

53.45 

15X20 

1.44 

22X32 

5.84 

30X60 

19.20 

56X72 

64.84 

15X24 

1.73 

22X36 

6.65 

30X72 

33.26 

60X60 

53.45 

15X30 

2.29 

22X40 

8.05 

32X32 

9.20 

60X62 

59.15 

15X32 

2.44 

22X48 

9.20 

32X34 

9.20 

60X64 

59.15 

15X36 

2.90 

24X26 

4.75 

32X36 

10.74 

60X66 

64.84 

15X40 

3.33 

24X28 

5.31 

32X40 

11.79 

60X68 

64.84 

fluctuations  in  the  selling  price  are  arranged  by  means  of  a  dis- 
count which  is  the  same  for  all  sizes.  At  the  present  time 
(July  1904)  the  discount  to  builders  is  about  80  and  5  off  at 
Denver.  Nearer  Pittsburgh  the  discount  is  greater  on  account 
of  lower  freight  charges.  This  discount  is  liable  to  sudden 
changes.  The  price-list  now  in  effect,  slightly  abridged,  is 
given  on  pp.  1420-1423. 

Examples  of  Figuring  Cost. — What  is  the  net  cost  of  a  light  of 
plate  glass  72X96  ins.,  the  discount  being  80  and  5  per  cent? 
Ans.  The  list  price,  in  table,  is  $173;  80  per  cent  =  $138.40; 
subtracting  from  $173  we  have  $34.60;  5  per  cent  off  from 
this  leaves  $32.87,  the  net  price. 

Odd  and  fractional  parts  of  inches  are  charged  at  the  price 
of  the  next  highest  even  inches.  Thus  31X120J  ins.  costs 
the  same  as  32X122  ins. 

The  average  weight  of  plate  glass  is  3£  Ibs.  to  the  square  foot. 


1418 


GLASS— KINDS  AND  PRICE-LISTS. 


Cost    of  Bending   Plate    and   Window   Glass, — 

Official  scale,  adopted  March  1,  1900: 

PLATE  GLASS. 

Plates  where  length  and  width  are  added,  less  than  76  inches.  .$0. 
"       of    76  or  more  but  less  than    90  united  hi 


90  " 

100 

100  " 

110 

110  " 

120 

120  "   "    "   " 

140 

•      ' 

140  " 
160  " 

160 
180 

'      • 

ISO  " 

200  "   "   "   " 

200 
210 

«       • 

210  " 
220  " 

220 
230 

inches.  .$0.60  s 
0.75 
1.00 

q.  ft. 

1   50 

t     it 

2  00 

i     44 

2  .  50 
3  00 

'     " 

3  .  50 

i     i* 

4  00 

.          14 

4  .  50 

1          14 

5  00 

»          14 

5  .  50 

1          44 

,.   6.00 

«          44 

WINDOW  GLASS. 

Lights  of  less  than  60   united   inches $0 . 25  sq.  ft. 

60  or  more  but  less  than    70  united  inches 0.30  " 

"      70  "       "        "       "        "        80       "  "     0.40  "     " 

"      80  ' "       "        90       "  "      0.50  "     " 

"      90  "       "        "       "       "100       "  "      0.60  "     " 

"    100  "       "  110  '     0.90  " 

Figured  Rolled  Glass. — The  Mississippi  Glass  Com- 
pany manufactures  nine  different  patterns  of  figured  rolled 
glass  for  use  in  doors,  transoms,  and  windows  where  an 
obscure  glass  is  desired,  or  for  purely  ornamental  effects.  The 
Maze  and  Ondoyant  patterns  are  especially  valuable  either 


FULL-SIZE  DETAIL  OF  FIGURED 
ROLLED-GLASS,  "FLORENTINE" 
PATTERN. 

Other  popular  patterns  specified 
•are  ''Ondoyant,"  "Maze,"  "Vene- 
tian/' "Syenite,"  "Oceanic,"  and 
"Figured  No.  1,"  "Figured  No.  2," 
and  "Figured  No.  3."  Thicknesses 
i  and  %6  in. ;  widths,  30,  40,  and  42 
ins.;  lengths  about  100  ins. 


FULL-SIZE  DETAIL  OF  ROLLED  WIRE 
GLASS,  "ROUGH" or  "HAMMERED •" 
STYLE. 

Other  popular  patterns  specified 
are  "Maze"  and  "Ribbed"  and 
"Polished."  i  in.  thick  is  standard 
and  is  the  only  thickness  "Polished." 
"Maze,"  "Ribbed,"  "Rough,"  or 
"Hammered"  can  be  had  f  in. 
thick;  widths  up  to  40  ins.;  lengths 
up  to  120  ins. 


GLASS— KINDS  AND   PRICE-LISTS.  1419 

in  outside  windows  or  skylights.  For  diffusing  the  light 
see  pp.  1300-1303.  The  Maze  pattern  may  be  had  either  with 
or  without  embedded  wire.  Ondoyant  glass  is  made  J  in. 
thick  and  30  ins.  wide.  The  Maze  and  several  other  patterns 
of  rolled  glass  are  made  J  and  %,  in.  thick,  and  42  ins.  wide. 

Maze  wired  glass  is  made  in  sheets  \  and  f  in.  thick,  up  to 
40  ins.  wide  and  100  ins.  long. 

Figured  glass,  on  account  of  its  greater  cleanliness  and  dif- 
fusing qualities,  has  almost  entirely  supplanted  ground  glass 
and,  to  a  considerable  extent,  chipped  glass. 

Wire  Glass  is  described  on  p.  765. 

Prismatic  Glass,  for  glazing  windows,  skylights,  and 
sidewalk  lights,  is  now  manufactured  in  a  large  number  of 
forms  in  both  prisms  and  sheets,  and  by  several  companies, 
the  more  important  of  which  are  as  follows: 

American  Luxfer  Prism  Co Chicago,  111. 

American  Prismatic  Light  Co Philadelphia,  Pa. 

Cleveland  Window  Glass  Co Cleveland,  Ohio. 

Daylight  Glass  Mfg.  Co Philadelphia,  Pa. 

Daylight  Prism  Co Chicago,  111. 

New  York  Prism  Co New  York,  N.  Y. 

Solar  Prism  Co. Cleveland,  Ohio. 

The  diffusing  properties  of  several  types  are  described  on 
pp.  1300-1303. 

Glass  for  Skylights. — Where  skylights  are  glazed  with 
clear  or  double  thick  glass,  it  may  be  used  in  lengths  of  from 
16  to  30  ins.  by  a  width  of  from  9  to  15  ins.  A  lap  of  at  least 
an  inch  and  a  half  is  necessary  for  all  joints.  This  is  the  cheapest 
mode  of  glazing.  The  best  glass,  however,  for  skylight  pur- 
poses, next  to  prism  or  wire  glass  (see  p.  1304),  is  fluted  or  rough 
plate  glass.  The  following  thicknesses  are  recommended  as 
proportionate  sizes: 

12  inches  by    48  inches  is  the  extent  for  glass  ^jo  inch  thickness. 

15       '•         "      60       "       "    ' K       " 

20       "         "    100       "       "    "         "         "       "     ?,/       " 
94      "         "    156       "       "    "         "         "       "     K       " 

WEIGHT  OF  ROUGH  GLASS   PER  SQUARE  FOOT. 

Thickness1 %     »/16        y±\    y8       14     y^        y4         \  m. 

Weight 2        2^       3}^'     5         7      8*4        10      12}£  Ibs. 

The  cost  of  skylights  with  galvanized-iron  frame,  glazed  with 
%-in.  or  J-in.  ribbed  glass,  ranges  from  40  to  60  cts.  per  square 
foot  of  area  covered. 

Cost  ot  Rolled  Glnss. — In  1904,  the  different  kinds  of 
glass  were  quoted  for  small  quantities  in  St.  Louis  about  as  fol- 
lows : 

%6-in.  ribbed  skylight  glass.  .  .  , 8  cts.  per  sq.  ft. 

M    "  12   " 

Ribbed  wire  glass,  V(  in.  thick 23   " 

Maze  '     23  " 

Factory  ribbed  glass,  '  s  in.  thick 9  " 

Ondoyant  glass,  Y*  in.  thick 10  " 

Maze  glass  (without  wire),  ^in.  thick 14   '' 

Maze  glass,  -Tn?  in.  thick 16  " 

Prismatic  glass  in  sheets from  25  to  50   " 


1420  GLASS— KINDS  AND  PRICE-LISTS. 

PRICE-LIST  OF  POLISHED  PLATE  GLASS. 
IN  EFFECT  SINCE  1894. 

Sizes  in  inches ;  prices  in  dollars  and  cents. 


! 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

32 

34 

12.80 
13.60 

14.90 
15.90 

17.10 
18.10 

19.20 
20.40 

21.30 
22.70 

23.50 
33.70 

34.70 
36.90 

37.60 
39.90 

40.50 
43.00 

43  40 
46.00 

36 

14.40  16.80 

19.20 

21.60 

24.00 

35.80 

39.00 

42.20 

45.50 

48.80 

38 

15.20 

17.70 

20.30 

22.80 

34.30 

37.80 

41.20 

44.60 

48.00 

51.50 

40 

16.00 

18.70 

21.30 

24.00 

36.10 

39.70 

43.40 

47.00 

50.60 

54.20 

42 

16.80 

19.60 

22.40 

34.10 

37.90 

41.70 

45.50 

49.30 

53.10 

56.90 

44 

17.6020.50 

23.50 

35.80 

39.70 

43.80 

47.70 

51.70 

55.60 

59.60 

46 

18.  40121.  50 

33.20 

37.40 

41.50 

45.70 

49.90 

54.00 

58.10 

62.30 

48 

19.20 

22.40 

34.70 

39.00 

43.40 

47.70 

52.00 

56.40 

60.70 

65.00 

50 

20.00 

23.30 

36.10 

40.60 

45.20 

49.70 

54.20 

58.70 

63.20 

70.90 

52 

20.80 

32.90 

37.60 

42.20 

47.00 

51.70 

56.40 

61.00 

68.70 

73.70 

54 

21.60 

34.10 

39.00 

43.90 

48.80 

53.60 

58.50 

63.40 

71.40 

76.50 

56 

22.40 

35.40 

40.50 

45.50 

50.60 

55.60 

60.70 

68.70 

74.10 

79.30 

58 

23.20 

36.70 

41.90 

47.10 

52.40 

57.60 

62.90 

71.20 

76.70 

82.20 

60 

24.00 

37.90 

43.40 

48.80 

54.20 

59.60 

65.00 

73.70 

79.30 

85.00 

62 

33.60 

39.20 

44.80 

50.40 

56.00 

61.60 

70.30 

76.10 

82.00 

88 

64 

34.70 

40.50 

46.20 

52.00 

57.80 

63.60 

72.50 

78.60  84.70 

91 

66 

35.80 

41.70 

47.70 

53.60  59.60 

68.60 

74.80 

81.10  87.30S  94 

68 

36.90 

43.00 

49.20 

55.30  61.40 

70.70 

77.10 

83.50 

89.90  96 

70 

38.00 

44.30 

50.60 

56.90 

63.20 

72.70 

79.30 

85.90 

92.50|  99 

72 

39.00 

45.50 

52.00 

58.50 

65.00 

74.80  81.60 

88.40 

95.20  102 

74 

40.10 

46.80 

53.40 

60.10 

69.90 

76.90  83.90 

90.90 

97.90  105 

76 

41.20 

48.10 

54.90 

61.80 

71.80 

79.00  86.10 

93.30 

101 

108 

78 

42.30 

49.30 

56.40 

63.40 

73.70 

81.10 

88.40 

95.70 

103 

110 

80 

43.40 

50.60 

57.80 

65.00 

75.60 

83.10 

90.70 

93.30 

106 

113 

82 

44.50 

51.90 

59.20 

69.70 

77.50 

85.20  92.90 

101 

108 

116 

84 

45.50 

53.10 

60.70 

71.40 

79.40 

87.30,  95.20 

103 

111 

119 

86 

46.60 

54.40 

62.10 

73.10 

81.30 

89.40  97.50 

106 

113 

122 

88 

47.70 

55.70 

63.60 

74.80 

83.10 

91.50  99.70 

108 

116 

125 

90 

48.80 

56.90 

65.00 

76.50 

85.00 

93.50  102 

110 

119 

127 

92 

49.90 

58.20 

69.50 

78.20 

86.90 

95.60  104 

113 

122 

130 

94 

51.00 

59.50 

71.00 

79.90 

88.80  97.70  107 

115 

124 

133 

96 

52.00 

60.70 

72.50 

81.60 

90.70  99.70  109 

118 

127 

136 

98 

53.10 

62.00 

74.10 

83.30 

92.60 

102 

111 

120 

130 

139 

100 

54.20 

63.30 

75.60 

85.00 

94.50 

104 

113 

123 

132 

142 

102 

55.30 

64.50 

77.10 

86.70J  96.40  106 

116 

125 

135 

144 

104 

56.40 

68.70 

78.60 

88.40  98.30108 

118 

128 

138 

147 

106 

57.50 

70.10 

80.10 

90.10 

100   U  10 

120 

130 

140 

150 

108 

58.50 

71.40 

81.60 

91.80 

102 

112 

122 

133 

143 

153 

110 

59.60 

72.70 

83.10 

93.50 

104 

114 

125 

135 

145 

165 

112 

60.70 

74.10 

84.60 

95.20 

106 

116 

127 

137 

148 

168 

114 

61.80 

75.40 

86.10 

96.90 

108 

118 

129 

140 

151 

171 

116 

62.90 

76.70 

87.60 

98.60 

110 

121 

131  . 

142 

162 

174 

118 

64.00 

78.00 

89.10 

100 

112 

123 

134 

145 

165 

177 

120 

65.00 

79.30 

90.70 

102 

114 

125 

136 

147 

168 

180 

122 

69.10 

80.70 

92.20  104 

115 

127 

138 

150 

171 

183 

124 

70.30 

82.00 

93.70  105 

117 

129 

141 

152 

174 

186 

126 

71.40 

83.30 

95.20  107 

119 

131 

143 

164 

176 

189 

128 

72.50 

84.70 

96.70^09 

121 

133 

145 

166 

179 

192 

130 

73.70 

86.00 

98.20 

110 

123 

135 

147 

169 

182 

195 

132 

74.80 

87.30 

99.70  112 

125 

137 

150 

172 

185 

198 

134 

76.00 

88.60 

101 

114 

126 

139 

152 

174 

188 

201 

136 

77.10 

89.  90  '103 

116 

128 

141 

163 

177 

190 

204 

138 

78.20 

91.30  104 

118 

130 

143 

166 

179 

193 

?07 

GLASS— KINDS  AND   PRICE-LISTS. 


1421 


PRICE-LIST   OF  POLISHED   PLATE   GLASS— (Continued). 

Sizes  in  inches ;   prices  in  dollars. 


A 

"& 
a 
o> 
A 

62 

64 

66 

68 

70 

72 

74 

76 

78 

80 

82 

84 

62 

91 

64 

94   97 

66 

97  100 

103 

68 

100 

103 

106 

109 

70 

102 

106 

109 

112 

116 

72 

105  109 

112 

116 

119 

122 

74 

108  112 

115 

119 

122 

126 

129 

76 

111  115 

118 

122 

126 

129 

133 

136 

78 

114 

118 

121 

125 

129 

133 

136 

140 

144 

80 

117 

121 

125 

128 

132 

136 

139 

144 

147 

151 

82 

120  j  124 

128 

132 

136 

139 

143 

447 

151 

164 

168 

84 

1231  127 

131 

135 

139 

143 

147 

151 

164 

168 

172 

176 

86 

126  130 

134 

138 

142 

146 

150 

163 

168 

172 

176 

181 

88 

129 

133 

137 

141 

145 

150 

163 

167 

172 

176 

180 

185 

90 

132 

136 

140 

144 

149 

153 

166 

171 

175 

180 

184 

189 

92 

135!  139 

143 

148 

152 

166 

170 

175 

179 

184 

189 

193 

94 

138!  142 

146 

151 

165 

169 

174 

179 

183 

188 

193 

197 

96 

141  145 

150 

163 

168 

173 

178 

182 

187 

192 

197 

202 

98 

143 

148 

153 

167 

171 

176 

181 

186 

191 

196 

201 

206 

100 

146 

151 

165 

170 

175 

180 

185 

190 

195 

200 

205 

210 

102 

149 

163 

168 

173 

178 

184 

189 

194 

199 

204 

209 

214 

104 

152 

166 

172 

177 

182 

187 

192 

198 

203 

208 

213 

218 

106 

164 

170 

175 

180 

185 

191 

196 

201 

207 

212 

217 

223 

108 

167 

173 

178 

184 

189 

194 

200 

205 

210 

216 

221 

227 

110 

170 

176 

181 

187 

192 

198 

203 

209 

214 

220 

225 

231 

112 

174 

179 

185 

190 

196 

202 

207 

213 

218 

224 

230 

235 

114 

177 

182 

188 

194 

199 

206 

211 

217 

222 

228 

234 

239 

116 

180 

185 

191 

197 

203 

209 

215 

220 

226 

232 

238 

244 

118 

183 

189 

195 

201 

206 

212 

218 

224 

230 

236 

242 

248 

120 

186 

192 

198 

204 

210 

216 

222 

228 

234 

240 

246 

252 

122 

189 

195 

201 

207 

213 

220 

226 

232 

238 

244 

250 

256 

124 

192 

198 

205 

211 

217 

223 

230 

236 

242 

248 

254 

260 

126 

195 

202 

208 

214 

220 

227 

233 

239 

246 

252 

258 

265 

128 

198 

205 

211 

218 

224 

230 

237   243 

250 

256 

262 

269 

130 

201 

208 

214 

221 

227 

234 

240 

.247 

253 

260 

266 

273 

132 

205 

211 

218 

224 

231 

238 

244 

251 

257 

264 

271 

277 

134 

208 

214 

221 

228 

234 

241 

248 

255 

261 

268 

275 

281 

136 

211 

218 

224 

231 

238 

245 

251 

258 

265 

272 

279 

286 

138 

214 

221 

228 

234 

241 

248 

255 

262 

269 

276 

283 

290 

140 

217 

224 

231 

238 

245 

252 

259 

266 

273 

280 

287 

294 

142 

220 

227 

234 

241 

248 

256 

263 

270 

277 

284 

291 

298 

144 

223 

230 

238 

245 

252 

259 

266 

274 

281 

288 

295 

302 

146 

226 

234 

241 

248 

255 

263 

270 

277 

285 

292 

299 

307 

148 

229 

237 

244 

252 

259 

266 

274 

281 

289 

296 

303 

311 

150 

232 

240 

247 

255 

262 

270 

277 

285 

292 

SCO 

307 

315 

152 

236 

243 

251 

258 

266 

274 

281 

289 

296 

304 

312 

319 

154 

239 

246 

254 

262 

269 

277 

285 

293 

300 

308 

316 

323 

156 

242 

250 

257 

265 

273 

281 

288 

296 

304 

312 

320 

328 

158 

245 

253 

261 

269 

276 

284 

292 

3t)0 

308 

316 

324 

332 

160 

248 

256 

264 

272 

280 

288 

296 

304 

312 

320 

328 

336 

162 

251 

259 

267 

275 

283 

292 

300 

308 

3  1  0 

324 

332 

340 

164 

254 

262 

271 

279 

287 

295 

303 

312 

320 

328 

336 

344 

166 

257 

266 

274 

282 

290 

299 

307 

315 

324 

332 

340 

349 

168 

260 

269 

277 

286 

294 

302 

311 

319 

328 

336 

344 

353 

i 

1422 


GLASS— KINDS  AND   PRICE-LISTS. 


PRICE-LIST  OF  POLISHED    PLATE   GLASS— (Continued}. 

Sizes  in  inches ;   prices  in  dollars. 


"S 

i 

A 

86 

88 

90 

92 

94 

96 

98 

100 

102 

104 

106 

108 

90 

193 

198 

202 

92 

198 

202 

207 

212 

94 

202 

207 

211 

216 

221 

96 

206 

211 

216 

221 

226 

230 

98 

211 

216 

220 

225 

230 

235 

240 

100 

215 

220 

225 

230 

235 

240 

245 

250 

102 

219 

224 

229 

235 

240 

245 

250 

255 

260 

104 

224 

229 

234 

239 

244 

250 

255 

260 

265 

270 

106 

228 

233 

238 

244 

249 

254 

260 

265 

270 

276 

281 

108 

232 

237 

243 

248 

254 

259 

265 

270 

275 

281 

286 

292 

110 

237 

242 

247 

253 

258 

264 

269 

275 

280 

286 

291 

297 

112 

241 

246 

252 

258 

263 

269 

274 

280 

285 

291 

297 

302 

114 

245 

251 

256 

262 

268 

274 

279 

285 

290 

296 

302 

308 

116 

250 

255 

261 

267 

273 

278 

284 

290 

296 

302 

307 

313 

118 

254 

260 

265 

272 

277 

283 

289 

295 

301 

307 

313 

319 

120 

258 

264 

270 

276 

282 

288 

294 

300 

306 

312 

318 

324 

122 

262 

268 

274 

281 

287 

293 

299 

305 

311 

317 

323 

329 

124 

267 

273 

279 

285 

291 

298 

304 

310 

316 

322 

329 

335 

126 

271 

277 

283 

290 

296 

302 

309 

315 

321 

328 

334 

340 

128 

275 

282 

288 

294 

301 

307 

314 

320 

326 

333 

339 

346 

130 

279 

286 

292 

299 

305 

312 

318 

325 

331 

338 

345 

351 

132 

284 

290 

297 

304 

310 

317 

323 

330 

337 

343 

350 

356 

134 

288 

295 

301 

308 

315 

322 

328 

335 

342 

348 

355 

402 

136 

292 

299 

306 

313 

320 

326 

333 

340 

347 

354 

400 

408 

138 

297 

304 

310 

317 

324 

331 

338 

345 

352 

359 

406 

414 

140 

301 

308 

315 

322 

329 

336 

343 

350 

357 

404 

412 

420 

142 

305 

312 

319 

327 

334 

341 

348 

355 

402 

410 

4J8 

426 

144 

310 

317 

324 

331 

339 

346 

353 

360 

408 

416 

424   432 

146 

314 

321 

328 

336 

343 

350 

358 

406 

414 

422 

430   438 

148 

318 

326 

333 

340 

348 

355 

403 

411 

419 

428 

436 

444 

150 

322 

330 

337 

345 

352 

360 

408 

417 

425 

433 

442 

450 

152 

327 

334 

342 

350 

357 

405 

414 

422 

431 

439 

448  '  456 

154 

331 

339 

346 

354 

402 

411 

419 

428 

436 

445 

453  !  462 

156 

335 

343 

351 

359 

407 

416 

425 

433 

442 

451 

459  !  468 

158 

340 

348 

355 

404 

413 

421 

430 

439 

448 

456 

465  !  474 

160 

344 

352 

360 

409 

418 

427 

436 

444 

453 

462 

470   480 

162 

348 

356 

405 

414 

423 

432 

441 

450 

459 

468 

477   75.9 

164 

353 

401 

410 

419 

428 

437 

446 

456 

465 

474 

755   769 

166 

357 

406 

415 

424 

433 

443 

452 

461 

470 

480 

764  i  778 

168 

401 

411 

420 

429 

439 

448 

457 

467 

476 

758 

773   787 

170 

406 

416 

425 

434 

444 

453 

463 

472 

753 

767 

782  i  797 

172 

411 

420 

430 

440 

449 

459 

468 

478 

761 

776 

791   806 

174 

416 

425 

435 

445 

454 

464 

474 

755 

770 

785 

801   979 

176 

420 

430 

440 

450 

460 

4C9 

479 

764 

779 

794 

810   990 

178 

425 

435 

445 

455 

465 

475 

757 

773 

788 

803 

983  1001 

180 

430 

440 

450 

460 

470 

480 

766 

781 

797 

812 

994  1012 

182 

478 

489  500 

511 

523 

758 

774 

790 

806 

986 

1005  1024 

184 

186 

483 

489 

495!  506 
500  511 

517 

523 

751 
759 

767 

775 

783 
791 

799 

807 

977 

988 

997 
1007 

1016  1035 
1027  1046 

188 

494 

506 

517 

751 

767 

783 

800 

979 

999 

1018 

1038  1057 

190 

500 

511 

522 

759 

775 

792 

808 

990 

009 

1029 

049  1069 

192 

688 

704 

720 

920 

940 

900 

980 

1000 

1020  11040 

1060  1080 

194 

695 

711 

909 

930 

950 

970 

990 

1010 

1031 

1051 

1071  1091 

196 

703 

719 

919 

939 

960 

980 

1000 

1021 

041 

1062 

1082  1102 

GLASS— KINDS  AND  PRICE-LISTS. 


1423 


PRICE-LIST    OF  POLISHED   PLATE   GLASS—  (Continued). 

Size  in  inches;  prices  in  dollars. 


A 

to 

J 

110 

112 

114 

116 

118 

120 

124 

128 

132 

136 

140 

144 

no 

112 

302 
308 

308 
348 

314 
355 

319 
361 

324 
367 

330 
373 

341 

386 

352 

398 

403 
411 

415 
423 

428 
436 

440 

448 

114 

314 

355 

361 

367 

374 

380 

393 

405 

418 

431 

443 

456 

116 

319 

361 

367 

374 

380 

387 

400 

412 

425 

438 

451 

464 

118 

324 

367 

374 

380 

387 

393 

406 

42jO 

433 

446 

459 

472 

12Q 

330 

373 

380 

387 

393 

400 

413 

427 

440 

453 

467 

480 

122 

335 

380  386 

393 

400 

407 

462 

478 

493 

507 

522 

762 

124 

341 

3861  393 

400 

406 

413 

470 

485 

501 

516 

753 

775 

126 

346 

392  j  399 

406 

413 

420 

477 

493 

508 

524 

766 

787 

128 

352 

398 

405 

412 

420 

427 

485 

501 

516 

756 

778 

800 

130 

357 

404 

412 

419 

426 

433 

493 

509 

525 

767 

790 

812 

132 

403 

411 

418 

425 

433 

440 

501 

516 

847 

873 

898 

990 

134 

409 

417 

424 

432 

439 

447 

509 

524 

860 

886 

977 

1005 

136 

415 

423 

431 

438 

446 

453 

516 

756 

873 

899 

992 

1020 

L38 

422 

429 

437 

445 

452 

460 

523 

767 

886 

977 

1006 

1035 

140 

428 

436 

443 

451 

459 

467 

753 

778 

898 

992 

1021 

1050 

142 

434 

442j  450 

457 

465 

473 

764 

789 

976 

1006 

1035 

1420 

144 

440 

448,  456 

464  472 

480 

775 

800 

990 

1020 

1050 

1440 

146 

446 

454  462 

470  '  479 

760 

786 

811 

1004 

1034 

1065 

1460 

148 

452 

460  469 

477  758 

771 

796 

987 

1017 

1048 

1079 

1480 

150 

458 

467 

475 

755 

768 

781 

807 

1000 

1031 

1062 

1094 

1500 

152 

464 

473  752 

765 

778 

792 

982 

1013 

1045 

1077 

1108 

1520 

154 

471 

479  762 

775 

789 

802 

995 

1027 

1059 

1091 

1123 

1540 

156 

477 

758  772 

785 

799 

812 

1007 

1040 

1072 

1105 

1327 

1560 

158 

754 

768  782 

795 

809 

987 

1020 

1053 

1086 

1119 

1344 

1580 

160 

764 

778  792 

805 

983 

1000 

1033 

1067 

1100 

1322 

1361 

1600 

162 

773 

787  802 

975 

996 

1012 

1046 

1080 

1114 

1339 

1378 

1620 

164 

783 

7971  812 

991 

1008 

1025 

1059 

1093 

1315 

1355 

1395 

1640 

166 

793 

807  i  986  1003 

1020 

1037 

1072 

1107 

1331 

1372 

1412 

1660 

168 

802 

980  ;  997 

1015 

1032 

1050 

1085 

1120 

1347 

1388 

1429 

1680 

170 

812 

992  1009 

1027 

1045 

1062 

1098 

1322 

1364 

1405 

1446 

1700 

172 

985 

1003  1021  j  1039 

1057 

1075 

1111 

1338 

1380 

1421 

1463 

1720 

174 

997 

1015  1033!l05lll069 

1087 

1124 

1353 

1396 

1438 

1480 

1740 

176 

1008 

1027  1045'  1063  1082 

1100 

1326 

1369 

1412 

1454 

1497 

2200 

178  1020 

1038  1057 

1075 

1094 

1112 

1341 

1384 

1428 

1471 

1514 

2225 

180 

1031 

1050  1069  1087 

1106 

1125 

1356 

1400 

1444 

1487 

1531 

22£0 

182  1043 

1062  108111100 

1119 

1327 

1371 

1416 

1460 

1504 

2212 

2275 

184  S1054 

1073  1092'1112 

1319 

1342 

1386 

1431 

1476  1521 

2236 

2300 

186  11066 

1085  1104j  1124 

1334 

1356 

1401 

1447 

1492  2196 

2260 

2325 

188  11077 

1097 

1116  1325 

1348 

1371 

1417 

1462 

1508  2219 

2285 

2350 

190  11089 

1108 

1316 

1339 

1362 

1385 

1432 

1478 

1524 

2243 

2309 

2375 

192  IllOO 

1120  1330  1353 

1376 

1400 

1447 

1493 

2200  2267 

2333 

2400 

194  1111 

1320  1344 

1367 

1391 

1415 

1462 

U09 

2223  2290 

2358 

2425 

196  J1123 

1334  1358 

1382 

1405 

1429 

1477 

1524 

2246  2314 

2382 

2450 

198 

1323 

1347 

1372 

1396 

1419 

1444 

1492 

2200 

2269  2337 

2406 

2475 

200 

1337 

1361 

1385 

1410 

1434 

1458 

1507 

2222 

2292  2361 

2431 

2500 

202 

1350 

1375  1399 

1424 

1448 

1473 

1522 

2244 

2315  2385 

2455 

204 

1364 

1388  1413 

1438 

1463 

1487 

2196 

2267 

2337  2408 

2479 

206 

1377 

1402  {1427 

1452 

1477 

1502 

2217 

2289 

2360  2432 

208 

1390 

1416 

1441 

1466 

1491 

1517 

2239 

2311 

2383  2456 

210 

1404 

1429 

1455 

1480 

1506 

1531 

2260 

2333 

2406 

2479 

212 

1417 

1443  1469 

1494 

1520 

2208 

2282 

2356 

2429 

214 

1430 

1456  1482 

1508 

2192 

2229 

2303 

2378 

2452 

216 

1444 

1470  1496 

1522 

2212 

2250 

2325 

2400 

2475 

1424  GLASS— KINDS  AND  PRICE-LISTS. 

Fal>oleum.* — During  the  past,  few  years  this  .material 
has  baen  introduced  as  a  substitu  e  for  glass,  particu- 
larly for  skylights  of  large  area,  and  in  all  places  where  the 
breakage  of  glass  constitutes  an  element  of  trouble,  expense, 
or  danger.  It  consists  of  wire  cloth,  embedded  in  a  translucent 
impervious  material,  which  is  strong  and  durable,  flexible  and 
elastic,  weather-proof  and  unbreakable.  It  is  a  non-conductor, 
is  easily  cleaned,  and  is  a  better  protection  against  fire  than 
glass.  It  transmits  a  large  amount  of  light  and  diffuses  it  well. 

The  fabric  is  not  damaged  in  the  slightest  by  rain  or  snow, 
cold  or  heat.  The  leaks  that  develop  in  glass  skylights,  due 
to  the  expansion  and  contraction  of  the  framework  under  the 
action  of  the  weather,  do  not  trouble  faboleum  because  it  is 
flexible  and  yielding. 

Faboleum  is  of  a  pale  amber  color,  and  the  light  it  transmits 
is  of  somewhat  the  same  tint,  being  very  soft  and  pleasant  to 
work  under.  The  amount  of  light  transmitted  is  not  quite 
equal  to  that  transmitted  by  ordinary  skylight  glass,  but,  on 
the  other  hand,  it  is  better  diffused.  "  Where  one  quarter  of 
the  roof  is  covered  with  fabric  the  lighting  is  practically  perfect. "t 
The  fabric  is  manufactured  in  sheets  3'  3"  wide  and  in  lengths 
from  4'  6"  to  9'  0".  The  cost  is  from  13  to  15  cts.  per  square 
foot  at  the  factory  at  Quincy,  Mass.  The  framework  for  fab- 
oleum is  best  made  of  v.  ood,  to  which  the  fabric  is  nailed. 
Wcoden  skyligh's  covered  with  this  fabric  cost  con  plete  from  25 
to  30  cts  per  square  fcot. 

Faboleum  was  employed  m  the  buildings  of  the  Tr  nnessei 
Centennial  Exposition  held  at  Nashville  in  1897,  and  nearly 
100,000  sq.  ft.  were  used  in  the  principal  buildings  of  the  Trans- 
Mississippi  and  International  Exposition  held  in  Omaha,  Neb., 
in  1898. 

Mirrors. 

Mirrors  are  made  by  silvering  the  back  of  glass.  Polished 
plate  glass  is  the  only  kind  that  is  suitable  for  mirrors.  The 
price  of  mirrors  is  based  on  the  price  of  the  glass  plus  the  cost 
of  silvering. 

Kinds  of  Mirrors. — "There  are  two  kinds  of  mirrors  on  the 
market,  one  the  old  time  reliable  mercury-back  mirror,  the 
other  the  nitrate  of  silver,  or  what  is  better  known  to  the  trade 
as  the  patent-back  mirror.  The  latter  is  now  and  has,  in  recent 
years,  been  most  extensively  sold  as  a  substitute  for  the  former. 

In  the  manufacture  of  mercury-back  mirrors  no  chemicals 
are  used,  only  two  metals,  mercury  and  tin-foil.  The  affinity 
of  mercury  for  tin  forms  an  amalgam  impervious  to  and  not 
affected  by  the  atmosphere. 

A  mercury-back  mirror  is  universally  considered  to  be  the 
only  durable  and  permanent  mirror. 

A  nitrate-of-silver  or  patent-back  mirror  is  produced  by  the 
precipitation  of  a  chemical  solution  of  nitrate  of  silver  arid 

*  Manufactured  by  the  Translucent  Fabric  Company,  Quincy,  Mass, 
t  M.  S.  Ketchum. 


MEMORANDA  ON  ROOFING,— SHINGLES.      1425 

other  media  on  the  surface  of  the  glass,  to  which  is  added  one 
coat  of  shellac  varnish  overlaid  with  one  or  more  coats  of  paint. 
This  mirror,  irrespective  of  the  quality  of  the  glass  from  which 
it  is  made,  will  steadily  deteriorate  from  the  date  of  its  manu- 
facture to  that  of  its  final  collapse,  which  may  occur  at  any 
time  from  a  few  months,  but  certainly  within  a  few  years." 

MEMORANDA   ON  ROOFING. 

Shingles.* — The  best  shingles  are  those  made  from  cypress, 
redwood,  or  cedar,  in  the  order  mentioned.  Redwood,  while 
perhaps  not  quite  as  durable  as  cypress,  is  less  inflammable; 
sawed  pine  shingles  are  inferior  to  cedar,  and  spruce  shingles 
are  not  suitable  for  good  work. 

Cypress  shingles  are  usually  18  ins.  long  and  J^g  in.  thick 
at  the  butt.  Those  from  all  other  woods  are  16  ins.  long,  and 
about  %  in.  thick  at  the  butt. 

Ordinary  roofing  shingles  are  of  random  widths,  varying 
from  2J  to  14  and  sometimes  16  ins.  They  are  put  up  in  bundles, 
usually  four  to  the  thousand.  A  " thousand"  common  shingles 
means  the  equivalent  of  1,000  shingles  4  ins.  wide. 

Dimension  Shingles  are  sawn  to  uniform  width,  either  4,  5, 
or  6  ins.  Dimension  shingles  with  the  butt  sawn  to  various 
patterns  are  also  carried  in  stock. 

NUMBER  OF  SQUARE  FEET  1000  SHINGLES  WILL  COVER,  f 

Laid.                                             Area  Covered.     No.  to  a  Square. 
4"      to  the  weather 100  sq.  ft.  1,000 


110 
120 
133 
145 
157 


910 
833 
752 
690 
637 


On  hip  roofs,  or  for  four  valleys,  add  5  per  cent,  for  cutting. 
On  irregular  roofs  with  dormer  windows,  add  10  per  cent.  It 
is  claimed  that  redwood  shingles  will  go  farther  than  cedar 
shingles. 

•  With  a  rise  to  the  roof  of  8  to  10  ins.  to  the  foot,  cedar  shingles 
should  be  laid  4  to  4J  ins.  to  the  weather;  with  rise  from  10 
to  12  ins.,  4|  to  4|  ins.  to  the  weather;  and  on  steeper  roofs 
they  may  be  laid  4^  to  5  ins.  Redwood  shingles  may  be  laid 
J  in.  more  to  the  weather. 

On  walls  cedar  shingles  are  commonly  laid  5  ins.  to  the 
weather,  and  redwood  shingles  6  ins. 

Labor. — An  average  shingler  should  lay  1,500  shingles  in 
9  hours  on  plain  work;  on  irregular  roofs  with  dormers,  1,000 
per  9  hours. 

It  requires  about  5  Ibs.  of  threepenny  or  7J  Ibs.  of  fourpenny 
nails  to  1,000  shingles. 

*  For  more  complete  information  see  Part  II,  Building  Construction 
and  Superintendence,  pp.  190-199. 

t  These  figures  are  intended  to  allow  for  some  waste. 


1426  MEMORANDA  ON   ROOFING. 

Cost. — Common  cedar  shingles  of  the  best  grade  cost  from 
$2.25  to  $3.50  per  M,  according  to  locality.  Redwood  shingles 
cost  from  $4  to  $5.  In  Denver,  shingles  are  laid  under  con- 
tract for  from  $1.25  to  $2.00  per  square,  all  materials  furnished. 

Slate  Roofs. 

Characteristics  of  Good  Slate. — A  good  slate  should  be  both 
hard  and  tough. 

If  the  slate  is  too  soft,  however,  the  nail-holes  will  become 
enlarged  and  the  slate  will  become  loose.  If  it  is  too  brittle 
the  slate  will  fly  to  pieces  in  the  process  of  squaring  and  holing 
and  will  be  easily  broken  on  the  roof.  "A  good  slate  should 
give  out  a  sharp  metallic  ring  when  struck  with  the  knuckles; 
should  not  splinter  under  the  slater's  axe;  should  be  easily 
'holed'  without  danger  of  fracture,  and  should  not  be  tender  or 
friable  at  the  edges." 

The  surface  when  freshly  split  should  have  a  bright  metallic 
lustre  and  be  free  from  all  loose  flakes  or  dull  surfaces. 

Most  slates  contain  ribbons  or  seams  which  traverse  the 
slate  in  approximately  parallel  directions.  Slates  containing 
soft  ribbons  are  inferior  and  should  not  be  used  in  good  work. 

Color. — The  color  of  slates  varies  from  dark  blue,  bluish 
black,  and  purple  to  gray  and  green.  There  are  also  a  few 
quarries  of  red  slate.*  The  color  of  the  slate  does  not  appear 
to  indicate  the  quality.  The  red  and  dark  colors  are  generally 
considered  the  most  effective,  and  the  greens  are  generally  used 
only  on  factories,  storehouses,  and  buildings  where  the  appear- 
ance is  not  of  so  much  importance. 

Some  slates  are  marked  with  bands  or  patches  of  a  different 
color,  and  the  dark-purple  slates  often  have  large  spots  of  light 
green  upon  them.  These  spots  do  not  as  a  rule  affect  the  dura- 
bility of  the  slate,  but  they  greatly  detract  from  its  appearance. 

Grading"  of  Slates. — The  Brownville,  Maine,  slates  are 
graded  as  follows:  No.  1.  Every  sheet  to  be  full  SA&"  thick,  both 
sides  smooth  and  all  corners  full  and  square.  No  pieces  to  be 
winding  or  warped. 

No.  2.  Thickness  may  vary  from  J"  to  \" ,  all  corners  square, 
one  side  generally  smooth,  one  side  generally  rough,  no  badly 
warped  slates. 

The  Bangor,  Penn.,     slates  are  graded: 

No.  I  Clear. — A  pure  slate  without  any  faults  or  blemishes. 

No.  I  Ribbon. — As  well  made  as  No.  1  Clear,  except  that  it 
contains  one  or  more  "ribbons"  (a  black  band  or  streak  across 
the  slate),  which,  however,  are  high  enough  on  the  slate  to  be 
covered  when  laid,  thus  presenting  a  No.  1  roof. 

No.  2  Ribbon. — This  contains  several  "ribbons,"  some  of 
which  cannot  be  covered  when  laid. 

No.  2  Clear. — A  slate  without  "ribbons,"  made  from  rough 
beds. 

*  The  best  red  slates  are  believed  to  be  those  quarried  by  the  Algonquin 
Red  Slate  Company  of  Worcester,  Mass.,  and  Mat  hews'  unfading  bright 
red,  the  Alden  Speare's  Sons  Company  of  New  York  City  selling  agents. 


SLATE   ROOFS.  1427 

Hard  Beds. — A  clear  Bangor  slate,  not  quite  as  smooth  as 
No.  1  Clear,  but  much  better  than  a  No.  2  Clear. 

Ordinary  Bent  Slate. — A  smooth  slate  similar  to  No.  1  Clear, 
but  bent  at  a  radius  of  about  12  ft. 

Punching. — Formerly  slates  were  punched  for  nail-holes 
on  the  job;  now,  however,  slates  are  bored  and  countersunk  at 
the  quarry,  when  so  ordered.  Architects  should  always  specify 
that  "  slates  be  bored  and  countersunk,"  as  punching  badly 
damages  the  slates. 

Sizes.—  The  sizes  of  slates  range  from  9"X7"  to  24"X14", 
there  being  some  thirty-seven  different  sizes;  the  more  common 
sizes,  however,  are  those  given  in  the  following  table. 

The  sizes  of  slates  best  adapted  for  plain  roofs  are  the  large 
wide  slate,  such  as  12"X16",  18"X12",  20" X 12", or  24"X14"; 
the  large  sizes  make  less  joints  in  the  roof,  require  less  nails, 
and  avoid  small  pieces  at  hips  and  valleys.  For  roofs  cut  up 
into  small  sections  the  smaller  sizes,  such  as  14"  X  7"  or  16"xS", 
look  the  best. 

Thickness. — Slates  vary  in  thickness  from  J  to  f  in.;  8/i6  in. 
is  the  usual  thickness  for  ordinary  sizes  (see  Grading  of  Slates) . 

Laying. — Slates  are  laid  either  on  a  board  sheathing  (rough 
or  tongued  and  grooved)  covered  with  tarred  or  water-proof  paper 
or  felt,  or  on  roofing-laths  2  to  3  ins.  wide  and  from  1  to  1-J-  ins. 
thick,  nailed  to  the  rafters  at  distances  apart  to  suit  the  gauge 
of  the  slates.  Each  slate  should  lap  the  slate  in  the  second 
course  below  3  ins. 

The  slates  are  fastened  with  two  threepenny  or  fourpenny 
nails,  one  near  each  upper  corner.  For  slates  20"XlO"  or 
larger,  fourpenny  nails  should  be  used.  Copper,  composition, 
tinned,  or  galvanized  nails  should  be  used.  Plain  iron  nails 
are  speedily  weakened  by  rust,  break,  and  allow  the  slates  to 
be  blown  off. 

On  iron  roofs  slates  are  often  placed  directly  on  small  iron 
purlins  spaced  at  suitable  distance  to  receive  them,  and  fastened 
with  wire  or  special  forms  of  fasteners. 

The  Gauge  of  a  slate  is  the  portion  exposed  to  the  weather, 
which  should  be  one  half  of  the  remainder  obtained  by  sub- 
tracting 3  ins.  from  the  length  of  the  slate. 

Roofs  to  be  covered  with  slate  should  have  a  rise  of  not  less 
than  6  ins.  to  the  foot  for  20-  or  24-in.  slates,  or  8  ins.  for  smaller 
sizes. 

Elastic  Cement. — In  first-class  work,  the  top  course  of  slate 
on  ridge,  and  the  slate  for  2  to  4  ft.  from  all  gutters  and  1  ft. 
each  way  from  all  valleys  and  hips,  should  be  bedded  in  elastic 
cement. 

Flashings. — By  "flashings"  are  meant  pieces  of  tin,  zinc,  or 
copper  laid  over  slate  and  up  against  walls,  chimneys,  copings, 
etc. 

Counter- flashings  are  of  lead  or  zinc,  and  are  laid  between  the 
courses  in  brick,  and  turned  down  over  the  flashings.  In 
flashing  against  stonework,  grooves  or  reglets  often  have  to  be 
cut  to  receive  the  counter-flashings. 

Close  and  Open  Valleys. — A  close  valley  is  where  the  slates 


1428 


MEMORANDA  ON   ROOFING. 


are  mitred  and  flashed  in  each  course  and  laid  in  cement.  In 
such  valleys  no  metal  can  be  seen.  Close  valleys  should  only 
be  used  for  pitches  above  45°. 

An  open  valley  is  where  the  valley  is  formed  of  sheets  of 
copper  or  zinc  15  or  16  ins.  wide,  and  the  slates  laid  over  these. 

Measurement. — Slates  are  sold  by  the  "square,"  by 
which  is  meant  a  sufficient  number  of  slates  of  any  size  to 
cover  100  sq.  ft.  of  surface  on  a  roof,  with  3  ins.  of  lap,  over 
the  head  of  those  in  the  second  course  below.  The  square  is 
also  the  basis  on  which  the  cost  of  laying  is  measured. 

"Eaves,  hips,  valleys,  and  cuttings  against  walls  or  dormers 
are  measured  extra — 1  ft.  wide  by  their  whole  length,  the  extra 
charge  being  made  for  waste  material  and  the  increased  labor 
required  in  cutting  and  fitting.  Openings  less  than  3  sq.  ft. 
are  not  deducted,  and  all  cuttings  around  them  are  measured 
extra.  Extra  charges  are  also  made  for  borders,  figures,  and 
any  change  of  color  of  the  work  and  for  steeples,  towers,  and 
perpendicular  surfaces."  : 

Cost. — The  cost  of  slates  varies  with  the  size,  color,  and 
quality.  The  prices  given  in  the  following  table  are  about  the 
average  for  blue-black  slate,  of  No.  1  grade,  at  the  quarry. 
It  will  be  seen  that  the  medium  sizes  cost  the  most,  and  the 
larger  and  smaller  sizes  the  least.  The  larger  sizes  make  the 
cheapest  roof. 

Red  slates  cost  from  60  to  150  per  cent,  more  than  black 
slates. 


NUMBER  AND    COST   OF    SLATES,  AND    POUNDS    OF    NAILS  TO 
100  SQUARE  FEET  OF  ROOF. 

(3-inch  Lap.) 


Sizes  of 
Slate. 

Exposed 
when  Laid. 

Number  to 
a  Square. 

Weight  of 
Galvanized 
Nails. 

Cost  per 
Square   at 
Quarry. 

ins. 

ins. 

Ibs.  oz. 

14X24 

loi 

98 

r  i    6 

$6  .  10 

12X24 

I0| 

115 

I    1     10 

6.60 

12X22 

»J 

126 

-dJ    1     12 

6.50 

11X22 

M 

138 

5 

1      15 

6.90 

12X20 

8f 

142 

2       0 

6.80 

10X20 

8i 

170 

2       6 

6.80 

12X18 

7* 

160 

1      13 

6.80 

10X18 

?4 

192 

2       3 

7.20 

9X18 
12X16 

8 

214 
185 

2       7 
2       2 

7.10 
6.80 

10X16 

8 

222 

2       8 

7.10 

9X16 

Bf 

247 

3       0 

7.00 

8X16 

g| 

277 

Si    3       2 

7.20 

10X14 

262 

3       0 

6.60 

8X14 

el 

328 

3     12 

6.60 

7X14 

si 

374 

|    4       4 

6.40 

8X12 

4} 

400 

4       9 

5.50 

7X12 

4* 

458 

5       3 

5.00 

6X12 

4* 

533 

I   6        1 

4.80 

*  The  Building  Trades  Pocket-book 


ROOFING  TILE.  1429 

The  cost  of  blue-black  slate  roofs,  complete,  varies  from 
$7  to  $13  per  square,  depending  on  the  class  of  work  and  re- 
moteness from  the  quarries. 

The  additional  cost  of  laying  slate  in  elastic  cement  varies 
from  $1.50  to  $2  per  square. 

An  experienced  roofer  will  lay  on  an  average  two  squares 
of  slate  in  ten  hours. 

Weight. — Slate  roofing  %  in.  thick  will  weigh  on  the  roof 
about  6|  Ibs.  per  square  foot,  and  J  in.  slates  8f  Ibs.,  the  smaller 
sizes  weighing  the  most  on  account  of  the  lap.  The  actual 
weight  of  a  square  foot  of  slate  \  in.  thick  is  3.63  Ibs. 


Roofing  Tile. 

The  term  roofing  tile  is  commonly  understood  to  refer  to 
exterior  roof  covering  made  from  clay  with  overlapping  edges. 
Clay  or  terra-cotta  roof  tiles  have  long  been  very  largely  used 
in  Europe,  where  their  cost  is  much  less  than  in  America. 

Since  the  year  1893  the  advance  here  in  the  character  and 
extent  of  roofing  tile  has  been  marked  and  rapid.  This  material 
can  now  be  had  for  half  the  prices  prevailing  twelve  years  ago, 
and  the  result  has  been  that  thousands  of  squares  of  terra-cotta 
tiles  have  been  placed  on  shops  and  factories  which  would 
under  former  conditions  have  been  covered  with  slate  or  metal. 

Whether  or  not  a  tile  roof  is  as  durable  and  satisfactory  as 
one  of  No.  1  slate  is  a  much-disputed  question.  The  author  is 
of  the  opinion  that,  considering  the  quantities  used,  slates  have 
given  better  satisfaction  than  tile. 

A  tile  roof,  however,  is  certainly  more  attractive  than  a 
slate  roof,  and  the  author  believes  that  there  are  many  roofing 
tiles  on  the  market  which  if  properly  laid  will  prove  as  tight 
and  durable  as  slate. 

There  are  so  many  patterns  of  roofing  tile  that  it  is  impos- 
sible here  to  enter  into  a  description  of  them.  Of  the  various 
patterns,  those  which  interlock  are  considered  to  make  the  most 
satisfactory  roof  from  a  practical  standpoint. 

Some  manufacturers  of  roofing  tile,  notably  the  Ludowici 
Roofing  Tile  Company,  make  glass  tiles,  of  the  same  pattern  as 
the  clay  tiles,  so  that  they  may  be  worked  in  with  them  and 
used  in  place  of  skylights.  Many  thousands  of  these  glass  tiles 
have  been  used  on  the  roofs  of  train-sheds,  shops,  and  factories. 

Roofing  tile  may  be  laid  on  felt  or  sheathing,  or  those  with 
a  proper  interlocking  device  may  be  laid  direct  on  wood  or  steel 
purlins  without  sheathing  or  inner  roof  of  any  kind.  When  so 
laid,  to  prevent  the  entrance  of  dust  or  dry  snow,  the  joints 
should  be  pointed  on  the  under  side  after  laying.  Most  tiles, 
particularly  of  the  older  patterns,  are  nailed  to  the  sheathing, 
but  this  is  a  defective  principle  of  fastening  and  is  superseded 
by  the  modern  practice  of  fastening  with  copper  wires  from  a 
pierced  lug  toward  the  lower  end  of  the  tile. 

Roofing  tiles  weigh  from  750  to  1,200  Ibs.  per  square  (100  sq. 
ft.). 


1430  MEMORANDA  ON  ROOFING. 

The  prices  of  tiles  vary  from  $6  to  $30  per  square,  according 
to  pattern  and  finish. 

The  cost  of  laying  varies  from  $1.50  to  $5  per  square,  accord- 
ing to  the  pattern  of  tile  used  and  the  character  and  extent 
of  the  roof. 

The  principal  manufacturers  of  roofing  tile  in  this  country 
are  the  Akron  Roofing  Tile  Company,  Akron,  Ohio;  Celadon 
Roofing  Tile  Company,  New  York,  N.  Y.;  C.  A.  Coiiway  &  Co., 
New  Philadelphia,  Ohio;  Federal  Roofing  and  Tile  Company, 
St.  Louis,  Mo.;  Ludowici  Roofing  Tile  Company,  Chicago,  111.; 
Mound  City  Roofing  Tile  Company,  St«  Louis,  Mo.;  National 
Tile  Roofing  Company,  Lima,  Ohio;  Ohio  Roofing  Tile  Com- 
pany, Ottawa,  Ohio — from  whom  catalogues  giving  full  infor- 
mation may  be  obtained. 

Sheet-metal  Tiles. — Roofing  tiles  stamped  from  sheet 
steel,  plain  or  galvanized,  and  also  from  sheet  copper,  in  imita- 
tion of  clay  tiles,  are  made  by  several  parties,  notably  Merchant 
&  Company  of  Philadelphia  and  W.  H.  Mullins  of  Salem,  Ohio, 
and  have  been  extensively  used. 

The  first  cost  of  these  tiles  (except  those  of  copper)  is  much 
less  than  that  of  clay  tiles  and  they  do  not  require  as  heavy 
roof  framing.  Tin  or  galvanized-iron  tiles,  however,  must  be 
painted  every  few  years,  so  that  for  a  long  period  of  years 
they  will  probably  cost  as  much  as  clay  tiles  and  more  than 
slate. 

Galvanized-iron  tiles  of  the  "Spanish"  pattern  cost  from  $13 
to  $15  per  square  laid  and  painted,  and  ordinary  tin  shingles 
from  $8  to  $10. 


Tin  Roofs. 

The  Sheets. — Roofing  plates  are  made  of  soft  steel  or 
wrought  iron  (more  commonly  of  the  former)  and  covered  with 
a  mixture  of  lead  and  tin,  and  are  designated  as  "terne  plates," 
in  distinction  from  plates  coated  only  with  tin  and  therefore 
called  "bright  tin."  Roofing  plates  are  coated  by  two  methods. 
The  original  manner  of  coating  the  plates  (commonly  designated 
"Old  Process")  was  by  dipping  the  black  plates  by  hand  into 
the  mixture  of  tin  and  lead,  and  allowing  the  sheets  to  absorb 
all  the  coating  that  was  possible;  and  several  brands  of  roofing 
tin  are  still  made  by  this  process.  The  other  process,  by  which 
the  majority  of  roofing  plates  are  now  made,  is  known  as  the 
"Patent  Roller  Process,"  by  which  the  plates  are  put  into  a 
bath  of  tin  and  lead,  and  are  passed  through  rolls,  the  pressure 
of  which  leaves  on  the  iron  or  steel  a  thickness  of  coating  which, 
to  a  great  extent,  determines  the  value  of  the  plate.  These 
rolls  can  be  so  adjusted  as  to  leave  a  good  amount  of  coating 
on  the  plate,  an  ordinary  coating,  or  a  very  scant  one;  the 
heavier  the  coating  the  more  valuable  the  plate. 

It  is  claimed  that  hand-dipped  plates  will  last  much  longer 
than  those  made  by  the  new  process,  although  the  latter  process 


TIN  ROOFS.  1431 

is  much  more  extensively  used  and  many  good  roofing  sheets 
are  made  by  it. 

The  best  roofing  plates  always  have  the  brand  stamped  on 
them,  and  as  the  manufacturers  have  a  pecuniary  interest  in 
keeping  up  the  reputation  of  these  brands,  the  only  way  of 
being  sure  of  a  good  tin  roof  is  to  specify  a  brand  of  tin  that 
has  a  reputation  for  quality  and  durability.  Some  of  the  best 
known  brands  are  Taylor's  "Old  Style,"  Merchant's  "Old 
Method,"  "M  F,"  "Scott's  Extra  Coated,"  "Margaret,"  and 
"Admiral." 

Sizes. — The  common  sizes  of  tin  plates  are  10X14  ins.  and 
multiples  of  that  measure.  The  sizes  more  generally  used  are 
14X20  ins.  and  20X28  ins.  The  larger  size  is  the  more 
economical  to  lay,  and  hence  roofers  prefer  to  use  it,  but  for 
flat  roofs  the  14X20  size  makes  the  better  roof. 

Thicknesses. — Terne  plates  are  made  in  two  thicknesses,  viz., 
I  C,  in  which  the  iron  body  weighs  about  50  Ibs.  per  100  sq.  ft., 
and  I  X,  in  which  it  weighs  62J  Ibs.  per  100  sq.  ft.  For  roofing 
the  I  C,  or  lighter  weight,  is  to  be  preferred,  because  the  seams 
will  not  suffer  as  much  from  contraction  and  expansion  as 
with  the  thicker  plates. 

For  spouts,  valleys,  and  gutters,  however,  I  X  plates  should 
always  be  specified,  and  should  preferably  be  used  for  flashings, 
as  they  are  stiffer  and  less  liable  to  be  dented  or  punched.  The 
thickness  of  the  iron  does  not  add  to  the  durability  of  the  plates, 
as  this  depends  entirely  upon  the  tin  coating. 

Weights. — The  standard  weight  of  14x20  in.  I  C  terne 
plates  is  107  Ibs.  to  112  sheets  (the  number  usually  packed 
in  one  box),  and  of  14x20  in.  I  X  sheets,  135  Ibs.  20x28  in. 
sheets  should  weigh  just  twice  as  much.  The  black  sheets 
before  coating  should  weigh,  per  112  sheets,  from  95  to  100  Ibs. 
for  I  C,  14X20  ins.,  and  from  125  to  130  Ibs.  for  I  X,  14X20  ins. 
The'  difference  between  the  weight  of  the  black  sheets  and  of 
the  finished  sheets  shows  the  weight  of  the  tin.  A  heavily 
coated  tin  should  weigh  from  115  to  120  Ibs.  per  112  sheets 
for  I  C,  14X20  ins.,  and  from  145  to  150  Ibs.  for  I  X,  14X20  ins. 
20X28  in.  sheets  should,  of  course,  weigh  twice  as  much. 

The  Roof. — Roofs  with  less  than  one  third  pitch  are  made 
with  flat  seams  and  should  preferably  be  covered  with  sheets 
14X20  ins.,  rather  than  from  sheets  20X28  ins.,  because 
the  larger  number  of  seams  stiffen  the  surface  and  help  to 
prevent  buckles  and  rattling  in  stormy  weather.  For  a  flat- 
seam  roof  1-in.  barbed  and  tinned  roofing  nails  should  be  used, 
not  over  6  ins.  apart,  well  under  the  edge.  They  should  be 
well  covered  up  and  the  seams  should  be  pounded  down  over 
the  edge  with  a  wooden  mallet.  Nails  must  never  be  exposed. 
The  seams  should  be  made  with  great  care;  sufficient  time  must 
be  taken  to  properly  "sweat"  the  solder  into  the  seams, 

Steep  tin  roofs  should  be  made  with  standing  seams  and  from 
sheets  20X2S  ins.  The  sheets  are  first  double-seamed  and 
soldered  together,  preferably  end  to  end,  into  long  strips  that 
reach  from  eaves  to  ridge.  The  sloping  seams  are  composed  of 


1432  MEMORANDA  ON  ROOFING. 

two  "upstands,"  interlocked  and  held  in  place  by  cleats.  The 
standing  seams  are  not  soldered,  but  are  simply  locked  together 
with  the  cleats  folded  in  from  15  to  18  ins.  apart.  Nails  should 
be  driven  into  the  cleats  only. 

The  use  of  acid  in  soldering  seams  in  a  tin  roof  is  to  be  care- 
fully avoided;  acid  coming  in  contact  with  the  bare  iron  on 
the  cut  edges  and  corners  where  the  sheets  are  folded  and  seamed 
together  will  cause  rusting.  No  other  soldering  flux  but  good 
rosin  should  ever  be  used. 

Durability. — A  tin  roof  of  good  material,  properly  put  on,  and 
kept  properly  painted,  will  last  from  thirty  to  forty  years.  It 
should  not  be  painted  for  the  first  time  until  it  has  been  well 
washed  by  rain,  to  get  the  grease  off  the  tin;  and  all  lumps  or 
rosin  left  on  the  roof  should  be  removed  as  soon  as  the  tin  is 
laid  and  soldered.  One  or  more  layers  of  felt-paper  should  be 
placed  under  the  tin,  to  serve  as  a  cushion,  and  also  to  deaden 
the  noise  produced  by  rain  striking  the  tin. 

The  durability  of  tin  roofing,  and  especially  of  gutters,  valleys, 
and  flashings,  is  generally  increased  by  painting  the  tin  on 
the  back  before  laying.  An  excellent  paint  for  tin  roofs  is 
composed  of  10  Ibs.  Venetian  red,  1  Ib.  red  lead,  1  gallon  pure 
linseed-oil. 

Number  of  Sheets  Required  to  a  Square. — For 
flat-seam  roofing  a  sheet  of  tin  14X  20  ins.  with  J-:n.  edges, 
measures  when  edged  or  folded  13X19  ins.,  or  247  sq.  ins.; 
consequently  the  number  of  sheets  required  to  a  square  equals 
14,400-247,  or  58J.  ,  1,000  sq.  ft.  requires  583  sheets.  A  box 
of  112  sheets  14X20  ins.  will  cover  approximately  192  sq.  ft. 

Sheets  20X28  ins.  measure  when  edged  or  folded  19X27  ins., 
or  513  sq.  ins.  To  cover  1,000  sq.  ft.  (10  squares)  requires  288 
sheets. 

The  standing  seams  and  locks  on  a  steep  roof  require  2J  ins. 
off  the  width  and  f  in.  off  the  length  of  the  sheet.  A  sheet 
20x23  ins.  with  the  seams  on  the  narrow  edges  will  cover 
486  sq.  ins.,  and  with  the  seams  on  the  long  edges  470  sq.  ins. 
The  former  requires  297  sheets  to  1,000  sq.  ft  ,  and  the  latter 
307  sheets. 

The  cost  of  tin  roofing  varies  from  $3  to  $11  per  square, 
according  to  the  grade  of  tin  used  and  the  scale  of  wages. 
Standing-seam  roofs  cost  about  50  cts.  a  square  less  than  fiat- 
seam  roofs. 


Slag  or  Gravel  Roofing*  (Composition  Roofing), 

The  ordinary  gravel  roofing  is  formed  by  first  covering  the 
surface  of  the  roof  with  dry  felt  (paper)  and  over  this  laying 
three,  four,  or  five  layers  of  tarred  or  asphalt ic  felt,  the  layers 
of  felt  lapping  each  other  like  shingles,  so  that  only  from  6  to 
10  ins.  of  each  layer  are  exposed. 


SLAG  OR  GRAVEL  ROOFING.  1433 

Flashing  -..against  walls,  chimneys,  curbs  of  skylights,  etc., 
is  done  by  turning  the  felt  up  4  ins.  against  the  wall.  Over 
this  is  laid  an  8-in.-  strip  with  half  its  width  on  the  roof.  The 
upper  edge  of  the  strip  and  of  the  several  layers  of  felt  is  then 
fastened  to  the  wall  by  nailing  wooden  strips  or  laths  over  the 
felt  and  into  the  walL 

A  better  method  is  to  lay  two  plys  of  tarred  felt  lapping 
each  other  17  ins.  and  then  spreading  a  coat  of  pitch  over  the 
entire  roof.  On  this  again  three  more  layers  of  felt  are  laid, 
then  coated  with  pitch,  into  which  the  crushed  slag  or  screened 
gravel  is  embedded.  Each  layer  of  felt  lapping  another  should 
be  mopped  2  ins.  more  than  its  exposed  surface  back  from  the 
edge. 

The  following  specification  prepared  by  the  Barrett  Manu- 
facturing Company  describes  the  latter  method,  as  also  the 
materials  that  should  be  used  to  secure  a  first-class  job:* 

Specification  for  Slag  or  Gravel  Koofing.f 

Over  the  entire  roof  shall  be  laid  a  five-  (5)  ply  coal-tar  pitch 
felt  and  slag  or  gravel  roof,  to  be  constructed  as  follows: 

The  rosin-sized  sheathing  paper  to  be  used  shall  weigh  not 
less  than  six  (6)  Ibs.  per  100  sq.  ft. 

The  felt  shall  weigh  not  less  than  fourteen  (14)  Ibs.  per  100 
sq.  ft.,  single  thickness. 

The  pitch  shall  be  the  best  quality  of  straight-run  coal-tar 
pitch  distilled  direct  from  American  coal-tar,  and  there  shall  be 
used  not  less  than  one  hundred  and  twenty  (120)  Ibs.  (gross 
weight)  per  100  sq.  ft.  of  completed  roof. 

The  nailing  shall  be  done  with  threepenny  barbed-wire 
roofing  nails  driven  through  tin  discs. 

The  slag  or  gravel  shall  be  of  such  a  grade  that  no  particles 
shall  exceed  five  eighths  (f )  of  an  inch  or  be  less  than  one 
fourth  (J)  of  an  inch  in  size.  It  shall  be  dry  and  free  from 
dust  or  dirt.  In  cold  weather  it  must  be  heated  immediately 
before  using.  Not  less  than  three  hundred  (300)  Ibs.  of  slag  or 
four  hundred  (400)  Ibs.  of  gravel  shall  be  used  per  100  sq.  ft. 

The  materials  shall  be  used  as  follows: 

First  lay  one  thickness  of  rosin-sized  sheathing  paper  (A) ,  lap- 
ping each  sheet  1  in.  over  the  preceding  one,  and  nailing  only  so 
often  as  may  be  necessary  to  hold  in  place  until  covered  with 
the  tarred  felt,  and  the  nailing  may  be  omitted  entirely  if 
practicable. 

*  For  specifications  for  ordinary  gravel  roofing,  including  flashing,  see 
Part  II,  Building  Construction  and  Superintendence,  p.  498. 
t  Known  as  Barrett's  specifications. 


1434 


MEMORANDA   ON   ROOFING. 


Over  the  rosin-sized  sheathing  lay  two  (2)  full  thicknesses  of 

tarred  felt  (B),  lapping  each 
sheet    seventeen     (17)    ins.* 


seventeen 

over  the  preceding  one,  and 
nailing  along  the  exposed 
edges  of  the  sheets  only  so 
often  as  may  be  necessary 
to  hold  the  sheets  in  place 
until  the  remaining  felt  can 
be  applied. 

Over  the  entire  surface  of 
the  felt  thus  laid  spread  a 
uniform  coating  of  pitch  (C), 
mopped  on.  Then  lay  three 
(3)  full  thicknesses  of  felt 
(D),  lapping  each  sheet 
twenty-two  (22)  ins.  over 
the  preceding  one,  and  nail- 
ing, as  laid,  every  three  (3) 
ft.,  not  more  than  ten  (10) 
ins.  from  the  upper  edge. 

When  the  felt  is  thus  laid 
and  secured,  mop  with  pitch 
(E)  the  full  width  of  twenty 
(20)  ins.  under  each  lap. 
Then  spread  over  the  entire 
surface  of  the  roof  a  uniform 
coating  of  pitch,  into  which, 
while  hot,  embed  slag  or 


Gravel  Roofing,  showing  Method 
of  Laying. 


gravel  (F). 

Note. — When  this  roof  is  to  be  laid  over  hydraulic  cement 
concrete,  as  in  fire-proof  construction,  omit  the  rosin  sheath- 
ing paper,  and  in  its  place  coat  the  concrete  with  hot  pitch. 

The  only  difference  between  slag  and  gravel  roofing  is  that 
for  the  former  crushed  slag  is  used  instead  of  gravel. 

As  there  are  several  different  weights  of  tarred  felt,  the 
•specifications  should  either  give  the  weight  per  100  sq.  ft.  or 
the  number  of  some  particular  brand,  as  Barrett's  No.  1,  2,  or  3. 

Temporary  roofs  may  be  made  with  three  or  even  two  thick- 
nesses of  tarred  felt. 

The  object  of  laying  dry  felt  or  rosin-sized  paper  on  the 
sheathing  is  to  prevent  the  pitch  from  dripping  through  the 
cracks.  The  minimum  weight  of  tarred  felt  that  should  ever 
be  used  on  temporary  jobs  is  12  Ibs.  per  100  sq.  ft.  and  the 


*  The  width    of  'roofing  felts  is   32  ins.      A  lap  of   17  ins.  gives  a  2-in. 
01  head-cover." 


ASPHALT  ROOFING.  1435 

minimum  amount  of  pitch  70  Ibs.  for  a  3-ply  roof  and  90  Ibs. 
for  a  5-ply  (i.e.,  four  layers  of  tarred  felt.)* 

Gravel  roofs  should  not  have  a  pitch  of  less  than  f  nor  more 
than  |  in.  to  the  foot  in  hot  climates,  or  in  the  Mountain  States. 
In  cold  and  damp  climates  the  pitch  may  be  as  great  as  4  ins. 
to  the  foot,  but  is  not  as  desirable  as  one  of  f  in.  to  1  in. 

Fire-resisting  Qualities. — While  it  cannot  be  called  fireproof, 
it  has  been  proved  by  carefully  conducted  tests  that  gravel  roof- 
ing will  protect  a  wooden  roof  better  than  tin. 

The  effect  of  fire  on  gravel  roofing  is  to  soften  the  asphalt 
and  pitch  in  the  roofing,  to  burn  out  the  inflammable  oil  in  the 
same,  and  to  cause  the  residue  to  swell  and  form  a  porous,  incom- 
bustible coke. 

Durability. — A  3-ply  gravel  roof  of  12-lb.  felt  and  70  Ibs. 
of  straight-run  distilled  pitch  should  last  for  from  four  to 
seven  years;  an  ordinary  6-ply  15-lb.  felt  and  100  Ibs.  pitch  from 
nine  to  ten  years,  and  a  roof  put  on  as  specified  above,  fifteen 
to  twenty  years,  and  under  favorable  circumstances  even  longer. 

Tar  roofing  is  not  readily  attacked  by  corrosive  gases  and  will 
consequently  last  longer  than  metal  on  buildings  exposed  to 
such  gases.  Creosote-oil  is  often  added  to  coal-tar  pitch,  par- 
ticularly in  cold  weather,  to  make  it  run  well  and  to  make  the 
slag  or  gravel  stick.  It  is  generally  considered  to  lessen  the  life 
of  the  pitch. 

Roofers  generally  give  a  five-year  guarantee  with  gravel  roofs. 

Cost. — The  cost  of  coal-tar  gravel  roofing  varies  with  the 
times  and  locality  from  $2.50  to  $3.50  per  square  for  3-ply, 
$3  to  $5  for  ordinary  5-ply,  and  about  $7  for  a  roof  as  above 
specified. 

Asphalt  Roofing  differs  from  coal-tar  roofing  principally 
in  the  substitution  of  asphalt  or  asphaltic  cement,  for  the  coal- 
tar  pitch,  for  saturating  the  felt  as  well  as  for  mopping  and 
surface  coating. 

It  is  claimed  that  the  oils  of  asphalt  do  not  evaporate  as 
quickly  as  do  those  of  coal-tar  pitch  under  ordinary  tempera- 
tures and  that  therefore  the  flexibility  and  life  of  asphaltic  felts 
and  coatings  are  not  as  quickly  destroyed.  As  a  matter  of  fact, 


*  In  the  Western  States  the  number  of  "ply"  is  construed  to  mean  the 
total  number  of  layers,  including  dry  as  well  as  saturated  felt,  and  the 
terms  3  ply,  5  ply,  etc.,  are  hereinafter  used  on  that  basis.  In  the  Eastern 
States,  3  ply,  5  ply,  etc.,  usually  refers  to  the  number  of  layers  of  saturated 
felt.  The  total  number  of  layers  should  always  be  specified. 


1436  MEMORANDA  ON   ROOFING. 

asphalt  roofs  do  not  always  last  longer  than  some  coal-tar  roofs, 
but  the  chances  are  that  they  will  last  fully  as  long  and  possibly 
longer,  depending  upon  the  quality  of  the  materials  and  the 
workmanship. 

The  asphalt  used  for  roofing  is  obtained  principally  from 
the  island  of  Trinidad. 

The  asphalt-roofing  materials  manufactured  by  the  Warren 
Chemical  and  Manufacturing  Company  of  New  York  have  been 
used  for  many  years  and  have  given  good  satisfaction. 

Specifications  for  Asphalt  Roofing.—  The  following 
specification  was  prepared  by  the  above-named  company.  The 
manner  of  laying  the  felting  differs  from  that  ordinarily  em- 
ployed for  coal-tar  roofing: 

Specifications.* — Cover  the  roof  with  two  thicknesses  of 
Warren's  Composite  Roofing  Felt,  mamlla-paper  side  down, 
lapping  each  sheet  17  ins.  over  the  preceding  one,  and  securing 
with  nails  through  tin  discs  about  2^  ft.  apart.  Over  the 
entire  surface  of  the  composite  felt  thus  laid  mop  an  even 
coating  of  Warren's  Anchor  Brand  Natural  'Asphalt  Roofing 
Cement.  Over  this  coating  of  cement  lay  one  thickness  of 
Anchor-brand  asphalt  felt,  lapping  each  sheet  at  least  2  ins. 
over  the  preceding  one,  sticking  these  laps  thoroughly  with 
the  hot  asphalt  roofing  cement,  and  securing  with  nails  through 
tin  discs.  Over  this  first  sheet  of  Anchor-brand  felt  mop  again 
an  even  coating  of  cement,  and  over  this  lay  a  second  sheet  of 
Anchor-brand  felt,  having  the  laps  come  in  the  middle  of  the 
first  sheet  of  Anchor-brand  felt  beneath,  sticking  the  2-in.  laps 
as  before,  and  securing  with  nails  through  tin  discs  about  1  \  ins. 
from  the  upper  edge  of  the  sheet.  Ove/  the  entire  surface  of 
the  felt  thus  laid  spread  an  even  coating  of  the  Anchor-brand 
cement,  covering  it  immediately  with  a  sufficient  body  of 
well-screened  dry  gravel.  If  the  roofing  is  applied  in  cold 
weather  the  gravel  must  be  heated. 

Asphalt  roofing  costs  a  little  more  than  coal-tar  roofing  of 
the  same  grade. 

An  asphalt  gravel  roof  should  not  have  a  slope  exceeding 
J  in.  to  the  foot,  on  account  of  the  liability  to  run  in  hot  weather. 

Ready  Roofing. — There  are  a  large  number  of  so-called  "  ready 
roofings,"  which  are  prepared  by  cementing  together  two, 
three,  or  more  layers  of  saturated  felt  or  felt  and  burlap  and 
then  coating  either  with  a  hard  solution  of  the  same  cementing 
material,  or  with  hot  pitch  or  asphalt  into  which  is  embedded 
sand  or  fine  gravel. 

These  roofings  are  commonly  put  up  in  rolls  36  ins.  wide  and 

*  The  Editor  has  been  notified  by  the  Warren  Chemical  and  Manufactur- 
ing Company  that  their  material  will  endure  at  a  pitch  of  five  to  seven  inches 
to  the  foot,  if  put  in  according  to  their  directions. 


READY  ROOFING.  1437 

are  applied  by  lapping  the  strips  2  ins.  with  a  coat  of  cementing 
material  between,  and  nailing  every  2  or  3  ins.  with  roofing 
nails  with  tin  caps.  A  sufficient  quantity  of  cement,  nails, 
and  tin  caps  is  packed  in  the  center  of  the  rolls. 
I  The  particular  advantage  of  these  roofings  is  that  no  previous 
experience  is  required  for  laying  them  and  no  kettles  are 
required;  for  this  reason  they  are  extensively  used  in  the 
country,  and  on  railroad  shops,  factories,  and  mill  buildings. 
In  cities  there  is  no  particular  advantage  in  using  them  except 
for  roofs  that  are  too  steep  for  coal-tar  pitch,  as  they  cost  on  the 
roof  about  the  same  as  good  gravel  roofing. 

Many  of  these  ready  roofings  are  as  durable  under  ordinary 
conditions  as  the  light-weight  gravel  roofs.  In  Colorado,  how- 
ever, it  has  been  found  that  they  are  badly  damaged  by  severe 
hail -storms,  probably  owing  to  the  lack  of  the  protecting  gravel. 

For  roofs  having  a  rise  of  1  inch  or  more  to  the  foot,  these 
roofings  make  an  economical  and  durable  roof,  and  for  some 
buildings  are  to  be  preferred  to  other  materials. 

The  best  known  and  most  extensively  used  of  these  ready 
roofings  are: 

Brand.  Name  of  Manufacturer. 

The  P.  &  B.  Ruberoid  Roofing Standard  Paint  Co.,  N.  Y. 

Malt  hold Paraffine  Paint  Co.,  San  Francisco. 

Arrow  Brands,  Asphalt  Roofing  ....    Asphalt  Ready  Roofing  Co.,  N.  Y. 

Elaterite  Roofing Western  Elaterite  RT g  Co.,  N.  Y. 

Elaterite  Roofing Elaterite  R'f'g  Co.,  San  Francisco. 

Standard  Asbestos  Roofing H.  W.  Johns-Man  ville  Co.,  N.  Y. 

Granite  Roofing •.  .    Eastern  Granite  R'f 'g  Co. ,  N.  Y. 

Carey's  Magnesia  Flexible  Roofing.  .  Philip  Carey  M'f'g  Co.,  Lockland,  O. 
Asphalt  Sand-surfaced  Roofing Warren  Chemical  &  M'f'g  Co.,  N.  Y. 

Corrugated  Iron  and  Steel  Sheets. 

Corrugated  sheets  of  iron  and  steel  are  very  extensively  used 
for  the  roofing  and  siding  of  mills,  sheds,  grain-elevators,  and 
warehouses. 

The  best  grades  of  corrugated  sheets  are  now  made  of  double- 
refined  box-annealed  iron  or  steel.*  The  corrugations  are 
usually  made  lengthwise  of  the  sheet,  either  by  passing  them 
through  rolls  or  by  pressing  the  plain  sheets  in  a  press  made  to 
give  the  desired  corrugation.  It  is  claimed  that  the  latter 

*  It  is  claimed  that  "the  life  of  a  genuine  puddled-iron  sheet  when  ex- 
posed only  to  the  pure  air  and  natural  elements  is  from  five  to  eight  times 
longer,  and  when  exposed  to  sulphurous  and  other  gases  ten  to  twenty 
times  longer,  than  that  of  steel  or  semi-steel  of  the  same  gauge,  or  a  light 
gauge  of  sheet  made  from  pure  puddled  pig  iron  will  wear  longer  than  the 
heaviest  gauges  of  steel  sheets,  or  than  galvanized  sheets  of  the  same  gauge." 


1438 


CORRUGATED   SHEETS. 


method  gives  the  more  perfect  and  uniform  corrugations.  The 
weight  and  thickness  of  the  metal  is  represented  by  the  gauge 
number  of  the  black  sheets  from  which  the  corrugated  sheets 
are  made.  The  standard  gauge  for  sheet  iron  and  steel  in  this 
country  is  that  established  by  act  of  Congress  March  3,  1893. 

The  following  table  gives  the  weight  and  thickness  of  the  dif- 
ferent gauges,  from  Nos.  7  to  30,  for  flat  black  sheets.  [The 
gauge  extends  from  No.  7-0,  J  in.  thick,  up  to  No.  40,  .005469  in. 
in  thickness,  but  sheet  steel  is  not  commonly  made  thinner  than 
No.  30,  and  above  %>  in.  the  thickness  is  generally  designated 
by  fractions  of  an  inch.] 
U.  S.  STANDARD  GAUGE  FOR  SHEET  IRON  AND  STEEL. 


Thickness. 

Weight. 

No.  of 
Gauge. 

Approximate 
Thickness  in 

Approximate 
Thickness  in 

Weight  per 
Square  Foot 

Weight  per 
Square  Foot 

Fractions  of 

Decimal  Parts 

in  Ounces 

in  Pounds 

an  Inch. 

of  an  Inch. 

Avoirdupois. 

Avoirdupois. 

•7 

3/16 

.1875 

120 

7.5 

8 

11/64 

.171875 

110 

6.875 

9 

5/32 

.15625 

100 

6.25 

10 

9/64 

.  140625 

90 

5.625 

11 

1/8 

.125 

80 

5. 

12 

7/64 

.109375 

70 

4.375 

13 

3/32 

.09375 

60 

3.75 

14 

5/64 

.078125 

50 

3.125 

15 

9/128 

.0703125    ' 

45 

2.8125 

16 

1/16 

.0625 

40 

2.5 

17 

9/160 

.05625 

36 

2.25 

18 

1/20 

.05 

32 

2. 

19 

7/160 

.04375 

28 

1.75 

20 

3/80 

.0375 

24 

1.50 

21 

11/320 

.034375 

22 

1.375 

22 

1/32 

.03125 

20 

1.25 

23 

9/320 

.028125 

18 

1.125 

24 

1/40 

.025 

16 

1. 

25 

7/320 

.021875 

14 

.875 

26 

3/160 

.01875 

12 

.75 

27 

11/640 

.0171875 

11 

.6875 

28 

1/64 

.015625 

10 

.625 

29 

9/640 

.0140625 

9 

.5625 

30 

1/80 

.0125 

8 

.5 

Section  3  of  the  act  of  Congress  provides  that  in  the  practical 
use  and  application  of  the  above  gauge  a  variation  of  2J  per  cent, 
either  way  may  be  allowed. 


CORRUGATED    ROOFING.  1439 

Galvanizing  the  sheets  adds  approximately  2£  ounces  per 
square  foot  to  the  above  weights. 

The  regular  sizes  of  the  corrugations  are  2J,  1J,  f ,  and  %  inch, 
measured  from  centre  to  centre. 

Besides  these  sizes,  5-in.,  3-in.,  and  2-in.  corrugations  are 
made  by  one  or  two  corrugating  companies. 

Corrugated  sheets  are  carried  in  stock  in  6-,  7-,  8-,  9-,  and 
10-ft.  lengths.  The  8-ft.  length,  however,  is  most  commonly 
used.  The  width  of  the  sheets,  as  a  rule,  is  24  ins.  between 
centres  of  the  outer  corrugations,  so  that  the  covering  width  is 
24  ins.  when  one  corrugate  is  used  for  side  lap.  This  applies  to 
all  sizes  of  corrugations,  although  one  or  two  mills  make  wider 
sheets. 

The  2-,  2  J-,  and  3-in  corrugated  sheets  are  made  in  all  gauges 
from  16  to  28,  the  If-in.  corrugated  sheets  are  made  from  Nos. 
22  to  28  gauge,  the  f-in  corrugated  sheets  from  Nos.  24  to  28, 
and  the  %-in.  corrugated  sheets  of  Nos.  26,  27,  and  28  gauges 
only.  No.  28  gauge  is  most  used  for  all  purposes.  The  sheets 
are  generally  painted  with  a  red  mineral  paint  before  shipping; 
galvanized  sheets  can  also  be  obtained  if  desired. 

All  corrugated  sheets  are  sold  by  the  square  (100  sq.  ft.), 
measuring  the  actual  width  and  length  of  the  corrugated  sheets. 

Corrugated  Roofing.* 

For  covering  roofs,  either  3-,  2J-,  or  2-in.  corrugates  should  be 
used,  the  2J-in.  being  the  most  common  size.  The  thickness 
or  gauge  will  depend  on  the  distance  between  the  supports  on 
which  the  sheets  are  laid. 

Nos.  26  to  28  gauges  should  be  laid  on  close  sheathing,  or 
strips  not  more  than  1  to  2  ft.  between  centres.  The  maximum 
distances  between  supports  for  other  gauges  should  be  as 
follows :  t 

For  No.  24  gauge,  2  to  2J  ft.  from  centre  to  centre. 

For  Nos.  22  and  20  gauge,  2  to  3  ft.  from  centre  to  centre. 

For  No.  18  gauge,  4  to  5  ft.  from  centre  to  centre. 

For  No.  16  gauge,  5  to  6  ft.  from  centre  to  centre. 

The  least  pitch  which  should  be  given  to  roofs  that  are  to  be 
covered  with  corrugated  sheets  is  3  ins.  to  the  foot,  and  for  truss 


*  Much  practical  information  regarding  the  use  of  corrugated  sheets  on 
mill  buildings,  witn  many  details,  is  contained  in  Steel  Mill  Buildings, 
by  Milo  S.  Ketchum,  C.E. 

t  For  strength  of  corrugated  sheets  see  Steel  Mill  Buildings,  p.  190. 


1440 


CORRUGATED  ROOFING. 


roofs  it  is  not  desirable  to  have  less  than  a  one  fourth  pitch  (6  ins. 
to  the  foot). 

When  laid  on  a  roof,  corrugated  sheets  should  have  a  lap  at 
the  lower  end  of  from  3  to  6  ins.,  according  to  the  pitch  of  the 
roof.  For  a  J  pitch,  a  3-in.  lap;  for  a  }  pitch,  a  4-iii.  lap; 
and  for  a  J  pitch,  a  5-in.  l&p»  For  the  side  lap  it  is  recommended 
that  each  alternate  sheet  be  laid  upside  down  and  lapped  as 
shown  in  Fig.  1.  By  this  method,  when  water  is  blown  through 


Fig.  1 

the  first  lap,  it  will  stop  and  not  pass  the  half  lap,  but  run  down 
and  out  at  the  end  of  the  sheet.  A  great  deal  of  roofing,  how- 
ever, is  laid  as  in  Fig.  2. 


Fig.  2 

In  applying  to  sheathing  or  wood  strips,  the  sheets  are  secured 
by  nailing  through  the  tops  of  the  corrugations,  the  nails  being 
driven  through  every  alternate  corrugation  at  the  ends,  and  about 
8  ins.  apart  at  the  sides. 

When  applied  to  iron  or  steel  purlins,  the  side  laps  should  be 
at  least  1J  corrugations,  and  the  sheets  should  be  riveted 
together  every  8  ins.  on  the  sides  and  at  every  alternate  corruga- 
tion at  the  ends.  The  Cincinnati  Corrugating  Company  makes 
a  patent  edge  corrugation  which  makes  a  tight  joint  with  a  lap 
of  only  one  corrugation.  To  fasten  the  sheets  to  the  purlins, 
which  are  usually  of  angles,  a  cleat  of  band  iron  f  or  J  of  an  inch 
wide  may  be  passed  around  or  under  the  purlins  and  riveted  at 
both  ends  to  the  sheet,  as  shown  in  Fig.  3.  By  contracting 
or  pressing  this  cleat  toward  the  web  a  tight,  secure  fastening 


CORRUGATED  ROOFING. 


1441 


is  made,  which  allows  for  contraction  and  expansion  of  the 
sheets. 

Cleats,  however,  are  generally  used  only  with  channel  or 
Z-bar  purlins.  For  angle-iron  purlins,  the  clinch-nail  (of  soft 
iron  wire)  is  most  commonly  used,  as  shown  by  Fig.  4;  it  makes 
a  very  satisfactory  fastening: 


Fig.  3 


Fig.  4 


Fig.  5  Fig.  6 

The  following  table  shows  the  size  of  clinch-nails  to  be  used 
with  different  sizes  of  angle  purlins  and  also  the  number  of  nails 
to  the  pound  in  each  instance: 

Purlin  angle 2X2  ins.    2}^ X 3  ins.    3% X 314  ins.    4 X 4^  ins. 

Length  of  nail 4  ins.  5  ins.  6  ins.  7  ins. 

No.  of  nails  per  Ib 48  38  33  27 

The  nails  should  be  placed  through  the  top  of  every  second 
or  third  corrugation. 

At  the  eaves  of  the  building  and  along  the  edge  of  the  venti- 
lator especial  pains  should  be  taken  in  fastening  the  roofing,  as 
this  is  where  the  wind  catches  it  and  strips  it  from  the  purlins. 
For  these  places  the  best  method  of  fastening  is  shown  by  Fig.  5. 

This  consists  of  a  strip  of  sheet  iron  about  2  inches  wider  than 
the  purlins,  made  of  No.  12  iron,  riveted  to  the  purlins  with  i-in. 
rivets  spaced  10  ins.  apart;  to  this  strip  the  corrugated  sheets 
are  riveted,  at  spaces  of  5  ins.  or  two  corrugates,  with  six-pound 
rivets.  The  method  of  fastening  shown  by  Fig.  6  also  answers 
very  well  and  is  less  expensive. 


1442 


CORRUGATED   SIDING. 


In  ordering  corrugated  sheets  an  allowance  must  be  made  for 
the  laps.  The  following  table  gives  the  number  of  square  feet 
necessary  to  cover  one  square  of  actual  surface,  using  sheets  8  ft. 
long.  If  shorter  sheets  are  used,  the  allowance  must  be  slightly 
increased : 

NUMBER  OF  SQUARE  FEET  OF  CORRUGATED  SHEETS  TO  COVER 
100  SQ.  FT.  OF  ROOF. 


End  laps.  .  . 

1  in 

2  ins 

3  ins 

4  ins 

5  in** 

6  ins 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Side  lap,  1  corrugation. 

110 

Ill 

112 

113 

114 

115 

"       "      H 

116 

117 

118 

119 

120 

121 

..       ,,     2 

123 

124 

125 

126 

127 

128 

APPROXIMATE  WEIGHT  IN  POUNDS  OF  100  SQ.  FT.  OF  2f-INCH 
CORRUGATED  SHEETS. 


Gauge  

No.  28 

No.  27 

No.  26 

84 
99 

No.  24 

111 
127 

No.  22 

138 
154 

No.  20 

No.  18 

No.  16 

Painted  
Galvanized.  .  . 

69 

86 

77 
93 

165 

182 

220 
236 

275 

291 

Aiiti-coiuleiisatioii  Lining. — Wherever  corrugated  steel 
is  laid  on  purlins  with  no  sheathing  or  paper  underneath,  if  the 
building  is  heated,  moisture  will  invariably  collect  on  the  under 
side,  and  if  the  air  in  the  building  is  warm  and  humid,  consider- 
able dripping  will  result.  To  prevent  this  dripping,  it  is  neces- 
sary to  protect  the  under  side  of  the  corrugated  steel  with  paper 
or  felt.  This  may  be  done  by  first  stretching  poultry-netting 
over  the  purlins,  from  eaves  to  ridge,  and  wiring  the  strips 
together  at  the  edges.  Over  this  should  be  laid  one  thickness 
of  asbestos  paper  and  one  or  two  layers  of  saturated  felt.  The 
corrugated  steel  may  then  be  fastened  to  the  purlins  in  the 
usual  way.  The  side  laps  may  be  secured  by  stove-bolts,  with 
1 "  X  -g"  X  4"  plate  washers  on  the  under  side,  to  support  the  lining. 

C or r n gated  Siding1. 

For  siding,  either  the  2J-,  2-,  or  IJ-in.  size  corrugations  are 
used.  The  IJ-in.  size,  however,  makes  the  best  appearance. 
For  the  lap,  one  inch  at  the  bottom  and  one  corrugation  at  the 
sides  is  sufficient. 

For  sheds,  etc.,  the  sheets  may  be  nailed  to  cross-pieces* cut  in 
between  the  studs  horizontally  and  spaced  from  2  to  3  ft.  apart, 
the  studs  being  from  3  to  4  ft.  on  centres.  For  elevators,  either 
cross-corrugated  sheets  or  sheets  not  more  than  3 2  ins.  long  should 
be  used.  The  nails  should  be  driven  in  the  trough  of  each  alter- 


FLOOR  AND  WALL  TILING.  1443 

nate  corrugation  2  ins.  above  the  lower  end  of  the  sheet,  which 
will  be  1  in.  above  the  top  end  of  the  under  sheet.  This  will 
allow  the  sheet  to  slide  1  in.  in  32  ins.  as  the  building  settles 
before  the  nail  will  strike  the  upper  end  of  the  lower  sheet.  The 
side  lap  should  not  be  nailed. 

Ceilings. — For  the  ceilings  of  stores,  stables,  etc.,  %-in.  or 
f-in.  corrugated  sheets  are  much  used;  they  make  an  excellent 
material  for  this  purpose. 

The  cost  of  corrugated  sheets  over  sheathing  is  about  $3.50 
a  square  and  on  steel  purlins  $4  to  $4.50. 

Galvanized  Iron. — This  term  is  commonly  applied  to  ail 
galvanized  sheet  metal,  although  most,  if  not  all,  of  the  galvan- 
ized sheets  of  the  present  day  have  a  steel  base. 

The  best  quality  of  galvanized  iron  bears  the  trade-mark 
"Appollo"  or  "  Apollo  Best  Bloom." 

Galvanized  sheets  come  in  Jerigths  of  6,  7,  and  8  ft.  in  U.  S. 
Gauge  Nos.  14,  16,  18,  20,  22,  24,  26,  27,  28,  and  30,  and  in 
widths  of  24,  26,  28,  30,  and  36  ins.  for  all  gauges  except  No.  30, 
which  is  made  only  in  widths  of  24,  26,  and  28  ins. 

Sheets  of  No.  28  gauge  are  also  made  in  widths  of  32  and 
34  ins.  The  widths  commonly  carried  in  stock  are  24,  28,  and 
30  ins. 

Most  of  the  galvanized  iron  used  for  cornices  and  ornamental 
work  is  No.  27  gauge.  No.  28  is  sometimes  used  for  gutters 
and  conductors. 

Cost. — The  net  price  per  100  Ibs.  of  flat  galvanized  sheets, 
in  car-load  lots  at  Pittsburg,  June,  1904,  is  as  follows:  For  Nos. 
10  to  14,  $2.35;  Nos.  15  and  16,  $2.50;  Nos.  17  to  21,  $2.60; 
Nos.  22  to  24,  $2.75;  Nos.  25  and  26,  $3.00;  No.  27,  $3.25; 
No.  28,  $3.50.  The  retail  price  in  cities  varies  from  3  cts. 
to  4J  cts.  per  lb.,  depending  largely  upon  the  freight  rate. 


FLOOR  AND  WALL,  TILING. 

Tile  floors  are  extensively  used  in  the  better  class  of  build- 
ings, and  particularly  in  those  portions  which  are  used  by  the 
public,  on  account  of  their  great  durability,  sanitary  qualities, 
and  decorative  effects.  As  a  matter  of  fact,  a  good  tile  floor 
is  also  cheaper  in  the  long  run  than  a  wooden  floor  if  it  is  sub- 
ject to  much  wear. 

The  materials  used  for  floors  are  tiles  made  from  different 


1444  FLOOR  AND  WALL  TILING. 

grades  of  clay,  marbles,  slate,  glass,  and  rubber.  Of  these  the 
most  durable  and  sanitary  are  the  vitreous  clay  tile. 

For  walls  and  wainscotings,  glazed  tiles,  marbles,  and  glass 
are  extensively  used. 

Clay  Tiles. — The  several  grades  of  clay  tile  are  known 
under  the  following  terms: 

A.  Floor  Tile. 

1.  Common  Encaustic   Tile. — The   cheapest  grade,   made  of 
naturally  colored  clays — red,  buff,  gray,  chocolate,  and  black. 
This  tile  is  of  a  porous,  absorbing  character  and  is  used  for 
common  floors  of  no  sanitary  requirements. 

2.  Semi-vitreous    Tile. — A    somewhat    better    grade    of    the 
former  article,  having  less  porosity  and  absorption. 

3.  Vitreous  Tile. — The  hardest  tile  known  (cannot  be  scratched 
by  steel  or  sand),  non-absorbent  and  thoroughly  aseptic.     It 
is  principally  in  use  for  floors  requiring  a  perfect  sanitary  con- 
dition;   is  manufactured  in  white,  blue,  gray,  green,  and  pink 
colors  of  great  delicacy. 

4.  "Ceramic"  Tile,  or  Ceramic  Roman  Mosaic. — This  material 
is    made   of  vitreous  clay   in   tesseral   pieces    representing  the 
tesserae  of  the  Roman  mosaic.     It  is  made  in  regular  tile  ranging 
from  J-in.  to  f-in.  squares  and  also  in  hexagonal  shapes  from  f 
in.  to  1  in.  in  size.     A  round  " lozenge"  is  also  manufactured  to 
be  laid  in  tesseral  paving. 

The  material  itself  is  of  great  hardness  and  is  well  suited 
for  work  of  monumental  or  public  character.  The  even  and 
regular  texture  of  the  tesserae  admits  the  adoption  of  damask 
designs  which  have  become  identified  and  associated  with  this 
material.  The  minuteness  of  the  tesserae  admits  great  range 
in  designing  and  can  therefore  follow  each  line  of  architecture. 
The  ceramic  Roman  mosaic  is  much  preferred  to  mosaic  con- 
sisting of  natural  marbles  on  account  of  the  great  variety  in 
colors  and  also  on  account  of  its  greater  durability,  the  vitreous 
clay  tile  being  perfectly  impervious  to  attacks  of  any  acids 
contained  in  the  atmosphere,  while  marble  especially  is  subject 
to  rapid  disintegration  caused  by  the  sulphuric  acid  contained 
in  the  smoke-laden  atmosphere  of  our  cities. 

5.  Florentine  Mosaic  and  Flint  Tile. — This  is  the  largest  and 
heaviest  tile  manufactured  in  this  country.     It  is  either  plain  or 
inlaid  and  is  in  use  especially  in  ecclesiastic  work  on  account  of 
its  relation  to  mediaeval  application.     The  material  is  vitreous 


FLOOR  AND  WALL  TILING.  1445 

annealed  and  is  more  tough  than  brittle.     It  is  also  in  use  for 
exterior  polychrome  work. 

6.  Aseptic  Tile. — A  large  and  heavy  thoroughly  vitreous  tile 
for  institute  work.  It  is  the  only  vitreous  tile  of  large  size  made 
in  this  country.  As  the  tile  is  large  and  generally  of  hexagonal 
shape,  the  joint  space  is  reduced  to  a  minimum,  and  it  is,  there- 
fore, especially  adapted  for  hospitals,  operating-rooms,  and 
contagious  wards  in  public  institutions. 

B.  Enamelled  or  Wall  and  Mantel  Tile. 

1.  White  Wall  Tile. — A  glazed  tile  for  wainscots.     This  tile 
has  a  white  soft  body  and  its  surface  is  covered  with  a  clear 
glaze.     The  brilliancy  of  this  glaze  and  its  reflecting  properties 
makes  the  white  wall  tile  especially  desirable  for  dark  passages. 

2.  Colored  Glaze  or  Enamel  Tile. — This  tile  is  about  the  same 
as  the  former  in  quality;    the  "glaze,"  or  "enamel,"  however, 
is  stained  with  metallic  oxides,  which  produces  a  brilliant  decora- 
tive effect. 

3.  Dull  Satin,  etc.,  Finished  Enamelled   Tile. — A  glazed  tile 
with  a  "dull"  or  "blind"  enamel.     The  dull  finish  is  either  pro- 
duced by  sandblasting  or  devitrifying  enamels.     It  is  princi- 
pally used  for  quaint  decorative  effects  in  mantel  work. 

4.  Glazed  Roman  Mosaic. — The  latest  style  of  enamelled  tiling 
which  has  great  decorative  possibilities.     It  has  the  same  tesseral 
texture  as  the  ceramic  floor  tile  and  finds  ready  application  to 
wainscots  and  mantel  work. 

Clay  tile  are  set  in  Portland-cement  mortar  as  a  rule,  and 
floors  should  always  be  provided  with  a  substantial  concrete. 
A  new  invention  which  has  been  placed  on  the  market  as  "Pli- 
caro"  mosaic  consists  of  the  ceramic  mosaic  laid  on  a  flexible 
base.  With  this  material  wood  floors  can  be  provided  with 
tile  floors,  and  owing  to  the  elasticity  and  lightness  of  the  mate- 
rial, floors  in  elevators,  boats,  and  other  ambulant  structures 
can  be  safely  tiled. 

Marble  Tiles  from  9  to  12  ins.  square  have  been  extensively 
used  for  floors,  principally  on  account  of  their  decorative  effect. 
None  of  the  marbles,  however,  are  as  hard  and  consequently 
as  durable  as  the  vitreous  and  ceramic  tile,  and  from  all  prac- 
tical standpoints  do  not  make  as  good  a  floor. 

When  used,  they  should  be  1|  ins.  thick  and  not  over  12  ins. 
square,  and  should  be  bedded  in  cement  on  a  concrete  base. 
Marbles  should  not  be  used  for  floors  in  hospitals,  as  they  yield 
rapidly  to  the  usual  antiseptic  floor  washes. 


1446  FLOOR  AND  WALL  TILING. 

Slate,  although  non-absorbent  and  not  affected  even  by 
dilute  mineral  acids,  is  too  cold  and  dingy  to  commend  itself  as  a 
floor  tile,  but  because  it  is  conveniently  handled  in  large  slabs 
it  is  valuable  as  a  cheap  base  and  as  a  cover  for  wiring  and 
pipe  trenches  in  the  floor.  As  these  often  follow  a  wall,  it  may 
serve  in  the  capacity  of  a  border  and  as  such  be  extended  around 
the  floor  space.  Slate  slabs  for  floors  should  be  about  1 J  ins. thick. 

Marbleithic  Tile  or  Slabs  are  made  of  small  pieces  or 
chips  of  marbles  of  irregular  shapes,  set  in  a  backing  of  sand  and 
Portland  cement,  and  after  the  cement  has  set,  the  top  surface  is 
rubbed  until  it  becomes  flat  and  smooth.  Marbleithic  resembles 
mosaic  or  Terazzo,  except  that  it  is  laid  in  the  form. of  tiles  in- 
stead of  being  put  down  on  the  floor  in  a  plastic  condition.  Much 
objection  has  been  made  to  Terazzo  because  of  the  cracks  which 
commonly  occur  in  it,  due  to  the  slight  settlements  which  are 
unavoidable  in  a  new  building.  With  tile  floors  of  any  mate- 
rial the  joints  allow  for  any  slight  movement  of  the  floor,  with- 
out producing  visible  cracks.  By  the  process  of  manufacture, 
marbleithic  is  made  much  harder  than  it  is  possible  to  make 
mosaic  floors  that  are  laid  in  a  plastic  condition,  so  that  they 
have  a  much  better  wearing  surface.  Floors  of  this  material 
have  now  (1904)  been  in  use  for  nine  years  and  they  have  been 
found  to  show  but  little  if  any  wear. 

Marbleithic  tiles  are  made  of  various  colored  marbles  and 
in  different  sizes,  shapes,  and  patterns,  so  that  a  great  variety  of 
effects  may  be  produced. 

Sanitary  coved  base,  stair  treads,  and  wainscoting  are  also 
made  of  it. 

Cast  Glass  Tile,  while  quite  resistant  to  a  blow  when  the 
polish  is  unbroken,  will  break  very  easily  when  the  surface  is 
scratched.  All  glass  tile  should,  therefore,  be  very  thick  and 
small  or  protected  by  metal  framing. 

Novns  Sanitary  Glass  *  is  a  sanitary  structural  glass 
manufactured  in  all  thicknesses  from  -|  in.  up  to  2  ins.  and  in  slabs 
of  all  widths  and  lengths  up  to  100  ins.  wide  and  180  ins.  long. 
It  is  made  in  various  colors  and  designs  and  in  the  following 
finishes:  natural  fire  finish,  hone,  semi-polished,  and  polished. 

This  material  can  be  worked  and  handled  the  same  as  marble, 
it  is  readily  drilled  and  shaped  to  accommodate  fixtures,  etc., 
and  is  very  handsome  in  appearance.  It  is  impervious  to 
discoloration  and  is  non-crazing. 

*  Made  by  the  Perm-American  Plate  Glass  Company,  Pittsburg,  Pa. 


FLOOR  AND  WALL  TILING.  1447 

These  qualities  make  it  especially  desirable  for  floors,  wain- 
scoting, tables,  shelves,  etc.,  in  all  places  where  an  absolute 
sanitary  condition  is  desired,  combined  with  a  handsome 
appearance. 

Interlocking  Rubber  Tiling. 

Several  years  ago  the  New  York  Belting  and  Packing  Company 
introduced  an  interlocking  rubber  tile,  which,  because  of  its  being 
noiseless,  non-slippery,  and  more  comfortable  to  the  feet  than 
inelastic  substances,  has  met  with  great  favor  for  floors  in  bank- 
ing-rooms, counting-rooms,  vestibules,  elevators,  stairs,  cafes, 
libraries,  churches,  etc.  For  elevators  it  is  the  most  durable 
and  practical  floor  that  can  be  laid;  it  is  also  especially  and 
peculiarly  adapted  for  floors  of  yachts  and  steamships.  The 
interlocking  feature  unites  the  tiles  into  a  smooth,  unbroken 
sheet  of  rubber,  unlimited  in  area.  The  tiles  do  not  pull  apart 
or  come  up,  and  each  being  distinct,  almost  any  color  scheme 
can  be  secured,  the  tiles  being  made  in  a  carefully  selected 
variety  of  colors.  The  tiles  are  laid  directly  over  the  original 
floor,  like  a  carpet  (except  that  they  are  not  fastened).  Expe- 
rience has  shown  that  they  are  very  durable. 

Each  tile  is  2f  ins.  square  and  f  in.  thick;  25.5  tiles  are 
required  to  the  square  foot.  Rubber  nosing  for  stairs  is  made 
to  interlock  with  the  tile. 

Cost  of  Different  Tiles. 

The  following  prices  are  approximately  the  cost  (to  the  trade) 
at  the  factory  at  the  present  time  (1904).  To  this  should  be 
added  freight  and  the  dealers'  profit.  The  cost  of  laying  the  tiles 
on  a  cement  base  (in  addition  to  the  cost  of  the  tiles)  should  not 
exceed  25  cents  per  square  foot. 

FLOOR  TILES. 

Factory  Price 
per  Sq.  Ft 

Common  encaustic  tile,  unglazed 15     cts. 

Vitreous  tile :  white 22Vio 

Colors  (large  sizes) from  23  to  26       '  * 

"Ceramic"  tile,  or  ceramic  Roman  mosaic,  from  20  to  35      " 
WALL  AND  MANTEL  TILE. 

Factory  Price 
per  Sq.  Ft. 

White  glazed  wall  tile 25     cts. 

Colored  glaze  or  enamel  tile 30 

Enamel  tile,  dull  satin  finish 40 

Marbleithic  costs  from  45  cts.  per  sq.  ft.,  upwards,  laid. 


1448  ASPHALTUM. 


ASPHALTUM. 

"Bitumen.  Asphaltum,  Asphalt. — Bitumen  is  the  name  used  to 
denote  a  group  of  mineral  substances,  composed  of  different 
hydrocarbons,  found  widely  diffused  throughout  the  world  in  a 
variety  of  forms  which  grade  from  thin  volatile  liquids  to  thick 
semi-fluids  and  solids,  sometimes  in  a  free  or  pure  state,  but 
more  frequently  intermixed  with  or  saturating  different  kinds 
of  inorganic  or  organic  matter. 

"To  designate  the  condition  under  which  bitumen  is  found, 
different  names  are  employed;  thus  the  liquid  varieties  are 
known  as  naphtha  and  petroleum,  the  semi-fluid  or  viscous  as 
maltha  or  mineral  tar,  and  the  solid  or  compact  as  asphalt  um 
or  asphalt."* 

Asphalt u ill  is  found  in  extensive  beds  or  lake-like  deposits 
on  both  continents ;  the  most  notable  of  these  are  the  pitch  lakes 
on  the  island  of  Trinidad,  and  at  Bermundez,  Venezuela. 

It  is  also  found  saturating  the  limestone  and  sandstone 
formations  in  certain  localities. 

Deposits  of  very  nearly  pure  asphaltum  are  found  in  Utah, 
Mexico,  Cuba,  and  various  parts  of  the  United  States. 

Elaterite,  gilsonite,  and  wurtzilite  are  varieties  of  very  nearly 
pure  asphaltum. 

Asphaltic  roofing  materials  are  manufactured  principally 
from  Trinidad  asphalt.  These  deposits  have  also  been  the 
main  source  of  supply  for  the  asphaltum  used  in  street-paving 
in  the  United  States. 

The  term  rock  asphalt  is  commonly  used  to  designate  the 
material  obtained  from  the  bituminous  limestone  deposits  at 
Seyssel  and  Pyrimoiit,  in  the  valley  of  the  Rhone,  France,  and 
in  the  Val-de-Travers,  canton  of  Neuchatel,  Switzerland,  and 
at  Ragusa,  on  the  island  of  Sicily.  It  is  extensively  employed 
for  paving  purposes  throughout  Europe,  and  is  considered 
to  make  a  much  more  durable  pavement  than  can  be  made 
with  asphaltum. 

Rock  asphalt  is  prepared  for  shipment  in  two  forms:  (a)  com- 
pressed asphalt  blocks,  which  are  used  for  paving  in  much  the 
same  way  as  stone  blocks,  and  (6)  mastic  asphalt,  which  is  put 
up  in  cakes  of  varying  shape,  generally  bearing  the  manu- 
facturer's trade-mark. 


*  Byrne,  Inspectors'  Pocket  Book. 


ROCK  ASPHALT.  1449 

In  the  Eastern  States  mastic  asphalt  is  used  for  floors  of 
cellars,  stores,  breweries,  malt-houses,  hotel  kitchens,  stables, 
laundries,  conservatories,  public  buildings,  carriage-factories 
sugar-refineries,  mills,  rinks,  etc.,  and  for  any  place  where  a 
hard,  smooth,  clean,  dry,  fire-  and  water-proof,  odorless,  and 
durable  covering  of  a  light  color  is  required,  either  in  basement 
or  upper  stories.  It  can  be  laid  either  over  cement  concrete, 
brick,  or  wood  in  one  sheet  without  seams;  also  over  cement 
concrete  for  roofs  for  fire  proof  buildings.  For  dwelling-house 
cellars,  especially  on  moist  or  filled  land,  this  material  is  especially 
adapted,  being  water-tight,  non-absorbent,  free  from  mould  or 
dust,  impervious  to  sewer-gases,  and  for  sanitary  purposes 
invaluable. 

Mastic  asphalt  is  also  valuable  for  damp  courses  over  founda- 
tions, and  for  covering  vaults  and  arches  under  ground. 

For  floors  of  cellars,  courtyards,  etc.,  laid  on  the  ground,  a 
base  of  cement  concrete  3  ins.  thick  should  first  be  laid ;  and  over 
this  a  layer  of  asphalt  from  }  in.  to  1J-  ins.  thick,  according 
to  the  use  to  which  it  is  to  be  put.  For  ordinary  cellar  floors, 
the  asphalt  need  not  be  more  than  f  in.  thick ;  for  yards  on  which 
heavy  teams  are  to  drive,  it  should  be  1^  ins.  thick.  In  specify- 
ing asphalt  pavement,  both  the  thickness  of  the  concrete  and  of 
the  asphalt  should  be  given;  it  should  also  be  remembered 
that  "asphalt  pavement"  does  not  include  the  concrete  founda- 
tion unless  so  specified. 

In  laying  asphalt  over  plank  or  boards,  a  layer  of  stout,  dry 
(not  tarred)  sheathing-paper  should  first  be  put  down  and  the 
asphalt  laid  on  this.  Asphalt  floors  for  stables  should  be  at  least 
1  in.  thick.  The  cost  of  rock  asphalt  in  the  large  cities  varies 
from  12  to  17  cents  per  square  foot  in  jobs  of  2,000  feet  and  over; 
this  does  not  include  the  concrete  foundation.  German  and 
other  cheap  asphalts  are  laid  for  somewhat  less,  while  imitation 
rock  asphalts  are  furnished  for  considerably  less. 

Architects  and  owners  desiring  to  employ  rock  asphalt  for  any 
of  the  above  purposes  should  be  careful  to  secure  the  genuine 
Val-de-Travers  or  Seyssel  or  Sicilian  rock  asphalt,  as  there  are 
imitations  which  are  of  but  little  value. 

The  bituminous  sandstones  of  California  have  been  exten- 
sively used  for  paving  streets  in  Western  cities.  They  are  pre- 
pared for  use  as  a  paving  material  by  crushing  to  powder.  With 
this  powder  a  considerable  proportion  of  sand  or  gravel  is  gen- 
erally mixed  and  the  mixture  is  then  heated  until  it  becomes 


1450  MINERAL  WOOL. 

plastic  and  then  spread  upon  the  street  and  compressed  by  roll- 
ing. 


MINERAL  WOOL.* 

There  are  at  least  two  kinds  of  mineral  wool  made  in  this 
country.  The  more  common  kind  is  made  by  converting  the 
slag  f  of  blast-furnaces,  mixed  with  certain  rocks  while  in  a 
melted  condition,  to  a  fibrous  state. 

Its  appearance  is  much  like  that  of  wool,  being  soft  and  fibrous, 
but  in  no  other  respect  are  the  materials  alike.  Mineral  wool 
made  from  slag  appears  in  a  variety  of  colors,  principally  white, 
but  often  yellow  or  gray  and  occasionally  quite  dark.  The 
color,  however,  is  said  to  be  no  indication  of  the  quality,  as  all 
of  the  peculiar  properties  of  the  material  are  present  in  equal 
proportions  in  any  of  the  shades.  The  other  kind  of  mineral 
wool  is  known  as  rock  wool,  and  is  made  from  granite  rock  raised 
to  3,000  degrees  of  temperature.  It  is  claimed  to  be  absolutely 
free  from  sulphur  and  the  only  odorless  wool  manufactured;  it 
has  been  approved  by  the  U.  S.  War  Department.  Its  color  is 
white  and  its  general  apparance  is  the  same  as  that  made  from 
slag.  The  peculiar  nature  of  both  kinds  is  that  of  a  mass  of 
very  fine,  pliant,  but  inelastic,  vitreous  fibres  interlacing  each 
other  in  every  direction  and  forming  an  innumerable  number 
of  minute  air-cells.  Its  great  value  in  the  insulation  and  pro- 
tection of  buildings  lies  in  the  number  of  air-cells  which  it  con- 
tains, combined  with  its  resistance  to  heat  or  fire.  In  common 
slag  wool  92  per  cent,  of  the  volume  consists  of  air  held  in  minute 
cells,  while  in  the  best  grade  the  proportion  of  air  reaches  as  high 
as  96  per  cent.  This  confined  air  makes  it  one  of  the  best,  if 
not  the  best,  of  the  non-conductors  of  heat,  and  to  a  less  degree  of 
sound.  Aside  from  these  qualities  it  is  very  durable,  contains 
nothing  that  can  decay  or  become  musty,  and  is  almost  a  sure 
protection  against  rats  and  vermin. 

Ordinary  mineral  wool  weighs  about  12  pounds  per  cubic  foot, 
and  is  put  up  in  bags  containing  from  40  to  60  pounds  in  each 
bag.  It  costs  at  the  works,  in  Stanhope,  N.  J.,  1  cent  per  pound, 
and  at  the  store  in  New  York  City  1 J  cents  per  pound. 

*  For  the  uses  of  mineral  wool  in  building  construction  see  Part  II,  Build- 
ing Construction  and  Superintendence,  p.  208. 

t  The  b,est  being  from  slag  that  does  not  contain  iron. 


ESTIMATING  COST  OF  STRUCTURAL  STEEL.   1451 

Extra  mineral  wool  weighs  about  9  pounds  per  cubic  foot,  and 
is  put  up  in  bags  containing  from  20  to  30  Ibs.  in  each  bag.  It 
costs  at  the  works  4  cents  per  pound,  and  at  the  store,  New 
York  City,  4J  cents  per  pound. 

In  estimating  the  quantity  of  wool  required  for  filling,  1  pound 
per  square  foot  should  be  allowed  for  each  inch  in  thickness  for 
ordinary  wool  and  f  pound  for  selected  wool. 

ESTIMATING  THE    COST   OF    STRUCTURAL    STEEL 
FOR   BUILDINGS. 

Structural  steel  for  buildings  is  commonly  made  up  of  I  beams, 
channels,  angles,  Z  bars,  and  plates,  which  may  be  used  as 
single  beams  or  braces,  or  built  into  riveted  girders,  columns, 
or  trusses.  The  cost  of  the  completed  steel  work  is  made  up 
of  the  following  items: 

(1)  Cost  of  the  plain  steel  at  the  mill,  plus  freight  and  dealers' 
profit. 

(2)  Extras  for  cutting,  punching,  fitting,  and  assembling  into 
girders,  columns,  or  trusses. 

(3)  Cost    of    the  fittings,  such  as  connection  angles,  gusset 
plates,  etc 

(4)  Shop  painting. 

(5)  Cost  of  erection  at  the  building. 

(6)  Painting  after  erection. 

Base  Price  of  Steel.— For  orders  of  any  considerable  size, 
the  cost  of  plain  steel  is  based  on  the  price  at  Pittsburg,  plus 
the  freight  to  the  point  of  delivery. 

The  base  price  at  Pittsburg  at  the  present  time  (July,  1904) 
is  SI. 60  per  100  Ibs.  for  beams  and  channels  15  ins.  and  less, 
and  for  angles  and  Z's,  3  to  6  ins. 

Beams  and  channels  over  15  ins.  cost  10  cts.  per  100  Ibs. 
extra,  and  T's  over  3  ins.,  5  cts.  extra. 

For  angles,  channels,  and  T's  under  3  ins.  the  base  is  $1.90 
from  Chicago  stock  (see  page  1456). 

For  plates  J  in.  thick  and  over  the  base  is  $1.60  per  100  Ibs. 
For  plates  %  in.  thick,  add  10  cts.  per  100  Ibs. 

Freight  Rates  at  present  are :  Pittsburg  to  Chicago,  16J  cts. 
per  100  Ibs.;  to  St.  Louis,  22  cts.;  to  New  York,  14J  cts.;  to 
Kansas  City,  42J  cts. ;  to  Denver,  92J  cts. ;  and  to  San  Francisco, 
85  cts. 

For  Pacific  coast  points,  a  discount  of  about  18  per  cent,  is 


1452     ESTIMATING  COST  OF  STRUCTURAL  STEEL. 

made  from  the  base,  at  Pittsburg,  on  account  of  the  high  freight, 
and  to  meet  European  competition.  On  account  of  the  ex- 
pense of  carrying  beams  in  stock,  local  dealers  usually  charge 
from  \  to  1  ct.  a  pound  extra  on  orders  supplied  from  stock. 

List  of  Extras  to  be  Added  to  Price  of  Plain 
Beams  and  Channels. —  If  any  kind  of  work  whatever  is 
done  on  the  plain  steel,  or  if  the  same  is  cut  to  length  with  a 
less  variation  than  f  in.,  an  extra  price  is  charged,  which  is 
based  on  the  following  list,  adopted  in  1902,  and  still  in  force. 
These  charges  are  common  to  all  shops  if  the  order  is  of  any 
size,  and  are  not  likely  to  be  changed  for  some  time. 

In  Effect  July  1,  1904. 

EXTRAS  TO  BE  ADDED  TO  BASE  PRICE  FOR  EACH  100  LBS. 

1.  For  cutting  to  length  with  less  variation  than  plus 

or  minus  f  in 15  cts. 

2.  Plain  punching  one  size  hole  in  web  only 15     " 

3.  Plain  punching  one  size  hole  in  one  or  both  flanges..  15      " 

4.  Plain  punching  one  size  hole  in  either  web  and  one 

flange  or  web  and  both  flanges 25    " 

5.  Plain  punching  each  additional  size  hole  in  eith^- 

web  or  flanges,  web  and  one  flange,  or  web  and 

both  flanges 15    ' ' 

6.  Plain  punching  one  size  hole  in  flange  and  another 

size  hole  in  web  of  the  same  beam  or  channel 40    * 

7.  Punching  and  assembling  into  girders 35     " 

8.  Coping,  ordinary  bevelling,  including  cutting  to  exact 

length,  with  or  without  punching;   including  the 
riveting  or  bolting  of  standard  connection  angles  .  .   35    ' 

9.  For  painting  or  oiling,  one  coat,  with  ordinary  oil 

or  paint . .    10    ' 

10.  Cambering,  beams  and  channels,  and  other  shapes 

for  ships  or  other  purposes 25    ' 

11.  Bending,  or  otb^r  unusual  work Shop  rates 

12.  For  fittings,  whether  loose  or  attached,  such  as  angle 

connections,  bolts,  and  separators,  tie-rods,  etc. . .     $1 . 55 

Tie-rods  in  all  cases,  where  estimated  upon  in  connection  with 
beams  or  channels,  to  be  classified  as  fittings. 

In  making  an  estimate  of  the  steel  work  from  the  framing 
plans,  the  weight  of  all  connection  angles,  gusset  plates,  sepa- 
rators, tie-rods,  etc.,  must  be  taken  off  separately,  and  the  cost 
figured  at  $1.55  per  100  Ibs,  above  the  base  price. 


ESTIMATING  COST  OF  STRUCTURAL  STEEL.     1453 

The  weights  of  standard  connections  are  given  on  pages  548 
and  549,  and  of  standard  separators  on  page  544. 

In  estimating  cost  of  riveted  columns  and  girders,  the  weight 
of  the  plain  bars  and  plates  of  which  the  column  or  girder  is  com- 
posed may  be  taken,  and  an  extra  added  to  the  price  per  pound 
to  cover  cost  of  rivets  and  assembling. 

This  extra  will  be  about  as  follows: 

Light  channel  or  Z-bar  columns 1 J   cts.  per  Ib. 

Heavy  channel  or  Z-bar  columns 1}     "     "    " 

Plate  girders,  24  to  48  ins.  deep .  .   1J     "      "    " 

Box  girders,  24  to  48  ins.  deep 1£     "     "    " 

Box  girders,  48  to  60  ins.  deep 1T\>   "     "    " 

Cost  of  Erecting1. — For  erecting  ordinary  beams  and  col- 
umns in  buildings  having  masonry  walls  the  cost  of  erection 
should  not  exceed  $10  per  ton  with  bolted  connections,  and 
will  sometimes  be  as  low  as  $6  per  ton. 

For  erecting  the  steel  work  of  skeleton  buildings  having 
riveted  connections,  it  is  common  to  allow  $10  per  ton. 

Cost  of  Painting'. — The  common  charge  for  shop  painting 
is  $1  per  ton,  but  if  done  in  accordance  with  the  specification 
on  page  1413  it  would  exceed  this  amount. 

For  painting  one  additional  coat  after  erection,  allow  $2  per 
ton. 

Roof-trusses. — In  lots  of  at  least  six,  the  shop  cost  of  ordi- 
nary roof-trusses  in  which  the  ends  of  the  members  are  cut  off 
at  right  angles  was  about  as  follows  in  1902:*  Trusses  weighing 
1,000  Ibs.  each,  $1.15  to  $1.25  per  100  Ibs.;  trusses  weighing 
1,500  Ibs.  each,  $0.90  to  $1.00  per  100  Ibs.;  trusses  weighing 
2,500  Ibs.  each,  $0.75  to  $0.85  per  100  Ibs. ;  and  trusses  weighing 
3,500  to  7,500  Ibs.,  $0.60  to  $0.75  per  100  Ibs.  Pin-connected 
trusses  cost  from  10  to  20  cts.  per  100  Ibs.  more  than  riveted 
trusses.  (M.  S.  Ketchum,  C.E.  in  Steel-Mill  Buildings.) 

Steel-mill  Buildings. — The  average  shop  cost  for  the 
frame  of  steel-mill  buildings,  including  draughting  is  about  $25.00 
per  ton,  and  the  cost  of  erection  from  $15.00  oc  $25.00  per  ton. 

(A  great  amount  of  data  pertaining  to  the  cost  of  steel-mill 
buildings  is  given  by  Mr.  Ketchum  in  the  book  above  men- 
tioned.) 

*  Under  present  conditions,  July  1,  1904,  those  figures  should  be  increased 
•5  per  cent. 


1454    ESTIMATING  COST  OF  STRUCTURAL  STEEL. 

Cost  of  Drafting. — Details  for  church  and  court-house 
roofs  having  hips  and  valleys  cost  from  $6.00  to  $8.00  per  ton; 
details  for  ordinary  mill  buildings  cost  from  $2.00  to  $4.00  per 
ton.  The  details  for  all  work  fabricated  by  the  Gillete-Herzog 
Mfg.  Co.,  with  the  exception  of  plain  beams  and  complicated 
tank-work,  were  made  in  1896  by  contract,  by  Mr.  H.  A.  Fitch, 
now  structural  engineer  for  the  Minneapolis  Steel  and  Machinery 
Co.,  Minneapolis,  for  $2.60  per  ton.  This  price  netted  the  con- 
tractor a  fair  profit.* 

Approximate  Estimates  of  tlie  Weight  of  Steel 
in  Building's.— According  to  H.  G.  Tyrrell,  C.E.,t  the  weight 
of  steel  in  any  proposed  new  building  may  be  roughly  estimated 
by  the  following  data,  which  is  a  fair  average  for  buildings  not 
over  eleven  stories  high,  designed  according  to  the  Building 
Laws  of  the  City  of  Boston : 

Per  Sq.  Ft. 
of  Floor. 

Apartment  houses  and  hotels,  with  outside  frame 14  Ibs. 

Apartment  houses  without  outside  frame 9     " 

Office  buildings,  with  outside  frame 23     ' ' 

Office  buildings,  without  outside  frame 15     " 

Warehouses,  with  outside  frame 28     ' 

Warehouses,  without  outside  frame 18     ' 

For  buildings  higher  than  eleven  stories,  the  weight  of  floors 
will  increase  in  direct  proportion  to  the  number  of  stories,  while 
the  weight  of  columns  will  increase  more  rapidly. 

For  the  approximate  weight  of  roof-trusses,  see  pages  947 
and  949. 

Cost  of  Merchant  Steel. — The  cost  of  merchant  iron  and 
steel  of  all  kinds  is  based  on  a  certain  size  of  each  particular 
shape,  which  is  taken  as  the  "base,"  and  the  price  of  all  other 
sizes  is  figured  at  a  certain  extra  above  the  base.  The  base 
price  may  fluctuate  and  be  changed  without  notice,  but  the 
extras  remain  constant,  and  are  the  same  in  all  localities.  Fol- 
lowing is  the 

*  M.  S.  Ketchura. 

t  Estimating  Structural  Steel,  in  Architects  &  Builders'  Magazine,  Jan., 
1903. 


ESTIMATING  COST  OF  STRUCTURAL  STEEL.     1455 


STANDARD  STEEL  CLASSIFICATION 

In  Effect  July  1,  1904. 
ROUNDS  AND  SQUARES. 


Extra  per 
100  Ibs. 

|       to  3     ins  Base 

3/ie  to  3i  ins 

Extra  per 
100  Ibs. 

0   15 

f       to  %  in.  .        .          $0  10 

3/^6  to  4     ins 

0  25 

i       to  %  in  0.20 

4/^5  to  4i  ins  .  . 

0  30 

%                  in  •  0.40 

4%  to  5     ins.  .  . 

0  40 

1                   in   0  .  50 

5|     to  5^  ins.  .  . 
5tj-     to  6     iris 

0.50 
0  75 

%                 in                       0  60 

I     and  3^  in                  .     0  .  70 

6-j-     to  6i  ins 

1  00 

^                 in  1.00 

6f     to  7J  ins.  .  . 

1  25 

%                 in  2.00 
FLAT  BARS  AND 
1     to  6    ins.  X     I    to     1    in.  . 

HEAVY  BANDS. 

Base 

1     to   6    ins  X    i  and  %  in.  . 

$0  20  extra 

per  100  Ibs. 

i  i      i  i      (i 

i  i           (  C           (  ( 
I          (  C           (  ( 
C              (           i  I 

I          <        1  1 

(         I       (  ( 

C              {           (  ( 

(          (       (  ( 
I          i        (  ( 
e        (  (        it 
i        1  1        1  1 
it        1  1        K 

per  100  Ibs. 

i      ii      ii 

i      1  1      1  1 
i      1  1      1  1 
i      1  1      1  1 
i      1  1      1  1 
i      ii      ii 
t      1  1      1  1 
t       in 

c          c        i; 
(          (        if 
ii          i        ii 
<  i         i        f  i 

t  C            t          ll 

1  1        I       1  1 
ll        t       ft 

%  to   %  in    X    ?    to     f     in.  . 

0.40      " 

%  to   %  in    X    i  and  %&  in.  . 

0  50     " 

%  and  |    in    X    f    to     i    in.  . 

0  50     '  ' 

%and£    in.   X    t  and  %  in.  . 
i                 in    X    i  and  %  in.  . 

0.70       ' 
0  90       ' 

in.   X    1  and  %  in.  . 

1.10       ' 

T^               in    X    3                  in.  . 

1  00       ' 

J^               in    X    T  and  /fe  in 

1  20       ' 

in    X    T  and  /{g    in.  . 

1  50       < 

1J   to   6    ins.X  1/ie  to    1%  ins. 
l|-  to   6    ins  X  IT    to     1^  ins.  . 

0  10       ' 

...      .   0  20       ' 

If  to  6    ins  X  If    to    2}  ins 

0  30       ' 

3^  to  6    ins  X  3     to    4      ins  . 

.    0  40        ' 

LIGHT  BARS  AND  BANDS. 

li  to  6      in.  XNos.  7,  8,  9  and  %  in.  .  .$0.40  extra 
l|  to  6      in.  XNos.  10,  11,  12  and  J  in.  .  0.60      rt 
1     to   1%  in.  XNos.  7,  8,  9  and  %>  in.  .  .   0.50      " 
1     to   1%  in.  XNos.  10,  11,  12  arid  \  in..  0.70     " 
%  to     %  in.  X  Nos.  /  ,  8,  9  and  %  in.  .  .   0  .  70     " 
%  to     %  in.  XNos.  10,  11,  12  and  J  in.  0.80     " 
%  and    f    in.  X  Nos.  7,8,9  and  %  in.  .  .    1  .  00     '  < 
%,and    I    in.  X  Nos.  10,  11,12,  and  i  in..   1.20     " 
%and    |    in.  XNos.  7,8,  9  and  %  in.  .  .    1.20      " 
%and    |    in.  XNos.  10,  11,  12  and  i  in.  .   1.30      " 
i                  in.  X  Nos.  7,  8,  9  and  %  in.  ..   1.30     " 
I                   in.  XNos.  10,  11,  12  and  -|  in..   1.50      " 
%                in.  X  Nos.  7,  8,  9  and  %  in.  ..    1.80     " 
J{£                 in.  XNos.  10,  11.  12  and  i  in..  2.10      ll 
f                  in.  X  Nos.  7,8,  9  and  %  in.  ..    1.90     " 
in.  X  Nos.  10,  11,  12  and  J  in..  2.40     " 

1456     ESTIMATING  COST  OF  STRUCTURAL  STEEL. 

For  intermediate  sizes,  the  next  higher  extra  to  be  charged  in 
all  cases. 

ANGLES. 

1J  X%Q  ins.  and  heavier,  but  under  3  ins Base 

1  to  liX/ie  ins.  and  heavier $0. 10  extra  per  100  Ibs. 

8  X  /fg  in 0 . 20 

.3.  v  $/  in  n  QH 

4  /\  /J6  HI U  .  OU 

f  X  |  in 2 . 00 

|X  J  in 3.00 

3  X  3  ins.  Xless  than  i  in.  thick 0.50 

Angles  }  in.  and  larger,  but  smaller  than 

3  ins.    %  in.  thick 0. 10  per  100  Ibs  over  %  in. 

CHANNELS. 

1  JX/ie  ins.  and  heavier,  but  under  3  ins Base 

1  to  IjXj^j  ins.  and  heavier $0. 10  extra  per  100  Ibs. 

iXjfein 0.20     "       "     "      " 

fand|X%in 0.30     "       «     "      " 

fXiin 0.60      "       "      "      " 

|xl  in.  and  thicker 1.00     "       "     "      " 

Channels  f  in.  and  wider,  but  under  3  ins. , 

£  in.  thick 0.10  per  100  Ibs.  over  %  in. 

TEES. 

1  i  X  %  ins.  and  heavier,  but  under  3  ins Base 

IJXJi  ms-  and  heavier $0. 10  extra  per  100  Ibs. 

1  to  1J  X  %  ins.  and  heavier 0  . 20      ' '       "     "      " 

in.  and  thicker 0.50      "       "      "      " 

in.  and  thicker 0.60     "       "     "      " 

in.  and  thicker 2.00     "       "      "      " 

Tees  1  in.  and  larger,  but  smaller  than  3 

ins.,  J  in.  thick 0 . 10  cts.  per  100  Ibs.  over  %  in. 

For  intermediate  sizes,  the  next  higher  extra  to  be  charged  in 
all  cases. 

The  base  for  all  of  the  above,  from  stock  in  Chicago,  on  full 
car-load  lots,  is  $1.90  (July  1,  1904).  For  other  principal  points^ 
the  base  may  be  obtained  by  adding  the  freight  rates  given  on 
page  1451. 

Example. — What  is  the  probable  cost  at  Kansas  City  of 
11"  X  i"  flat  steel  bars.  Ans.  Base  =  $1.90  per  100  Ibs. 

Extra    =    0.20    "      "      " 
Freight  =   0.42J  "      "      " 

Total     -  $2.52|  per  100  Ibs. 

or  about  2J  cts.  a  pound  in  car-load  lots.    For  small  lots,  about 
3  cts.  per  pound  might  be  charged. 


COST  OP  BUILDINGS  PER  CUBIC  FOOT.     1457 


COST  OF   BUILDINGS  PER   CUBIC   FOOT. 

The  most  accurate  method  of  estimating  the  cost  of  any  pro- 
posed building,  before  the  plans  and  specifications  are  sufficiently 
complete  for  taking  off  the  actual  quantities,  is  by  means  of  the 
cubic  contents. 

Two  buildings  built  in  the  same  style,  and  for  the  same  pur- 
pose, of  the  same  materials,  and  on  the  same  scale  of  wages  and 
and  prices  of  materials,  should  cost  the  same,  or  very  nearly  the 
same,  per  cubic  foot,  although  one  building  be  somewhat  larger 
than  the  other  and  of  different  shape. 

It  therefore  follows  that  if  we  know  the  cost  per  cubic  foot  of 
different  classes  of  buildings,  in  different  localities,  we  can  ap- 
proximate quite  closely  the  cost  of  any  proposed  building  by 
multiplying  its  cubic  contents  in  feet  by  the  known  cost  per  cubic 
foot  of  a  similar  building  already  built  in  that  locality. 

Conversely,  if  the  cost  of  a  proposed  building  must  be  kept 
absolutely  within  a  certain  sum,  the  size  of  the  building  should 
be  proportioned  so  that  the  cubic  contents  shall  not  exceed  the 
quotient  obtained  by  dividing  the  amount  appropriated  by  the 
average  cost  per  cubic  foot  of  similar  buildings.  Even  then  it 
may  be  found,  when  the  bids  are  opened,  that  they  exceed  the 
appropriation,  but  the  excess  will  probably  not  be  so  great  but 
that  the  necessary  reductions  can  be  made  without  altering  the 
main  features  of  the  building. 

In  estimating  the  cost  by  the  cubic  contents,  it  is  of  course 
necessary  that  the  contents  be  computed  on  the  same  basis,  in 
both  the  proposed  building  and  the  one  already  built.  In  the 
following  examples,  the  cubic  contents  are  computed  from  the 
basement  or  cellar  floor,  to  the  average  height  of  a  flat  roof,  or, 
if  a  pitch  roof,  the  finished  portion  of  the  attic  is  included,  or 
that  part  which  might  be  finished,  but  mere  air-spaces  and  open 
porches  are  not  included.  Vaults  and  areas  under  sidewalks, 
etc. ,  are  included  as  part  of  the  basement.  All  measurements  are 
to  the  outside  of  the  walls  and  foundations.  Cost  does  not,  as  a 
rule,  include  the  architect's  fee.  A  few  of  the  examples,  that 
were  not  compiled  by  the  author,  may  not  be  computed  closely 
by  the  above  rule,  but  it  is  to  be  presumed  that  they  are. 

It  should  be  remembered  in  using  this  table,  that  wages  and 
building  materials  were  considerablv  higher  during  the  years 
1901—1903  than  in  the  years  from  1893—98,  thereby  increasing 
the  cost  per  cubic  foot  from  14  to  22  per  cent. ;  also  that  the  cost 


1458    COST  OF  BUILDINGS  PER  CUBIC  FOOT. 

i 

of  first-class  fire-proof  buildings  is  greater  in  the  Western  and 
Southern  States  than  in  the  Eastern  States,  because  of  the  dis- 
tance from  the  great  steel  and  material  centres. 

TABLE  FOR  ESTIMATING  THE  APPROXIMATE  COST  OF 
A  NEW  BUILDING,  OR  THE  VALUE  OF  AN  EXISTING 
BUILDING. 

(Based  on  prices  for  labor  and  materials  as  they  were  in  1902.) 
FARM  AND  COUNTRY  PROPERTY.* 

Dwellings,  frame :  Small  box  house,  no  cornice 4 

Dwellings,  frame:   Shingle  roof,  small  cornice,  no  sash 

weights,  plain 5  to  6 

Dwellings,  brick :   Same  class 7  to  8 

Dwellings,   frame:    Shingle  roof,   good   cornice,   sash 

weights,  blinds  (good  house) 7  to  8 

Dwellings,  brick:  Same  class  (good  house) 9  to  10 

Barns,  frame:  Shingle  roof,  not  painted,  plain  finish.  .    1^  to  2J 

Barns,  frame:  Shingle  roof,  painted,  good  foundation.   2^  to  3 

Stores,  frame:  Shingle  roof,  painted,  plain  finish 5  to  7 

Stores,  brick:  Shingle  roof,  painted,  good  cornice,  well 

finished 7  to  9 

Ordinary  wood  churches  and  schoolhouses :   country .  .      5  to  7 

Brick  churches  and  schoolhouses:  country 8  to  10 

If  slate  or  metal  roof,  add  J  ct.  per  ft.  to  above. 

CITY  AND  VILLAGE  PROPERTY.* 
Dwellings,  frame:   Shingle  roof,  pine  floors  and  finish, 

no  bathroom  or  furnace,  plain  finish  (good  house) .      6  to    7 

Dwellings,  brick:  Same  class 8  to    9 

Dwellings,  frame:  Shingle  roof,  hard-wood  floor  in  hall 

and  parlor,  bath,  furnace,  and  fair  plumbing 8  to    9 

Dwellings,  brick:  Same  class 8  to  10 

Dwellings,  frame:  Shingle  roof,  hard  wood  in  first  floor, 
good  plumbing,  furnace,  artistic  design,  some  inte- 
rior ornamentation,  well  painted 10  to  12 

Dwelling  brick:  With  good  plumbing,  bath,  hot  and 
cold  water,  pine  finish,  well  painted,  no  hard-wood 
finish 11  to  12 

MISCELLANEOUS  BUILDINGS.! 

Abattoirs  and  other  slaughter-houses 14  to  16 

Asylums — lunatic — per  cubic  foot,  complete,  including  patients' 
wards,  administrative  buildings,  chapel,  hospital,  mortuary, 
laundry,  workshops,  and  all  other  accessories,  16  to  25  cts., 
or  from  $1,350  to  $1,600  per  patient. 

*  These  figures  were  compiled  by  James  N.  Brown  of  St.  Louis,  Mo.,  and 
form  part  of  instructions  furnished  by  insurance  companies  to  their  ad- 
justers. 

t  The  following  data  is  from  an  article  by  Fred  T.  Hodgson  in  the  Archi- 
tects and  Builders'  Magazine,  May,  19J2. 


COST  OF   BUILDINGS  PER  CUBIC   FOOT.     1459 

Bath-houses,  complete,  or  for  barracks,  but  not  supplied  with 
hot  water,  per  cubic  foot,  45  to  50  cts.,  or  per  bath,  $280  to 
$320. 

Baths,  public,  comprising  swimming-baths,  slipper-baths,  laun- 
dry, caretaker's  quarters,  machinery,  etc.,  complete,  per  cubic 
foot,  30  to  36  cts. 

Breweries,  complete,  including  buildings,  cellarage,  boilers,  en- 
gine, machinery,  coppers,  liquor-baths,  mash-tubs,  coolers, 
refrigerator,  ice  storage,  pumps,  and  all  other  requirements, 
per  cubic  foot,  14  to  20  cts. 

Churches,  plain,  per  cubic  foot,  from 16  to  22  cts. 

Per  square  foot,  from $4.50  to  $6.50 

Per  sitting,  from $40  to  $55 

Churches,  ornamental,  per  cubic  foot,  from 22  to  39  cts. 

Per  square  foot,  from $7.00  to  $12.50 

Per  sitting,  from $65  to  $120 

Cotton  mills,  as  generally  constructed: 

Per  cubic  foot 9  to  12  cts. 

Per  spindle 22  to  30  cts. 

Cow-stables,  complete,  with  iron  finishings  and  fittings: 

Per  cubic  foot 14  to  16  cts. 

Per  square  foot $2.20  to  $2.80 

Per  cow $170  to  $190 

Second-class  stable  with  common  fittings : 

Per  cubic  foot •. 11  to  13  cts. 

Per  square  foot $1.65  to  $2.00 

Per  cow ". $130   to  $145 

Third  class,  for  farm,  wood  fittings: 

Per  cubic  foot 7 J  to  10  cts. 

Per  square  foot $1.45  to  $1.50 

Per  cow $90  to  $105 

Drill-halls  or  sheds  for  infantry: 

Per  cubic  foot 11  to  14  cts. 

Per  square  foot $1.60  to  $1.70 

Electric  stations  of  power-houses,  buildings  erected  complete, 
exclusive  of  machinery  and  plant,  per  cubic  foot,  14  to  17  cts. 

Flats,  as  constructed  in  New  York,  comprising  ornamental  brick- 
work in  front,  elevators,  fire-resisting  floors,  and  the  whole 
well  finished  in  ordinary  wood  throughout : 
Per  cubic  foot 28  to  36  cts. 

Hospitals,  complete,  including  administrative  buildings,  etc. : 

Per  cubic  foot 20  to  30  cts. 

Per  bed. $1,550  to  $2,300 

Cottage  hospitals  for  small  towns: 

Per  cubic  foot 17  to  22  cts. 

Per  bed $1,050  to  $1,550 

Hospitals,  isolated,  including  all  nursery  buildings: 

Per  cubic  foot 17  to  22  cts. 

Per  bed *. $1,800  to  $2,300 

Hotels,  complete  in  every  particular: 

First-class,  per  cubic  foot 31  to  41  cts. 

Second-class,  per  cubic  foot , 23  to  31   cts. 

Third-class,  per  cubic  foot , 20  to  24  cts. 


1460    COST  OF  BUILDINGS  PER  CUBIC  FOOT. 

Houses,  complete,  in  brickwork  and  good  substantial  finishings : 

First  class — Large  mansion  with  elaborate  finish: 
Main  building,  16-ft.  ceiling,  per  cubic  foot,  30  to  40  cts. ;    per 

square  foot,  $5.50  to  $6.50.* 
Additions,  11-ft.  ceilings,  per  cubic  foot,  16  to  20  cts. ;  per  square 

foot,  $2.50  to  $3.00. 

Second  class — Large  mansion  of  ordinary  character: 
Main  building,  14-ft.  ceiling,  per  cubic  foot,  22  to  30  cts.;    per 

square  foot,  $3.50  to  $4.50. 
Additions,  per  cubic  foot,  15  to  20  cts.;   per  square  foot,  $1.65 

to  $2.15. 

Third  class — Country  houses: 
Height  of  ceiling,  11  ft.,  per  cubic  foot,  15  to  20  cts.;  per  square 

foot,  $2.15  to  $2.65. 

Fourth  class — Speculative  buildings: 
Ceilings,  10  ft.,  per  cubic  foot,  13  to  15  cts.;    per  square  foot, 

$1.30  to  $1.55. 

Fifth  class — Tenements  and  cottages  to  rent: 
Ceilings,  9  ft.,  per  cubic  foot,  10  to  12  cts. ;  per  square  foot,  $1.10 

to  $1.35. 
Libraries,  public,  complete  in  every  particular: 

Per  cubic  foot 16  to  22  cts. 

Municipal  lodging-houses  for  cities  and  large  towns: 

Per  cubic  foot 15  to  18  cts. 

Per  bed $300  to  $375 

Museums,  public: 

For  large  cities,  per  cubic  foot 22  to  33  cts. 

Towns 19  to  26  cts. 

Music  halls,  complete,  per  head  of  accommodation: 

For  large  cities $80  to  $130 

For  small  cities  and  towns $40  to    $70 

Town  halls,  complete: 

Large  cities,  per  cubic  foot 31  to  36  cts. 

Small  cities  and  towns 22  to  30  cts. 

Alternative  prices: 

Basement,  per  cubic  foot 2(?  to  24  cts. 

Superstructure,  per  cubic  foot 27  to  35  cts. 

Ornamental  towers,  per  cubic  foot.  .  „ 39  to  46  cts. 

Theatres,  complete,  per  head  of  accommodation: 

In  large  cities $82  to  $108 

Small  cities  and  towns $50  to    $80 

Per  cubic  foot 28  to  38  cts. 

Chimney  shafts,  plain,  as  for  factories,  etc.,  complete,  including 

foundations,  iron  cap,  etc.,  height  measured  from  surface  of 

ground  to  top  of  cap: 

Per  foot  in  heght. 

Not  exceeding  100  ft.  in  height $40  to  $46 

100  ft.  to  180  ft.  high $45  to  $52 

180  ft.  to  250  ft.  high • $50  to  $56 

*The  prices  per  square  foot,  in  this  and  following  paragraphs,are  evidently 
per  sq.  ft.  of  floor  area,  counting  all  of  the  floors  above  the  basement. — 
Author. 


COST  OF   BUILDINGS  PER  CUBIC  FOOT.     1461 

EXAMPLES  OF  THE  ACTUAL  COST  OF  BUILDINGS  PER 
CUBIC  FOOT. 

COMPILED  BY  THE  AUTHOR. 

Office  Buildings. 


Cost 

Name  of  Building. 

Date. 

Character  of  Construction  and 
Finish. 

per 
Cu.  Ft. 

Cts. 

Chamber    of    Com-  ) 

merce,         Boston,  > 
Mi 

1891-2 

f  Seven  stories  ;  pitch  roof,  iron  and  ") 
slate;  granite  walls,  pile  founda-  ( 
tion;      fire-proof     construction; 

29 

ass.                        ) 

I     marble  and  oak  finish. 
(Thirteen  stories  ;  granite  and  Ohio  ! 

"Ames      Building,"  ( 
Boston.                     f 

1889-91 

stone  fronts;  flat  roof;  fire-proof  ! 
construction  ;    marble    and   oak  [ 

53 

I     finish. 

Exchange  Building,  ) 
Boston.                     J 

1889-91 

i  Nine  stories  ;    granite  front  ;    flat  1 
roof  ;       fire-proof     construction  V 
f     marble  and  oak  finish.                    ) 

40 

United  States  Trust  ) 
Co.  Building,  New  v 

"V       1                                            ( 

1888 

f  Ten  stories  ;  flat  roof  ;  massive  gran-  ! 
Iite  front  ;  fire-proof  construction  ;  ! 
extra  foundation;    fixtures,  rich  f 

60 

York. 

marble  work  and  finish. 

Seven-story     Office  "| 
Building,      New! 
York  (R.  W.  Gib-  f 
son). 

1890 

(  Two  massive   stone   fronts  ;    fire-  ) 
-\      proof  construction  ;    usual  ma-  f 
(     chinery,  fixtures,  etc.,  complete.  ) 

37 

Six-story  Office  ] 

f  Three  brick  and  terra-cotta  fronts;! 

Building,      New! 
York  (R.  W.  Gib-  f 

non-fire-proof,    but   with  metal  1 
!      lathing  ;  terra-cotta  furring  ;  ma-  j 

26 

son). 

t     chinery,  elevators,  etc. 

fTwo   stories   and   basement;    tilel 

Herald        Building,  \ 
New  York  City.      f 

1893 

)      and   fire-proof   roof,    brick   and  1 
1      stone  fronts  ;  fire-proof  construe-  f 

46 

(     tion.                                                     J 

Auditorium     Build-  1 
ing,  Chicago.            f 

1887-9 

(See  description  elsewhere.) 

36 

f  Eleven  stories  ;  flat  roof  ;  fire-proof] 

Rookery     Building,  ^ 
Chicago.                    j 

1886 

1      construction  ;  oak  finish,  marble  ! 
!      floor  and  wainscot  ;    eleven  -ele-  f 

32 

[     vators. 

f  Twenty  stories  ;   pitch  roof  ;  gran-  ! 

Masonic        Temple,  1 
Chicago.                    1 

1891 

ite  and  terra-cotta  fronts  ;  skele- 
ton construction  ;  fire-proof  ;  rich  }- 
marble  and  metal  work  ;    four-  j 

58 

[.     teen  elevators. 

f  Seventeen  stories  ;  flat  roof  ;  Bed-  ! 

Old    Colony    Build-) 

1893-4 

ford  stone,  white  brick,  and  ter- 
-{      ra-cotta    fronts  ;     skeleton    con-  }• 

41 

ing,  Chicago.            ) 

i      struction  ;  fire-proof  ;  rich  marble 

t     and  metal  work  ;   six  elevators. 

(Twelve  stories  ;  flat  roof  ;  first  three' 

N.    Y.    Life    Insur-1 

stories    dressed    granite;    terra- 

ance Building,  La  ! 

0 

cotta    above;     riveted    skeleton  ! 

A7 

Salle  and  Monroe  j 

1893—4 

construction  ;  fire-proof;  machin-  [ 

'±< 

Streets,  Chicago.    J 

|      ery  ;  rich  marble  work  and  finish; 

t     small  vaults  ;   five  elevators.         J 

Stock         Exchange^ 
Building,  La  Salle  ! 
and     Washington  j 
Streets,  Chicago.    J 

1893-4 

(  Thirteen  stories  ;    flat  roof  ;   skele-  J 
ton  construction;  fire-proof;  rich  > 
(     terra-cotta  facing.                            ) 

35j^ 

Manhattan      Build-  \ 
ing,  Chicago.*          f 

1892 

(  Sixteen  stories;  five  elevators;  two  ) 
•/      fronts;      pressed      brick,    terra-  V 
f      cotta,  and  gfanite.                            \ 

,7* 

*  Jenney  and  Mundie,  architects;  see  Inland  Architect  for  March,  1902. 


1462    COST  OF  BUILDINGS  PER  CUBIC  FOOT. 


ACTUAL  COST  OF  BUILDINGS— (Continued). 
Office  Buildings. 


Cost 

Name  of  Building. 

Date. 

Character  of  Construction  and 
Finish. 

per 
Cu.  Ft. 

Cts. 

Fort     Dearborn) 
Building,     Chi-  >• 
cago.*                       ) 

about 
1893 

j  Twelve  stories  ;  pressed  brick  and  [ 
1      terra-cotta.                                           j 

361/io 

Isabella      Building,  |_ 
Chicago.*                  f 

1893 

(Twelve  stories  ;  granite  and  terra-) 
,     cotta  ;   exposed  on  three  sides  :  > 
(     tile  roof.                                              \ 

57j.| 

Board      of      Trade  l 

Building,        Mon-  > 

1892-3 

20 

treal,  Canada.          \ 

Chamber    of    Com-  ( 
merce,  Cincinnati,  f 

1887-8 

i  Pitch  roof  ;   seven  stories  ;   granite  / 
I      fronts  ;  fire-proof  construction,     f 

26 

f  Ten  stories  ;  flat  roof  ;  stone  facing] 

Wainwright,  Build-  \_ 
ing,  St.  Louis.         f 

1890 

first    and    second    stories  ;     rich  | 
{     terra-cotta  above  ;  skeleton  con-  j* 
struction  ;    fire-proof  ;    four  ele- 

24%0 

L    vators. 

f  Nine  stories  ;  flat  roof  ;  granite  front  ] 

Equitable  Building,  j 
Denver.                     j 

1891-2 

two  stories  ;  light  brick  and  terra-  > 
•\      cotta  above  ;  fire-proof  construe-  }• 
tion;    rich  marble  work;    eight  i 

42 

elevators.                                            J 

Ernest  and  Cramer  I 
Building,  Denver.  \ 

1890 

|  Eight    stories;     flat    roof;     brick; 
front;     mill    construction;     o*k> 
(     finish;    three  elevators.                   \ 

19 

Three  stories  ;  flat  roof  ;  one  front  1 

Bailey  Block,  Den-) 
ver.                             f 

1890 

!      store  facing  ;   ordinary  brick  and  1 
1      timber  construction  ;    plumbing  [ 

8X 

[     and  steam  heat  ;  pine  finish.         J 

Ten  stories  ;    flat  roof  ;    brick  and  } 

Crocker       Building,  ( 
San  Francisco.        \ 

1890 

terra-cotta  fronts  ;  skeleton  con-  1 
j      struction;    fire-proof;    elaborate! 

63 

[     finish,  marble,  etc. 

f  Five  stories  ;   flat  roof  ;   buff  brick  J 

Bradbury  Building,  j 
Los  Angeles,  Cal.    j 

1891 

J      and  terra-cotta  walls  ;  fire-proof  ( 
J      construction  ;     oak  finish  ;    two  [ 

32 

[     elevators. 

f  Seven  stories;    flat  roof;   pressed-  1 

Endicott     Building,  \ 
St.  Paul,  Minn.        j" 

1887-9 

j      brick  front  ;    fire-proof  construe-  1 
|      tion  ;      marble     wainscot  ;      five  f 

29 

(     elevators. 

f  Three  stories;    two  stone  fronts;] 

—  Office     Building,  ) 

fire-proof  ;  usual  plumbing,  heat-  | 

Connecticut      (11.  V 

1891 

ing   plant,    fixtures,    etc.  ;     rich  }• 

50 

W.  Gibson).             j 

marble  work  ;   stories  of  moder-  | 

(     ate  height 

Five    Office    Build-  ( 
ings  in  Minnesota,  j 

1893-6 

I  Eight-  to    twelve-story  buildings  ) 
-<      about   of  the   character  of   the  >• 
f      Rookery,  Chicago.                            ) 

29i-35 

Board    of    Trade) 
Building,  Duluth,  V 
Minn.                         ) 

1895 

f  Seven    stories;     two    fronts;    fire-] 
proof;       handsomely     finished;  ! 
]      equal    to    the    Old    Colony    in  [ 
[     Chicago. 

38 

Seven-story     Office  ) 
Building,        Mon-  >- 

1903 

1  One  front;    fire-proof;    about  the  ) 
<     type  of  the  Union  Trust  Build-  [ 

36 

treal.                           ) 

(     ing  in  St.  Louis.                                 ) 

Ten  -  story    O  ffi  c  e  [ 
Building,  Chicago.  ) 

1903 

ilqual  to  Old  Colony  Building. 

37| 

*  Jenney  and  Mundie,  architects. 


COST  OF  BUILDINGS   PER  CUBIC  FOOT.     1463 


ACTUAL  COST  OF  BUILDINGS— (Continued). 
Warehouses  and  Stores. 


Name  of  Building. 

Date. 

Character  of  Construction  and 
Finish. 

Cost 
per 
Cu.  Ft. 
Cts. 

Eight-story      Office  ) 
and    Bank   Build-  V 

1902 

j  One  front  ;  fire-proof  ;  equal  to  the  I 

39 

ing,  San  Francisco  ) 

|      Brown  Hotel,  Denver.                     j 

Eight-story       Bank 
and  Office  Build-  V 

1904 

Fire-proof;  quite  elaborate. 

41 

ing,  Atlanta.            ) 

Warehouse,   Minne-  <_ 
sota.                           \ 

1896 

(  Five  stories,  fire-proof  ;    for  very  ) 
•<      heavy  goods  ;  good  front  ;  steam  V 
(     heat  ;   plenty  of  elevators,  etc.      J 

m 

Seven-story    Ware-  ) 
house,  Minnesota,  f 

1898 

J  Mill     construction  ;     plain     brick  ) 
1     walls.                                                    f 

9Vis 

Seven-story     Ware-  1 
house,  Cincinnati.  I 

1904 

j  Fire-proof  ;     cement    floors  ;     no  f 
I      finish.  .                                                 f 

25.V6 

Store  Building,  New  | 

1903 

j  Four    stories;     fire-proof;     plain  ( 

31 

Orleans. 

1      finish.                                                   f 

Department    Store,  I 
Chicago.                    j 

1900 

j  Six  stories  ;  fire-proof  construction  ;  ) 
1      one  front,  modern.                            ] 

29 

Leiter  Building,  Chi-  I. 
cago.*                       J 

1892 

(Wholesale  and  retail  store;  eight) 
K     stories  ;  granite  three  sides  ;  brick  V 
(     on  alley.                                             ) 

19M 

Athletic  Club  Build-  { 
ing,  Denver,  Colo,  j 


Hotels  and  Apartment  Buildings. 

f  Fourteen  stories;  brick  and  terra-  ] 
cptta  front ;  skeleton  construe-  { 
tion,  riveted;  fire-proof;  usual! 
plumbing,  machinery,  etc.  j 

Triangular    plan;     three    stone5) 
fronts;      considerable     carving; 
nine  stories;  .flat  roof;  all  rooms 
face  street;  350  guest  rooms, 160 
private  baths,    17  public    toilet  - 
rooms,  all  tiled;   steel  construc- 
tion;   fire-proof;    provided  with 
electric  light,  ice  and  refrigerator  . 
plant ;  laundry ;  4  elevators.        J 

Fireproof;  elaborately  finished. 

(  Fire-proof,  but  no  more  elaborate  ) 
than  above.  f 

Fire-proof;  hard-wood  finish;  not) 
elegant;  two  elevators.  ) 

Five  stories ;  flat  roof ;  pressed-  J 
brick  front ;  partly  slow-burning  V 
construction.  ) 

Club  Buildings,  Y.  M.  C.  A.,  Etc. 

f  Four  stories;;  flat  roof;  one  front  1 
pressed  brick ;  thoroughly  equip- 
ped with  swimming  and  Turk- 
ish baths,  gymnasium,  hand-ball 
room,  billiard-room,  social 
rooms,  etc. ;  brick  walls,  wood 
construction. 


—  Hotel,  New  York  ) 

(R.  W.  Gibson).      [ 

" 

Brown  Palace  Hotel,  ) 
Denver.                    j 

1892     «| 

Eight-story    Apart-  ) 

ment  House,  New  > 

1901     I 

York.                         1 

Two   Apartment^ 
Houses,  New  York  f 

1903 

Seven-story    Apart-  j 
ment  House,  Pitts-  V 

1903      - 

burg.                           ) 

The  Lenox  (Apart- 
ments), Cleveland,  V 
Ohio.                          i 

about 
1889 

1890-1 


*  Jenney  and  Mundie,  architects. 


1464    COST  OF  BUILDINGS  PER  CUBIC  FOOT. 
ACTUAL  COST  OF  BUILDINGS— (Continued) 
Club  Buildings,  Y.  M.  C.  A.,  Etc. 


Name  of  Building. 

Date. 

Character  of  Construction  and 
Finish. 

Cost 
per 
Cu.  Ft. 
Cts. 

Denver  Club  Build-  | 
ing,  Denver,  Colo,  f 

Standard  Club  Ho.,) 

1887-8 
1887 

|  Three  stories  and  high-pitch  roof;"] 
j      stone  ashlar,   four  sides;     slate  \ 
j      roof;     wood   construction;    oak  f 
[     and  pine  finish.                                j 

24 
129/lo 

Chicago.                   J 
Y.  M.  C.  A.  Build-/ 

13 

ing,  Cleveland,  O.  J 

School,  College,  and  Seminary  Buildings. 


?  Three  stories  and  basement  ;  recita-  ! 

Wingate  Hall,  State  j 

tion-  and  drawing-rooms;  brick 

College,        Orono,  > 

1891-2 

with   granite    trimmings;     slate  }- 

10/2 

Me.                             ) 

'      roof;    wood   floors;    brtck   par- 

titions. 

fTwo     stories     and     basement;! 

Grammar-s  chool  ) 
Building,  Denver,  V 

1891-2 

pressed-brick  walls;   shingle  and 
-j      tin  roof;    wooden  floors;     brick  }~ 

Qy2 

Colo.,  8  rooms.        ) 

partitions;  cost,  basement  floor 
t     to  second-story  ceiling. 

(Pressed  brick;  wooden-floor  con-! 

Smedley    School,) 
Denver,  4   rooms,  f 

1902 

J      struction  ;     shingle    roof  ;     slate  { 
1      blackboard;    janitor's  rooms  in  f 
[     basement  ;  two  large  furnaces.    J 

lOVs 

Clayton    School,! 
Denver,  15  rooms, 
2    lunch-rooms,    6  ' 
rooms  for  janitor,  ' 
and  large  hall  in 

1901 

f  Light  pressed  brick  ;  wooden-floor"! 
j      construction;      otherwise     first-  1 
1      class  building  ;  fan  system  heat-  f 
I     ing  and  ventilation. 

10 

attic. 
Ursuline     Convent,  1 

1890 

(  Three  stories  ;    pitch  roof  ;    brick  ) 
•<      with  stone  trimmings  ;   ordinary  V 

15 

Cleveland,  O.          f 

f      wood  construction. 

Six   buildings   grouped   around   a! 

Hill  Theological) 
Seminary,   St.V 

quadrangle;    ordinary  construe-  | 
tion;    library,   gymnasium,  and! 
}     staircases     fire-proof;      corridor 

11 

Paul,  Minn.             ) 

walls    face    brick;     oak    finish; 

1      cost  per  cubic  foot  above  grade.     \ 
fThis  building,  covering  21,000  feet! 

Lelancl  Stanford  Jr.  ) 
Museum,      P  a  1  o  > 

1891 

and   containing   over    1,100,000  j 
!      cubic  feet  of  space,  is  built  en-  [ 
\      tirely  of    Portland-cement  con-  f 

18 

Alto,  Cal.                  ) 

crete  —  walls,  floors,  and  roof  — 

[     and  is  fireproof  throughout. 

f  A  large  three-story  building,  most-  ! 

Newark       High  ) 
School,     Newark,  V 
N.  J.                           ) 

1897-8 

ly  fire-proof  construction.    Cubi- 
cal contents  from  basement  floor 
<{      to  mean  point  in  roof,  1,803,000  }• 
cu.  ft.     For  description  of  build- 

J 

ing,  list  of  contracts,   etc.,  see 

L     American  Architect,  July  9,  1898.  J 

COST  OF  BUILDINGS  PER  CUBIC  FOOT.      1465 
ACTUAL  COST  OF  BUILDINGS— (Continued). 
School-houses. 


Character  of  Construction  and 
Finish. 

Cost 

Name  of  Building. 

Date. 

per 
Cu.  Ft. 

Cts. 

Cost  per 

St.  Louis. 

Room. 

Eugene  Field  School 

1 

f  $5,600 

15& 

Edward  Wyman  Sch. 
Horace  Mann  School. 

All    first-class    buildings, 

5,600 
6,007 

14 

149/10 

Ralph   Waldo    Emer- 

}•    described  in  Brickbuilder  • 

son  School. 

for  October,  1903. 

5,636 

14^ 

Cote  Brilliante  School 

6,758 

17 

Henry  Blow  School. 

J 

6,243 

16 

School-houses  of  entirely  fire-proof  construction,  built  in  Boston,  1892- 
1903,  cost  from  22.39  cts.  per  cu.  ft.  for  the  South  Boston  High  School 
to  24.98  cts.  for  the  Heath  Street  School.  The  Dorchester  High 
School,  which  is  fire-proof  construction  except  for  a  plank  roof,  cost 
16.33  cts.  Schools  of  ordinary  construction  range  from  16.58  to  24 
cts.  per  cu.  ft. — Brickbuilder,  August,  1903. 

Libraries. 


Public  Library,  New  \ 
London,  Conn.         j 

1889-90 

{  One-story    stone    building;     ordi-  ) 
)     nary  construction.                            j" 

36^ 

Howard      Memorial  j 
Library,  New  Or-  v 

1888 

44 

leans,  La.                  \ 

| 

Congressional,  / 
Washington,  D.C.  f 

Including  some  of  its  furnishings. 

67^ 

Hospitals. 

f  Seven  stories;  pressed-brick  front;"! 

Hospital     Building,  ) 
New  York  (R.  W.  V 

1890-5 

stone      trimmings  ;        fireproof  ; 
{      thorough  heating  and  ventilat-  Y 

40 

Gibson).                    j 

I      ing    plant  ;      plumbing  ;      much 

[     marble  and  tiling. 

Hospital     Building,  ) 
New  York  (R.  W.  V 
Gibson).                   ) 

1890-5 

fSix  stories;    pressed-brick  front;! 
1      stone  trimmings  ;  part   fireproof  | 
[      and  part  non-fireproof,  but  with  J- 
metal  lathing  and  terra-cotta  f  ur- 

32 

(.     ring  ;  plumbing,  steam  plant,  etc.  J 

Churches. 

Grace  M.E.  Church,  ) 

f  Two-story  wooden  building  ;  tower  1 
i      and   spire;     slate   roof;    copper  | 

Cambridgeport,  V 

1886-7 

metal-  work  ;     cost  includes  fur-  }• 

8^ 

Mass.                           ) 

|      naces,  pews,  frescoing,  and  gas-  | 

L     fixtures. 

f  Two-story    stone    church;     stone] 

I      tower  71  feet  high,  with  wood  | 

Christ  M.E.  Church,  ) 
Denver,  Colo.          f 

1889-91 

j      spire     108     feet     high,    above;  1 
j      .shingle  roof  ;  steam  heat  ;  oak  fin-  f 

21 

ish  in  second  story;   pews,  fres- 

L     coing,  etc.                                          J 

Zion  Temple,  Syna-  ) 

gogue,  Ogden  Av.,  V 

1885 

7!}io 

Chicago.                     j 

1466     COST  OF   BUILDINGS  PER  CUBIC   FOOT. 


ACTUAL  COST  OF   BUILDINGS.— (Continued). 
Theatres, 


Name  of  Building. 

Date. 

Character  of  Construction  and 
Finish. 

Cost 
per 
Cu.  Ft. 
Cts. 

Six  stories;  brick,  stone,  and  terra- 

Theatre,       Duluth,  \ 

1893 

cotta;     two     fronts     absolutely 

<TCV 

Minn.*                        J 

fireproof    and    elegantly    deco- 

OO/6 

rated  and  finished. 

Schiller  Building,  or  ) 
German    Theatre,  V 
Chicago.                    ) 

1891 

Seventeen  stories;  fiat  roof,  faced 
with   terra  -cotta;   skeleton   con- 
struction; fireproof;  rich  marble 
work;  theatre  in  four  stories. 

309-1  o 

Miscellaneous. 

Built  in  middle  West;  all  wood  and 

Park  pavilion  . 

1898 

47  / 

dancing-hall,  etc. 

Large  car  barn  

1895 

Exposed    iron    construction    and 
brick  walls. 

9M» 

American      Express  / 
stables,  Chicago,  t  f 

1893 

Steel     construction,     fire-proofed, 
Sioux  Falls,  Jasper;   first  story, 
pressed  brick  above;  tile  arches;  j 

10VS 

four  stories  and  basement.            j 

27  cts. 


*  Traphagen  &  Fitzpatrick,  architects,     t  Jenney  &  Mundie,  architects. 

Dwelling's. 

(See  also  pages  1458,  1460  ) 

City  dwellings  in  Chicago,  designed  by  Adler  &  Sullivan,  architects. 

Cost  per  cubic  foot  from 17  to  20  cts. 

Of  dwellings  designed  by  the  author  and  built  in  Boston  in  1886, 
the  average  cost  of  eight-  and  ten-room  wooden  houses  per 
cubic  foot  of  habitable  space,  including  cellar,  was  about 11  cts. 

In  Denver,  Colo.,  the  cost  of  a  first-class  stone  house  (isolated), 
with  hard- wood  finish,  indirect  steam  heat,  extra  plumbing,  dec- 
orations, etc.,  complete,  was  in  1890  about 

Brick  houses  of  ten  rooms,  pine  finish,  furnace  heat,  good  plumb- 
ing, etc.,  cost  above  cellar  floor,  but  not  including  unoccupied 
roof  space,  in  1892 14  cts. 

Cheap  eight-room  brick  cottages  of  one  and  one-half  or  two  stories ; 
bath-room  and  furnace ;  cubic  space  reckoned  from  cellar  floor, 
but  not  including  unoccupied  roof  space,  were  built  in  Den- 
ver, in  1894,  for  about ' 10  cts. 

Cost  of  Different  Kinds  of  Work  per  Cubic  Foot 
of  Building. 

In  Fireproof  for  March,  1903,  Mr.  F.  W.  Fitzpatrick  gave  some 
figures  showing  the  proportionate  cost  of  the  different  branches 
of  work  which  go  to  make  up  the  completed  building.  Believ- 
ing that  these  data  will  be  found  useful  in  making  up  approxi- 
mate estimates,  the  author  obtained  permission  to  use  them 
herein. 

The  following  figures  represent  the  actual  cost  of  a  prominent 
ten-story  office  building,  60' X  ISO7,  built  in  the  middle  West, 
a  No.  1  high  grade  fire-proof  structure,  with  two  street  fronts 
faced  with  granite;  pile  foundation. 


COST  OF   BUILDINGS   PER   SQUARE  FOOT.   1467 

(Figures  are  in  cents  per  cubic  foot  of  building.) 


The  foundation  cost. . 

Steel  framing 2> 

Granite  and  all  masonry liy 

Cornice,  roofs,  and  skylights. .  .  £; 

Fire-proof  floors ^ 

Partitions  (tile) 2/l 

All  plastering  and  stucco 1^ 

Elevator  fronts  and  all  orna- 
mental metal-work 2 

Marble-work 3>; 

Hardware 2/ 

Joiner  work 1^ 

Glass ^ 

Painting  and  varnish '  7/ 

Electric  wiring ^ 


Heating 


Plumbing % 

Elevators 1 

Stairs,  scenic  structural  fram- 
ing, "making  ends  meet," 
lamp  fixtures,  etc.  What 
might  be  called  a  fair  amount 
for  "contingencies  "  in  such 
a  building,  including  lesser 
items  not  mentioned  here 

but  grouped  together 423/120 

Architect  'a  fee 1% 


Total.  . 34V12 


The  Chicago  post-office,  a  building  of  12,000,000  cubic  feet 
and  of  monumental  character  and  finish,  cost,  in  some  of  its 
items,  as  follows: 

(Figures  are  in  cents  per  cubic  foot  of  entire  building.) 


Its  foundation  cost 
The  steel  framing 
Granite  and  masonry 
Fire-proof  floors 


Ornamental  metal -work 

Marble 

Plumbing 

Heating 


Plaster,  plain  and  ornamental .     1 

It  may  be  noticed  that  the  relative  cost  of  several  of  these 
items  was  identically  the  same  as  in  the  office  building.  The 
total  cost  of  this  building  was  42|  cts.  per  cubic  foot. 

COST    OP   BUILDINGS   PER    SQUARE   FOOT. 

One-story  buildings  of  large  area,  such  as  exposition  buildings, 
etc.,  may  be  estimated  almost  as  accurately  by  the  square  foot 
as  by  the  cubic  foot,  as  there  are  few  or  no  interior  partitions, 
and  usually  no  plastering  or  interior  finish. 

Iron  Building's. — "Roughly  speaking,  the  cost  of  one-story 
iron  buildings,  complete,  is,  for  sheds  and  storage-houses,  40  to 
GO  cts.  per  square  foot  of  ground,  and  for  such  buildings  as  ma- 
chine-shops, foundries,  and  electric-light  plants,  that  are  pro- 
vided with  travelling  cranes,  the  cost  is  from  60  to  90  cts.  per 
square  foot  of  ground  cohered."  (H.  G.  Tyrrell.) 
Textile  Factories.— See  pages  723-725. 
Exposition  Building's. — The  cost  of  the  World's  Fair 
buildings  (Chicago,  1893)  per  square  foot  of  ground  covered,  in- 
cluding sculpture  and  decoration,  as  given  by  E.  C.  Shankland, 
chief  engineer,  was  as  follows: 

Manufactures  and  Liberal  Arts  Building.  .  .  .$1 .39 

Transportation  Building 1 . 08 

Electricity  Building 1 . 69 

Machinery  Hall ' 2. 12 

Agricultural  Building 1 . 44 

Administration  Building 9.18 

Horticultraul  Building 1.41 

Mines  and  Mining  Building 1 . 04 

Fisheries  Building 2 . 35 

Forestry  Building 75 


1468 


DEPRECIATION   OF  BUILDINGS. 


Cost  of  Structures  for  the  St.  Louis  Exposition 

(1904). — The  following  figures  are  issued  by  Isaac  S.  Taylor, 
Director  of  Works,  of  the  World's  Fair,  showing  the  area  and 
cost  of  the  principal  exhibition  buildings.  The  total  area  of 
twenty-two  buildings  is  123.51  acres,  and  the  total  cost  $6,939,- 
992.26.  The  cost  is  for  the  bare  buildings,  and  does  not  include 
sculptural  or  other  decorations,  or  the  architect's  compensation. 


Dimensions. 

Area 
in 
Acres 

Cost. 

Cost 
per 
Sq.  Ft. 

Art  Building 

161'X346' 
144'  X  423' 
106'  XI  50' 
200'  X  736' 
136'  X  136' 
525'  X  750' 
525'  X  750' 
525'  X  758' 
525'  XI,  200' 
525'  X  758' 
525'  XI,  200' 
525'  XI,  000' 
301'X326f 
525'  XI,  300' 
374'  X  782' 
500'  XI,  600' 
300'  X  600' 
195'  in  diam- 
eter, exclusive 
of  annex. 

1.42 

3.14 
0.41 
3.86 
0.42 
9.08 
8.80 
7.70 
13.47 
6.67 
10.28 
9.48 
2.25 
15.70 
5.42 
18.62 
4.07 

V  1.09 

[$967,833.90 

39,388.99 
328,980.00 
45,000.00 
488,848  .  50 
471,820.95 
323,950.75 
711,510.00 
408,531.57 
704,067.96 
509,110.50 
135,480.00 
674,853.42 
225,342.27 
520,491.07 
168,883.38 

215,899.00 

$5.45 

2.48 
2.23 
2.43 
1.24 
1.20 
0.81 
1.13 
1.03 
1.12 
0.97 
1.38 
0.99 
0.77 
0.58 
0.94 

Two  Art  Pavilions,  each.         .  .  . 

Art  Building  Annex  

Government  Building. 

Government  Fisheries  Building 
Mines  and  Metallurgy  

Liberal  Arts.  .  . 

Education  and  Social  Economy.. 
Manufactures.  . 

Electricity 

Varied  Industries.  .  . 

Machinery 

Steam,  Gas,  and  Fuel  Building.  . 
Transportation 

Horticulture. 

Agriculture  

Forestry,  Fish,  and  Game. 

Festival  Hall   ....                  •) 

Cost  of  United  States  Government  Buildings.— 

There  was  published  in  1900,  by  the  Treasury  Department,  a 
history  of  the  public  buildings,  giving  the  cost,  and  in  the 
Architects  and  Builders'  Magazine  for  Aug.  1902  and  the  Inland 
Architect  for  April  1902,  was  published  a  list  of  287  buildings, 
giving  the  cost  per  cubic  foot,  material  used  for  walls,  and  date 
of  erection.  As  a  rule  these  buildings  have  cost  more  than 
private  buildings,  so  that  their  cost  cannot  be  used  as  a  guide, 
except  for  government  buildings. 

DEPRECIATION   OF   BUILDINGS. 

TIFFANY'S  ESTIMATE  OF  DEPRECIATION.     (Used  by  U.  S.  Gov't.) 
The  figures  given  on  page  1458  are  for  NEW  buildings.       To 
ascertain  the  present  value,  a  discount  between  old  and  new 
should  be  made  as  follows: 

Per  Cent  per  Year, 

Brick,    occupied  by  owner 1    to  1} 

Brick,  * '   tenant 1 J  to  1 J 

Frame,         "          "   owner 2    to  2| 

Frame,         "          "   tenant , , 2J  to  3 


DEPRECIATION  OF  BUILDINGS. 


1461) 


If  built  of  "long-leaf"  yellow  pirie,  or  of  spruce,  found  in  New 
England  States,  add  20  to  30  per  cent.,  or  if  of  "short-leaf"  yel- 
low pine,  add  40  to  50  per  cent,  to  his  figure.  If,  of  redwood  or 
cedar,  found  on  Pacific  Coast,  charge  only  about  half  his  esti- 
mates, which  are  for  white  pine  or  white  pine  with  oak  framing 
timbers. 

These  figures  for  depreciation  are  to  include  buildings  where 
ordinary  repairs  have  been  made.  If  extraordinary  repairs  have 
been  made,  the  discount  should  not  be  so  heavy.  Exercise  good 
judgment  as  to  depreciation. 

The  Wear  and  Tear  of  Building  Materials.— At 
the  tenth  annual  meeting  of  the  Fire  Underwriters '  Association 
of  the  Northwest,  held  at  Chicago  in  September,  1879,  Mr.  A.  W. 
Spalding  read  a  paper  on  the  wear  and  tear  of  building  ma- 
terials and  tabulated  the  result  of  his  investigations  in  the  fol- 
lowing form: 


Frame 
Dwelling. 

Brick 
Dwelling 

(Shingle 
Roof). 

Frame 
Store. 

Brick 

Store 
(Shingle 
Roof). 

Material  in  Building. 

2 

°|s 

6 

3 

*  J| 

oT 

'Ji 

I 

^Jl 

§i  2 

HI 

III 

|E 

III 

a 

§D  £ 

111 

U     QJ 

>?* 

£Q  c. 

>K* 

feQ  c, 

>^ 

ojQ  ft 

>i^ 

£P  a 

< 

PH 

< 

PH 

<1 

PH 

2 

li 

Brick 

75 

li 

66 

H 

Plastering  

20 

5 

30 

3* 

16  ' 

.  _  .  . 

30 

2  1 

Painting,  outside. 

5 

20 

7 

14 

5 

20 

6 

16 

Paintin0"   inside      . 

7 

14 

7 

14 

5 

20 

6 

16 

Shingles  

16 

6 

16 

6 

16 

6 

16 

6 

Cornice  

40 

40 

30 

40 

Weather-boarding  

30 

3-j- 

30 

3i 

Sheathing.  .  . 

50 

2 

50 

'2    ' 

40 

50 

2 

Flooring  

20 

5 

20 

5 

13 

8 

13 

8 

Doors,  complete.  .  . 

30 

3^ 

30 

25 

4 

30 

Windows,  complete  

30 

3} 

30 

3l 

25 

4 

30 

3i 

Stairs  arid  newel  

30 

si 

30 

3i 

20 

5 

20 

5 

Base.  ... 

40 
30 

3* 

40 
30 

2* 

30 
30 

1! 

30 
30 

it 

Inside  blinds 

Building  hardware 

20 

5 

20 

5 

13 

8 

13 

8 

Piazzas  and  porches.  .  .  . 

20 

5 

20 

5 

20 

5 

20 

5 

Outside  blinds      .  . 

16 

6 

16 

6 

16 

6 

16 

6 

Sills  and  first-floor  joists. 

25 

4 

40 

25 

4 

30 

3i 

Dimension  lumber  

50 

2 

75 

H 

40 

2* 

66 

if 

These  figures  represent  the  averages  deduced  from  the  replies 
made  by  eighty-three  competent  builders  unconnected  with  fire- 
insurance  companies  in  twenty-seven  cities  and  towns  of  the 
eleven  Western  States. 


1470  DIMENSIONS  OF  FURNITURE. 


DIMENSIONS    AND    DATA    USEFUL   IN    THE     PRE- 
PARATION  OF    PLANS. 

Dimensions  for  Furniture. — For  the  convenience  of 
draughtsmen  when  designing  furniture  or  providing  space  for  a 
special  article  the  following  dimensions  are  given :  * 

Chairs  and  Seats. — The  average  figures  taken  from  a  variety  of 
good  chairs  are :  Height  of  the  seat  above  the  floor,  18" ;  depth 
of  the  seat,  19";  the  top  of  the  back  above  the  floor,  38". 
Usually  the  seat  increases  in  depth  as  it  decreases  in  height, 
while  the  back  is  higher  and  slopes  more.  Twenty  inches  inside 
is  a  comfortable  depth  for  a  seat  of  moderate  size.  Chair-arms 
are  about  9"  above  the  seat.  The  slope  of  the  back  should  not 
be  more  than  one  fifth  the  depth  of  the  seat.  A  lounge  is  6'  long 
and  about  30"  wide. 

Tables  vary  in  shape  and  size  almost  as  much  as  chairs.  Writ- 
ing- and  dining-tables  are  made  2'  5"  high,  and  the  species  of 
sideboard  called  a  carving-table  is  made  3'  high  to  the  principal 
shelf  but  tables  for  general  use  are  2'  6"  high. 

Dining-tables  are  made  from  3'  6"  to  4'  wide  and  to  extend 
from  12'  to  16'  feet  by  means  of  slides  within  the  frame.  This 
frame  should  not  be  so  deep  as  to  interfere  with  the  knees  of  any 
one  sitting  at  the  table;  that  is,  there  must  be  about  2'  clear 
space  between  it  and  the  floor. 

The  smallest  size  practicable  for  the  knee-holes  of  desks  and 
library  tables  is  2'  high  by  I'  8"  wide,  the.  width  to  be  in- 
creased as  much  as  possible. 

Bedsteads  are  classed  as  single,  three  quarters,  and  double.  A 
single  bed  is  3'  to  4'  wide  inside;  a  three-quarter  bed,  4'  to 
4'  6";  a  double  bed,  5'.  All  bedsteads  are  6'  6"  to  6'  8"  long 
inside.  Footboards  are  from  2'  6"  to  3'  6"  and  headboards 
from  5'  to  6'  6"  high.  Single  beds  for  dormitories  are  often  made 
only  2'  8"  wide. 

Bureaus  vary  in  shape  and  size  to  such  an  extent  that  it  is 
impossible  to  say  that  any  dimension  is  fixed. 

Convenient  sizes  are:  body,  3'  5"  wide,  1'  6"  deep,  2'  6"  high; 
or  4'  wide,  1'  8V  deep,  3'  high. 

*  Many  of  these  dimensions  were  first  contributed  to  the  American  Archi- 
tect of  November  10,  1894,  by  Mr.  Alvin  C.  Nye. 


DIMENSIONS  OF   PLUMBING   FIXTURES.       1471 

Commodes  are  1'  6"  square  on  the  top  arid  2'  6"  high. 

Chiffoniers  are  about  3'  wide,  V  8"  deep,  4'  4"  high. 

Cheval  glasses  are  made,  if  large,  6'  4"  high,  3'  2"  wide.  If 
small,  5'  high,  I/  8"  wide.  If  medium,  5'  6"  high,  2'  wide. 

Wash-stands  of  large  sizes  are  3'  long,  1'  6"  wide,  and  2'  7" 
high.  Small  sizes  are  2'  4"  to  2'  8"  long. 

Trardrqfres  may  be  8'  high,  2'  deep,  and  4'  6"  wide;  or,  0'  9'' 
high,  1'  5"  deep,  and  3'  wide. 

Sideboards  may  be  4'  to  6'  long  and  from  20"  to  2'  2"  deep. 

Upright  pianos  vary  from  4'  10"  to  5'  6"  in  length,  from  4 
to  4'  9"  in  height,  and  are  about  2/  4"  deep  over  all. 

Square  pianos  are  about  6'  8"  long  by  3'  4"  deep. 

Billiard-tables  (Collender),  4/X8/,  4'  2"X9',  and  5'XlO'. 
Size  of  room  required  13'Xl7',  14/X18/,  and  15/X20/  respec- 
tively, 

Dimensions  of  Plumbing-  Fixtures. — Enamelled-iron 
Bath-tubs. — Standard  sizes  for  roll-rim  baths  with  sloping  end 
are:  Nominal  lengths,  4',  4J',  5',  5J',  and  6';  width  over  all,  30" 
to  34".  Specially  narrow  tubs  are  made  25"  to  29"  wide.  The 
actual  length  over  rim  is  usually  1"  or  2"  more  than  the  nominal 
length,  and  2"  will  include  ordinary  overflow-pipe. 

Wash-basins. — Crockery  basins,  to  go  with  marble  slabs,  are 
made  round  and  oval.  Round  bowls  are  made  10",  12",  13" 
14",  and  16"  in  diameter,  measured  from  the  outside  of  the  rim. 
Oval  bowls,  14"X17",  15"X19",  and  16"X21".  The  12"  and 
14"  round,  and  15"X19"  oval,  are  most  commonly  used. 

Marble  basin-slabs  may  be  20"X24",  20"X30",  22"X28",  or 
24"  X30",  the  last  being  a  very  common  size.  Can  be  made  any 
size  to  order.  They  should  be  1|"  thick,  countersunk  on  top, 
and  should  have  moulded  edges  where  exposed. 

Corner  slabs  are  commonly  made  21"X21"  and  24"X24". 
Marble  backs  are  usually  8"  or  10"  high,  and  sometimes  12". 

Enamelled-iron  wash-basins  or  lavatories  made  in  one  piece: 
Common  sizes  are  16"X20",  11"X14"  basin;  18"X21",  11"X 
15"  basin;  18"X24",  12"Xl5"  basin;  back,  10i"  high.  The 
smallest-size  wash-basin  is  13"  wide  at  the  back. 

Corner  basins,  12|"Xl2i",  12"  round  basin;  15"X15",  11" X 
14"  basin,  16"X16",  11"X14"  basin,  19"X19",  11"X15"  basin. 
The  standard  height  of  wash-basins  is  2/  6"  from  the  floor. 

Foot-baths,  enamelled  iron,  roll  rim,  are  22^"X19";  width,  in- 
cluding fittings,  V  11";  height  17";  depth  inside  11". 


1472      DIMENSIONS  OF   PLUMBING   FIXTURES. 

Seat-baths,  enamelled  iron,  average  about  32"  long  over  fittings, 
and  27"  wide. 

Water-closets. — The  dimensions  of  water-closet  bowls  vary  con- 
siderably, the  following  being  about  an  average:  Width  of  bowl 
over  all,  13";  depth  from  wall  to  front  of  seat,  23"',  height  from 
floor  to  seat,  17"',  width  of  seat,  15"  to  16".  Closets  with  low- 
down  tanks  measure  about  28"  from  front  of  seat  to  wall.  The 
distance  from  centre  of  outlet  opening  to  the  walls,  or  the 
11  roughing  in"  dimensions,  are  given  in  manufacturers'  cata- 
logues, as  they  vary  with  different  closets.  The  smallest  space 
permissible  for  water-closet  compartments,  where  doors  open 
out,  is  2'  4"X4'  0".  If  the  door  opens  in,  the  compartment 
should  be  3'X5'. 

Closet-ranges,  used  in  schools  and  factories,  are  made  24",  27", 
and  30",  centre  to  centre  of  partitions.  For  grade  schools,  24" 
is  ample,  and  for  factories;  27".  The  range  usually  occupies  a 
space  28"  in  depth  if  set  against  a  wall. 

Urinal-stalls  should  be  24"  to  27",  centre  to  centre  of  parti- 
tions, depth  of  partitions,  20"  or  22";  of  ends,  2';  of  bottom 
slab,  2'',  height  of  partitions,  4"  6"  to  5'  6". 

Kitchen-sinks  of  cast  iron  are  made  in  a  great  variety  of  sizes, 
those  most  commonly  used  being  16'VX24",  18"X30",  18"X36", 
20'''X30"  and  20"X36"  ;  24"X50"  being  the  largest  size  for 
enamelled  sinks.  The  depth  inside  for  the  sizes  given  is  6". 
Plain  cast-iron  sinks  are  made  as  large  as  32"  X  56"  or  28"  X  78". 
Steel  sinks  are  made  in  all  of  the  above  sizes  up  to  20"  X  40". 

Common  sizes  of  Porcelain  sinks  are  20"X30",  23"X36",  24" 
X42". 

Cast-iron  slop-sinks,  common  sizes,  are  16"X16",  16"X20", 
18"X22",  20/'X24";  12"  deep. 

Copper  Pantry-sinks. — €ommon  sizes  are  12"Xl8",  14//X20", 
and  16"X24". 

Laundry-tubs  of  slate  or  soapstone  are  commonly  made  2!  wide 
over  all,  and  16"  in  depth.  Lengths  over  all,  two-part  tubs, 
4'  0"  and  4'  6";  three-part  tubs,  6'  0",  &  6",  and  7'. 

Earthen  and  porcelain  tubs  come  separately,  and  are  connected 
up  as  required. 

The  dimensions  of  each  tub  are  2'  or  2'  7|"  in  length,  2'  1$" 
in  width,  and  15"  in  depth  inside. 

The  length  required  for  two  2'  tubs  is  4'  l"j  for  three  tubs, 
6'  2";  and  for  four  tubs,  8'  3". 


DIMENSIONS  OF  CARRIAGES  AND  CARS.     1473 

Wolff's  roll-rim  enamelled-iron  wash-tubs  are  55"  over  all,  for 
two  tubs,  and  82"  for  three  tubs. 

Range-boilers  are  12"mdiameter  for  30-gallon  boilers,  14"  for 
40-gallon,  16"  for  52-  and  63-gallon,  22"  for  100-  and  120-gallon. 

Dimensions  of  Carriages. — Covered  Buggy  (Goddard). — 
Length  over  all,  14';  width,  5';  height,  7'  4".  "Will  turn  in 
space  from  14'  to  20'  square,  according  to  skill. 

Coupe.— Length  over  all,  18';  width,  6';  height,  6'  6". 

Buggy  (Piano  Box).—  Length  over  all,  14';  width,  4'  10". 

Landau.—  Length  over  all,  19'  6";  width,  6'  3";  height,  6'  3"; 
length  of  pole,  8'  0". 

Stanhope  Gig  (2  Wheels).—  Length  over  all,  10'  6";  width,  5' 
8";  height,  7'  6". 

Victoria. — Length,  without  pole,  9'  6";  length  of  pole,  8'; 
width  over  all,  5'  4". 

Light  Brougham. — Length,  without  pole  or  shaft,  9'  to  11'; 
width  over  all,  5'  4";  height,  6'  4". 

Dimensions  and  Weight  of  Fire-Engines. — From 
measurements  of  different  fire-engines  belonging  to  the  city  of 
Boston,  it  was  found  that  the  greatest  length,  including  pole, 
was  22'  6".  The  widths  varied  from  5'  to  5'  11",  the  average 
height  being  8'  8". 

The  average  weight  of  29  engines  is  8,000  Ibs. ;  the  greatest 
weight  being  9,420  Ibs.,  and  the  least  4,780  Ibs. 

Dimensions  and  Weight  of  Hose  Carriages. — Ex- 
treme length  with  horse,  19'  6",  withoilt  horse,  17' 6";  width, 
%  9"  to  7'  0";  height,  from  6'  8"  to  7'  0";  average  weight  of  11 
carriages,  2,943  Ibs.;  greatest  weight,  3,500;  least  weight,  2,120. 

Dimensions  and  Weight  of  Ladder  Wagons. — 
Length  of  truck,  33';  total  length,  with  ladders  on,  45';  width, 
6'  2";  average  weight  of  12  wagons,  6,G60  Ibs.;  greatest  weight, 
8,800;  least,  4,350. 

Dimensions  of  Locomotives  and  Cars, — The  dimen- 
sions of  locomotives  and  freight-cars  vary  considerably,  but  the 
following  will  cover  those  in  common  use: 

Locomotives. — 15'  4"  to  15'  10"  to  top  of  stack  from  top  of 
rail;  extreme  width  of  cab,  10'  2".  Doors  to  admit  locomo- 
tives should  be  12'  to  13'  wide  and  18'  high. 

Furniture-cars  are  14'  1",  top  of  track  to  top  of  brake-staff; 
floor  3'  8"  from  track;  extreme  width,  9'  10". 

Stock-cars,  13'  5",  top  of  track  to  top  of  brake-staff;  floor, 
4'  0"  from  track;  extreme  width,  9'  8". 


1474     DIMENSIONS  OF  CARS,  HORSE-STALLS,  ETC. 

Refrigerator-cars,  14'  6",  top  of  track  to  top  of  brake-staff; 
floor,  4'  0"  from  track;  extreme  width,  9'  1" . 

Ordinary  freight-cars  are  about  13'  (3"  high  to  top  of  brake- 
staff  and  9'  4"  in  extreme  width.  The  height  of  floor  of  freight- 
cars  varies  from  3'  8"  to  4'  0"  above  top  of  track,  for  stand- 
ard gauge,  and  3'  0"  to  3'  6"  for  narrow-gauge  cars. 

Passenger-coaches  vary  from  14'  to  16'  in  height  and  10'  to  11' 
in  width.  Doors  to  admit  cars  'should  give  at  least  12"  clearance 
on  each  side,  and  2'  overhead. 

Street  trolley-cars  are  about  8'  6"  wide  for  the, car  proper,  and 
the  steps  project  about  8".  Height  from  track  to  top  of  coach, 
11'  6";  trolley-stand  is  18"  higher.  Length  up  to  42'.  Trucks 
for  a  41'  6"  car  are  about  24'  apart.  Wheel-base,  4'  centre  to  cen- 
tre. Radius  of  shortest  curve  in  Denver,  35'  to  midway  between 
rails. 

The  gauge  of  a  railroad  track  is  the  distance  between  the 
inner  sides  of  the  heads  of  the  two  rails.  The  standard  or 
"broad"  gauge  is  4'  8i";  standard  narrow  gauge,  3'  3J". 

Capacity  of  Freight-cars. — Car-loads. — The  capacity  of 
freight-cars,  and  the  minimum  car-load,  varies  so  greatly  that  no 
accurate  general  information  can  be  given.  For  heavy  freight, 
25  tons  is  an  average  load;  for  light  freight,  12  to  15  tons;  for 
household  goods,  10  tons  is  about  the  minimum;  for  lime,  15  tons 
is  about  a  minimum  load;  for  cement,  20  tons.  The  minimum 
car-load,  to  obtain  car-load  rates,  varies  with  different  roads, 
and  also  with  the  rate  made;  a  low  rate  is  usually  made  on  the 
basis  of  a  big  load.  Thirty  tons  is  a  good  load  for  heavy  freight, 
and  40  tons  is  about  the  maximum,  except  for  special  cars. 

Miscellaneous  Dimensions. — Horse-stalls. — Width,  3' 
10"  to  4',  or  else  5'  or  over  in  width,  9'  long.  Width  should  never 
be  between  4'  and  5',  as  the  horse  is  liable  to  cast  himself. 
i  Dimensions  of  Standard  Bowling  Alley. — Length  of  alley,  60'; 
width  from  centre  to  centre,  5'  6";  width  of  bed,  3'  6";  troughs 
each  side.  Pit  5';  to  drop  one  foot  at  end  below  level  of  bed; 
runway,  11'  6". 

Dimensions  of  Drawings  for  Patents  (United  States). — 10"X  15" 
with  border-line  1"  inside  all  around. 

Dimensions  of  a  Barrel. — Diameter  of  head,  17";  bung,  19"; 
length,  28";  volume,  7,680  cu.  ins. 

Miscellaneous  Memoranda. — Weight  of  Men  and 
Women. — The  average  weight  of  twenty  thousand  men  and 
women  weighed  at  Boston,  1864,  was, — men,  141J  Ibs.;  women, 
124i  Ibs. 


DIMENSIONS  OF  SCHOOLROOMS,  ETC.        1475 

Avenues  of  City  of  New  York  run  28°  50'  30"  east  of  north. 

Flagpoles. — For  a  flagpole,  extending  from  30'  to  60'  above 
the  roof,  the  following  proportions  give  satisfactory  results: 
The  diameter  at  the  roof  should  be  BV  the  height  above  the  roof, 
and  the  top  diameter  J  the  lower.  To  profile  the  pole,  divide 
the  height  into  quarters ;  make  the  diameter  at  the  first  quarter 
above  the  roof,  %  of  the  lower  diameter;  at  the  second  quarter, 
J,  and  at  the  third  quarter,  f  the  lower  diameter.* 

Dimensions  of  Schoolrooms,  Boston  Schools. — 
The  sizes  of  the  rooms  in  the  Boston  schools,  as  adopted  by  the 
School  board,  are,  for  grammar  schools,  28/X32'Xl3/  6"  high; 
for  primary  schools,  24/X32'Xl2/.  This  accommodates  56 
scholars  per  room,  in  each  grade,  allowing  216  cu.  ft.  per  scholar 
in  the  grammar  schools,  and  165  cu.  ft.  in  the  primary  grade. 

A  width  of  27'  is  very  satisfactory  for  schoolrooms,  and  is 
commonly  adopted  because  it  permits  of  the  use  of  28'  joists 
without  waste. 

Height  of  Blackboards  in  Schoolroom. — The  height 
from  floor  to  top  of  chalk-rail  should  be  about  as  follows: 

3d  and  4th  grades,  chalk-moulding 2' 1"    from  floor 

5th  grade,  "  2' 2J"     "       " 

6th  grade,  "  2'  4"      "       " 

7th  and  8th  grades,  "  2'  6"      "       " 

Slate  blackboards  are  made  3'  6",  4'  0",  and  4'  6"  high, 
4'  being  a  very  common  and  satisfactory  height. 

SIZES    OF   CHAIRS    AND    DESKS    FOR    SCHOOLS    AND 
ACADEMIES. 


Age  of  Scholar. 

Height  of  Chair. 

Height  of  Desk 

(Next  Scholar). 

Space  Occupied 
by  Desk  and 
Chair  (Back  to 

Back  of  Desk). 

16  to  18  years. 

16^ 

inches. 

29*  inches. 

2  feet  9  inches.  ' 

14  to  16 

15 

28 

2 

9 

12  to  14 

27* 

2 

8 

10  to  12 

14 

26* 

2 

7 

8  to  10 

13- 

25* 

2 

5 

7  to    8 

12 

24 

2 

4 

6  to    7 

11* 

22* 

2 

3 

5  to    6 

10* 

21 

2 

2 

4  to    5 

9* 

19 

2 

0 

Desks  for  two  scholars  are  3  ft.  10  ins.  long,  and  for  a  single  scholar,  2  ft. 
long. 

Aisles  are  2  ft.  to  2  ft.  4  ins.  wide,  according  to  age  of  scholars  and  size  of 
room. 


*  The  Building  Trades  Pocket-book. 


1476  STAIRS. 

Stairs.* — The  "rise"  of  a  stair  is  the  height  from  the  top 
of  one  step  to  the  top  of  the  next.  The  " total  rise"  is  the 
height  from  floor  to  floor.  The  "run"  is  the  horizontal  dis- 
tance from  the  face  of  one  riser  to  the  face  of  the  next.  "Risers " 
are  the  upright  boards  forming  the  face  of  the  steps,  and  the 
"treads"  are  the  horizontal  boards  on  which  the  feet  tread. 
Treads  are  usually  from  1J  to  1J  ins.  wider  than  the  run,  on 
account  of  the  nosing. 

The  "rise"  of  any  stairs  is  found  by  dividing  the  "total 
rise"  by  the  number  of  risers.  The  "run"  of  the  stairs  may 
be  fixed  at  will  unless  the  space  is  cramped,  but  to  secure  a 
comfortable  stair  the  run  must  bear  a  certain  relation  to  the 
rise. 

Rules  for  Proportion  of  Treads  and  Risers. — For  ordinary 
use  a  rise  of  7  to  7J  ins.  makes  a  very  comfortable  stair.  In 
schools  and  for  stairs  used  by  children  the  rise  should  not  exceed 
6  ins,  Stairs  having  a  rise  greater  than  7J  ins.  are  steep. 

The  width  of  the  run  should  be  determined  by  the  height  ol 
the  rise;  the  less  the  rise  the  greater  should  be  the  run,  and  vice 
versa.  Several  rules  have  been  given  for  proportioning  the  run 
to  the  rise,  viz.: 

(1)  The  sum  of  the  rise  and  run  should  be  equal  to  from  17 
to  17J  ins. 

(2)  The  sum  of  two  risers  and  a  tread  should  not  be  less  than 
24  nor  more  than  25  ins. 

(3)  The  product  of  the  rise  and  run  shall  not  be  less  than 
70  nor  more  than  75. 

These  rules  apply  only  to  stairs  with  nosings.  Stone  stairs 
without  nosings  should  have  at  least  12-in.  treads  to  be  com- 
fortable for  adults. 

Height  of  Hand-rail. — In  dwellings,  hotels,  apartments,  etc., 
the  height  of  the  rail  should  be  about  2  ft.  6  ins.  above  the  tread, 
on  a  line  with  the  face  of  the  riser.  For  grand  staircases  the 
height  may  be  reduced  to  2  ft.  4  ins.  On  steep  stairs  the  height 
should  be  from  2  ft.  7  ins.  to  2  ft.  9  ins.  The  rail  should  also 
be  raised  over  winders.  On  landings  the  height  of  the  rail 
should  be  equal  to  the  height  of  the  stair-rail  measured  at  the 
centre  of  the  tread,  the  usual  height  in  residences  being  2  ft. 
8  ins.  to  2  ft.  10  ins. 


*  This  subject  is  quite  fully  treated  in  Pare  II,  Building  Construction  and 
Superintendence. 


SASH  WEIGHTS. 


1477 


s. — The  weights  ordinarily  used  for  balancing 
windows  are  made  of  a  cheap  grade  of  cast  iron,  in  the  form  of 
a  solid  cylinder,  with  an  eye  cast  in  the  upper  end.  On  account 
of  the  limited  space  in  the  weight-box,  the  weights  should  never 
be  of  greater  diameter  than  the  thickness  of  the  sash;  conse- 
quently for  balancing  heavy  sash,  the  weights  must  be  quite 
long.  For  wide  and  low  windows  the  ordinary  sash-weight 
may  be  too  long  to  permit  the  sash  to  be  raised  or  lowered  its 
entire  height,  and  in  special  cases  it  is  often  necessary  to  use 
square  sash-weights,  and  frequently  it  is  necessary  to  use  lead 
weights,  lead  being  about  58  per  cent,  heavier  than  cast  iron. 

The  length  of  sash-weight  in  inches  required  to  balance  a 
given  weight  may  readily  be  found  by  dividing  the  given  weight 
by  the  values  in  the  following  table.  To  the  quotient  thus 
obtained  1  in.  should  be  added  to  cover  the  eye. 

WEIGHT  OF  IRON  AND  LEAD  SASH-WEIGHTS  PER  LINEAL  INCH. 


Diameter,  or 
Side  of  Square. 

Round 
Cast  Iron. 

Square 
Cast  Iron. 

Square 
Lead. 

Inches. 

Pounds. 

Pounds. 

Pounds. 

H 

0.32 

0.40 

0.64 

if 

0.46 

0.5S 

0.92 

l! 

0.62 

0.79 

1.25 

2 

0.81 

1.04 

1.64 

21 

1.03 

1.31 

2.07 

2i 

1.27 

1.62 

2.56 

2J 

1.54 

1.96 

3.10 

3 

1.83 

2.34 

3.69 

3i 

2.50 

3.18 

5.02 

4 

3.26 

4.16 

6.56 

The  approximate  diameters  of  the  common  stock  cast-iron 
sash-weights  are:  for  weights  of  8  Ibs.  and  under,  1J  ins.;  for 
weights  between  8  and  16  Ibs.  inclusive,  If  ins.;  for  weights 
between  16  and  20  Ibs.;  2  ins.  and  for  weights  between  20  and  30 
Ibs. ,  2J  ins.  Weights  above  30  Ibs.  are  usually  square  in  cross- 
section. 

Weight  of  Sash  and  Glass. — For  approximating  the  weight 
of  windows,  the  weight  of  the  glass  may  be  taken  at  3J  Ibs. 
per  square  foot  for  plate  glass,  1J  Ibs.  for  double-strength  glass, 
and  1  Ib.  for  single-strength  glass. 

For  the  weight  of  the  wooden   sash,  add  together   the   height 


1478         SEATING  SPACE  IN   CHURCHES,  ETC. 

and  width  of  each  sash  (in  feet)  and  multiply  by  2.1  for  2J-in. 
sash,  1§  for  If-in.  sash,  and  1J  for  If-in.  sash. 

The  exact  weight,  however,  can  only  be  obtained  by  weighing 
each  sash,  as  the  glass  varies  considerably  in  weight. 

In  hanging  sashes,  the  weights  for  the  upper  sash  should 
be  about  \  Ib.  heavier  than  the  sash,  and  for  the  lower  sash 
J  Ib.  lighter. 

Seating  Space  in  Churches  and  Theatres.  —  The 
minimum  spacing  for  pews,  back  to  back,  is  30  ins.  This  spacing 
is  fairly  comfortable  to  occupants,  but  is  a  little  cramped  for 
persons  to  pass  by  others  into  or  out  of  the  pew.  A  spacing 
of  32  ins.  is  to  be  preferred,  and  if  there  is  abundance  of  room^ 
the  spacing  may  be  made  33  ins.;  anything  ov,er  33  ins.  is  a 
waste  of  room.  18  ins.  in  the  length  of  the  pew  is  considered 
as  a  "  sitting." 

For  dimensions  of  pew  bodies  see  p.  48  of  " Churches  and 
Chapels." 

Opera  or  Assembly  Chairs  are  made  19,  20,  21,  and  22  ins. 
wide,  centre  to  centre-  of  arms,  and  in  arranging  them  in  rows 
where  the  aisles  converge,  the  ends  are  brought  to  a  line  on 
the  aisles  by  using  a  few  chairs  that  are  either  narrower  or 
wider  than  the  standard  width.  For  churches,  a  standard 
width  of  20  ins.  is  the  least  that  is  desirable. 

For  theatres,  21-  or  22-in.  chairs  are  commonly  used  in  the 
parquet,  20-  or  21-in.  in  the  dress  circle,  and  20-  and  19-in.  in 
balcony  and  gallery,  although  there  is  no  accepted  rule  in  this 
respect. 

On  account  of  the  seat  lifting,  opera  or  assembly  chairs  may 
be  comfortably  spaced  30  ins.  back  to  back,  and  this  is  the 
usual  spacing  in  halls  and  churches. 

In  theatres  the  chairs  are  usually  set  on  steps.  In  the  upper 
gallery  these  steps  should  not  be  more  than  30  ins.  wide;  in 
the  balcony  they  are  usually  made  either  30  or  31  ins.  wide, 
and  in  the  parquet  31  or  32  ins.  wide.  As  a  rule  the  higher- 
priced  seats  are  more  commodious  than  the  lower-priced. 

Estimating  Seating  Capacity. — The  actual  seating  capacity 
of  theatres  and  audience-rooms  can  be  determined  only  by 
drawing  the  seats  to  an  accurate  scale,  on  the  floor  plan,  and 
then  counting  the  number  of  chairs,  or  measuring  the  lineal 
feet  of  pews. 

For  approximate  purposes  the  seating  capacity  or  required 
size  of  room  may  be  determined  by  allowing  from  7  to  8  sq.  ft. 


CAPACITY  OF  CHURCHES  AND  THEATRES.     1479 

to  each  seat,  or  sitting,  when  on  a  curve,  and  6  to  7  sq.  ft.  to 
each  sitting  when  in  straight  rows,  the  smaller  number  being 
used  only  for  large  rooms.  This  allows  for  aisles  and  pulpit 
platform.  For  small  concert  halls  and  narrow  rectangular 
rooms  6  sq.  ft.  per  sitting  will  usually  be  sufficient  allowance, 
provided  only  the  actual  floor  space  utilized  for  seats  and  aisles 
is  considered. 


CAPACITY  OF  SEVERAL  CHURCHES,  THEATRES,  AND 
OPERA-HOUSES. 

CHURCHES. 
(Estimating  a  person  to  occupy  an  area  of  19.7  ins.  square.) 


St  Peter's 

54,000 

Notre  Dame,  Paris. 

21  000 

Milan  Cathedral.          

37,000 

Pisa  Cathedral.  .            

13,000 

St  Paul's   Rome      .  . 

32,000 

St.  Stephen's,  Vienna.  . 

12  400 

St.  Paul's,  London  

25,600 

St.  Dominic's,  Bologna  .... 

12,000 

St   Petronio's,  Bologna 

24,400 

St.  Peter's,  Bologna. 

11,400 

Florence  Cathedral 

24,300 

Cathedral  of  Sienna.  .  . 

11  000 

Antwerp  Cathedral                .  . 

24,000 

St.  Mark's,  Venice  

7,000 

St   Sophia's   Constantinople. 

23,000 

Spurgeon's  Tabernacle.  .  . 

7,000 

St  John  Lateran  's 

22  900 

THEATRES  AND    OPERA-HOUSES. 
EUROPEAN. 


Carlo  Felice,  Genoa 

2,560 

Drury  Lane,  London. 

1  948 

Opera-house,  Munich  
Alexander,  St.  Petersburg. 

2,370 
2,332 

Co  vent  Garden,  London  .  .  . 
Opera  House,  Berlin.  .  . 

3,000 
1,636 

San  Carlos,  Naples.  .  . 

2  240 

Adelphi,  London.  .  .. 

2  300 

Imperial,  St.  Petersburg.  .  .  . 

2,160 

Lancaster,  London  

1,850 

La  Scala,  Milan.  ... 

2,113 

Globe,  London  

1,100 

Academy  of  Paris.  . 

2  092 

The  Auditorium,  Chicago.  .  . 
Metro')'  t'n  Opera  House  N  Y. 

4,200 
3,200 

Abbey's  Theatre,  N.  Y  
Empire  Theatre,  N.  Y.  .  . 

1,450 
1,150 

Philadelphia  Academy  
Boston  Theatre,  Boston.  .  .  . 
American  Theatre,  N.  Y.  .  .  . 

3,124 
3,000 
2,500 

Fifth  Ave.  Theatre,  N.  Y.  . 
Castle     Square     Theatre,  I 
Boston  ( 

1,400 
1,600  to 
1,800 

Proctor's    Pleasure    Palace, 
N.  Y  

2,100 

Gaiety  Theatre,  Boston.  .  -j 

nearly 
3,000 

Lyric  Theater,  N.  Y  

1,543 

Grand     Opera-house,    Cin- 

1,736 

1480 


DIMENSIONS  OF  THEATRES. 


DIMENSIONS   OF  THEATRES  AND  OPERA-HOUSES. 

The  following   are   the  dimensions,   in   feet,  of  some   of  the 
prominent  theatres  in  this  country  and  in  Europe: 


Name  and  Location. 

Auditorium. 

Prose    i. 
Opening. 

Stage. 

i 

-8 

g 

d 
a 

& 

<3 

,d 

3 

a> 

w 

,d 
•5 

s 

| 

-S 

jtj 

$ 

j 

a 
<r> 
Q 

1 

« 

a> 

Alexander,  St.  Petersburg 
,  Berlin. 

58 
51 
71 
74 
47 
66 
51 
56 

76 
78 
95 
73 
56 
76 
66 
64 
71 
87 
78 
65 
61 

58 
47 
64 
83 
57 
66 

56 
41 
49 
52 
37 
43 
32 
32 
46 
48 
48 
30 
31 

54 

50 

75 
92 

86 
66 
80 
78 
86 
48 
87 
83 
90 
62 
68 

100 
110 
67 
40 
71* 
80 
77i 

70 
67* 

67 

68 
60 

84 
76 
78 
74 
69 
82 
55 
80 
68 
71 
72 
38 
46 

73 

70 
30 

65* 
28* 
35 
43* 

40, 
30f 

41 

45* 
42 

88 
95 
65 

73* 
70 

70 

La  Scala,  Milan  

San  Carlo,  Naples.  . 

Grand  Theatre,  Bordeaux 
Salle  Lepelletier,  Paris.  .  . 
Covent  Garden,  London  . 
Drury  Lane,  London.  .  .  . 
Boston  Theatre,  Boston.  . 

'58*' 
"74" 

Academy  of  Music,  N.  Y.. 
Opera-house,  Phila.  . 

62 
66 
60 
68 

Globe  Theatre,  Boston.  .  . 
Museum,  Boston.  . 

Metrop't'n  Opera  House, 
New  York*  

The  Auditorium,  Chicago. 

Empire  Theatre,  N.  Y. 
Abbey's  Theatre,  N.  Y.  .  . 
Harrigan's  Theatre,  N.  Y. 
Fifth  Ave.  Theatre,  N.  Y. 

69 
70f 
56i 

66 
79 
52 

'47P 

34 
35 

27 

34 
34 

American,  N.  Y.  .  .  . 

74* 

74* 
67* 

67 

79* 

77 

74* 

74* 
67 

69 

85* 
80f 

702 

39 

34 
32 

36 
40 

39 

345 
30 

34 
34 

Proctor's    Pleasure    Pal- 
ace, N.  Y. 

Hudson  Theatre,  N.  Y.  .  . 
Grand  Opera-house,  Cin- 
cinnati   .    .    . 

Castle    Square    Theatre, 
Boston6  

Gaiety  Theatre,  Boston  .  . 

1  From  the  curtain  or  back  line  of  proscenium  opening. 

2  Measured  from  stage  to  centre  of  ceiling. 

3  To  the  "gridiron"  or  rigging-loft. 

4  As  remodelled  in  1893. 

5  Can  be  enlarged  to  40'  X  40' . 

6  The  plan  of  this  theatre  is  in  the  shape  of  a  horseshoe. 

Notes  on  Theatre  Dimensions.*— "The  utmost  dis- 
tance from  the  front  of  the  stage  to  the  rear  ought  not  to  exceed 
75  ft.,  or  the  limit  the  voice  is  capable  of  expanding  in  a  lateral 
direction." 

"  Measured  from  the  curtain  line,  the  Theatre  of  San  Carlos  at 
Naples  is  73  ft.;  at  Bologna  74  ft.  Of  the  London  theatres,  the 


*  From  "The   Planning   and  Construction   of  American   Theatres,"  by 
Wm.  H.  Birkmire 


GUTTERS  AND  CONDUCTORS.  1481 

Adelphi  is  74  ft.,  Covent  Garden  80  ft  ,  the  Gaiety  53  ft.  6  ins., 
Lancaster  5S  ft.  4  ins.,  Marylebone  74  ft.,  and  the  Globe  47  ft. 
6  ins." 

The  width  of  the  ideal  theatre,  between  inside  walls,  should  be 
from  70  to  75  ft.,  arid  "the  ceiling  should  be  55  to  65  or  even 
70  ft.  above  the  stage  level." 

"  The  depth  of  the  parquet  floor  at  the  orchestra-rail  is 
governed  by  the  stage  level,  and  is  generally  from  3  ft.  6  ins.  to 
4  ft.  3  ins.  below  the  stage.  A  depth  of  3  ft.  9  ins.  is  a  good 
height,  as  it  fixes  the  eye  of  the  spectator  5  ins.  above  the  stage 
level." 

"  The  height  of  the  stage,  i.e.,  from  the  floor  to  the  bottom  of 
the  'gridiron'  or  rigging-loft,  should  be  2  or  3  ft.  over  twice  the 
height  of  proscenium  opening,  that  the  fire-curtain  may  be 
raised  the  full  height  of  the  opening."  There  should  be  a  height 
of  7  ft.  above  the  gridiron  to  enable  the  flymen  to  adjust  their 
ropes  with  facility. 

Proportioning-  Gutters  and  Conductors  to  Root 
Surface. — The  size  of  gutters  and  down-spouts  and  their 
distance  apart  for  roofs  (of  Mill  Buildings)  with  -J  pitch  and  of 
different  spans  are  shown  by  the  following  table :  * 

One  half  roof  span,  ft 10  20  30  40  50  60  70  80 

Size  of  gutter,  in 5  5  6  6  7  7  8  8 

"     "  down-spouts,  ins.  ...3  3  4  4  5  5  6  6 

Spacing  of  down -spouts,  ft. .  .   50  50  50  50  40  40  40  40 

The  specifications  of  the  American  Bridge  Company  provide 
as  follows  for  the  size  of  gutters  and  conductors  :f 


Span  of  Roof. 

Up  to    50  ft. 

50  to    70  " 

Gutter. 
6  ins. 

7   " 

Conductor. 
4  ins.  every  40  ft. 
5    '/.       "      40  " 

70  to  100  " 

8    " 

5   "        "      40  " 

Hanging  gutters  should  have  a  slope  of  about  1  in.  to  16  ft. 

"The  Produce  Exchange  Building  in  New  York  City,  with  a 
roof  area  of  three-fourths  of  an  acre,  roughly  speaking,  has 
twelve  leaders  of  about  5  ins.  diameter.  The  roof,  which  is  paved 
with  fire-brick,  is  graded  with  slopes  of  perhaps  one  in  fifty  toward 

*  H.  G.  Tyrrell,  C.E. 
tM,  S.  Ketchum,  C.E, 


1482  ELEVATORS. 

the  points  at  which  the  leader  openings  are  placed,  most  of  these 
draining  surfaces  being  about  40X  70  ft.  each.  The  provision 
here  made  is  equivalent  to  about  1  sq.  in.  of  leader  opening  to 
140  sq.  ft.  of  roof  surface.  On.  the  Sloane  Building,  on  19th 
Street  and  Broadway,  New  York  City,  with  a  roof  area  of  18,000 
or  20,000  sq.  ft.,  sloping  one  in  twenty-five,  there  are  two  leaders 
of  about  6  ins.  in  diameter,  and  a  third  rectangular,  4X  6  ins. 
This  gives  an  allowance  of  240  sq.  ft.  of  surface  to  the  square 
inch  of  leader  opening,  while  on  the  Massachusetts  Hospital 
Life  Insurance  Company's  Building,  and  the  Hemenway  Build- 
ing, in  Boston,  the  proportion  is  only  from  60  to  70  sq.  ft  to  the 
square  inch  of  opening."  * 


ELEVATORS— SPECIFICATIONS    FOR.f 

Conditions  which  should  be  Considered  and  made 
Definite  by  the  Architect,  Preliminary  to  the 
Elevator  Specifications. 

(a)  The  System:  Electric  or  Hydraulic. — If  electric,  whether 
of  the  drum  or  friction-drive  type.  If  hydraulic,  whether  of  the 
horizontal  cylinder,  the  vertical  cylinder,  or  the  plunger  type. 

Where  a  reliable  and  sufficient  direct-current  supply  is  avail- 
able for  one  or  two  elevators,  the  electric  is  unquestionably  the 
best  system.  For  batteries  of  three  or  more  the  system  must 
be  determined  by  the  special  conditions  which  exist  in  every 
plant,  and  are  relative  to  the  other  mechanical  equipment,  and 
should  be  decided  only  after  mature  deliberation  and  consul- 
tation with  unprejudiced  engineers  and  elevator  builders. 

(6)  Location  of  Hoistways  and  Machinery  Room. — The  location 
of  the  hoist  ways  is  rather  a  matter  for  the  good  judgment  of  the 
architect,  having  reference  to  facility  of  ingress  and  egress  of 
passengers,  so  as  to  avoid  crowding  and  confusion  at  the  main 
entrance. 

The  machinery-room  should  be  immediately  adjacent  to  the 
hoistways,  well  ventilated,  and  protected  from  dust,  large  and 
high  enough  to  permit  easy  access  to  all  parts  of  the  machines 
for  inspection  and  repairs. 

(c)  Number  and  Sizes. — The  number  and  sizes  will  be  deter- 
mined, first,  by  the  space  available  for  hoistways;  second,  the 


*  Mr.  Dwight  Potter  in  "  The  Technology  Quarterly." 
}  Prepared  by  Sydney  F.  Weston. 


ELEVATORS.  1483 

number  of  passengers  to  be  carried  during  the  rush  hours;  third, 
the  frequency  of  car  departures  from  the  ground  floor,  or 
"schedule." 

Having  determined  the  square  feet  of  cross-section  to  be  used, 
the  next  thing  to  determine  is  the  number.  Three  cars,  each 
carrying  one-third  the  passengers,  is  preferable  to  two,  each 
carrying  one-half,  because  the  car  departures  are  more  frequent, 
reducing  the  time  the  passengers  must  wait  at  the  ground-floor, 
and  therefore  lessening  the  liability  of  over-congestion  and 
loss  of  patience  by  those  waiting. 

Every  machine  is  likely  to  need  repairs;  therefore  the  more 
units  in  the  battery  the  less  will  the  one  out  of  commission  be 
missed.  It  is  far  greater  economy  to  have  an  excess  capacity 
than  even  a  slight  under  capacity,  especially  against  the  time 
when  it  may  be  imperative  to  shut  down  one  or  more  machines. 

In  determining  the  load  for  passenger  service,  allow  80  Ibs. 
per  sq.  ft.  of  platform  area,  and  150  Ibs.  per  passenger. 

(d)  Loads  and  Speeds. — The  loads  and  speeds  determine  the 
sizes  of  machines.     The  loads  having  been  decided  as  above, 
the  question  of  speed  is  next,  and  is  a  most  important  factor. 

Generally  the  local  ordinances  limit  the  car  speed,  as  in  New 
York,  to  a  maximum  of  400  ft.  per  min.  for  cars  that  stop  at 
every  floor;  and  to  500  ft.  per  min.  for  express  cars,  those  that 
go  the  first  two-thirds  of  their  travel  without  stop. 

The  best  elevator  insurance  companies  will  not  permit  electric 
drum  elevators  to  travel  over  about  350  ft.  per  min.,  whereas 
the  electric  friction-drive,  or  the  hydraulic  types,  are  safe  and 
under  perfect  control  for  the  higher  speeds.  Four  hundred  feet 
per  minute  is  about  as  high  a  speed  as  the  human  system  can 
stand  without  unpleasant  sensation,  and  is  ample^for  the  best 
schedules. 

In  hydraulic  systems  it  is  necessary  for  figuring  the  pumps 
and  tanks  that  the  maximum  number  of  round  trips  per  hour  be 
specified. 

(e)  Hoistways. — The  hoistways  should  be  finished  to  plumb- 
line  dimensions,  so  that  the  car  running  on  guide-rails  set  to 
plumb-line  will  at  all  points  have  the  same  clearance. 

Provide  supports  adjacent  to  the  hoistway  for  the  overhead 
beams  at  a  distance,  if  possible,  of  at  least  6  ft.  from  the  top  of 
the  car  frame  when  the  car  platform  is  flush  with  the  top  land- 
ing, and  more  is  better,  in  order  to  have  ample  "runby,"  i.e., 
the  distance  between  the  top  of  the  car  frame  anj  the  lowest 


1484  ELEVATORS. 

point  of  the  overhead  work,  so  that  should  the  car  slide  by  the 
top  landing  a  little  before  the  automatic  limits  shut  off  the  mo- 
tive power,  there  would  be  a  minimum  danger  of  running  into 
the  overhead  work. 

For  the  same  purpose  there  should  be  a  pit  at  the  bottom  of 
the  shaft  at  least  5  ft.  deep  below  the  bottom  landing. 

The  distance  from  the  above-mentioned  supports  for  overhead 
beams,  in  the  clear  below  the  skylight,  varies  from  4  or  5  to  10 
ft.,  and  should  be  determined  by  the  elevator-maker. 

(/)  Counterweight,  Location  of. — In  New  York,  the  Building 
Department  requires  that  the  ' '  counterweights  shall  be  run  in  a 
separate  shaft  from  the  car,  or  in  a  chace  separated  from  the 
car  shaft  by  a  substantial  screen  or  partition  for  the  full  height 
of  the  hoist."  These  chaces  should  be  at  least  8  ins.  deep  by 
36  ins.  long. 

(g)  The  Bureau  of  Buildings  for  the  Borough  of  Manhattan  on 
April  24,  1902,  issued  regulations  governing  the  construction, 
inspection,  and  operation  of  passenger  elevators,  which  were 
published  in  the  "Record  and  Guide/'  May  10,  1902,  and  are 
especially  called  to  the  attention  of  all  architects,  as  not  only 
obligatory  in  New  York,  but  excellent  practice  at  all  times. 

(h)  The  foregoing  is  intended  to  give  an  idea  of  what  the  archi- 
tect must  provide  in  the  building  for  the  reception  of  the  elevator 
apparatus,  and  what  he  must  determine  to  enable  the  maker  to 
intelligently  design  and  lay  out  his  machines. 

Above  all  things,  avoid  specifying  apparatus  of  special  con- 
struction. Utilize  standard  design  as  much  as  possible,  as,  first, 
it  is  more  apt  to  be  well  designed,  tested,  and  built;  second, 
repair  parts  can  be  easily  and  quickly  obtained. 

Specifications. — These  should  state: 

(1)  Kinds  of  service  and  number  of  elevators  for  each  service. 

(2)  Maximum   load.     (3)   Speed    with   maximum   load.     (4) 
Maximum  speed.     (5)  Load  with  maximum  speed. 

(6)  Maximum  number  of  round  trips  per  hour  for  each  elevator. 

(7)  Method  of  car  control. 

(8)  Sizes  of  hoist  ways  and  area  of  car  platforms. 

(9)  Travel  of  car  platform  in  feet;   and  the    number  of  car 
landings. 

(10)  System. — If  electric,  the  current  and  voltage;  if  hydraulic, 
the  steam  pressure  for  the  pumps,  or  the  water  pressure  if  the 
purchaser  provides  the  pumps,  tanks,  or  other  source  of  water- 
pressure  supply. 


ELEVATORS.  1485 

(11)  An  elevation  sketch  showing  landings,  supports  for  over- 
head beams,  space  for  the  overhead  sheaves  and  rimbys  at  top 
and  bottom;  a  plan  sketch  showing  size  and  shape  of  hoistways, 
entrances,   position  of  car  and  counterweight  guide-rails,  and 
location  of  space  available  for  machines,   pumps,  tanks,   etc., 
with  reference  to  the  hoistways. 

(12)  Car  and  counterweight  guide-rails,  whether  of  wood  or 
steel. 

(13)  Posts  or  supports  for  fastening  the  rails,  whether  of  wood 
or  iron,  carried  all  the  way  up  from  the  bottom;  or  iron  brackets 
bolted  to  the  building  framework  at  each  floor. 

(14)  Finished  car  or  cage,  value  of;  i.e.,  the  specified  amount 
to  be  allowed  for  each,  the  design  to  be  subject  to  the  approval 
of  the  architect. 

(15)  Ropes,  the  number  and  size  of,  if  not  left  to  the  judgment 
of  the  maker.     Always  require  the  largest  sheaves  possible,  as 
this  factor  determines  largely  the  life  of  the  ropes. 

(16)  Signals,  system  of;  i.e.,  (a)  annunciators  in  the  cars  with 
push-buttons  at  the  landings;  or  (6)  "up"  and  "down"  signals 
in  the  cars,  with  "up"  and  "down"  buttons  at  the  landings,  so 
arranged  that  a  car  going  up  receives  only  "up"  signals,  and  a 
car  going  down  receives  only  "down"  signals,  each  signal  being 
automatically  reset  by  the  first  car  that  passes  that  floor  in  the 
direction  for  which  the  signal  is  given.  The  latter  system  adds 
greatly  to  the  efficiency  of  a  battery  of  elevators,  in  that  it  avoids 
the  confusion  of  more  than  one  car  answering  a  signal,  or  a  car 
going  in  one  direction  stopping  for  a  passenger  going  in  the  oppo- 
site direction.  Always  specify  the  number  of  floors  at  which 
each  car  is  to  land. 

(17)  Indicators,  whether  at  the  ground-floor  only  (for  the  in- 
formation of  the  starter  as  to  the  position  of  the  cars)  or  at  all 
floors. 

Indicators  are  unnecessary  with  the  automatic  signals  last 
described,  except  at  the  ground-floor,  there  being  at  each  floor 
an  "up"  and  a  "down"  signal  to  show  the  first  available  car  in 
either  direction. 

(18)  Source  of  power.    Specify  whether  the  connection  will  be 
brought  to  the  elevator  apparatus  by  the  purchaser  or  by  the 
elevator  contractor;    if  by  the  latter,  give  sketch  showing  the  dis- 
tance, and  for  the  electric  system  specify  whether  the  wiring  is 
to  be  open  (i.e.,  on  cleats),  in  moulding,  or  in  conduit;   the  sizes 
of  wire,  and  the  switches,  cutouts,  etc.;  for  an  hydraulic  system, 


1486  ELEVATORS. 

the  size  of  pipe  for  steam  supply.     Leave  the  sizes  of  water-pip- 
ing to  the  elevator  contractor,  and  hold  him  responsible  for  them. 

(19)  Pumps  and  tanks  in  hydraulic  plants  to  be  furnished  by 
the  contractor.    Specify  whether  the  capacity  is  to  be  just  ample 
to  do  the  work,  or  whether  there  is  to  be  a  reserve  capacity,  with 
reserve  units,  to  provide  against  interfering  with  the  service  in 
case  of  accident  to  a  pump  or  tank,  but  leave  the  sizes  and  design 
to  the  judgment  of  a  responsible  elevator  maker. 

(20)  Foundations  for  the  machine — whether  to  be  provided 
by  the  purchaser  or  by  the  contractor. 

(21)  Miscellaneous. — Gratings  underneath  the  overhead  work, 
pit-pans,  painting  in  addition  to  the  standard  factory  finish,  and 
all  items  not  above  mentioned,  are  generally  furnished  by  the 
purchaser  under  separate  contract,   but  by  whom   should    be 
specified  in  the  elevator  specifications. 

Safety. — Under  the  subject  of  "safety"  must  be  considered  the 
most  vital  feature  of  the  entire  apparatus — the  mechanical  de- 
vice, or  "  car  safety ,"  for  gripping  the  rails  and  stopping  the  car 
in  case  the  ropes  break,  or  for  other  reason  the  car  acquires  a 
falling  speed  in  excess  of  that  for  which  the  mechanism  is  designed. 

There  are  innumerable  safeties  on  the  market,  but  only  one  or 
two  fulfilling  the  ideal  conditions  of  first  "cushioning,"  or  grad- 
ually checking  the  fall,  and  then  positively  and  mechanically 
gripping  the  rails  with  a  power  that  increases  until  the  car  stops. 

I)ata  as  to  Size  and  Number  of  Elevators  Re- 
quired.*— An  idea  of  the  practice  in  elevator  installations 
may  be  obtained  from  Table  No.  1,  which  gives  the  story  heights, 
the  approximate  area  of  office  space  above  the  first  floor,  the 
number  of  cars,  the  office  area  per  car,  and  the  area  of  each  car, 
as  actually  installed. 

To  determine  the  number  of  trips  and  car-travel  per  hour,  ob- 
servations were  made  at  four  office  buildings  in  Philadelphia: 
Drexel  Building,  ten  stories  high;  Stephen  Girard  Building, 
thirteen  stories  high;  Land  Title  and  Trust  Building,  fifteen 
stories  high ;  Real  Estate  Trust  Building,  seventeen  stories  high. 

In  the  Drexel  Building,  which  has  six  elevators,  one  elevator 
ran  from  the  first  to  the  fourth  story;  one  elevator  from  the  first 
to  the  fifth  story;  two  elevators  from  the  first  to  the  tenth  story, 

*  Extract  from  a  paper  by  Mr.  Charles  G.  Darrach  read  before  the  Amer- 
ican Society  of  Civil  Engineers,  October  2,  1901,  and  published  in  the  Amer- 
ican Architect,  October,  1901. 


ELEVATORS. 


1487 


stopping,  if  required,  at  any  of  the  floors;  and  two  elevators  ran 
to  the  fifth  story  " express,"  and  served  all  the  stories  above. 


TABLE  NO.  1. 


Office  Area 

No. 

Square 

Area  of 

Building. 

Stories. 

above 
First  Floor, 

of 
Cars. 

Feet  per 
Car. 

Car, 
Sq.  Ft. 

Sq.  Ft. 

St.  Paul  Building,  New  York 

25 

83,200 

6 

13,900 

23.6 

Empire  Building,  New  York. 

21 

150,000 

10 

15,000 

42.0 

N.  American  Building,  Phila- 

delphia   

18 

90,500 

5 

18,100 

27.6 

Real  Estate,  Philadelphia.  .  . 

17 

155,650 

10 

15,560 

23.7 

Bowling  Green,  New  York.  .  . 
Land  Title,  Philadelphia.  .  .  . 

16 
15 

222,000 
66,400 

9 
5 

24,700 
13,300 

29.'  6 

Stephen  Girard,  Philadelphia. 

13 

67,000 

4 

16,750 

29.0 

Drexel  Building,  Philadelphia 

10 

130,000 

6 

21,700 

21.4 

At  the  Stephen  Girard  Building  there  were  four  elevators,  which 
ran  " accommodation"  through. 

At  the  Land  Title  and  Trust  Company's  Building  there  were 
five  elevators  which  ran  on  schedule  time,  " accommodation"  to 
all  floors  except  the  second. 

At  the  Real  Estate  Building  all  the  cars  ran  " accommodation" 
through. 

Table  No.  2  shows  the  results  obtained. 

TABLE  NO.  2. 


Building. 

Stories. 

Height, 
Feet. 

Travel 
per  Trip, 
Feet. 

Trips 
per 
Hour. 

Average 
Feet  per 
Minute. 

Drexel  Building  . 

4 

40 

80 

60 

80 

5 

50 

52 

87 

1  1            <  < 

101 

108 

216 

35 

«  «            « 

101 

108 

216 

35 

1  ?fi 

Stephen  ^Jirard  Building  
Land  Title  Trust  Building.  .  . 

Real  Estate  Trust  Building.  '.  '. 

13 
15 
15 

17 

150 
180 
180 
200 

300 
360 
360 
400 

30 

271 
242 
25 

150       i 

1442 
167 

1  Actual. 


2  Estimated. 


From  observations  at  the  Drexel  Building  in  1897,  during  the 
noon  hour,  the  up-travel  from  the  first  floor  reached  800  passen- 
gers, with  a  maximum  of  12  to  13  passengers  in  the  car.  The 
cars  were  also  overtaxed  all  day,  from  10  A.M.  until  4  P.M. 

At  the  Land  Title  Building,  running  twenty-four  trips  per  hour, 
the  service  was  very  satisfactory.  There  was  a  slight  crowding 
during  the  noon  hour;  this,  however,  can  be  remedied  by  the  use 
of  the  improved  car-signalling  apparatus. 


1488 


ELEVATORS. 


At  the  Stephen  Girard  Building,  the  cars  are  crowded  during 
the  noon  hour,  and  also  between  three  and  five  in  the  afternoon. 

All  three  of  these  buildings  are  well  filled. 

The  Real  Estate  Building  was  not  fully  occupied,  so  that  the 
elevator  service  there  could  not  be  fairly  judged. 

Using  the  trips  per  hour  as  observed  and  estimated,  and  equat- 
ing the  car  area  by  the  formula : 


TX22' 

in  which  a  =  square  feet  of  car  area; 

A  =  square  feet  of  office  area; 
T  =  total  trips  per  hour. 

we  derive  the  following  table: 

TABLE  NO.  3.— EQUATED  CAR  AREAS. 


Building. 

Stories. 

Num- 
ber of 
Cars. 

Sq.  Ft.  of 
Office  Area 
per  Car. 

Actual 
Car  Area 
in  Sq.  Ft. 

Equated 
Car  Area 
in  Sq.  Ft. 

Estimated 
Trips  per 
Hour. 

St  Paul 

25 

6 

13,900 

23  6 

31  5 

120 

Empire  
Real  Estate.  .  .  . 
Bowling  Green. 

21 
17 
16 

10 
10 
9 

15,000 
15,560 
24,700 

42.0 
23.7 

31.0 
28.3 
43.1 

220 
250 
234 

Land  Title. 

15 

5 

13,300 

22.4 

135 

Stephen  Girard. 

15 
13 
10 

5 
4 
6 

13,300 
16,750 
21,700 

29.6 
23 

21.4 

25 
25.4 

28.2 

120 
120 
210 

At  the  Drexel  Building  the  two  cars  which  ran  "express"  to 
the  fifth  floor,  and  the  two  cars  which  ran  " accommodation" 
through,  made  the  same  number  of  trips,  and  carried  practically 
the  same  number  of  passengers.  It  would  be  interesting  to  know 
whether  similar  results  are  obtained  in  any  other  buildings,  and 
the  advantage  gained  in  arranging  the  travel  of  the  various  cars 
to  serve  " accommodation"  through  the  entire  trip,  "express" 
part  way,  or  providing  separate  service  to  different  heights  in  the 
building. 

Using  the  same  formula,  and  equating  to  obtain  the  square 
feet  of  office  space  per  car,  with  given-sized  cars,  and  the  number 
of  through  trips  heretofore  used,  we  have  the  following  resultsi 
with  cars  of  25  and  30  sq.  ft.  area: 


ELEVATORS. 


1489 


TABLE  NO.  4.— SQUARE  FEET  OF  OFFICE  AREA  PER  CAR. 


Stories. 

Car  Area  =  25  sq.  ft. 

Car  Area  =  30  sq.  ft. 

25      . 

11,000  sq. 
12,100 
13,750 
14,300 
14,850 
16,500 
19,250 

ft.  p< 

3r  c< 

ir 

13,200  sq. 
14,500 
16,500 
17,160 
17,820 
19,800 
23,100 

tft.  p< 

3r  a 

ir 

21  

17  

16 

15  

13  

10  

Additional  data  furnished  by  Mr.  Kloman  of  the  Otis  Elevator 
Co: 


Name  of  Building,  all  in  New 
York  City. 

No.  of 
Eleva- 
tors. 

No.  of 
Floors. 

Total 
Floor 
Area. 

Floor 
Area  per 
Eleva- 
tor. 

18 

20 

465,540 

25,864 

Park  Row  (Ivins  Syndicate)  

10 

25 

315,000 

31,500 

Atlantic  Mutual 

6 

18 

162,000 

27,000 

American  Exchange  Bank  

3 

16 

72,000 

24.000 

Bank  of  Commerce.  .  . 

7 

19 

172,000 

24,571 

S.E.  cor.  Broadway  and  Maiden  Lane 

6 
10 

18 
20 

129,000 
170,000 

21,500 
17,000 

The  Empire  Building  is  said  to  be  noted  for  its  quick  service, 
and  the  Park  Row  Building  for  slowness. 

According  to  Mr.  Kloman,  the  officers  of  the  Otis  Elevator 
Co.  have  come  to  the  conclusion  that  the  best  service  is  obtained  . 
with  a  large  number  of  small  cars  having  a  capacity  of  not  over 
15  passengers,  rather  than  with  fewer  large  cars. 

Electric  Elevator  with  Push-button  Control. — 
This  is  perhaps  the  most  important  of  the  latest  improvements 
in  elevators,  as  it  permits  of  the  installation  of  elevators  in  resi- 
dences and  other  buildings  where  a  constant  attendant  would 
be  both  expensive  and  undesirable.  This  type  of  elevator  is 
particularly  adapted  to  private  residences,  apartment  houses, 
hospitals,  and  other  places  where  the  service  is  intermittent  and 
it  is  desired  to  do  away  with  the  expense  of  an  attendant. 

"The  elevator  is  always  ready  for  service,  and  it  is  equipped 
with  every  safeguard  which  human  ingenuity  can  devise  against 
the  possibility  of  accident." 

The  operation  of  the  elevator  is  as  follows:  A  passenger  desir- 
ing to  use  the  elevator  presses  a  button  placed  near  the  elevator 
shaft,  and  the  car,  if  not  in  use,  immediately  travels  to  that  floor 
and  stops  automatically.  When  the  car  has  come  to  rest  at  that 


1490 


ELEVATORS. 


floor,  the  door  can  be  opened.  The  passenger  then  enters  the 
car  and  closes  the  door.  The  car  will  not  leave  that  floor  unless 
the  door  is  tightly  closed.  Inside  the  car  there  is  a  series  of  push- 
buttons, numbered  to  correspond  with  the  various  floors.  The 


FIG.  A.  WOOD  GUIDES.  SI.DE  POST. 

MACHINE  AND  COUNT ERWEJG.HT  AT  BACK 

OR  MACHINE  OVER.HEAD.  / 


With  machine  and  counter- 
weight at  side,  the  width  of 
hatch  must  be  increased  3  ins., 
and  the  depth  may  be  5  ins. 
less.  Steel  guides  effect  a 
saving  in  width  of  hatch  of 
1  to  2  ins. 


With  steel  corner  guides, 
depth  of  hatch  is  same  as  in 
Fig.  B,  but  width  is  £  in.  less. 


RG.  B..  WOOD  GUIDES.  CORNER  POST. 

MACHINE  AT  BACK  OR  OVERHEAD. 

COUNTERWEIG.HT  AT  SIDE. 

passenger  pushes  the  proper  button  and  the  car  proceeds  to  the 
desired  landing  and  stops  automatically.  Not  until  the  passen- 
ger has  left  the  car  and  closed  the  door  can  the  elevator  be  con- 
trolled from  any  other  floor.  Should  the  passenger  desire,  for 
any  reason,  to  stop  the  car  at  any  point  of  its  travel,  he  can  do 


MAIL  CHUTES.  1491 

so  instantaneously,  by  merely  pushing  the  safety  button  with 
which  the  car  is  provided. 

Standard  Relations  of  Hatchway,  Platform,  and 
Car  Sizes. — In  their  1903  Catalogue  the  Otis  Elevator  Co.  (which 
furnishes  a  large  proportion  of  the  elevators  in  the  United  States) 
published  sixteen  engravings  showing  the  required  size  of  hatch- 
way and  car  platforms  under  different  conditions,  taking  the  in- 
side dimensions  of  the  car  as  a  base. 

As  these  relative  dimensions  apply  to  all  elevators — electric, 
hydraulic,  steam,  and  belt-driven — they  will  be  found  very  use- 
ful for  reference  in  the  preparation  of  plans, 

The  diagrams  for  two  of  the  most  common  installations  are  re- 
produced on  opposite  page. 

MAIL  CHUTES. 

The  Cutler  patent  system  of  mailing  letters  from  each  floor, 
by  means  of  a  specially  constructed  chute  connected  with  the 
receiving-box  at  the  bottom,  has  come  into  such  general  use  in 
public  buildings,  apartment  houses,  and  hotels  that  architects 
should  be  informed  in  regard  to  the  restrictions  affecting  the 
same  and  what  is  required  in  the  way  of  preparation.  The 
system  is  installed  by  the  patentees,  under  regulations  of  the 
Post  Office  Department  governing  its  construction  and  location. 
It  may  be  placed  in  any  building  of  more  than  one  story  used 
by  the  public,  where  there  is  free  delivery  and  collection  service, 
in  the  discretion  of  the  local  postmaster,  subject  to  whose  ap- 
proval the  contracts  are  made. 

The  chute  must  extend  in  a  vertical  line,  must  be  exposed  to 
view,  and  accessible  throughout  its  entire  length.  It  is  made  in 
removable  sections,  to  facilitate  clearing  it  in  the  event  of  acci- 
dent. 

The  requirements  for  " preparatory  work"  are  described  in 
Part  II,  Building  Construction  and  Superintendence,  p.  520. 
Before  the  final  completion  of  plans,  however,  architects  or  owners 
should  submit  the  same  to  the  Cutler  Mfg.  Co.,  Rochester,  N.  Y., 
with  whom  contracts  for  the  installation  must  be  made.  The 
whole  apparatus,  when  erected  and  the  Government  lock  put 
on  the  box,  passes  under  the  exclusive  care  and  control  of  the 
Post  Office  Department. 


1492 


REFRIGERATORS. 


REFRIGERATORS. 

The  following  information  is  given  as  a  guide  to  architects  in 
providing  for  refrigerators  in  fine  residences,  hotels,  club 
buildings,  etc. 

A  consultation  with  some  reliable  refrigerator  builder,*  how- 
ever, is  always  wise  before  deciding  in  relation  to  space  to  be 
occupied  by  refrigerators,  refrigerating  rooms,  freezers,  etc.,  as 
a  satisfactory  refrigerator  cannot  be  adapted  to  a  badly  proportioned 
space.  Care  should  be  taken  to  select  a  refrigerator  simple  in  its 
working  and  easily  cleansed,  as  modern  sanitary  science  has 
traced  much  sickness  to  poor  refrigeration.  Thorough  insula- 
tion is  one  of  the  most  important  features  in  a  refrigerator,  as 
upon  this  depends  economy  in  the  use  of  ice,  the  keeping  of  the 
cold  air,  and  the  consequent  perfect  preser- 
vation of  the  food. 

Fig.  1  is  a  kitchen  refrigerator  for  use  in 
families  of  ordinary  size,  and  has  the  ice 
located  in  the  centre.     Depth  should  not  be 
over  3   ft.    nor  under  2   ft.     Height  may 
4  to  7  ft.     Length  of  front  largely  de- 
'x    termines  the  capacity,  and  should  be,  say, 
Fig.  1  from  5  to  7  ft. 

Fig.  2  shows  greater  capacity,  and  is  better 

adapted   for  use   in  large   families,   entertaining  considerably, 
and    for    small    clubs,    boarding-houses,    restaurants,    private 
hospitals,   etc.     This  style  is  known  as  a  "combination"   re- 
frigerator, from  the  fact  that  it 
contains  separate  compartments 
for  the   various  kinds   of    food. 
The  large  compartment   at  the 
left  is  specially  for  large  meats, 
and    packages   in   bulk,  and   is 
fitted    with    shelves  and  meat- 
hooks.     The  right  end  of  the  re- 
frigerator is  divided  by  a  parti-  Fig.  2 
tion  into  two  compartments,  the 
drawers  being  for  steaks,  chops,  jellies,  etc.,  and  the  door  above 

*  The  leading  builders  of  high-class  refrigerators  are:  The  Lorillard  Re- 
frigerator Co.,  New  York;  McCray  Refrigerator  Co.,  Kendallville,  Ind. ; 
Monroe  Refrigerator  Co.,  Lockland,  Ohio;  Wickes  Refrigerator  Co., 
Chicago,  111. 


REFRIGERATORS.  1493 

for  vegetables  and  sundries.  The  compartment  to  the  right 
of  this  is  specially  for  milk  and  butter,  and  should  be  absolutely 
separate  from  all  other  compartments.  One  ice-tank  supplies 
cold  air  to  all  compartments,  and  is  filled  through  a  door  in 
the  front. 

A  convenient  arrangement  is  a  window  in  the  wall  at  back  of 
refrigerator,  through  which  ice  may  be  passed  into  refrigerator. 

Refrigerators  over  two  feet  in  depth  should  be  built  in  sections 
bolted  together,  rendering  them  easy  to  transport  and  handle 
in  contracted  space. 

Fig.   3  is  a  refrigerator  for  use  in   butler's  pantries,  where 
economy    of    space    is    important.     The 
ice-tank    is    arranged  to  come  out  on  a 
runway,  for  convenience  in  filling.     When 
the  ice-tank  is  pushed  back,  this  runway 
folds  up,  and  an  outside  door  closes  over 
it.     This   does   away  with  the  necessity  ' 
of  cutting  through  the  counter-top,  and 
permits  the  ice-tank  to  be  readily  taken 

out  for  cleansing  purposes.  The  height  should  be  about  2  ft. 
8  ins.,  depth  about  2  ft.  Length  of  front  determines  capacity, 
but  should  never  be  less  than  2  ft.  10  ins.  In  every  3  ft  or 
3  ft.  6  ins.  one  ice-tank  is  allowed.  The  finish,  wood,  trim,  and 
hardware  should  correspond  with  other  fittings. 

Drainage. — A  short,   accessible,  well-trapped  drain   is  im- 
perative, and  should  be  as  nearly  under  the  centre  of  the  ice 
compartment  as  possible.     It  is  well  to  have 
refrigerators  on  casters,  so  they  can  be  easily 
moved  for  cleaning  about  them. 

-^i&'  ^  snows  a  good  drainage  arrange- 
ment,  permitting  removal  of  refrigerator  at 
will. 

F '9-  4  Plumber's  pan  for  reception  of  refrigerator 

drip  should  be  countersunk  in  floor. 

Where  a  very  low  temperature  is  required,  as  for  game  or 
fish  carried  in  large  quantities,  or  in  medical  colleges  where  the 
object  is  to  preserve  bodies,  it  is  absolutely  necessary  that  ice 
should  go  into  the  tanks  from  top. 

Usual  complement  of  refrigerators  for  use  in  ordinary  families : 
one  in  kitchen;  one  in  butler's  pantry.  Large  families  same, 
with  greater  capacity.  Small  clubs,  small  restaurants,  etc., 
one  general  storage;  one  wine;  one  in  or  near  kitchen,  for  cook's 


1494  LIBRARY  STACKS. 

use;  one  fish.  Large  hotels,  clubs,  restaurants,  etc. :  one  storage 
for  large  meat;  one  in  or  near  kitchen,  for  cook's  use;  one  fish; 
one  milk  and  butter ;  one  in  storeroom ;  one  ice-cream  (in  hotels) ; 
one  wine.  Private  hospitals:  one  large  storage;  one  for  cook's 
use,  in  or  near  kitchen ;  one  for  milk  and  butter ;  one  iron-lined 
box  for  broken  ice.  Large  hospitals  same,  but  increased  capacity, 
and  a  small  refrigerator  in  each  ward.  Isolated  hospitals  should 
have  large  storage  ice-houses  in  addition.  Medical  colleges,  for 
preserving  bodies,  with  accommodations  for  eight  bodies:  di- 
mensions about  8  ft.  6  ins.  front,  7  ft.  6  ins.  deep,  and  9  ft. 
high.  Ice  going  into  tanks  from  top. 

Revolving  Doors. — A  great  improvement  over  the  ordi- 
nary doors,  or  storm-doors,  for  many  purposes.  For  description 
see  Part  II,  Building  Construction  and  Superintendence. 

Tower  Clocks— Dimensions  of  Clock  Faces. — For 
description  of  requirements  of  installation  of  tower  clocks,  see 
Churches  and  Chapels,  p.  154. 

Rule  for  Diameter  of  Dials. — "To  look  well  and  show  plainly, 
dials  should  be  1  ft.  diameter  for  every  10  ft.  of  elevation  and 
should  set  out  flush  with  or  close  to  the  line  of  the  building  or 
tower."  * 

DIMENSIONS  OF  SOME  LARGE  CLOCK  FACES. 

Tower  Clock,  Depot  of  the  Central  Railroad  of  New  Jersey,  at 
Communipaw. — Diameter  of  single  dial,  14  ft.  3  ins.;  minute 
hand  is  7  ft.  long,  weighs  40  Ibs.;  hour  hand  is  5  ft.  long,  weighs 
28  Ibs.  The  motive  power  is  furnished  by  a  weight  of  700  Ibs., 
hung  from  a  f-in.  steel  cable. 

Four-dial  Clock,  New  York  Produce  Exchange. — Diameter  of 
each  dial,  12  ft.  6  ins. 

Four-dial  Clock,  Chronicle  Tower,  San  Francisco. — Diameter 
of  each  dial,  16  ft.  6  ins.;  length  of  minute  hands,  8  ft.;  length 
of  hour  hands,  5  ft.  6  ins.  The  mechanism  of  the  clock  is  6  ft.  1 
in.  high  and  weighs  3,000  Ibs. 

Pneumatic  Clock,  City  Hall  and  Court  House,  Minneapolis. — 
Dials,  23  ft.  4  ins.  in  diam. 

LIBRARY    STACKS— CAPACITY  OF    SHELVING. 

General  Description  of  the  Library  Stack  Sys- 
tem, using  Iron  or  Steel  Stacks.— The  unit  of  the  sys- 
tem is  the  shelf  compartment,  or  the  space  between  two  adjacent 

*  Seth  Thomas  Clock  Co. 


CAPACITY  OF  LIBRARY  SHELVING.          1495 

partitions  or  shelf  supports.      A  row  of  compartments,  side  by 
side,  constitutes  a  range.     A  number  of  ranges  form  a  stack. 

When  the  compartments  are  placed  against  walls,  and  are  acces- 
sible from  only  one  side,  they  are  called  single- faced;  and  when 
placed  free  from  walls,  thus  accessible  on  both  sides,  they  are 
double-faced. 

A  standard  single-faced  compartment  is  3  ft.  long,  8  or  10  ins. 
wide,  and  7  ft.  high.  A  standard  double-faced  compartment  is 
16  or  20  ins.  wide,  other  dimensions  the  same.  Standard  shelves 
are  3  ft.  long  and  8  or  10  ins.  wide.  The  aisles  between  the 
ranges  vary  from  2  ft.  8  ins.  to  3  ft.  4  ins.  in  width. 

The  shelf  supports  are  made  in  various  ways,  differing  with 
each  manufacturer.  They  should  not  seriously  break  the  smooth 
surface  at  the  side,  or  expose  the  last  book  to  damage.  The 
shelves  are  usually  constructed  of  steel.  The  weight  of  stacks 
and  shelves  (as  made  by  the  Snead  &  Co.  Iron  Works)  with  their 
load  of  books  is  about  30  Ibs.  per  cubic  foot  of  stack. 

When  there  are  upper  floors  they  are  usually  referred  to  as 
decks;  the  height  from  deck  to  deck  varies  from  7  ft.  to  7  ft.  6  ins., 
7  ft.  being  the  standard.  The  deck  framing  consists  of  steel  tees,, 
angles,  and  bars,  and  the  floor  covering  is  of  marble  or  rough  plate 
glass.  The  weight  of  deck  framing  and  floor  covering  is  about 
24  Ibs.  per  sq.  ft.  for  marble  and  18  Ibs.  for  glass. 

Capacity  of  Library  Shelving". — The  capacity  of  a 
library  depends  upon  its  character;  for  an  ordinary  circulating 
library  the  capacity  is  about  ten  volumes  per  lineal  foot  of  shelf; 
for  the  Library  of  Congress  it  is  about  eight  and  a  half  volumes 
per  lineal  foot,  and  this  is  about  the  average  for  an  ordinary 
collection  of  books. 

The  number  of  books  a  room  will  hold  may  be  estimated  as 
follows : 

Let  us  suppose  that  the  cases  are  7  ft  high,  16  ins.  deep,  and 
have  books  011  each  side;  that  the  width  of  passageway  between 
the  cases  is  the  minimum  of  32  ins.;  and  that  each  shelf  is  36  ins. 
in  length.  The  floor-space  that  one  division  of  one  side  of  the 
case  will  take  is  half  the  width  of  the  case  (8  ins.)  plus  half  the 
width  of  passageway  (16  ins.),  multiplied  by  the  length  of  the 
shelf  (36  ins.),  which  gives  a  result  of  6  sq.  ft.  If  the  average 
number  of  shelves  in  the  division  is  7,  and  there  are  8J  books 
to  the  foot,  the  capacity  of  the  division  is  180  volumes,  or  an 
average  of  30  books  to  the  square  foot  of  floor  area.  In  this 
calculation  no  account  has  been  taken  of  the  stairs,  windows, 


1496  CLASSICAL  MOULDINGS. 

doors,  or  cross  gangway,  and  only  a  minimum  width  of  passage- 
way has  been  allowed.  If  space  for  these  is  taken  into  con- 
sideration, a  conservative  estimate  of  shelving  capacity  of  a 
room  will  work  out  at  about  22  volumes  to  the  square  foot,  for 
each  deck  or  story  7  ft.  high. 

In  the  Congressional  Library  at  Washington  the  double-faced 
compartments  are  24  ins.  wide  over  all,  and  the  aisles  between 
3  ft.  4  ins.  wide,  making  5  ft.  4  ins.  between  centres  of  compart- 
ments. The  stack  rooms  are  nine  stories  high,  each  story  being 
7  ft.  from  floor  to  floor.  The  floors  proper  are  thin  white-marble 
slabs,  with  polished  side  down  for  reflecting  the  light. 

CLASSICAL   MOULDINGS* 

Mouldings  are  so  called  because  they  are  of  the  same  shape 
throughout  their  length  as  though  the  whole  had  been  cast  in  the 
same  mould  or  form.  The  regular  mouldings,  as  found  in  re- 
mains of  classic  architecture,  are  eight  in  number,  and  are  known 
by  the  following  names: 

.      Annulet,  baud,  cincture,  fillet,        Astragal,  or  bead.  ",-vrr/^  » 

listel,  or  square.  Ogee. 

-x  I 7  Some  of  these  terms  are  de- 

.J  IV  rived  thus:    Fillet,   from    the 

French  word  fil,  "thread"; 
astragal,  from  astragalos,  "a 
bone  of  the  heel,"  or  "the 
curvature  of  the  heel";  bead, 
because  this  moulding,  when 


Cymatium,  or  cyma-reota.       Inve  ted  cymatium,  or          properly     Carved,    rCSCmbleS     B 

string  of  beads;  torus,  or  tore, 

the  Greek  for  rope,  which  it  resembles  when  on  the  base  of  a 
column;  scotia,  from  skotia,  "darkness,"  because  of  the  strong 
shadow  which  its  depth  produces,  and  which  is  increased  by  the 
projection  of  the  torus  above  it;  ovolo,  from  ovum,  "an  egg," 
which  this  member  resembles  when  carved,  as  in  the  Ionic 
capital;  cavetto,  from  cavus,  "hollow";  cymatium,  from  kuma- 
ton,  "a  wave." 

Characteristics  of  Mouldings. — Neither  of  these 
mouldings  is  peculiar  to  any  one  of  the  orders  of  architecture ; 
and  although  each  has  its  appropriate  use,  yet  it  is  by  no  means 
confined  to  any  certain  position  in  an  assemblage  of  mouldings. 

*  See  also  Glossary,  under  Moulding. 


THE  CLASSICAL  ORDERS.  1497 

The  use  of  the  fillet  is  to  bind  the  parts,  as  also  that  of  the  astra- 
gal and  torus,  which  resemble  ropes.  The  ovolo  and  cyma- 
reversa  are  strong  at  their  upper  extremities,  and  are  therefore 
used  to  support  projecting  parts  above  them. 

The  cy ma-recta  and  cavetto,  being  weak  at  their  upper  ex- 
tremities, are  not  used  as  supporters,  but  are  placed  uppermost 
to  cover  and  shelter  the  upper  parts.  The  scotia  is  introduced 
in  the  base  of  a  column  to  separate  the  upper  and  lower  torus, 
and  to  produce  a  pleasing  variety  and  relief. 

The  form  of  the  bead  and  that  of  the  torus  are  the  same ;  the 
reasons  for  giving  distinct  names  to  them  are  that  the  torus,  in 
every  order,  is  always  considerably  larger  than  the  bead,  and  is 
placed  among  the*  base  mouldings,  whereas  the  bead  is  never 
placed  there,  but  on  the  capital  or  entablature.  The  torus,  also, 
is  seldom  carved,  whereas  the  bead  is;  and  while  the  torus,  among 
the  Greeks,  is  frequently  elliptical  in  its  form,  the  bead  retains  its 
circular  shape.  While  the  scotia  is  the  reverse  of  the  torus,  the 
cavetto  is  the  reverse  of  the  ovolo,  and  the  cy  ma- recta  and  cyma- 
reversa  are  combinations  of  the  ovolo  and  cavetto. 

THE    CLASSICAL    ORDERS.* 

"In  the  classical  styles  several  varieties  of  column  and  entab- 
lature are  in  use.  These  are  called  the  orders.  Each  order 
comprises  a  column  with  a  base,  shaft,  and  capital,  with  or 
Yv'ithout  a  pedestal,  with  its  base,  die,  and  cap,  and  is  crowned 
by  an  entablature,  consisting  of  architrave,  frieze,  and  cornice. 
The  entablature  is  generally  about  one  fourth  as  high  as  the 
column,  and  the  pedestal  one  third,  more  or  less. 

"Among  the  Greeks  the  forms  used  by  the  Doric  race,  which 
inhabited  Greece  itself  and  had  colonies  in  Sicily  and  Italy, 
were  much  unlike  those  of  the  Ionic  race,  which  inhabited  the 
western  coast  of  Asia  Minor,  and  whose  art  was  greatly  in- 
fluenced by  that  of  Assyria  and  Persia.  Besides  the  Ionic  and 
Doric  styles,  the  Romans  devised  a  third,  which  employed 
brackets,  called  modillions,  in  the  cornice,  and  was  much  more 
elaborate  than  either  of  them;  this  they  called  the  Corinthian. 

*  The  paragraphs  in  quotation-marks  are  taken  from  "The  American 
Vignola"  by  Prof.  Wm.  R.  Ware,  by  permission  of  the  owners  of  the  copy- 
right, the  International  Text-book  Company,  proprietors  of  the  Interna- 
tional Correspondence  Schools.  The  engravings  were  made  especially  for 
this  book,  and  correspond  with  the  original  drawings  prepared  by  Giacomo 
Barozzi  da  Vignola. 


1498 


THE  CLASSICAL   ORDERS. 


They  used  also  a  simple  Doric  called  the  Tuscan,  and  a  cross 
between  the  Corinthian  and  Ionic  called  the  Composite.  These 
are  the  five  orders.  The  ancient  examples  vary  much  among 


Cymatium 


<-5 


Corona 

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Dimensions  are  in  Slths  of  Diameter.     -  - 

Fig.  I 

The  Tuscan  Order. 

themselves  and  differ  in  different  places,  and  in  modern  times 
still  further  varieties  are  found  in  Italy,  Spain,  France,  Ger- 
many, and  England.  The  best  known  and  most  admired  forms 
for  the  orders  are  those  worked  out  by  Giacomo  Barozzi  da 


THE  CLASSICAL  ORDERS. 


1499 


Vignola  in  the  sixteenth  century  from  the  study  of  ancient 
examples." 

The  Tuscan  Order. — "The  distinguishing  characteristic 
of  the   Tuscan   order  is   simplicity.     Any   forms   of   pedestal, 


F 


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Dimensions  are  in  Slths  of  Diameter 

Fig.  2 
The  Doric  Order. 

column,   and   entablature  that  show   but  few   mouldings,   and 
those  plain,  are  considered  to  be  Tuscan." 


1500  THE  CLASSICAL   ORDERS. 

The  Doric  Order. — "The  distinguishing  characteristics 
of  the  Doric  order  are  features  in  the  frieze  arid  in  the  bed-mould 
above  it  called  triglyphs  and  mutules,  which  are  supposed  to 
be  derived  from  the  ends  of  beams  and  rafters  in  a  primitive 
wooden  construction  with  large  beams.  Under  each  triglyph, 
and  beneath  the  tsenia  which  crowns  the  architrave,  is  a  little 
fillet  called  the  regula.  Under  the  regula  are  six  long  drops, 
called  guttse,  which  are  sometimes  conical,  sometimes  pyramidal. 
There  are  also  either  eighteen  or  thirty-six  short  cylindrical 
guttse  under  the  soffit  of  each  mutule.  The  guttse  are  supposed 
to  represent  the  heads  of  wooden  pins,  or  treenails. 

"Two  different  Doric  cornices  are  in  use — the  mutulary  with 
bracket  and  the  denticulated  with  dentils,  the  principal  difference 
being  in  the  bed-mould."  The  order  shown  by  Fig.  2  has  the 
denticulated  cornice. 

The  Ionic  Order. — "The  prototypes  of  the  Ionic  order 
are  to  be  found  in  Persia,  Assyria,  and  Asia  Minor. 

"It  is  characterized  by  bands  in  the  architrave  and  dentils 
in  the  bed-mould,  both  of  which  are  held  to  represent  small 
sticks  laid  together  to  form  a  beam  or  a  roof.  But  'the  most 
conspicuous  and  distinctive  feature  is  the  scrolls  which  deco- 
rate the  capital  of  the  column.  These  have  no  structural 
significance,  and  are  purely  decorative  forms  derived  from 
Assyria  and  Egypt.  Originally  the  Ionic  order  had  no  frieze 
and  no  echinus  in  the  capital.  These  were  borrowed  from 
the  Doric  order,  and,  in  like  manner,  the  dentils  and  bands  in 
the  Doric  were  borrowed  from  the  Ionic.  The  Ionic  frieze  was 
introduced  in  order  to  afford  a  place  for  sculpture,  and  was 
called  by  the  Greeks  the  Zoophorus,  or  Figure-bearer. 

"The  typical  Ionic  base  is  considered  to  consist  mainly  of  a 
scotia,  as  in  some  Greek  examples.  It  is  common,  however,  to 
use  instead  what  is  called  the  Attic  base,  consisting  of  a  scotia 
and  two  fillets  between  two  large  toruses,  mounted  on  a  plinth, 
the  whole  half  a  diameter  high.  The  plinth  occupies  the  lower 
third,  or  one  sixth  of  a  diameter.  Vignola  adopted  for  his 
Ionic  order  a  modification  of  the  Attic  base,  substituting  for 
the  single  large  scotia  two  small  ones,  separated  by  one  or  two 
beads  and  fillets,  and  omitting  the  lower  torus."  This  is  the 
base  shown  in  the  engraving. 

"The  Ionic  frieze  is  plain,  except  for  the  sculpture  upon  it. 
It  sometimes  has  a  curved  outline,  as  if  ready  to  be  carved,  and 


THE  CLASSICAL  ORDERS. 


1501 


Dimensions  are  in  2±ths  of  Diameter. 

Fig.  3 

The  Ionic  Order. 


1502 


THE  CLASSICAL  ORDERS. 


is  then  said  to  be  pulvinated,  from  pulvinar,  a  bolster,  which  it 
much  resembles. 

"The  shaft  of  the  column  is  ornamented  with  twenty-fou* 
flutings,  semicircular  in  section,  which  are  separated  not  by  an 
arris,  but  by  a  fillet  of  about  one  fourth  their  width.  This 
makes  the  flutings  only  about  two  thirds  as  wide  as  the  Doric 
channels,  or  about  one-ninth  of  a  diameter,  instead  of  ono 
sixth." 

To  Describe  the  Ionic  Volute. — There  are  several 
methods  of  doing  this,  the  simplest  being  by  means  of  centres 
found  as  shown  by  the  diagram  Fig.  3a.  First  locate  the  centre 
of  the  eye  \D  vertically  below  the  point  A,  Fig.  3.  Then  describe 
a  circle  with  a  diameter  equal  to  TVA  to  form  the  eye.  Inside  oi 
this  circle  inscribe  a  square  at  45  degrees  to  a  horizontal;  then 
"  draw  the  axes  1-3  and  2-4,  and  divide  each  of  these  into  six  equal 
parts.  Then  with  the  point  1  as  a  centre,  and  a  radius  extending 
to  A,  Fig.  3,  draw  a  quarter-circle  to  line  1-2  produced,  with  2  as  a 

centre,  continue   the  curve 
-  i  until  it  intersects   2-3  pro-, 

duced,  and  so  on.  The 
centres  for  the  outer  curve  of 
the  volute  are  at  the  points 
1,2,  3,  4,5,  6,  etc.  For  the 
centres  for  the  inner  curve, 
start  with  a  point  one  third 
the  way  from  1  to  5,  then  a 
point  one  third  the  way  from 
2  to  6,  and  so  on. 

The  Corinthian  Or- 
der.—"The  three  distin- 
guishing characteristics  of 
the  Corinthian  order  are  a 
tall,  bell-shaped  capital,  a 
series  of  small  brackets  called  modillions,  which  support  the 
cornice  instead  of  mutules,  in  addition  to  the  dentils,  and  a 
general  richness  of  detail  which  is  enhanced  by  the  use  of  the 
acanthus  leaf  in  both  capitals  and  modillions. 

"Here,  again,  the  Attic  base  is  commonly  used,  but  some- 
times, especially  in  large  columns,  a  base  is  used  which  resembles 
Vignola's  Ionic  base,  except  that  it  has  two  beads  between  the 
scotias  instead  of  one,  and  also  a  lower  torus.  The  shaft  is 
fluted  like  the  Ionic  shaft,  with  twenty-four  semicircular  flut- 


Fig.  3a 


THE  CLASSICAL  ORDERS. 


1503 


IT 


<-— lOJfr— >f 


=  e  "If  UL~L1 

!Mlg 

":ff 

-9  > 

\$% 
j 

If 

44- 

£ 


\ 

-4- 


? 


-t- 

4  ! 

---J-  I 


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L 


ilh 


j 


Dimensions  are  in  24ths  of  Diameter 

THE  CORINTHIAN  OR.DEI^ 

Fig.  4 


II  ! 

_l_i_^.-i:-. 


1504  THE  CLASSICAL  ORDERS. 

ings,  but  these  are  sometimes  filled  with  a  convex  moulding  or 
cable  to  a  third  of  their  height. 

"  Almost  all  the  buildings  erected  by  the  Romans  employ 
the  Corinthian  order. " 

The  Composite  Order.  — "The  Composite  order  is  a 
heavier  Corinthian,  just  as  the  Tuscan  is  a  simplified  Doric.  The 
chief  proportions  are  the  same  as  in  the  Corinthian  order,  but 
the  details  are  fewer  and  larger.  It  owes  its  name  to  the  capi- 
tal, in  which  the  two  lower  rows  of  leaves  and  the  caulicoli  are 
the  same  as  in  the  Corinthian.  But  the  caulicoli  carry  only  a 
stunted  leaf -bud,  and  the  upper  row  of  leaves  and  the  sixteen 
volutes  are  replaced  by  the  large  echinus,  scrolls,  and  astragal  of 
a  complete  Ionic  capital. 

"Vignola's  composite  entablature  differs  from  his  Ionic 
chiefly  in  the  shape  and  size  of  the  dentils.  They  are  larger, 
and  are  more  nearly  square  in  elevation,  being  a  fifth  of  a  diam- 
eter high  and  one  sixth  wide,  the  interdentil  being  one  twelfth, 
and  they  are  set  one  fourth  of  a  diameter  apart,  on  centres. 

"The  composite  capital  is  employed  in  the  Arch  of  Titus  in 
Rome,  and  elsewhere,  with  a  Corinthian  entablature,  and  the 
block  cornice  occurs  in  the  so-called  frontispiece  of  Nero,  as 
well  as  in  the  temple  at  Athens,  in  connection  with  a  Corinthian 
capital." 

Egyptian  Style.* — The  architecture  of  the  ancient  Egyp- 
tians is  characterized  by  boldness  of  outline,  solidity,  and 
grandeur. 

The  principal  features  of  the  Egyptian  style  of  architecture 
are:  uniformity  of  plan,  never  deviating  from  right  lines  and 
angles;  thick  walls,  having  the  outer  surface  slightly  deviating 
inwardly  from  the  perpendicular;  the  whole  building  low; 
roof  flat,  composed  of  stones  reaching  in  one  piece  from  pier  to 
pier,  these  being  supported  by  enormous  columns,  very  stout 
in  proportion  to  their  height;  the  shaft  sometimes  polygonal, 
having  no  base,  but  with  a  great  variety  of  handsome  capitals  the 
foliage  of  these  being  of  the  palm,  lotus,  and  other  leaves; 
entablatures  having  simply  an  architrave,  crowned  with  a 
huge  cavetto  ornamented  with  sculpture;  and  the  intercolum- 
niation  very  narrow,  usually  1J  diameters  and  seldom  exceed- 
ing 24. 

A  great  dissimilarity  exists  in  the  proportion,  form,  and  gen- 
eral feature  of  Egyptian  columns.  For  practical  use  the  column 

*  From  "The  American  House  Carpenter,"  by  R.  G.  Hatfield. 


LIGHTNING  CONDUCTORS. 


1505 


shown  in  Fig    5  may  be  taken  as  a  standard  of  the  Egyptian 
style. 


FIG.  5. — EGYPTIAN  ARCHITECTURE. 
(Diameter  divided  into  60  parts.) 


LIGHTNING   CONDUCTORS. 

The  following  rules  for  the  erection  of  lightning  conductors 
were  issued  in  1882  by  the  Explosive  Department  of  the  English 
Home  Office  to  the  occupiers  of  all  factories  and  magazines  for 
explosives,  and  to  those  local  and  police  authorities  upon  whom 
devolves  the  inspection  of  stores  of  explosives : 


1506  LIGHTNING  CONDUCTORS. 

1.  Material  of  Rod. — Copper,  weighing  not  less  than  6  oz.  per 
foot  run,  the  electrical  conductivity  of  which  is  not  less  than  90 
per  cent,  of  that  of  pure  copper,  either  in  the  form  of  rod,  tape,  or 
rope  of  stout  wires,  no  individual  wire  being  less  than  No.  12 
B.  W.  G.  (.109  in.).     Iron  may  be  used,  but  should  not  weigh 
less  than  2J  Ibs.  per  foot  run. 

2.  Joints.  —  Every   joint,    besides   being  well    cleaned    and 
screwed,  scarfed,  or  riveted,  should  be  thoroughly  soldered. 

3.  Form  of  Points. — The  point  of  the  upper  terminal  *  of  the 
conductor  should  not   have  a  sharper  angle  than  90°.     A  foot 
below  the  extreme  point  a  copper  ring  should  be  screwed  and 
soldered  on  to  the  upper  terminal,   in  which  ring  should  be 
fixed  three  or  four  sharp  copper  points,  each  about  6  ins.  long. 
It  is  desirable  that  these  points  should  be  so  platinized,  gilded, 
or  nickel-plated  as  to  resist  oxidation. 

4.  Number  and  Height  of  Upper  Terminals. — The  number  of 
conductors  or  upper  terminals  required  will  depend  upon  the 
size  of  the  building,  the  material  of  which  it  is  constructed, 
and  the  comparative  height  above  ground  of  the  several  parts. 
No  general  rule  can  be  given  for  this,  except  that  it  may  be 
assumed  that  the  space  protected  by  the  conductor  is,  as  a  rule, 
a  cone,  the  radius  of  whose  base  is  equal  to  the  height  of  the 
conductor  from  the  ground. 

5.  Curvature. — The  rod  should  not  be  bent  abruptly  around 
sharp  corners.     In  no  case  should  the  length  of  a  curve  be  more 
than  half  as  long  again  as  its  chord.     A  hole  should  be  drilled 
in  string-courses  or  other  projecting  masonry,  when  possible, 
to  allow  the  rod  to  pass  freely  through  it. 

6.  Insulators. — The  conductor  should  not  be  kept  from  the 
building  by  glass  or  other  insulators,  but  attached  to  it  by 
fastenings  of  the  same  metal  as  the  conductor  itself  is  composed 
of. 

7.  Fixing. — Conductors  should  preferentially  be  taken  down 
the  side  of  the  building  which  is  most  exposed  to  rain.     They 
should  be  held  firmly,  but  the  holdfasts  should  not  be  driven  in 
so  tightly  as  to  pinch  the  conductor  or  prevent  contraction 
and  expansion  due  to  change  of  temperature. 

8.  Other  Metal  Work. — All  metallic  spouts,  gutters,  iron  doors, 
and  other  masses  of  metal  about  the  building  should  be  elec- 
trically connected  with  the  conductor. 

*  The  upper  terminal  is  that  portion  of  the  conductor  which  is  between 
the  top  of  the  edifice  and  the  point  of  the  conductor. 


ADHESIVE  STRENGTH  OF  SULPHUR,  ETC.     1507 

9.  Earth   Connection. — It   is   most   desirable   that,   whenever 
possible,  the  lower  extremity  of  the  conductor  should  be  buried 
in   permanently   damp   soil.     Hence,    proximity   to   rain-water 
pipes  and  to  drains  or  other  water  is  desirable.     It  is  a  very  good 
plan  to  bifurcate  the  conductor  close  below  the  surface  of  the 
ground,  and  to  adopt  two  of  the  following  methods  for  securing 
the  escape  of  the  lightning  into  the  earth:    (1)  A  strip  of  copper 
tape  may  be  led  from  the  bottom  of  the  rod  to  a  gas  or  water 
main  (not  merely  to  a  leaden  pipe),  if  such  exist  near  enough, 
and  be  soldered  to  it;    (2)  a  tape  may  be  soldered  to  a  sheet  of 
copper,  3  ft.  X3  ft.  XA-  in.  thick,  buried    in   permanently  wet 
earth  and  surrounded  by  cinders  or  coke;    (3)  many  yards  of 
copper  tape  may  be  laid  in  a  trench  filled  with  coke,  having 
not  less  than  18  sq.  ft.  of  copper  exposed. 

10.  Protection  from  Theft,  etc. — In  places  where  there  is  any 
likelihood  of  the  copper  being  stolen  or  injured,  it  should  be 
protected  by  being  enclosed  in  an  iron  gas-pipe,  reaching  10  ft. 
(if  there  is  room)   above  ground  and  some  distance  into  the 
ground. 

11.  Painting. — Iron  conductors,  galvanized  or  not,  should  be 
painted,     It  is  optional  with  copper  ones, 

12.  Inspection. — When  the  conductor  is  finally  fixed  it  should 
5n  all  cases  be  examined  and  tested  by  a  qualified  person,  and 
this  should  be  done  in  the  case  of  new  buildings  after  all  work 
on  them  is  finished. 

Periodical  examination  and  testing,  should  opportunities 
offer,  are  also  very  desirable,  especially  when  iron  earth  con- 
nections are  employed. 

ADHESIVE    STRENGTH    OF    SULPHUR,    LEAD,   AND 
PORTLAND    CEMENT   FOR   ANCHORING   BOLTS. 

The  following  test  of  these  materials  is  reported  in  the  Amer- 
ican Architect,  page  105,  vol.  xxiv. : 

"  Fourteen  holes  were  drilled  in  a  ledge  of  solid  limestone, 
seven  of  them  being  If  ins.  in  diameter  and  seven  of  them  If 
ins.  in  diameter,  all  being  3J  ft.  deep.  Seven  f-in.  and  seven 
1-in.  bolts  were  prepared  with  thread  and  nut  on  one  end  and 
plain  at  the  other  end  but  ragged  for  a  length  of  3J  ft.  from  the 
blank  end. 

"Tour  were  anchored  with  sulphur,  four  with  lead,  and  six 
with  cement,  mixed  neat.  Half  of  each  were  f -in.  and  half  1-in. 


1508          EFFLORESCENCE  ON   BRICKWORK. 

bolts,  and  all  of  them  were  allowed  to  stand  till  the  cement  was 
two  weeks  old.  At  the  expiration  of  this  time  a  lever  of  suffi- 
cient power  was  rigged  and  all  the  bolts  were  pulled  with  the 
following  result: 

"Sulphur. — Three  bolts  out  of  four  developed  their  full 
strength,  16,000  and  31,000  Ibs.  One  1-in.  bolt  failed  by  draw- 
ing out  under  12,000  Ibs. 

"Lead. — Three  bolts  out  of  four  developed  their  full  strength, 
as  above;  one  1-in.  bolt  pulled  out  under  13,000  Ibs. 

"Cement. — Five  of  the  bolts  out  of  six  broke  without  pulling 
out;  one  1-in.  bolt  began  to  yield  in  the  cement  at  26,000  Ibs., 
but  sustained  the  load  a  few  seconds  before  it  broke. 

"While  this  experiment  demonstrated  the  superiority  of 
cement,  both  as  to  strength  and  ease  of  application,  yet  it  did 
not  give  the  strength  per  square  inch  of  area.  To  determine 
this,  four  specimens  of  limestone  were  prepared,  each  10  ins. 
wide,  18  ins.  long,  and  12  ins.  thick,  two  of  them  having  IJ-in. 
holes,  and  two  of  them  2}-in.  holes  drilled  in  them.  Into  the 
small  holes  1-in.  bolts  were  cemented,  one  of  them  being  per- 
fectly plain  round  iron,  and  the  other  having  a  thread  cut  on 
the  portion  which  was  imbedded  in  the  cement.  Into  the  2f- 
in.  holes  were  cemented  2-in.  bolts  similarly  treated,  and  the 
four  specimens  were  allowed  to  stand  thirteen  days  before  com- 
pleting the  experiment.  At  the  end  of  this  time  they  were  put 
into  a  standard  testing-machine  and  pulled.  The  plain  1-in. 
bolt  began  to  yield  at  20,000  Ibs.,  and  the  threaded  one  at  21,000 
IbSo  The  2-in.  plain  bolt  began  to  yield  at  34,000  Ibs.,  and  the 
threaded  one  at  32,000  Ibs.,  the  strain  in  all  cases  being  very 
slowly  applied.  The  pump  was  then  run  at  a  greater  speed, 
and  the  stones  holding  the  2-in.  bolts  split  at  67,000  Ibs.  in  the 
case  of  the  smooth  one  and  at  50,000  Ibs.  in  the  case  of  the 
threaded  one. 

"It  is  thus  seen  that  cement  is  more  reliable,  stronger,  and 
easier  of  application  than  either  lead  or  sulphur,  and  that  its  re- 
sistance is  from  400  to  500  Ibs.  per  square  inch  of  surface  ex- 
posed. It  is  also  a  well-ascertained  fact  that  it  preserves  iron 
rather  than  corrodes  it.  The  cement  used  throughout  the  ex- 
periment was  an  English  Portland  cement." 

EFFLORESCENCE  ON  BRICKWORK. 

There  are  at  least  three  different  substances  which  may  cause 
the  white  efflorescence  often  seen  on  the  face  of  brickwork. 


RELATIVE  HARDNESS  OF  WOODS. 


1509 


Of  these,  carbonate  of  soda  is  the  most  common  upon  new 
work,  after  the  lime  stains  have  been  removed.  This  is  due  to 
the  action  of  the  lime  mortar  upon  the  silicate  of  soda  in  the 
bricks.  Silicate  of  soda  seldom  occurs  in  brick  unless  the  clay 
used  is  a  salt  clay. 

The  only  other  white  efflorescence  of  importance  is  chiefly 
composed  of  sulphate  of  magnesia.  This  is  due  to  pyrites  in 
the  clay,  which,  when  burned,  gives  rise  to  sulphuric  acid,  and 
the  latter  unites  with  magnesia  in  the  lime  mortar. 

The  above  are  the  results  of  actual  examinations  by  Mr. 
Samuel  Cabot,  chemist.  The  conclusions  arrived  at  are  these: 

I.  The  efflorescence  is  never  due  to  the  bricks  alone,   and 
seldom  to  the  lime  alone. 

II.  To  avoid  it,  the  bricks  should  be  covered  with  an  oily  pre- 
servative capable  of  keeping  the  salts  from  exuding.     Linseed 
oil  cannot  fill  the  requirements,  as  it  is  injured  by  the  mortar. 

RELATIVE    HARDNESS    OF   WOODS. 

Taking  shell-bark  hickory  as  the  highest  standard  of  our  forest- 
trees,  and  calling  that  100,  other  trees  will  compare  with  it  for 
hardness  as  follows: 


Shell-bark  hickory 100 

Pignut  hickory 96 

White  oak 84 

White  ash 77 

Dogwood 75 

Scrub  oak 73 

White  hazel 72 

Apple-tree 70 

Red  oak 69 

White  beech 65 

Black  walnut 65 

Black  birch 62 


Yellow  oak 60 

Hard  maple 56 

White  elm 58 

Red  cedar 56 

Wild  cherry 55 

Yellow  pine 54 

Chestnut 52 

Yellow  poplar 51 

Butternut 43 

White  birch 43 

White  pine 30 


WEIGHT  OF  ROUGH  LUMBER  PER  1,000  FEET. 

BOARD  MEASURE   (APPROXIMATE). 
(For  weight  of  various  woods  see  table,  pp.  1341  to  1344.) 


Dry. 

Partly 
Seasoned. 

Green  . 

Pine  and  hemlock  

2,500  Ibs. 

2,700  Ibs. 

3,000  Ibs. 

Norway  and  yellow  pine.  .  .  . 
Oak  and  walnut   .  .       . 

3,000    " 
4  000    " 

4,000    " 
5  000   " 

5,000    " 

Ash  and  maple  

3,500    " 

4,000    " 

1510 


FORCE  OP  THE  WIND. 


FORCE  OF  THE  WIND. 

According  to  experiments  made  in  1890  or  thereabouts,  by 
Asst.  Prof.  C.  F.  Marvin,  U.  S.  Signal  Service,  the  relation  be- 
tween wind  pressure  and  velocity  is  given  very  accurately  by 
the  formula  p  =  .004F2,  where  p  =  pressure  in  pounds  per  square 
foot  on  a  flat  surface  normal  to  the  direction  of  the  wind,  and 
V  denotes  velocity  in  miles  per  hour.  Smeaton  considered 
the  pressure  as  equal  to  .005F2. 

The  following  table  based  on  Marvin's  formula  is  quoted  by 
Profs.  Turneaure  and  Ketchum.  See  also  Trautwine's  Pocket- 
book,  p.  321,  note. 


Miles 
Hour. 

Feet 
per 
Minute. 

Feet 
per 

Second. 

Force,  in 
Pounds,  per 
Square  Foot. 

Description. 

1 

88 

1.47 

0.004 

Hardly  perceptible 

2 
3 

176 

264 

2.93 
4.4 

0.014  | 
0.036  j 

Just  perceptible 

4 
5 

352 
440 

5.87 
7.33 

0.064/ 
0.1       f 

Gentle  breeze 

10 
15 

880 
1,320 

14.67 
22 

0.4      ) 
0.9      f 

Pleasant  breeze 

20 
25 

1,760 
2,200 

29.3 
26.6 

1.6      1 
2.5      f 

Brisk  gale 

30 
35 

2,640 
3,080 

44 
51.3 

3.6      | 

4.9      j" 

High  wind 

40 
45 

3,520 
3,960 

58.6 
66 

6.4      / 

8.1      f 

Very  high  wind 

50 

4,400 

73.3 

10.0 

Storm 

60 
70 

5,280 
6,160 

88 
102.7 

14.4      ) 
19.6      f 

Great  storm 

80 
100 

7,040 
8,800 

117.3 
146.6 

25.6      I 
40.0      f 

Hurricane 

TO   MAKE    BLUE-PRINT   COPIES   OF   TRACINGS. 

The  following  directions,  taken  from  The  Locomotive,  cover 
the  whole  ground.  The  sensitized  paper  can  be  procured  at 
stores  where  artists'  materials  are  sold,  all  prepared,  so  that 
the  process  of  preparing  the  paper  by  means  of  chemicals  can 
then  be  omitted. 

The  materials  required  are  as  follows: 

1.  A  board  a  little  larger  than  the  tracing  to  be  copied.  The 
drawing-board  on  which  the  drawing  and  tracing  are  made  can 
always  be  used. 


BLUE-PRINT  COPIES  OF  TRACINGS.          1511 

2.  Two  or  three  thicknesses  of  flannel  or  other  soft  white  cloth, 
which  is  to  be  smoothly  tacked  to  the  above  board,  to  form  a 
good  smooth  surface,  on  which  to  lay  the  sensitized  paper  and 
tracing  while  printing. 

3.  A  plate  of  common   double-thick  window-glass,   of  good 
quality,  slightly  larger  than  the  tracing  which  it  is  wished  to 
copy.       The  function  of  the  glass  is  to  keep  the  tracing  and 
sensitized  paper  closely  and  smoothly  pressed  together  while 
printing. 

4.  The   chemicals   for  sensitizing  the   paper.     These   consist 
simply  of  equal  parts,  by  weight,  of  citrate  of  iron  and  ammonia, 
and  red  prussiate  of  potash.     These  can  be  obtained  at  any 
drug-store.     The  price  should  not  be  over  eight  or  ten  cents  per 
ounce  for  each. 

5.  A  stone  or  yellow  glass  bottle  to  keep  the  solution  of  the 
above  chemicals  in.     If  there  is  but  little  copying  to  do,  an  ordi- 
nary glass  bottle  will  do,  and  the  solution  made  fresh  whenever  it 
is  wanted  for  immediate  use. 

6.  A  shallow   earthen  dish  in  which  to   place  the  solution 
when  using  it.     A  common  dinner-plate  is  as  good  as  anything  for 
this  purpose. 

7.  A  brush,  a  soft  paste-brush  about  4  ins.  wide,  is  the  best 
thing  we  know  of. 

8.  Plenty  of  cold  water  in  which  to  wash  the  copies  after 
they   have  been  exposed  to  the  sunlight.     The  outlet   of  an 
ordinary  sink  may  be  closed  by  placing  a  piece  of  paper  over  it 
with  a  weight  on  top  to  keep  the  paper  down,  and  the  sink 
filled  with  water,  if  the  sink  is  large  enough  to  lay  the  copy  in. 
If  it  is  not,  it  would  be  better  to  make  a  water-tight  box  about 
5  or  6  ins.  deep,  and  6  ins.  wider  and  longer  than  the  drawing 
to  be  copied. 

9.  A  good  quality  of  white  book-paper. 

Dissolve  the  chemicals  in  cold  water  in  the  following  propor- 
tions: 1  oz.  of  citrate  of  iron  and  ammonia,  1  oz.  of  red  prus- 
siate of  potash,  8  oz.  of  water  They  may  all  be  put  into  a 
bottle  together,  and  shaken  up.  Ten  minutes  will  suffice  to 
dissolve  them. 

Lay  a  sheet  of  the  paper  to  be  sensitized  on  a  smooth  table  or 
board;  pour  a  little  of  the  solution  into  the  earthen  dish  or 
plate,  and  apply  a  good  even  coating  of  it  to  the  paper  with 
the  brush;  then  tack  the  paper  to  a  board  by  two  adjacent 
corners,  and  set  it  in  a  dark  place  to  dry;  one  hour  is  sufficient 


1512  HORSE-POWER,  ETC. 

for  the  drying;  then  place  its  sensitized  side  up,  on  the  board 
on  which  you  have  smoothly  tacked  the  white  flannel  cloth; 
lay  your  tracing  which  you  wish  to  copy  on  top  of  it;  on  top  of 
all  lay  the  glass  plate,  being  careful  that  paper  and  tracing  are 
both  smooth  and  in  perfect  contact  with  each  other,  and  lay 
the  whole  thing  out  in  the  sunlight.  Between  eleven  and  two 
o'clock  in  the  summer-time,  on  a  clear  day,  from  six  to  ten  min- 
utes will  be  sufficiently  long  to  expose  it;  at  other  seasons  a 
longer  time  will  be  required.  If  your  location  does  not  admit 
of  direct  sunlight,  the  printing  may  be  done  in  the  shade,  or 
even  on  a  cloudy  day;  but  from  one  to  two  hours  and  a  half 
will  be  required  for  exposure.  A  little  experience  will  soon 
enable  any  one  to  judge  of  the  proper  time  for  exposure  on 
different  days.  After  exposure,  place  your  print  in  the  sink  or 
trough  of  water  before  mentioned,  and  wash  thoroughly,  letting 
it  soak  from  three  to  five  minutes.  Upon  immersion  in  the 
water,  the  drawing,  hardly  visible  before,  will  appear  in  clear 
white  lines  on  a  dark-blue  ground.  After  washing,  tack  up 
against  the  wall,  or  other  convenient  place,  bv  the  corners,  to 
dry.  This  finishes  the  operation,  which  is  very  simple  and 
thorough. 

After  the  copy  is  dry,  it  can  be  written  on  with  a  common  pen 
and  a  solution  of  common  soda,  which  gives  a  white  line. 


HORSE-POWER,   PULLEYS,   GEARS,   BELTING, 
AND    SHAFTING. 

Horse-power. — A  horse  can  travel  400  yds.  at  a  walk  in 
4J  minutes,  at  a  trot  in  2  minutes,  and  at  a  gallop  in  1  minute; 
he  occupies  at  a  picket  3  ft.  by  9  ft.;  and  his  average  weight 
equals  1,000  Ibs. 

An  average  horse  carrying  225  Ibs.  can  travel  25  miles  in  a  day 
of  eight  hours. 

A  draught-horse  can  draw  1,600  Ibs.  23  miles  a  day,  weight  of 
carriage  included. 

In  a  horse-mill  a  horse  moves  at  the  rate  of  3  ft.  in  a  second. 
The  diameter  of  the  track  should  not  be  less  than  25  ft. 

A  horse-power,  in  machinery,  is  estimated  at  33,000  Ibs., 
raised  1  ft.  in  a  minute;  but  as  a  horse  can  exert  that  force  but 
six  hours  a  day,  one  machinery  horse-power  is  equivalent  to 
that  of  4  horses. 


PULLEYS,   GEARS  AND    BELTING.  1513 

Rules  to  Determine  the  Size  and  Speed  of 
Pulleys  or  Gears, — The  driving  pulley  is  called  the  driver, 
and  the  driven  pulley  the  driven. 

If  the  number  of  teeth  in  gears  are  used  instead  of  diameter, 
in  these  calculations,  number  of  teeth  must  be  substituted 
wherever  diameter  occurs. 

To  find  the  diameter  of  driver,  the  diameter  of  the  driven  and 
its  revolutions,  and  also  revolutions  of  driver,  being  given: 
Multiply  the  diameter  of  driven  by  its  revolutions,  and  divide 
the  product  by  the  revolutions  of  the  driver;  the  quotient 
will  give  the  diameter  of  the  driver. 

To  find  the  diameter  of  driven,  the  revolutions  of  the  driven, 
also  diameter  and  revolutions  of  the  driver,  being  given:  Mul- 
tiply the  diameter  of  driver  by  its  revolutions,  and  divide  the 
product  by  the  revolutions  of  the  driven;  the  quotient  will 
give  the  diameter  of  the  driven. 

To  find  the  revolutions  of  the  driver,  the  diameter  and  revolu- 
tions of  the  driven,  also  diameter  of  the  driver,  being  given: 
Multiply  the  diameter  of  driven  by  its  revolutions,  and  divide 
the  product  by  the  diameter  of  driver;  the  quotient  will  give 
the  revolutions  of  driver. 

To  find  the  revolutions  of  the  driven,  the  diameter  and  revolu- 
tions of  the  driver,  also  diameter  of  the  driven,  being  given: 
Multiply  the  diameter  of  driver  by  its  revolutions,  and  divide 
the  product  by  the  diameter  of  driven;  the  quotient  will  give 
the  revolutions  of  driven. 

Horse-power  Belting-  will  Transmit. — The  ability 
of  belting  to  transmit  power,  or  to  turn  a  wheel  or  " pulley," 
depends  upon  the  width  and  thickness  of  the  belt,  the  arc  con- 
tact with  the  pulley,  whether  the  belt  is  horizontal,  vertical,  or 
at  an  angle,  and  upon  the  velocity.  The  greater  the  velocity 
and  the  thicker  the  belt,  the  more  power  it  will  transmit.  A 
belt  running  vertically  or  inclined  will  transmit  less  power  than 
one  running  horizontally,  but  in  figuring  the  horse-power  ca- 
pacity of  belting  only  the  velocity,  width,  and  thickness  of  belt 
are  usually  considered,  it  being  assumed  that  the  pulleys  are 
of  proper  size  and  located  so  that  the  belt  will  be  nearly  hor- 
izontal. Belts  are  commonly  assumed  to  be  of  leather,  unless 
otherwise  designated. 

The  term  single  belt  is  used  to  designate  a  belt  made  of  a 
single  thickness  of  cowhide  leather. 

A    double  belt  is  made    by  cementing  and  riveting  together 


1514  NOTES  ON  BELTING. 

two  thicknesses  of  leather.  There  is  no  standard  thickness  for 
either  single  or  double  belts. 

RULES. — Many  rules  have  been  given'  for  determining  the 
horse-power  belting  will  transmit.*  Those  most  commonly 
used  are: 

For  Single  Belts. — Multiply  the  width  (in  inches)  by  the 
velocity  in  feet  per  minute  and  divide  by  1,000. 

For  Double  Belts. — Multiply  the  width  by  the  velocity  and 
divide  by  700.  The  answer  is  the  number  of  horse-power. 

Some  authorities  give  divisors  of  800  and  733  for  single  belts, 
and  550  and  513  for  double  belts. 

For  the  velocity  of  the  belt  multiply  the  number  of  revolu- 
tions per  minute  of  either  pulley  by  the  circumference  of  that 
pulley. 

Notes  oil  Belting'. — For  continuous  use  a  double  belt  is 
the  most  economical,  in  the  long  run,  except  on  very  small  pul- 
leys or  for  very  light  duty. 

Triplex  and  quadruple  belts  are  sometimes  used  for  very 
heavy  duty,  but  such  belts  are  not  commonly  carried  in  stock. 

Single  belts  should  always  be  used  with  the  hair  side  next 
the  pulley. 

The  belt  speed  for  maximum  economy  should  be  from  4000 
to  4500  ft.  per  minute. 

Idler  pulleys  work  most  satisfactorily  when  located  on  the 
slack  side  of  the  belt  about  one  quarter  way  from  the  driving- 
pulley. 

Belts  are  more  durable  and  work  more  satisfactorily  made  nar- 
row and  thick,  rather  than  wide  and  thin. 

As  belts  increase  in  width  they  should  also  be  made  thicker. 

For  dynamo  work  or  electric  motors  the  ends  of  the  belt 
should  be  fastened  together  by  splicing  and  cementing,  instead 
of  lacing. 

For  all  other  cases  the  ends  are  fastened  by  hooks  or  lacing. 

Belts  should  be  cleaned  and  greased  every  five  to  six  months. 

Distance  Centre  to  Centre  of  Shafts.*— In  the 
location  of  shafts  that  are  to  be  connected  with  each  other  by 
belts,  care  should  be  taken  to  secure  a  proper  distance  one 
from  the  other.  This  distance  should  be  such  as  to  allow  of 
a  gentle  sag  to  the  belt  when  in  motion. 

A  general  rule  may  be  stated  thus:  Where  narrow  belts  are 
to  be  run  over  small  pullevs  15  ft.  is  a  good  average,  the  belt 

*  For  discussion  of  belting,  belt-dressing,  care  of,  etc.,  see  Kent's  M.  E. 
Pocketbook,  6th  edition,  pp.  876-887. 


BELTS   AND    PULLEYS.  1515 

having  a  sag  of  1J  to  2  ins.  The  minimum  distance  between 
shafts  is  about  10  ft. 

For  larger  belts,  working  on  larger  pulleys,  a  distance  of  20 
to  25  ft.  does  well,  with  a  sag  of  2J  to  4  inches. 

For  main  belts  working  on  very  large  pulleys,  the  distance 
should  be  25  to  30  ft.,  the  belts  working  well  with  a  sag  of  4  to 
5  ins. 

If  too  great  a  distance  is  attempted,  the  belt  will  have  an 
unsteady  flapping  motion,  which  will  destroy  both  the  belt 
and  machinery. 

Arrangement  of  Belts  and  Pulleys.* — If  possible 
to  avoid  it,  connected  shafts  should  never  be  placed  one  directly 
over  the  other,  as  in  such  case  the  belt  must  be  kept  very 
tight  to  do  the  work.  For  this  purpose  belts  should  be  carefully 
selected  of  well-stretched  leather. 

It  is  desirable  that  the  angle  of  the  belt  with  the  floor  should 
not  exceed  45°.  It  is  also  desirable  to  locate  the  shafting  and 
machinery  so  that  belts  should  run  off  from  each  shaft  in  opposite 
directions,  as  this  arrangement  will  relieve  the  bearings  from 
the  friction  that  would  result  when  the  belts  all  pull  one  way 
on  the  shaft. 

If  possible,  machinery  should  be  so  placed  that  the  direction 
of  the  belt  motion  shall  be  from  the  top  of  the  driving  to  the  top 
of  the  driven  pulley,  when  the  sag  will  increase  the  arc  of  con- 
tact. 

The  pulley  should  be  a  little  wider  than  the  belt  required  for 
the  work,  and  should  have  a  crowning  face,  except  where  the 
belt  is  to  be  shifted. 

The  motion  of  driving  should  run  with  and  not  against  the 
laps  of  the  belts. 

Rubber  belts  are  cheaper  than  leather  belts  and  should 
always  be  used  in  wet  places,  but  for  ordinary  use  in  dry  places 
they  are  not  as  durable  as  leather  belts. 

They  should  always  be  kept  free  from  grease  or  animal  oils. 
If  they  slip,  moisten  the  inside  of  the  belt  with  boiled  linseed 
oil.  Some  fine  chalk,  sprinkled  on  over  the  oil,  will  help  the 
belt. 

Rule  for  Finding  the  Length  of  Belts.— Add  the 
diameter  of  the  two  pulleys  together,  multiply  by  3|,  divide 
the  product  by  2,  add  to  the  quotient  twice  the  distance 

*  Kent,  p.  885. 


1516 


SHAFTING— CHAIN  BLOCKS. 


between  the   centre  of   the   shafts,  and    the    sum  will  be  the 
required  length. 

Horse-Power  Shafting  will  Transmit. 


Diameter  of 
Shaft  in 

Revolutions  per  Minute. 

Inches. 

100 

150 

200 

250 

300 

350 

400 

ins. 

16ths. 

H.P. 

H.P. 

H.P. 

H.P7 

~n7pT 

H.P. 

H.P. 

0 

15 

1.2 

1.7 

2.4 

3.1 

3.6 

4.3 

5.0 

1 

3 

2.4 

3.7 

4.9 

6.1 

7.3 

8.5 

9.7 

1 

7 

4.3 

6.4 

8.5 

10.5 

12.7 

14.8 

16.9 

1 

11 

c  .  7 

10.1 

13.4 

16.7 

20.1 

23.4 

26.8 

1 

15 

10.0 

15.0 

20.0 

25.0 

30.0 

35.0 

40.0 

2 

3 

14.3 

21.4 

28.5 

35.6 

42.7 

49.8 

57.0 

2 

7 

19.5 

29.3 

39.0 

48.7 

58.5 

68.2 

78.0 

2 

11 

26.0 

39.0 

52.0 

65.0 

78.0 

87.0 

104.0 

2 

15 

33.8 

50.6 

67.5 

84.4 

101.3 

118.2 

135.0 

3 

3 

43.0 

64.4 

85.8 

107.3 

128.7 

150.3 

171.6 

3 

7 

53.6 

79.4 

107.2 

134.0 

158.8 

187.6 

214.4 

3 

11 

65.9 

97.9 

121.8 

164.8 

195.7 

230.7 

243.6 

3 

15 

80.0 

120.0 

160.0 

200.0 

240.0 

280.0 

320  .  0 

4 

7 

113.9 

170.8 

227.8 

284.7 

341.7 

398.6 

455.6 

4 

15 

156.3 

234.4 

312.5 

390.6 

468.7 

546.8 

625.0 

CHAIN   BLOCKS. 

These  are  portable  hoisting  devices  which  enable  one  man 
to  raise  a  very  heavy  load  and  which  will  sustain  the  load  at  any 
point.  In  general,  they  resemble  pulleys  operated  by  chains. 
Since  the  invention  of  the  differential  pulley-block  by  Thos.  A. 
Weston,  about  the  year  1863,  chain  blocks  have  come  into  very 
general  use  for  economical  hoisting,  and  particularly  where  it  is 
desired  to  hold  the  load  at  any  point. 

Chain  blocks  are  of  three  general  classes: 

A.  The  differential  block,  which  is  the  original  and  simplest 
and  cheapest  form  of  self-sustaining  pulley. 

B.  Screw-  or  worm-geared  blocks,  of  which  the  Yale  &  Towne 
duplex  blocks  are  the  most  efficient  type;   and 

C.  Triplex  blocks,  spur-geared. 

Differential  and  worm-geared  blocks  of  all  kinds  depend  upon 
friction  to  prevent  the  load  from  running  down.  In  the  triplex 
block  a  separate  device  is  introduced  which  automatically  holds 
the  load  safely,  and  yet  enables  it  to  be  lowered  with  slight 
effort  and  at  high  velocity  but  without  acceleration  or  danger. 
This  is  the  most  efficient  of  all  chain  blocks,  and  the  most 
economical  wherever  quick  work  is  wanted  and  economy  in 


CHAIN    BLOCKS. 


1517 


time  and  labor  sought.  For  information  as  to  the  kind  of  block 
best  adapted  to  any  particular  service,  the  manufacturers 
should  be  consulted.  The  following  data  on  the  power  and 
efficiency  of  chain  blocks  were  supplied  by  the  Yale  &  Towne 
Manufacturing  Company. 

Power  and  Efficiency  of  Chain  Hoists. — The  table 
below  gives  the  work  to  be  done  by  the  operator  at  the  hand- 
pulling  chain  with  each  size  of  various  kinds  ot  chain  blocks 
in  lifting  the  stated  capacity-,  i.e.,  the  amount  of  work  or  pull- 
ing required  to  lift  this  load  one  foot  by  stating  the  force  exerted 
in  pounds  and  the  distance  in  feet  of  operating  chains  to  be 
pulled.  The  product  of  these  two  factors  determines  the  effici- 
ency of  the  block  and  the  ease  and.  speed  of  hoisting. 


Capacity 
in  Tons. 

Triplex 
(Spur-geared). 

Duplex 
(  Worm  -geared  ). 

Differential. 

Lbs.      Ft. 

Lbs.      Ft. 

Lbs.      Ft. 

i 

62  X  21 

68  X  40 

122X24 

1 

82  X  31 

87  X  59 

216X30 

li 

110X  35 

94  X  80 

246X36 

2 

120  X   42 

115X  93 

308X42 

3 

114  X   69 

132X126 

557X38 

4 

124  X   84 

142X155 

5 

110X126 

145X195 

6 

130X126 

145X252 

8 

135X168 

160X310 

10 

140X210 

160X390 

12 

130X126 

16 

135X168 

20 

140X210 

These  blocks  have  two  hand  chains.  The  figures  give  the 
number  of  feet  to  be  operated  on  each  hand  chain. 

A  man  cannot  pull  more  than  his  own  weight  on  the  operating 
chains,  and  can  pull  faster  in  proportion  as  the  pull  required  is 
lighter.  82  Ibs.  is  maximum  pull  usually  required  of  one  man, 
and  he  will  do  more  work  with  less  fatigue  if  the  hand-chain 
pull  is  not  over  40  Ibs.,  because  he  can  then  pull  the  chain  hand 
over  hand  a  little  more  than  twice  as  fast  as  he  could  when  pulling 
twice  as  hard.  When  the  hand-chain  pull  is  less  than  20  Ibs, 
the  speed  of  hoisting  an  equal  load  is  diminished  because  the 
man  is  tired  by  moving  his  arms  too  rapidly,  and  cannot  do 
as  much  work  as  with  a  heavier  pull. 


1518 


PROPORTIONS   OF  HOOKS. 


The  best  result  is  obtained  by  using  a  chain  block  having 
a  capacity  double  the  usual  load. 

The  operator  then  works  to  the  best  advantage  with  average 
loads,  and  occasional  heavy  loads  are  easily  handled  without 
overstraining  either  the  operator  or  the  chain  block,  which 
should  never  be  used  beyond  its  capacity  for  fear  of  stretching 
the  chain  so  that  it  will  not  work  smoothly. 

Proportions  of  Hooks.* — For  economy  of  manufac- 
ture each  size  of  hook  is  made  from  some  regular  commercial 
size  of  round  iron.  The  basis,  or  initial  point,  in  each  case  is, 
therefore,  the  size  of  iron  of  which  the  hook  is  to  be  made,  which 
is  indicated  by  the  dimension  A  in  the  diagram.  The  dimen- 
sion D  is  arbitrarily  assumed.  The  other  dimensions,  as  given 
by  the  formulae,  are  those  which,  while  preserving  a  proper 

bearing-face*  on  the  interior  of 
the  hook  for  the  ropes  or  chains 
which  may  be  passed  through 
it,  give  the  greatest  resistance  to 
spreading  and  to  ultimate  rup- 
ture which  the  amount  of  mate- 
rial in  the  original  bar  admits 
of.  The  symbol  A  is  used  in 
,  the  formulae  to  indicate  the 
nominal  capacity  of  the  hook  in 
x\.  tons  of  2,000  Ibs,  The  formulae 
which  determine  the  lines  of  the 
other  parts  of  the  hooks  of  the 
several  sizes  are  as  follows,  the 
measurements  being  all  expressed 


in  inches : 


£>=.5J  +1.25 
#=.644+1.60 
F=.33J+  .85 


£=.75  D 
0=.363J+    .66 
Q=.64J  +1.60 


M=   .50A 

J-120A  N=   .855 -.16 

#=1.13A  U=   .866A 

EXAMPLE, — To  find  the  dimension  D  for  a  2-ton  hook, 
formula  is: 


The 


*  By  Henry  R.  Towne,  in  his   Treatise  on  Cranes,  as  the  result  of  an 
extensive  experimental  and  mathematical  investigation. 


THE  LONGEST  BRIDGES  IN  THE  WORLD.   1519 

and  as  J  =  2,  the  dimension  D  by  the  formula  is  found  to  be  2J 
ins. 

The  dimensions  A  are  necessarily  based  upon  the  ordinary 
merchant  sizes  of  round  iron.  The  sizes  which  it  has  been  found 
best  to  select  are  the  following: 

Capacity  of  hook    i      i      £     1         1^-2       34568      10    tons. 
Dimension  A £      }J     f     1TV    H      1*      1*     2     2£     2*     2|      3£  inches 

The  formulae  which  give  the  sections  of  the  hook  at  the  sev- 
eral points  are  all  expressed  in  terms  of  A  and  can  therefore 
be  readily  ascertained  by  reference  to  the  foregoing  scale. 

EXAMPLE. — To  find  the  dimension  /  in  a  2-ton  hook.  The 
formula  is  /=  1  33^4,  and  for  a  2-ton  hook  A  =  If  in.  Therefore 
7,  in  a  2-ton  hook,  is  found  to  be  1%  ins 

Experiment  has  shown  that  hooks  made  according  to  the 
above  formulae  will  give  way  first  by  opening  of  the  jaw,  which, 
however,  will  not  occur  except  with  a  load  much  in  excess  of 
the  nominal  capacity  of  the  hook.  This  yielding  of  the  hook 
when  overloaded  becomes  a  source  of  safety,  as  it  constitutes  a 
signal  of  danger  which  cannot  easily  be  overlooked,  and  which 
must  proceed  to  a  considerable  length  before  rupture  will  occur 
and  the  load  be  dropped.  A  comparison  of  these  hooks  with 
most  of  those  in  ordinary  use  will  show  that  the  latter  are,  as 
a  rule,  badly  proportioned,  and  frequently  dangerously  weak. 


THE  LONGEST   BRIDGES   IN   THE   WORLD. 

Forth  Bridge,  9,200  ft. 

Montreal  Bridge,  over  the  St.  Lawrence}  8,791  ft 

The  Baltimore  &  Ohio  Bridge,  at  Havre  de  Grace,  6,OOC  ft. 

Brooklyn  Bridge,  over  the  East  River,  N.  Y. : 

Length  of  river-span,  1,595  ft.  6  ins. 

Length  of  each  land-span,  930  ft. 

Length  of  Brooklyn  approach,  971  ft. 

Length  of  New  York  approach,  1,562  ft.  6  Ins. 

Total  length  of  bridge,  5,989  ft.     Width  of  bridge,  86  ft. 

Number  of  cables,  4;  diameter  of  each,  15f  ins. 

Clear  height  of  bridge  in  centre  of  river-span  above  high 
water  at  90°  F.,  135  ft. 


1520  THE  LONGEST  BRIDGES  IN  THE  WORLD. 

Williamsburg  Bridge,  crossing   the  East  River  at  Grand  St. 

Ferry  to  Brooklyn: 

Extreme  length,  7,250  ft.;   central  span,  1,600  ft. 
Estimated  cost    $21,000,000. 
Manhattan  Bridge,  over  East  River,*  2,920  ft.  long  in  three 

spans.     Length  between  terminals,  9,900  ft.     Estimated 

cost,  $13,000,000. 
Blackwell's  Island  Bridge,*  extending  over  Blackwell's  Island, 

N.  Y.: 

Total  length,  7,449  ft.     Estimated  cost,  $18,000,1)00. 
Wooden  bridge  at  Columbia,  Pa.,  5,366  ft. 
Monongahela  Bridge,  near  Homestead,  5,300  ft. 
Louisville  Railroad  Bridge,  over  the  Ohio,  5,218  ft. 
Volga,  over  the  Syzran,  Russia,  4,947  ft. 
Moerdyck,  Holland,  4,927   ft. 
Dnieper,  near  Jekaterinoslaw,  Russia,  4,213  ft. 
Cincinnati  Southern  Railroad,  over  the  Ohio,  3,950  ft. 
Kiev,  over  the  Dnieper,  3,607  ft. 
Dauphin  Bridge,  over  the  Susquehanna,  3,590  ft. 
Barrage  Bridge,  Delta  of  the  Nile,  3,353  ft. 
Havre  de  Grace  Bridge,  over  the  Susquehanna,  3,271  ft. 
Kronprinz  Rudolph,  over  the  Danube  at  Vienna,  3,266  ft. 
Dnieper,  near  Krementchong,  Russia,  3,250  ft. 
Brommel,  over  the  Meuse,  Holland,  3,060  ft. 
Plattsmouth  Bridge,  over  the  Missouri,  3,000  ft. 
Two  bridges  of  Rotterdam,  over  the  Meuse,  2,833  ft. 
Quincy  Bridge,  over  the  Mississippi,  2,847  ft. 
St.  Louis  Bridge,  over  the  Mississippi,  2,574  ft. 
Omaha  Bridge,  over  the  Missouri,  2,750  ft. 
Saint-Esprit,  over  the  Rhone,  France,  2,460  ft. 
Kiulmbourg,  over  the  Rhine,  Holland,  2,347  ft. 
Cincinnati,  over  the  Ohio,  2,233  ft. 
Keokuk,  la.,  over  the  Mississippi,  2,008  ft. 
Chaumont  Viaduct,  valley  of  the  Suize,  France,  2,000  ft. 
Menai,  England,  1,957  ft. 
Poughkeepsie  Bridge,  N.  Y.,  total  length  6,759  ft. 

*In  process  of  construction. 


OTHER  NOTABLE  BRIDGES.  1521 


OTHER   NOTABLE   BRIDGES. 

The  following  bridges  are  notable  either  from  their  size  or 
historical  connection. 

The  Lagong  Bridge,  built  over  an  arm  of  the  China  Sea,  is 
5  miles  long,  with  300  arches  of  stone,  70  ft.  high  and  70  ft. 
broad,  and  each  pillar  supporting  a  marble  lion  21  ft.  in  length. 
Its  cost  is  unknown,  but  much  exceeds  that  of  the  Forth  Bridge. 

The  new  London  Bridge  is  constructed  of  granite,  from  the 
designs  of  L.  Rennie,  and  considered  amongst  the  finest  speci- 
mens of  bridge  architecture.  It  was  commenced  in  1824,  and 
completed  in  seven  years,  at  a  cost  of  about  $7,500,000. 

The  Bridge  of  Sighs,  at  Venice,  over  which  the  condemned 
prisoners  were  transported  from  the  Judgment  Hall  to  the 
place  of  their  execution,  was  built  in  the  Armada  year,  1588. 

The  Bridge  of  the  Holy  Trinity,  at  Florence,  consists  of 
three  beautiful  elliptical  arches  of  white  marble,  and  stands 
unrivalled  as  a  work  of  art.  It  is  322  ft.  long,  and  was  com- 
pleted in  1569. 

The  Niagara  Suspension  Bridge  was  built  in  1852-1855.  It 
is  245  ft.  above  high  water,  821  ft.  long,  and  the  strength  is 
estimated  at  12,000  tons. 

The  Rialto,  at  Venice,  said  to  have  been  built  from  the  designs 
of  Michael  Angelo,  consists  of  a  single  marble  arch,  98  ft.  6  ins. 
long,  and  was  completed  in  15S9. 

The  Britannia  Bridge  crosses  the  Menai  Straits,  Wales,  at 
an  elevation  of  103  ft.  above  high  water.  It  is  entirely  of 
wrought  iron,  1,511  ft.  long,  and  was  finished  in  1850.  Cost, 
$3,000,000. 

The  oldest  bridge  in  England  is  a  triangular  bridge  at  Croy- 
land,  in  Lincolnshire,  which  is  said  to  have  been  erected  about 
A.D.  868.  It  is  formed  of  three  semi-arches,  whose  bases  stand  in 
the  circumference  of  a  circle,  equidistant  from  each  other,  and 
uniting  at  the  top. 

Clifton  Suspension  Bridge,  near  Bristol,  has  a  span  of  703  ft., 
and  a  height  of  245  ft.  above  the  water.  The  carriageway  is 
20  ft.  wide,  and  footway  5£  ft.  wide.  Cost,  $500,000. 

Coalbrookdale  Bridge,  over  the  Severn,  has  the  reputation  of 
being  the  first  cast-iron  bridge  built  in  England.  It  was  erected 
in  1779.  It  consists  of  one  arch  100  ft.  wide.  Total  weight, 
378J  tons. 


1522 


DIMENSIONS  OF  CHURCH  BELLS. 


DIMENSIONS    AND    WEIGHT    OF    CHURCH    BELLS 

MANUFACTURED  BY  MENEELY  BELL  Co.,  TROY,  N.  Y. 


Bell. 

Mountings. 

Weight. 

Medium 
Tone. 

Diameter. 

Size  of  Frame, 
Outside. 

Diameter  of 
Wheel. 

400  Ibs. 

D 

27  in. 

42X42  in. 

4  ft.  4  in. 

450    " 

c3 

28 

42X42 

4 

4  " 

500     " 

c 

29 

45X47 

4 

4  " 

550    " 

c 

30 

45  X  47 

4 

4  " 

600 

' 

B 

31 

45X47 

4 

9  " 

700 

1 

B 

33 

48X48 

5 

6  " 

800 

1 

Bb 

34 

48X54 

5 

6  " 

900 

' 

A 

36 

54X54 

5 

9  " 

1000 

4 

A 

37 

54  X  54 

5 

9  " 

1100 

1 

A 

38 

54X59 

5 

9  " 

1200 

1 

Ab 

39 

56X59 

6 

3  " 

1300 

1 

Ah 

40 

56X59 

6 

3  " 

1400 

1 

GU 

41 

60X60 

6 

6  " 

1500 

1 

G 

42 

60X60 

6 

6  " 

1600 

' 

G 

43 

60X60 

6 

6  " 

1800 

t 

F# 

45 

65X68 

7 

2000 

' 

F* 

46 

65X68 

7 

2100 

' 

F 

47 

65X68 

7 

2300 

4 

E 

49 

70X72 

7 

6  " 

2500 

1 

E 

50 

70X72 

7 

6  " 

2800 

' 

Eb 

51 

74X78 

8 

3000 

1 

Eb 

53 

74X78 

8 

3500 

' 

D17 

56 

74X78 

8 

6  " 

4000 

i 

c  a 

58 

78X81 

9 

4500 

c  * 

61 

78X81 

9 

5000 

' 

c 

63 

84X84 

9 

5500 

1 

B, 

65 

84X84 

9 

6000 

* 

Bb 

67 

84X84 

9 

6  " 

6500 

' 

BP 

68 

90X90 

9 

6  " 

The  actual  weights  usually  exceed  the  patterns,  noted  above,  from  two 
to  three  per  cent. 

MENEELY  SCHOOL  BELLS. 


Bell. 


Mountings. 


Weight. 

Diameter. 

Size  of  Frame,  Outside. 

100  pounds 
125        " 

17    inc 
18* 

hes 

2fe 
2 

et  6  inc 
6 

hes  b 

y  2  f  e 

1  2 

3t  8  inc 
8      . 

ics 

150 

19* 

2 

6 

2 

8 

175 

20| 

2 

8 

3 

0 

200        " 

21^ 

2 

8 

3 

0 

225 

22 

2 

8 

3 

0 

250 

23 

3 

0 

3 

2 

275        " 

24 

3 

0 

3 

2 

300 

24^ 

3 

0 

3 

4 

325        " 

25 

3 

0 

3 

4 

350 

26 

3 

0 

3 

4 

375        ** 

26^ 

3 

0 

3 

4 

SIZE  OF  ROPE  FOR  BELLS. 

For  bells  of  less  than  500  pounds | 

"       "     "  500  to  800  pounds f 

"       "     "  800  to  1,800  pounds | 

"       "     above  1,800  pounds J  to  1 


inch  diameter 


LARGEST  RINGING  BELLS  IN  THE  WORLD.  1523 


THE    LARGEST  RINGING   BELLS  IN  THE  WORLD.* 


Names  and  Location 
of  Bdls. 

1 

o 

1 

a 
Q 

1733 


Actual 
Vibration. 

0) 

3 

Q 

>> 

0> 

w 

D 

Fft 

Gtt 

Diameter, 
Inches. 

Sound-bow. 

Weight, 
Pounds. 

Inches. 

Stroke. 

Moscow  Tzar  Kolokol  . 

74 
94 
105 

272 
203? 
185 
156 
155 
151 
136.3? 
112 
114.25 
121 
118 
113.5 
103.6 
103 
103 
100 
97.25 
84 
95 
95.81 
88 
82.85 
81 
76 
75.5 
72 

23 
16? 
14.75 

0.84 
0.80 
0.80 

443,772 
201,600 
127,350 
120,000 
95,000 
69,664 
60,736 
45,000 
42,000 
40,320 
40,200 
35,620 
30,800 
28.670 
28,560 
24,080 
18,000 
17,024 
16,016 
15,848 
13,000 
12,096 
11,500 
10,080 
9,856 
8,960 

Burmah,  Mengoon  .,  .  .  . 

Moscow,  St    Ivan's 

1819 

Pekin,  Great  Bell.  .  .  . 

Burmah,  Maha  Ganda.  .  . 

125 
125 

141 

B 
B 

Ctf 

12.5 
12 
10.6 

0.80 
0.80 
0.80 

Nishni  Novgorod  

Moscow,  Church  of  Redeemer 
Nankin,  China  

1879 

London,  St.  Paul's  

1881 

157 

157 
157 
166 
176 
166 
176 
187 
187 
210 
198 
210 
1981 
210 
222 
210 
249 
249 

E? 

EP 

EP 
E 

F 
E 
F 

Ftt 
Ftt 

G8 

G 

Gtt 
G 

GS 

A 

G8 

B 
B 

8.75 
9.125 
9.5. 
9.375 
9.75 
7.5 
7.8 
8 
7.5 
6.125 
7.2 
7.75 
6.375 
6 
6.08 
5 
5.94 
5.75 

0.76 
0.75 
0.80 
0.83 
0.75 
0.73 
0.76 
0.80 
0.77 
0.73 
0.76 
0.71 
0.73 
0.73 
0.75 
0.66 
0.78 
0.79 

Olmutz,  Bohemia  

Vienna,  Austria  

1711 
1856 
1487 
1680 
1847 
1845 
1786 
1680 
1477 

Westminster,  London  

Montreal,  Canada 

York,  England 

St.  Peter's    Rome     . 

Great  Tom,  Oxford  

Cologne,  Germany  

Brussels,  Belgium   

State-house,  Philadelphia.  .  .  . 

875 
834 
1716 
1675 
1610 
1857 

Exeter,  England  

Old  Lincoln,  England  

Westminster,  London  

*  John  W.  Nystrom,  in  the  Journal  of  the  Franklin  Institute. 


1524  SYMBOLS  FOR  THE  APOSTLES  AND  SAINTS. 


SYMBOLS  FOR  THE  APOSTLES  AND  SAINTS. 

From  the  constant  occurrence  of  symbols  in  the  edifices  of  the 
Middle  Ages  and  many  of  the  cathedrals  of  the  present  day,  the 
following  list  of  symbols,  as  commonly  attached  to  the  apostles 
and  saints,  may  be  found  useful: 

Holy  Apostles. 

St.  Peter. — Bears  a  key,  or  two  keys  with  different  wards. 

St.  Andrew. — Leans  on  a  cross  so  called  from  him;  called  by 
heralds  the  saltire. 

St.  John  the  Evangelist. — With  a  chalice,  in  which  is  a  winged 
serpent.  When  this  symbol  is  used,  the  eagle,  another  sym- 
bol of  him,  is  never  given. 

St.  Bartholomew. — With  a  flay  ing-knife. 

St.  James  the  Less. — A  fuller's  staff  bearing  a  small  square 
banner. 

St.  James  the  Greater. — A  pilgrim's  staff,  hat,  and  escalop-shell. 

St.  Thomas., — An  arrow,  or  with  a  long  staff. 

St.  Simon. — A  long  saw. 

St.  Jude. — A  club. 

St.  Matthias. — A  hatchet. 

St.  Philip. — Leans  on  a  spear  or  has  a  long  cross  in  the  shape 
of  at. 

St.  Matthew. — A  knife  or  dagger. 

St.  Mark. — A  winged  lion. 

St.  Luke.— A  bull. 

St.  John. — An  eagle. 

St.  Paul. — An  elevated  sword,  or  two  swords  in  saltire. 

St.  John  the  Baptist. — An  Agnus  Dei. 

St.  Stephen. — With  stones  in  his  lap. 

Saints. 

St.  Agnes. — A  lamb  at  her  feet. 

St.  Cecilia. — With  an  organ. 

St.  Clement. — With  an  anchor. 

St.  David. — Preaching  on  a  hill. 

St.  Denis. — With  his  head  in  his  hands. 

St.  George. — With  the  dragon. 

St.  Nicholas. — With  three  naked  children  in  a  tub,  in  the  end 

whereof  rests  his  pastoral  staff. 
St.  Vincent. — On  the  rack. 


HEIGHTS  OF  COLUMNS,  TOWERS,  AND  DOMES.  1525 


HEIGHTS  OF  COLUMNS,  TOWERS,  DOMES,  SPIRES, 

ETC. 

COLUMNS. 


Name. 

x  Place. 

Feet 

Alexander  «,.... 

St.  Petersburg  

175 

Bunker  Hill  

Chariest  own,  Mass.  .  .  . 

221  \ 

Chimney  (St  Rollox)  

Glasgow  

455  i 

Chimney  (Musprat's)  

Liverpool  

406 

City.  . 

London  

202 

July        

Paris  

157 

132 

Nelson's  

Dublin  

134 

Nelson's  

London  

171 

Place  Vendome    

Paris  

136 

Pompey's  Pillar  

Effvpt.  .  . 

114 

Trajan  

Rome  

145 

Washington  

Washington  

555 

York  

London  

138 

TOWERS  AND  DOMES.* 


Name. 

Place. 

Feet. 

Eiffel  Tower  

Paris  

985 

Tower   . 

Babel 

680 

Tower.                    

Baalbec  

500 

Cathedral  (spire).  . 

Cologne.  .  .  . 

516f 

Cathedral.                      

Rouen  

49  If 

Cathedral  (spire).  . 

Antwerp.  .  .  . 

476 

St.  Nicholas  

Hamburg  

473 

Cathedral. 

Anvers.  .  .  . 

472 

St.  Peter's  (cupola)  

Rome  

469* 

Cathedral. 

Cremona  

392 

Cathedral 

Escurial 

200 

Cathedra]  

Florence  

384 

Cathedral 

Milan. 

438 

Cathedral 

St    Petersburg 

363 

Capitol  (dome).  .  .  . 

Washington 

287J 

Leaning  Tower  

Pisa  

188 

Porcelain.  .  .  . 

China 

200 

St   Paul's 

London 

366 

St.  Mark's  

Venice 

328 

City  Hall. 

Philadelphia 

5371 

*  See  also  next  page. 


1526     HEIGHT  AND  DIAMETER  OF  NOTED  DOMES. 


HEIGHT  OF  SPIRES. 


Name. 

Place. 

Feet. 

Cathedral  
Cathedral  new  

Strasburg  
New  York 

465J 
325 

Grace  Church    

New  York 

216 

Cathedral       

Salisbury.  .  . 

450 

St  John's  

New  York 

210 

St   Paul's  

New  York  

200 

St   Mary's  

Liibeck  

404 

St   Peter's  

Rome  

391 

St   Stephen's     

Vienna. 

465 

Trinity  Church  

New  York   . 

286 

Balustrade  of  Notre  Dame.  .  .  . 

Paris  

216 

Hotel  des  Iiivalides  

Paris  

344 

Pyramid  of  Cheops  

Egypt.  .  . 

520 

Pyramid  of  Sakara  

EsrvDt 

356 

LIST  OF  THE  PRINCIPAL  DOMES  IN  THE  WORLD. 

Their  diameter  and  height  from  the  ground. 
(Gwilt's  Encyclopaedia.) 


Place. 


Pantheon,  at  Rome 

Duomo,  or  Sta.  Maria  del  Fiore,  at  Florence .  .  . 

St.  Peter's,  at  Rome 

Sta.  Sophia,  at  Constantinople 

Baths  of  Caracalla  (ancient) 

St.  Paul's,  London 

Mosque  of  Achmet 

Chapel  of  the  Medici 

Baptistery,  at  Florence 

Church  of  the  Invalids,  at  Paris 

Minerva  Medica,  at  Rome 

Madonna  della  Salute,  Venice 

St.  Gene  vie  ve,  at  Paris  (Pantheon) 

Duomo,  at  Sienna 

Duomo,  at  Milan 

St.  Vitali's,  at  Ravenna 

Val  de  Grace,  at  Paris 

San  Marco,  Venice 

United  States  Capitol,  Washington 


Diam., 
Feet. 


142 

139 

139 

115 

112 

112 
92 
91 
86 
80 
78 
70 
67 
57 
57 
55 
55 
44 

124f 


Height, 
Feet. 


143 
310 
330 
201 
116 
215 
120 
199 
110 
173 

97 
133 
190 
148 
254 

94 
133 

307i 


DIMENSIONS   OF  ENGLISH  CATHEDRALS.     1527 


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Chester  
Rochester  
Carlisle  
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Bristol  
Oxford  

1528        DIMENSIONS  OF  VARIOUS  OBELISKS. 


DIMENSIONS   OF   THE   VARIOUS   OBELISKS    EXIST- 
ING   AT   THE   PRESENT   TIME. 

(Gwilt's  Encyclopaedia.) 


Situation. 


Two  large  obelisks  mentioned  by  Diodorus  Sicu- 

lus 158 . 2 

Two  obelisks  of  Nuncoreus,  son  of  Sesostris,  ac- 
cording  to    Herodotus,   Diodorus   Siculus,    and 

Pliny 121 .8 

Obelisk  of  Rhameses,  removed  to  Rome  by  Con- 

stantius 118.4 

Two  obelisks,  attributed  by  Pliny  to  Smerres  and 

Eraphius 106 . 0 

Obelisks  of  Nectanabis,  erected  near  the  Tomb  of 

Arsinoe  by  Ptolemy  Philadelphus 105.5 

Obelisk  of  Constantius,  restored  and  erected  in  front 

of  S.  Giovanni  Laterano,  at  Rome 105.5 

Part  of  one  of  the  obelisks  of  the  son  of  Sesostris, 

in  the  centre  of  the  piazza  in  front  of  St.  Peter's.  .  82.4 

Two  at  Luxor 79.1 

Obelisk  of  Augustus,  from  the  Circus 

Maximus,  now  in  the  Piazza  del  Popola  at  Rome.  .  78.2 

Two  in  the  ruins  at  Thebes,  still  remaining 72.8 

Obelisk    of   Augustus,  raised   by   Pius  VI.    in   the 

Piazza  di  Monte  Citorio 

Two  obelisks:    one  at  Alexandria,  vulgarly  called 

Cleopatra's  Needle,  and  the  other  at  Heliopolis.  .  67.1 

Obelisk  by  Pliny,  attributed  to  Sothis 63 . 3 

Two  obelisks  in  the  ruins  at  Thebes 63 . 3 

Great  obelisk  at  Constantinople 59. 

Obelisk  in  the  Piazza  Navona,  removed  from  the 

Circus  of  Caracalla 54 . 9 

Obelisk  at  Aries 50. 1 

Obelisk  from  the  Mausoleum  of  Augustus,  now  in 
front  of  the  Church  of  Sta.  Maria  Maggiore,  at 

Rome 48.3 

Obelisk  in  the   Gardens  of  Sallust,  according  to 

Mercati 48 . 3 

Obelisk  at  Bijije,  in  Egypt 42 . 9 

Small  obelisk  at  Constantinople,  according  to  Gyl- 

lius 34 . 2 

The  Barberini  Obelisk 30.0 

Obelisk  of  the  Villa  Mattel 26.4 

Obelisk  in  the  Piazza  della  Rotunda 20 . 1 

Obelisk  in  the  Piazza  di  Minerva 17.6 

Obelisk  of  the  Villa  Medici 16.1 


Height 

in 

English 
Feet. 


SOME  WELL-KNOWN  EUROPEAN   BUILDINGS.  1529 

DIMENSIONS  OF  SOME  WELL-KNOWN  EUROPEAN 
BUILDINGS.* 

The  body  of  Milan  Cathedral,  from  the  great  doorway  to  the 
end  of  the  apse,  measures  148  metres  and  10  centimetres,  with  a 
breadth  of  57  metres.  The  total  length  of  the  transepts  with  the 
chapels  is  87  metres.  The  nave  is  47  metres  high  by  19  in  width, 
and  the  total  height,  from  the  centre  to  the  feet  of 'the  statue  of 
the  Virgin  which  crowns  the  central  tower,  is  108.5  metres. 

The  Cathedral  of  York,  burned  in  1828,  and  which  had  already 
been  rebuilt  in  1705,  has  a  length  of  142  English  feet,  a  breadth 
of  105  feet  at  the  western  extremity,  and  109  feet  at  the  opposite 
end.  The  total  height  of  the  nave  is  99  feet;  the  ceiling  of  the 
central  tower  is  213  feet  from  the  ground.  A  window  which  opens 
at  the  extremity  of  the  gallery,  and  which  is  entirely  filled  with 
stained  glass,  is  65  English  feet  in  height  by  32  in  width. 

The  Cathedral  of  Cordova,  built  in  the  year  792  by  King 
Abderame,  is  134  feet  long  and  387  wide.  This  church  contains 
nine  naves  formed  by  1,018  columns,  the  smallest  of  which  are 
7  feet  and  the  largest  11  feet  and  3  inches  high. 

The  Escurial,  begun  in  1557,  to  which  was  given  the  form  of  a 
gridiron,  in  honor  of  St.  Lawrence,  is  51  feet  in  height  and  637 
feet  in  length. 

In  the  Alhambra  at  Granada,  an  ancient  Moorish  fortress,  the 
Lion  Court  is  100  feet  square. 

The  Church  of  St.  Denis,  near  Paris,  is  335  feet  long  by  90  feet 
high.  It  was  built  in  1152  by  Suger. 

The  famous  Column  of  the  Grand  Army  on  the  Place  Vendome, 
Paris,  is  136  feet  high. 

The  Church  of  St.  Genevieve,  at  Paris,  to-day  transformed  into 
the  Pantheon,  is  one  of  the  most  remarkable  structures  by  reason 
of  the  vastness  of  its  proportions.  The  diameter  of  the  dome  is 
68  feet.  The  32  columns  which  surround  it  are  34  feet  in  height, 
and  the  highest  point  of  the  edifice  is  237  feet  from  the  sidewalk. 

The  Cathedral  at  Rheims,  which  Stendhal  considers  one  of  the 
most  beautiful  churches  in  France,  was  built  in  840,  and  measures 
430  feet  in  length  by  110  in  height. 

The  Cathedral  at  Strasburg,  which  is  perhaps  the  only  purely 
Gothic  monument  on  the  Continent  of  Europe,  was  finished  in 
1275.  The  first  stone  was  laid  in  1015.  The  tower,  finished  in 

*  Taken  from  an  article  on  Milan  Cathedral,  published  in  the  American 
Archiiect,  August  25,  1888. 


1530  DIMENSIONS  GRAND  OPERA  HOUSE,  PARIS. 

1439,  is,  without  contradiction,  the  highest  bit  of  masonry  which 
exists  in  Europe.  Its  height  is  426  feet;  width  of  nave,  43  feet; 
length,  145  feet,  inside  measurements. 

The  tower  of  St.  Etienne  at  Vienna  is  414  feet  high,  4  feet 
less  than  that  at  Strasburg. 

The  tower  of  St.  Michael  at  Hamburg  is  390  feet. 

The  famous  tower  of  Pisa  measures  193  feet,  but  it  leans  toward 
the  south  about  12  feet,  which  gives  it  a  mean  inclination  of  6 
feet  in  the  hundred. 

St.  Sophia,  at  Constantinople,  measures  270  feet  in  length  by 
240  feet  in  width,  from  north  to  south.  The  height  of  the  dome 
above  the  level  of  the  ground  is  only  165  feet. 

The  towers  of  Notre  Dame,  at  Paris,  measure  240  feet  in  height. 
The  total  length  of  this  church  is  409  feet.  Its  interior  width  at 
the  crossing  is  150  feet;  the  width  of  the  nave  is  40  feet. 

The  Church  of  St.  Paul,  at  London,  is  500  feet  in  length  by  169 
feet  in  width.  The  height  of  the  dome  is  319  feet. 

St.  Peter's,  at  Rome;  total  length,  including  the  portico  and 
thickness  of  the  walls,  is  660  feet.  The  foundation  walls  are  21 
feet  and  7  inches  thick.  The  walls  of  the  peristyle  are  8  feet  and 
9  inches  thick,  and  the  peristyle  is  39  feet  and  3  inches  in  width. 
The  interior  length  of  the  crossing  of  St.  Peter's  is  98  feet.  The 
interior  width  of  the  nave,  without  the  aisles  and  chapels,  is  82 
feet.  The  total  height  from  the  floor  to  the  summit  of  the  cross 
which  surmounts  the  dome  is  408  feet.  The  height  of  the  dome 
under  the  key-stone  is  249  feet.  The  interior  height  of  the  fagade 
is  259  feet. 

DIMENSIONS  OF  THE  GRAND  OPERA-HOUSE,  PARIS. 

Superficial  area,  37,317  square  feet,  and  cubical  contents, 
428,660  metres. 

The  width  of  the  fagade  is  230  feet. 

Greatest  width  of  building,  408  feet. 

Height  above  the  ground  level,  184  feet. 

From  foundation  to  summit,  266  feet. 

No  less  than  fifteen  eminent  painters,  fifty-six  eminent  sculp- 
tors, besides  nineteen  sculptors  of  ornament,  were  engaged  on 
the  external  and  internal  decorations. 

M.  Gamier,  the  architect,  gave  his  entire  and  unremitting  at- 
tention to  it,  and,  with  the  aid  of  his  assistants,  produced  more 
than  30,000  drawings.  The  building  was  in  course  of  construc- 
tion for  thirteen  years. 


TALLEST  BUILDINGS  IN  UNITED  STATES.    1531 


HEIGHT   OF    SOME   OF   THE   TALLEST  BUILDINGS 
IN  THE   UNITED   STATES. 

BUILDINGS  IN  NEW  YORK  CITY. 

Height  above 
Sidewalk. 

Ivins  Syndicate  (Park  Row);Buildingi..29  stories 386  ft. 

New  Times  Building  " 22       "      375*  ' ' 

Manhattan  Life  Building  2 18       "     and  tower 348  ' ' 

International  Bank  Bld'g.3  60  Wall  St. .26       "      Pine  St.  wing 345  " 

Wall  St.  Exchange  3 25       "     340  ' ' 

St.  Paul  Building  5 26       "     313  ' ' 

American  Surety  Building 6 21       "     312  " 

Pulitzer  (World)  Building  5 16       "     and  dome 309  " 

Hanover  National  Bank  10 22       '  * •  • 

American  Tract  Society  Building  1 ....  21       "     306  ' ' 

Empire  Building  2 20       "     304  ' ' 

Commercial  Cable  Building  7 20       "     304  * ' 

Whitehall  (Battery  Place)  Building1?.  .20       "     

Forty-two  Broadway  Building 19 20       "     " 

Madison  Square  Garden  s to  top  of  tower 300  ' ' 

Gillender  Building  9 19  stories  and  tower 300  " 

Fuller  (Flat  Iron)  Building  21 21        "      285  " 

Trinity  Church  spire 284  '  * 

Standard  Oil  Building  2  (remodelled) .  .  19  stories 280  " 

Broad  Exchange  Building  3 20       "      276  '  * 

Bank  of  Commerce  Building  10 19       "      264  '" 

Broadway-Maiden  Lane  Building  3.  ...  18       "     234  '* 

Broadway  Chambers  14 18       "     '  • 

Home  Life  Insurance  Building11 16                and  tower 257  '* 

Washington  Building 12 13        "         "        "       250  ' ' 

New  York  Life  Building  8 12       "         '  *        "     244  ' ' 

S.  L.  Mitchell  Estate  Building 15       "     230  " 

Mutual  Life  Building  4 14       "     230  * ' 

Manhattan  Hotel 16       "     225  '  * 

Produce  Exchange  Building5 9       "       and  tower 225  '* 

Queens  Insurance  Co.  Building 7 17       "     '  * 

Bowling  Green  Building  13 16       *  *     224  * ' 

St.  James  Building 6 16       "     '•• 

American  Exchange  Bank 3 16       "     •  • 

New  Netherlands  Hotel 16       "     220  '  • 

Blair  Building 15 16       "     •• 

Bank  of  the  Metropolis  6 16       "     *  * 

Beaver  Building  3 15       "     v '  * 

Dun  Building  7 15       '  *     223  '  * 

Central  Bank  Building  20 15       "     219  " 

Hudson  Building 16       "     218  '  * 

Lords  Court  Building ls 15       ' '     214  * ' 

Johnston  Building 15       "      212  '  * 

Syndicate  Building 15       "     207  " 

*  430  ft.  above  footings. 


1532  TALLEST  BUILDINGS  IN  UNITED  STATES. 

Height  above 
Sidewalk. 

Continental  Ins.  Co.  Building 14  stories 215    ft. 

Union  Trust  Building  5 to  top  of  tower 194     ' ' 

Postal  Telegraph  Building  7 13  stories 192     " 

Havemeyer  Building  5 14       "     192     ' ' 

Mutual  Reserve  Building, 13       "     184     '  * 

Times  Building  (old)  s 183     " 

Silk  Exchange  Building 13  stories 180     '  * 

ARCHITECTS. — *  R.  H.  Robinson.  2  Kimball  &  Thompson.  3  Clinton  & 
Russell.  4  C.  W.  Clinton.  5  Geo.  B.  Post.  6  Bruce  Price.  7  Geo.  Edward 
Harding  &  Gooch.  8  McKim,  Mead  &  White.  9  Berg  &  Clark.  10  James  B. 
Baker.  »  N.  Le  Brun  &  Sons.  12  E.  H.  Kendall.  13  Audsley  Bros.  14  Cass 
Gilbert.  15  Carrere  &  Hastings.  *6  Cyrus  L.  W.  Eidlitz.  "  Henry  J.  Har- 
denbergh.  18  John  T.  Williams.  ™  Henry  Ives  Cobb.  20  Wm.  H.  Birkmire. 
M  D.  H.  Burnham  &  Co. 

CHICAGO. 

Height  above 
Sidewalk. 

Masonic  Temple  22 20  stories Roof  line  278     ft. 

To  top  of  skylight 303     " 

Auditorium  23 17  stories  and  tower 265     '  * 

Fischer  Building  2; 18       •  •         "    attic 235     ' ' 

Old  Colony  Building  2* 17       "     213     '  * 

Schiller  Theatre  23 17       "     

Katahdin  &  Wachusett  Building 17       "     203£  ' ' 

Unity  Building 17       "     210"    " 

Railway  Exchange  Building  21 17       "      

Marquette  Building 2* 16       "      207     ' ' 

Monadnock  Building 16       "     215     ' ' 

Ashland  Block 16       "     200$  ' ' 

The  New  Great  Northern  Building  21.  .  .  16       "     200     ' ' 

Manhattan  Building  » 16       "     197     " 

Reliance  Building  21 14       "     200     ' ' 

Security  Building 14       "      200     " 

Title  &  Trust  Building 16       "     198 

Woman 's  Temple  22 13       "     Ridge  198     '  * 

Champlain  Building  2* 15       '  *     189     " 

BOSTON. 

Ames  Building  25 Top  of  cornice 186     ft. 

Chamber  of  Commerce  25 Top  of  tower 172£  '  * 

BUFFALO,  N.  Y. 
Guaranty  Building  23 13  stories 

CINCINNATI. 
Ingalls  Building27 15  stories  (concrete-steel construct'n) 


DESCRIPTION  OF  AMERICAN   BUILDINGS.    1533 

PHILADELPHIA. 

City  Hall To  top  of  tower 537     ft. 

Land  &  Title  Building 22  stories 317     ' ' 

PITTSBURG. 

Allegheny  County  Court  House  26 To  top  of  finial 319     ft. 

Farmers'  Bank  Building  28 25  stories 

SAN  FRANCISCO. 
Spreckels  Building  29 16  stories  and  tower 215     ft. 

MISCELLANEOUS. 

U.  S.  Capitol,  Washington Top  of  dome 307£  ft. 

State  Capitol,  Hartford,  Conn Top  of  figure  on  dome 256      ' ' 

ARCHITECTS.—21  D.  H.  Burnham  &  Co.  22  Burnham  &  Root.  23  Adler 
&  Sullivan.  2*  Holabird  &  Roche.  2S  Shepley,  Rutan  &  Coolidge.  26  H. 
H.  Richardson  and  Shepley  Rutan  &  Coolidge.  27  Elzner  &  Anderson. 
28  Alden  &  Harlow.  29  Reid  Bros.  »  Jenney  &  Mundie. 


DESCRIPTION   OF   NOTABLE    AMERICAN 
BUILDINGS. 

THE  UNITED  STATES  CAPITOL. 

[From  ' '  King 's  Hand-book  of  Washington. ' '] 

The  site  of  the  building  is  89J  ft.  above  ordinary  low  tide  in 
the  Potomac.  Entire  length  of  building,  751  ft.;  greatest 
depth  (breadth  of  wings),  324  ft.;  area  covered  by  building, 
3J  acres.  The  central  building  is  352  ft.  long;  corridors,  44  ft. 
long;  wings,  143  ft.  front,  239  ft.  deep,  exclusive  of  porticos  and 
steps.  Central  building  is  freestone  from  quarries  about  40 
miles  below  Washington.  This  is  painted  white. 

The  wings  are  of  white  marble  from  Lee,  Mass.  Appropria- 
tions made  by  Congress  from  1800  to  date  for  the  erection  and 
remodelling  of  the  Capitol  amount  to  $15,000,000. 

Dome  designed  by  T.  U.  Walter,  to  replace  a  smaller  one 
removed  in  1856.  Exterior  height  crest  of  statue  above  base- 
line, 307J  ft.;  top  of  lantern  above  balustrade  of  building, 
218  ft.;  height  of  Statue  of  Freedom  on  the  apex,  19J  ft.; 
diameter  of  dome,  135J  ft. 

The  dome  rests  on  an  octagonal  base  93  ft.  above  the  base- 
ment floor,  and  as  it  leaves  the  top  line  of  the  building  consists 
of  a  peristyle,  124  ft.  in  diameter,  of  36  iron-fluted  columns  27 
ft.  high  and  weighing  6  tons  each. 


1534    DESCRIPTION  OF  AMERICAN  BUILDINGS. 

The  lantern  is  15  ft.  in  diameter  and  50  ft.  high. 

The  weight  of  iron  in  the  superstructure  of  the  dome  is  8,009,- 
200  Ibs.  This  rests  on  a  substructure  of  masonry  and  40  interior 
massive  stone  columns  supporting  heavy  groined  arches,  upon 
which  also  rests  the  pavement  of  the  Rotunda. 

Height  from  floor  of  Rotunda  to  canopy,  180  ft.;  diameter 
of  Rotunda,  96  ft. 

The  canopy  consists  of  an  inner  shell  of  iron  ribs  and  lathing, 
laid  with  plaster  suitable  for  frescoing.  It  is  65i  ft.  in  diameter, 
and  21  ft.  vertical  height. 

Supreme  Court  Room. — Seventy-five  ft.  long,  45  ft.  wide,  and 
45  ft.  high. 

Hall  of  Representatives. — Length,  139  ft.;  width,  93  ft.; 
height,  36  ft.;  floor,  115  ft.  by  67  ft.  Galleries  will  seat  about 
2,500  persons. 

The  ceiling  of  the  hall  is  of  cast  iron,  panelled,  painted,  and 
gilded,  and  highly  enriched  with  gilt  mouldings.  The  panels 
are  filled  with  glass,  with  stained  centre-pieces  representing 
the  arms  of  the  States.  Above  the  ceiling  is  the  illumination- 
loft,  with  1,500  gas-jets,  for  lighting  the  hall  for  night  sessions. 

Senate  Chamber.— Length,  113J  ft.;  width,  80}  ft.;  height, 
39  ft. 

Floor  is  83  ft.  long,  51  ft.  wide.  Galleries  seat  1,200  persons. 
The  ceiling  is  of  iron  with  glass  panels,  lighted  same  as  Repre- 
sentatives' Hall. 

The  Congressional  Library. — In  response  to  an 
invitation  for  competitive  plans,  28  designs  were  submitted, 
from  among  which  that  of  Messrs.  Smithmeyer  &  Pelz  of  Wash- 
ington was  selected  as  the  best,  and  they  were  entrusted  with 
the  work.  Mr.  Smithmeyer  was  early  retired,  and  in  1892  Mr. 
Pelz  was  also  retired,  and  after  that  Mr.  Edward  P.  Casey  took 
up  the  work.  In  many  respects  it  is  one  of  the  most  notable 
buildings  in  this  country. 

The  dimensions  of  the  ground  plan  are:  Length  of  frontage, 
470  ft.,  depth,  340  ft.  The  reading-room  is  100  ft.  inscribed 
diameter.  The  niches  are  18  ft.  additional,  making  the  open 
space  between  opposite  walls  136  ft.  The  stair  hall  is  4S'X  80', 
but  with  adjoining  corridors  and  between  walls,  is  94'X  136'.  The 
longest  rooms,  the  north  and  south  wings,  are  210'X  35'.  There 
are  three  book  repositories,  with  a  total  capacity  of  about  2,000,000 
volumes.* 

*  The  Architects'  and  Builders'  Magazine,  July,  1900. 


DESCRIPTION  OF  AMERICAN  BUILDINGS.   1535 

Treasury  Building. — Dimensions:  468  ft.  north  to 
south,  264  ft.  east  to  west;  inclusive  of  porticos  and  steps, 
582  ft.  by  300  ft.  Cost,  $6,000,000. 

Architects — Robert  Mills,  T.  U.  Walter,  Young,  Rogers,  and 
A.  B.  Mullett. 

State,  War,  and  Navy  Building.— A.  B.  Mullett, 
architect.  Extreme  dimensions  north  to  south,  567  ft.;  east 
to  west,  342  ft.;  exclusive  of  projection,  471  ft.  north  to  south, 
and  253  ft.  east  to  west.  Cost,  $5,000,000. 

New  City  Hall,  Philadelphia;  John  McArthur,  Jun., 
architect. 

Dimensions  of  Building 

From  north  to  south 486  ft.  6  ins. 

"      east  to  west 470  ft. 

Area 4J  acres 

Number  of  rooms  in  building 520 

Total  amount  of  floor-room 14}  acres 

Height  of  main  tower 537  ft.  4  ins. 

Width  at  base 90  " 

Centre  of  clock-face  above  pavement 361   " 

Diameter  of  clock-face 20  " 

State  Capitol,  Hartford,  Conn.;  R.  M.  Upjohn,  archi- 
tect, New  York  City. 

Exterior  is  of  marble;  building  is  of  fire-proof  construction, 
with  brick  and  iron  floors. 

Length 296  ft. 

Depth 199  " 

Height  to  top  of  roof 99  " 

Height  to  top  of  figure  on  dome.  .  .  .  256  " 

Senate  chamber .  .  50  "  X  40  ft.,  35  ft.  high 

Representatives'  hall 84  "  X  56  "     48  "   high 

Supreme  Court  room 50  "  X  31   "     35  "   high 

Cost  of  building,  $2,500,000.00. 

The  Washington  Monument,  at  Washington,  D.C.,  is 
555  ft.  5  ins.  high,  and  has  a  base  of  55  ft.,  with  an  entasis  of 
1  ft.  in  every  34  in  height.  The  monument  is  faced  with  white 
marble  and  backed  with  blue  granite  to  the  height  of  452  ft.; 
above  that  the  walls  are  entirely  of  marble.  The  average  settle- 
ment of  the  structure  at  each  corner  is  1.7  ins.  The  monu- 


1536    DESCRIPTION  OF  AMERICAN  BUILDINGS. 

ment  is  a  simple  plain  obelisk  with  no  embellishments  what- 
ever. 

The  weight  of  the  monument  is  80,470  tons,  or  3.6  tons  per 
square  foot;  the  area  covered  by  the  foundation  being  22,400 
sq.  ft. 

The  corner-stone  of  the  monument  was  laid  July  4,  1848,  and 
the  cap-stone  was  set  Dec.  6,  1884. 

The  Madison  Square  Garden,  New  York  City.— 
Messrs.  McKim,  Mead  &  White,  architects.  This  building  covers 
the  block  bounded  by  East  Twenty-seventh  Street,  Fourth 
Avenue,  Twenty-sixth  Street,  arid  Madison  Avenue.  It  was 
opened  to  the  public  June  16,  1890,  and  cost  $3,000,000. 

It  combines  an  immense  amphitheatre,  a  restaurant  (80'X90'), 
a  ball-room,  a  concert  hall,  an  open-air  roof  garden  (SO'X20Q£), 
and  a  theatre. 

The  amphitheatre  is  an  enormous  room,  310'X  194'  and  80' high, 
with  an  arena  containing  30,000  sq.  ft.  The  room  is  semi- 
circular at  each  end,  and  is  provided  with  permanent  seats 
for  7,800  people,  with  sufficient  standing  space  left  to  give 
room  for  a  total  of  15,000  persons.  This  vast  arena,  covered 
by  the  immense  roof  without  central  support,  is  entirely  open 
and  free  from  side  to  side  and  from  end  to  end.  For  summer 
performances  the  roof  can  be  opened  by  machinery. 

The  theatre  has  a  seating  capacity  of  about  1,200,  with  stand- 
ing room  for  400  more. 

The  open-air  garden  extends  over  the  roof  along  the  Madison 
Avenue  front.  It  will  hold  from  3,000  to  5,000  people. 

The  building  is  surmounted  by  an  immense  tower  300  ft.  high. 

Auditorium  Building,  Chicago,  111, ;  Adler  &  Sulli- 
van, architects. 

This  building  was  built  during  the  years  1887-89  and  includes: 

1.  The  Auditorium. — Permanent  seating  capacity,  over  4,000; 
for  conventions,  etc.  (for  which  the  stage  will  be  utilized),  about 
8,000.     Contains  the  most  complete  and  costly  stage  and  organ 
in  the  world. 

2.  Recital  Hall— Seats  over  500. 

3.  Business  Portion  consists  of  stores  and  136  offices,  part  of 
which  are  in  the  tower. 

4.  Tower  Observatory,  to  whir,h  the  public  are  admitted. 
Above  four  departments  of  the  building  are  managed  by  Chi- 
cago Auditorium  Association. 

5.  Auditorium  Hotel  has  400  guest  rooms.     The  grand  dining- 


ARCHITECTS  OF  NOTED   PUBLIC  BUILDINGS.    1537 

room  (175  feet  long)  and  the  kitchen  are  on  the  top  floor.  The 
magnificent  banquet  hall  is  built  of  steel,  on  trusses,  spanning 
120  feet  over  the  Auditorium. 

Area  covered  by  building,  about  one  and  one-half  acres. 

Cost  of  building,  $3,200,000. 

ARCHITECTS  OF  NOTED  PUBLIC  AND  SEMI-PUBLIC 
BUILDINGS  IN  THE  UNITED  STATES. 

BUILDINGS  ARRANGED  ACCORDING  TO  LOCATION. 

GOVERNMENT  BUILDINGS  IN  WASHINGTON,  D.  C. 

Architects. 
United  States  Capitol Messrs.  Hallet,  Hadfield,  Hoban, 

Latrobe,     Bulfinch,     Walter, 

and  Clark. 

National  Museum Cluss  &  Schulye. 

State,  War  and  Navy  Building.  A.  B.  Mullett. 

Treasury  Building Robert    Mills,    T.    U.    Walter, 

Young,    Rogers,    and    A.    B. 

Mullett. 
The  Congressional  Library Smithmeyer  &  Pelz,  Edward  P. 

Casey.* 

United  States  Post  Offices  and  Court-houses: 
Location. 

Baltimore,  Md James  G.  Hill. 

Boston,  Mass A.  B.  Mullett. 

Chicago,  111.  (old) A.  B.  Mullett. 

Chicago,  111.  (new) Henry  Ives  Cobb. 

Cincinnati,  O A.  B.  Mullett. 

Detroit,  Mich M.  E.  Bell. 

Kansas  City,  Mo James  G.  Hill. 

New  York,  N.  Y A.  B.  Mullett. 

St.  Louis,  Mo A.  B.  Mullett. 

Other  Government  Buildings. 

Immigrant  Station,  Ellis  Island, 

N.  Y.  Harbor Boring  &  Tilton. 

New  Naval  Academy,  Annapolis, 

Md Ernest  Flagg. 

*  See  p.  1534. 


1538  ARCHITECTS  OF  NOTED  PUBLIC  BUILDINGS. 

STATE  CAPITOLS. 
Capitol  of: 

Architects. 

Colorado,  at  Denver E.  E.  Meyers  &  Son. 

Connecticut,  at  Hartford R.  M.  Upjohn. 

Illinois,  at  Springfield A.  H.  Piquenard. 

Indiana,  at  Indianapolis Edwin  May. 

Iowa,  at  Des  Moines A.  H.  Piquenard. 

Georgia,  at  Atlanta W.  J.  Edbrook  &  F.  P.  Burn- 
ham. 
Louisiana,  at  Baton  Rouge. .  .W.  A.  Freret. 

Maine,  at  Augusta Charles  Bulfinch. 

Massachusetts,  at  Boston Charles  Bulfinch;  Brigham  & 

Spofford. 

Michigan,  at  Lansing E.  E.  Meyers. 

Minnesota,  at  St.  Paul, Cass  Gilbert. 

Capitol  of: 

New  York,  at  Albany Messrs.    Fuller,    Eidlitz,    and 

H.  H.  Richardson. 

Ohio,  at  Columbus Henry  &  Wm.  Walter. 

Rhode  Island,  at  Newport.  .  .  James  Munday. 

Tennessee,  at  Nashville John  Strickland. 

Texas,  at  Austin E.  E.  Meyers  &  Son. 

Virginia,  at  Richmond Thomas  Jefferson. 

COUNTY  BUILDINGS. 

Court-house,  Baltimore Wyatt  &  Nolting. 

Suffolk  County  Court-house, 

Boston,  Mass Geo.  A.  Clough. 

Cook  County  Court-house,  Chi- 
cago, 111 J.  J.  Egan. 

Arapahoe  County  Court-house, 

Denver,  Col E.  E.  Meyers  &  Son;  P.  Eberley. 

Jefferson  Market  Court-house, 

New  York F.  C.  Withers. 

The  Appellate  Division  Court- 
house, New  York James  Brown  Lord. 

Allegheny  County  Court-house 

and  Jail,  Pittsburgh,  Pa H.  H.  Richardson. 

Court-house,  Providence,  R.  I. .Stone  &  Carpenter. 


ARCHITECTS  OF  NOTED  PUBLIC  BUILDINGS.   1539 

CITY  AND  TOWN  HALLS. 
City  Hall: 

Albany,  N.  Y H.  H.  Richardson. 

Boston,  Mass Oilman  &  Bryant. 

Detroit,  Mich James  Anderson. 

New  York,  N.  Y.  (1803-12).  .John  McComb. 

(New)  Philadelphia,  Pa John  Me  Arthur,  Jr.  , 

Worcester,  Mass Peabody  &  Stearns. 

Town  Hall,  North  Easton,  Mass.  .H.  H.  Richardson. 

LIBRARIES. 

Name  and  Location.  Architect. 

Public  Library,  Boston,  Mass McKim,  Mead  &  White. 

Public  Library,  Chicago,  111 Shepley,  Rutan  &  Coolidge. 

Newberry  Library,  Chicago Henry  Ives  Cobb. 

Lenox  Library,  New  York R.  M.  Hunt. 

Free  Circulating  Library,  N.  Y. 

Branch  No.  1  * James  Brown  Lord. 

Chatham  Sq.  Branch  N.  Y.  Pub. 

Library  * McKim,  Mead  &  White. 

Blackstone  Memorial  Library,  Bran- 
ford,  Conn S.  S.  Beman. 

Public  Library,  Erie,  Pa Alden  &  Harlow. 

Public  Library,  Mankato,  Minn.*.  .    Jardine,  Kent  &  Jardine. 

Public  Library,  Milton,  Mass Shepley,  Rutan  &  Coolidge. 

Public  Library,  Tacoma,  Wash.  .  . .  Jardine,  Kent  &  Jardine. 

Public  Library,  Milwaukee,  Wis.  .  .    Ferry  &  Class. 

Public  Library,  Newark,  N.  J Rankin  &  Kellogg. 

Public  Library,  Schenectady,  N.  Y.*  Penn  Varney. 

Carnegie  Library,  Syracuse,  N.  Y.  .  Jas.  A.  Randall. 

Carnegie  Library,  Paducah,  Ky.  ...  A.  L.  Lassiter. 

Carnegie  Library,  East  Orange,  N.  J.  Jardine,  Kent  &  Jardine. 

Carnegie  Library,  Sandusky,  O.  .  . .  D'Oench  &  Yost 

ART  INSTITUTES  AND  MUSEUMS. 

Museum  of  Fine  Arts,  Boston Sturgis  &  Brigham. 

Academy  of  Fine  Arts,  Chicago.  .    .  Burnham  &  Root. 

Art  Institute,  Chicago Shepley,  Rutan  &  Coolidge. 

Art  Museum,  Detroit James  Balfour. 

Museum  of  Fine  Arts,  St.  Louis  . . .  Peabody  &  Stearns. 

*  Carnegie  Libraries. 


1540 


LIST  OF  NOTED  ARCHITECTS. 


LIST  OF  NOTED  ARCHITECTS. 

(Gwilt.) 
BEFORE  CHRIST. 


Name  of  Architect. 

Century. 

Principal  Works. 

Theodoras,  of  Samos. 

7th 

Labyrinth  at  Lemnos,  some  buildings  at 

Sparta,  and  the  Temple  of  Jupiter  at 

Samos. 

Ictinus,  of  Athens. 

6th 

Parthenon  at  Athens,  Temple  of  Ceres 

and  Prosperpine  at  Eleusis  ,  Temple  of 

Apollo  Epicurius  in  Arcadia. 

Callicrates,  of  Athens. 

6th 

Assisted  Ictinus  in  the  erection   of  the 

Parthenon. 

Mnesicles,  of  Athens. 

6th 

Propylaea  of  the  Parthenon. 

Dinocrates,  of  Macedonia. 

4th 

Rebuilt  the  Temple  of  Diana  at  Ephesus, 

engaged  on  works  at  Alexandria,  was 

the  author  of  the  proposition  to  trans- 

form   Mount    Athos   into   a   colossal 

figure. 

Andronicus,  of  Athens. 

4th 

Tower  of  the  Winds  at  Athens. 

Callimachus,  of  Corinth. 

4th 

Reputed    inventor    of    the    Corinthian 

order. 

Sostratus,  of  Cnidus. 

4th 

The  Pharos  of  Alexandria. 

Cossutius,  of  Rome. 

2d 

Design    for    the    Temple    of    Jupiter 

Olympus  at  Athens. 

Hermodorus?  of  Salamis. 

2d 

Temple  of  Jupitor  Stator  in  the  Forum 

at  Rome,  Temple  of  Mars  in  the  Cir- 

cus Flaminius. 

Fussitius,  of  Rome. 

1st 

Several  buildings  at   Rome;    the  first 

Roman  who  wrote  on  architecture. 

AFTER  CHRIST. 


Virtmvius  Pollio,  of  Fano. 

1st 

Basilica    Justitiae    at    Fano;    a    great 

writer  on  architecture. 

Metrodorus,  of  Persia. 

4th 

Many    buildings    in    India    and    some 

at    Constantinople;    the   first-known 

Christian  architect. 

Aloisius,  of  Padua. 

5th 

Assisted   in   the   erection   of  the   cele' 

brated  rotunda  at  Ravenna,  the  cu- 

pola of  which  is  said  to  have  been  of 

one  stone,  thirty-eight  feet  in  diame^ 

ter  and  fifteen  feet  thick. 

Anthemius,  of    Trales,  of 

6th 

St.  Sophia,  at  Constantinople. 

Lydia. 

Saxulphus,    Abbot    of 

7th 

Built    the   Monastery   of   Medeshamp- 

Peterborough,       after- 

stede,   afterwards    called    Peterbor- 

wards made  Bishop  of 

ough. 

Lichfield,  of  England. 

Egbert,    Archbishop     of 

8th 

Rebuilt  York  Cathedral. 

York,  of  England. 

Romualdus.  of  France. 

9th 

The  Cathedral  of  Rheims,  the  earliest 

example  of  Gothic  architecture. 

LIST  OF  NOTED  ARCHITECTS. 


1541 


AFTER  CHRIST. 


Name  of  Architect. 

Century. 

Principal  Works. 

Buschetto,  of  Dulichium. 

10th 

The  Cathedral,  or  Duomo,  of  Pisa,  the 

earliest    example    of    the    Lombard 

ecclesiastical    style    of    architecture. 

It  was  built  in  1016. 

Pietro   di   Ustamber,  of 

10th 

Cathedral  of  Chartres. 

Spain. 

Lanfranc,  Archbishop  of 

10th 

Choir  of  Canterbury  Cathedral,  burnt  in 

Canterbury,     of     Eng- 

1174. 

land. 

Remigius,  Bishop  of  Lin- 

llth 

Part  of  Lincoln  Cathedral. 

coln,  of  England. 

Walke'yn.  Bishop  of  Win- 

llth 

Said  to  have  erected  the  oldest  part  of 

chester,  of  England. 

Winchester  Cathedral. 

Mauritius,  Bishop  of  Lon- 

12th 

Built  old  St.  Paul's  in  1033. 

don,  of  England. 

Alexander,      Bishop      of 

12th 

Rebuilt  Lincoln  Cathedral. 

Lincoln,  of   England. 

Dioti  Salvi,  of  Italy. 

12th 

Baptistery   of    Pisa,    near   the    Campo 

Santo.     His  works  were  in  the  Lom- 

bard style  and  were  overloaded  with 

minute  ornaments. 

Buono,  of  Venice. 

12th 

The  Tower  of  St.  Mark  at  Venice,  which 

is  three  hundred  and  thirty  feet  high 

and  forty  feet  square,  built  in  1154;  a 

design   for  enlarging  the   Church  of 

Santa  Maria  Maggiore,  at  Florence,  of 

which    the    master-walls    still    exist; 

the    Vicaria    and    the    Castello    del' 

Novo,  at  Naples;    Church  of  St.  An- 

drew, at  Pistola;  la  Casa  della  Citta; 

Campanile  at  Arezzo. 

Wilhelm,  or  Guglielmo,  of 

12th 

The  Leaning  Tower  of  Pisa    built  in 

Germany. 

1174.     Bonnano    and    Tomaso,    two 

sculptors  of  Pisa,  were  also  engaged 

upon  it. 

William,  of  Sens,  of  Eng- 

12th 

Canterbury  Cathedral. 

land. 

Peter,  of  Colechurch,  of 

13th 

Began  London  Bridge. 

England. 

Robert,  of  Lusarches,  of 

13th 

Cathedral  of  Amiens,  which  was  con- 

France. 

tinued  by  Thomas  de  Cormont  and 

finished  by  his  son  Renauld. 

Poore,  Bishop   of  Salis- 

13th 

Began  Salisbury  Cathedral. 

bury,  of  England. 

Pietro  Perez,  of  Spain. 

13th 

The  Cathedral  of  Toledo. 

Robert    de    Courcy,    of 

13th 

Rebuilt  the  Cathedral  at  Rheims. 

France. 

Juan  Rari.  of  France. 

14tn 

Finished  the  building  of  the  Church  of 

Notre  Dame,  of  Paris. 

1542  LIST  OF  NOTED  ARCHITECTS. 

AFTER  CHRIST. 


Name  of  Architect. 

Century 

Principal  Works. 

Rafaelle     d'Urbino,     of 

16th 

Continued  the  erection  of  St.  Peter's  at 

Urbino. 

Rome  after  the  death  of  Bramante, 

his  master  in  architecture;    engaged 

on  the  buildings  of  the  Farnese  Pal- 

ace; Church  of  Santa  Maria,  in  Navi- 

cella,  repaired  and  altered;  stables  of 

Agostino,  near  the  Palazzo  Farnese; 

Palazzo     Caffarelli,     now     Stoppani; 

the    gardens    of    the    Vatican;     the 

facade  of  the  Church  of  San  Lorenzo, 

and  of  the  Palazzo  Uggoccioni,  now 

Pandolfmi,  at  Florence. 

Bolton,     W.,     Prior     o 

16th 

Supposed  to  have  designed  Henry  VII.  's 

St.   Bartholomew's,    o 

Chapel,  where  he  was  master  of  the 

England. 

works. 

Giovanni  Gil  de  Honta- 

16th 

Plan  of   the  Cathedral   of  Salamanca, 

non,  of  Spain 

etc. 

Michael  Angelo  di  Buona- 

16th 

Library  of  the  Medici,  generally  called 

rotti,  of  Florence. 

the  Laurentian  Library,  at  Florence; 

model  for  the  facade  of  the  Church  of 

San   Lorenzo,    commonly   called   the 

Capella    dei    Depositi;     Church    San 

Giovanni,   which  he  did  not  finish; 

fortifications  at  Florence  and  at  Monte 

San   Miniato;     monument    of   Julius 

II.  ,  in  the  Church  of  San  Pietro  in 

Vincoli,  at  Rome;    plan  of  the  Cam- 

pidoglio,  Palace  of  the  Conservator!, 

building  in  the  centre,  and  the  flight 

of  steps  in  the  Campidoglio,  or  Cap- 

itol,  at  Rome;    continuation  of  the 

Palace  Farnese  and  several  gates  at 

Rome,  particularly  the  Porta  Nomen- 

tana  or  Pia;    steeple  of  St.  Michaele, 

at  Ostia  ;  the  gate  to  the  Vineyard  de 

Patriarea  Grimani;    Tower  of  S.  Lo- 

renzo,   at   Ardea;    Church   of   Santa 

Maria,  in  the  Certosa,  at  Rome  ;  many 

plans  of  palaces,  churches,  and  chap- 

els.    He  was  employed  on  St.  Peter's 

after  the  death  of  San  Sallo. 

Martino    de    Gainza,    of 

16th 

The  Chapel  Royal  at  Seville. 

Spain. 

Machuca,  of  Spain. 

16th 

Royal  Palace  of  Granada. 

Theodore  Havens,   of 

16th 

Caius     College,     Cambridge.     A     good 

England. 

specimen  of  the  architecture  of  the 

day. 

LIST  OF  NOTED  ARCHITECTS. 
AFTER  CHRIST. 


1543 


Name  of  Architect. 

Century 

Principal  Works 

Carlo  Maderno,  of  Lom- 

16th 

Altered  Michael  Angelo's  design  for  St. 

bardy. 

Peter's  at  Rome  from  a  Greek  to  a 

Latin    cross;     began    the    palace    of 

Urban  VIII. 

Sir  H.  Watton,  of  Eng- 

17th 

Author  of    "The    Elements    of   Archi- 

land. 

tecture,"    published    in    London    in 

1624. 

Inigo  Jones,  of  England. 

17th 

Banqueting  House;    chapel,    Lincoln's 

Inn;    Surgeon's  Hall;    arcade,   Cov- 

ent    Garden,    London;,     and   a  vast 

number  of  other  important  works. 

Claude        Perrault,       of 

17th 

Facade  of  the  Louvre,  Chapel  of  Sceaux, 

France. 

Chapel  of  Notre  Dame  in  the  Church 

of  the  Petits  Peres. 

Sir  Christopher  Wren,  of 

17th 

St.  Paul's;  planned  the  city  of  London 

England. 

after  the  fire,  nearly  all  the  churches 

therein,  Hampton  Court,  etc. 

Jules  Hardouin  Mansard, 

17th 

The  dome  of  the  H6tel  des  Invalides. 

of  France. 

Gallerie  du  Palais  Royal,  the  Place 

de    Louis    de    Grand,  des  Victoires, 

etc.     He  was  the  nephew  of  Francois 

Mansard,  the  reputed  inventor  of  the 

Mansard  roof. 

Alexander  Jean  Baptiste 

18th 

L'Hotel  de  Vendome,  in  the  Rue  d'En- 

le  Blond,  of  France. 

fer,  at  Paris.    He  was  employed  much 

in  Russia  by  Peter  the  Great. 

Galli    da    Bibbiena,     of 

18th 

Theatre  at  Verona,  theatre  at  Vienna; 

Italy. 

author  of  two  books  on  architecture. 

James  Gibbs,  of  Scotland. 

18th 

Radcliffe's  Library,   Oxford;    the  new 

church  in  the  Strand;  St.-Martin's-in- 

the-Fields;     King's    College,    Royal 

Library,    and    Senate    House,    Cam- 

bridge. 

Sir  William  Chambers,  of 

18th 

Somerset  House  and  many  other  works  ; 

England. 

author  of  a  treatise  on  civil  architec- 

ture. 

Hobert  Adam,   of  Scot- 

18th 

Architect  to  George  III.;    author  of  a 

land. 

work  on  the  ruins  of  Spalatro      His 

principal  works  are  the  Register  Office 

at  Edinburgh,  infirmary  at  Glasgow, 

the    Edinburgh     University,     Luton 

House,  Adelphi  Terrace. 

Sir  John  Soame,  of  Eng- 

18th 

Bank    of    England,    Board    of    Trade, 

land. 

State-Paper  Office. 

Charles  Percier,  of  France 

18th 

Architect  of  the  Tuileries  :  restorations, 

etc.,  at  Louvre  and  Tuileries. 

1544  LIST  OF  NOTED  ARCHITECTS. 

AFTER  CHRIST. 


Name  of  Architect. 

Century. 

Principal  Works. 

James  Essex,  of  England. 

18th 

The  earliest,  in  modern  times,  who  prac- 

tised solely  mediaeval  art  ;  restoration 

of  Ely  and  other  cathedrals;    altera- 

tions at  various  colleges  at  Cambridge 

and  Oxford. 

James    Wyatt,    of    Eng- 

18th 

The  Pantheon  Assembly  rooms,  palace 

land. 

at  Kew,  Fonthill  Abbey,  Doddington 

Hall,  Ashridge  House,  and  many  res- 

torations. 

Augustus  Pugin,  of  Eng- 

18th 

Published   "  Specimens    of   Gothic   Ar- 

land. 

chitecture,"    "Examples    of    Gothic 

Architecture,"  "Antiquities  of  Nor- 

mandy," and  other  works. 

John  Nash,  of  England. 

19th 

Brighton  Pavilion,  Haymarket  Theatre, 

Buckingham   Palace,   Regent's   Park 

and  its  terraces  of  dwellings,  Regent 

Street    and   the   Quadrant   improve- 

ments. 

Thomas     Rickman,     of 

19th 

New  court  of  St.  John's  College,  Cam- 

England. 

bridge;    restoration  of  the  Bishop  of 

Carlisle's    palace,    Cumberland;     up- 

wards of  twenty-five  churches  in  the 

midland     counties,     several     private 

dwellings.     Published    "Attempt    to 

Discriminate  the  Styles  of  Architec- 

ture in  England." 

Carl  Friedrich  Schinkel, 

19th 

Hauptwache     Theatre     and    Museum, 

of  Prussia. 

Werder-Kirche    (Gothic),    Bauschule 

and   Observatory  at   Berlin,   theatre 

at    Hamburg,    Schloss    Krzescowice, 

Charlottenhof,      and      the      Nicolai- 

Kirche   at   Potsdam.     Published   his 

designs,    many    of    which    were    not 

executed. 

Guillaume    Abel    Blouet, 

19th 

Published    supplement    to    Roudelet's 

of  France. 

"L'Art   de   Batir,"   and   revised   the 

tenth  edition  of  that  work. 

Ernst  Friedrich  Zwirner, 

19th 

Restoration      of      Cologne      Cathedral, 

of  Prussia. 

church  at  Remagen. 

David  Hamilton,  of  Scot- 

19th 

The  Nelson  Monument,  the   Royal  Ex- 

land. 

change,  the  Western  Club-house,  and 

other  buildings  at  Glasgow;  Hamilton 

Palace  and  Lennox  Castle,  Scotland. 

Mr.  Joseph  Gwilt. 

19th 

Compiler    of    the    "Encyclopedia    of 

Architecture." 

NOTED  AMERICAN  ARCHITECTS. 
AFTER  CHRIST. 


1545 


Name  of  Architect. 

Century. 

Principal  Works. 

James  Fergusson,  d.  Jan., 

19th 

Author   of   the    "History   of  Architec- 

1886. 

ture." 

John    Henry    Parker,    b. 

19th 

Author  of  the  "Glossary  of  Architec- 

in  London,    1806;    d. 

ture,"  "The  Domestic  Architecture  of 

Jan.  31,  1884, 

the  Middle  Ages,"  a  revised  edition 

of  Rickman's  "Gothic  Architecture." 

George  Edmund  Street. 

19th 

The  Law  Courts,  London. 

William  Burges. 

19th 

Cork  Cathedral,   restoration   of  Cardiff 

Castle. 

Sir  Gilbert  Scott. 

19th 

Hamburg  Cathedral,  Edinburgh  Cathe- 

dral,   the  Albert   Memorial,  Midland 

Station   and  Hotel   at   St.    Pancras, 

England. 

LIST  OF   NOTED  AMERICAN   ARCHITECTS. 

CHARLES  BULFINCH,  the  first  New  England  architect,  b.  1763, 
d.  1844.  Designed  the  first  theatre  in  Boston,  1793;  the  Mass. 
State  House,  1795;  the  first  Catholic  church  in  Boston,  1803; 
Faneuil  Hall,  enlarged,  1808;  University  Hall  at  Harvard  Col- 
lege, 1814;  the  McLean  Asylum  at  Somerville,  1792-1817,  and 
the  Mass.  General  Hospital,  1818.  Architect  of  the  Capitol  at 
Washington  from  1797-1818. 

JOHN  HAVILAND,  b.  1792,  d.  1825. 

Principal  works:  Pittsburgh  Penitentiary;  Eastern  Peniten- 
tiary at  Cherry  Hill;  Hall  of  Justice,  New  York;  Naval  Asylum, 
Norfolk;  New  Jersey  State  Penitentiary;  and  many  other  jails, 
asylums,  and  public  halls. 

JONATHAN  PRESTON,  b.  1801,  d.  July,  1884;  practised  in  Bos- 
ton, Mass. 

Principal  works:  .The  first  building  of  the  Massachusetts  Insti- 
tute of  Technology,  and  the  building  of  the  Boston  Society  of 
Natural  History. 

WILLIAM  WASHBURN,  b.  in  Lyme,  N.  H.,  1808,  d.  in  Boston, 
November  8,  1890;  practised  in  Boston. 

Principal  works :  The  Fifth  Avenue  and  Victoria  Hotels  in  New 
York,  and  the  Parker  House,  Tremont  House,  Revere  House, 
Adams  House,  Young's  Hotel,  and  the  American  House  in  Bos- 
ton; the  Tremont  Temple,  Boston;  Charlestown  City  Hall,  and 
many  other  public  and  private  buildings. 


1543  NOTED  AMERICAN  ARCHITECTS. 

THOMAS  USTICK  WALTER,  LL.D.,  b.  1804,  d.  October  30,  1887; 
practised  in  Philadelphia,  Pa.;  was  one  of  the  original  mem- 
bers of  the  American  Institute  of  Architects,  and  president  for 
many  years;  received  the  degree  of  LL.D.  from  Harvard  Uni- 
versity, being  the  first  architect  to  receive  that  degree  in  this 
country. 

Principal  works:  The  five  original  buildings  of  Girard  College, 
designed  in  1833  and  completed  in  1847.  Extension  of  the  Na- 
tional Capitol,  1851-65;  also  the  extensions  of  the  Patent  Office, 
Treasury  and  Post-office  buildings,  the  dome  on  the  old  Capitol, 
the  Congressional  Library,  and  the  Government  Hospital  for  the 
Insane;  also  numerous  other  buildings  of  lesser  importance.  Mr. 
Walter  was  a  member  of  the  Franklin  Institute  and  of  many 
literary  and  scientific  associations. 

ARTHUR  GILMAN;  practised  in  New  York  and  Boston,  in 
partnership  with  Mr.  Bryant. 

Principal  works:  Boston  City  Hall;  First  Church,  on  Arlington 
Street,  Boston,  and  numerous  dwelling-houses  in  New  York  and 
Boston.  In  association  with  Mr.  Edward  Kendall,  designed  the 
Equitable  Life  Assurance  Company's  building  on  Broadway,  New 
York. 

R.  G.  HATFIELD,  b.  in  Elizabeth,  N.  J.,  1815,  d.  February,  1879; 
author  of  the  American  House  Carpenter  and  Transverse  Strains; 
associated  for  thirty-five  years  with  his  brother,  Oliver  P.  Hatfield. 
The  firm  became  widely  known  as  experts  and  consulting  archi- 
tects in  matters  pertaining  to  building  construction. 

Principal  works:  House  of  Refuge,  Randall's  Island,  N.  Y.; 
Westchester  County  Buildings,  White  Plains,  N.  Y. ;  New  York 
Institution  for  the  Deaf  and  Dumb ,  Seaman's  Bank  for  Savings, 
City  Bank  building,  Security  Insurance  Co.  Building,  all  of  New 
York  City. 

OLIVER  P.  HATFIELD,  d.  April,  1891. 

JOHN  Me  ARTHUR,  Jr.,  b.  in  Scotland  in  1823,  d.  January,  1890; 
practised  in  Philadelphia,  Pa. 

Principal  works:  House  of  Refuge,  Continental  Hotel,  Girard 
House,  Public  Ledger  Building,  First  National  Bank  Building,  the 
Assembly  Building,  the  Broad  Street  Presbyterian  Church,  and 
the  City  Hall,  all  of  Philadelphia.  Also  the  Hospital  for  the 
Insane,  at  Warren,  Pa.;  Lafayette  College,  Easton,  Pa.;  and 
numerous  other  public  and  private  buildings  in  Pennsylvania 
and  other  States.  Was  twice  tendered  the  position  of  Supervis- 
ing Architect  to  the  United  States  Government,  but  declined. 


NOTED  AMERICAN  ARCHITECTS.  1547 

EBENEZER  L.  ROBERT,  b.  1825;    practised  in  New  York  City. 

Principal  works:  Standard  Oil  Company's  Building,  on  Broad- 
way; the  Ninth  National  Bank;  the  Baptist  Church  of  the  Epiph- 
any, on  Madison  Avenue;  St.  Paul's  Methodist  Church,  on  Fourth 
Avenue,  all  of  New  York  City;  and  the  Phoenix  Insurance  Com- 
pany's Building,  Brooklyn,  N.  Y. 

ALEXANDER  R.  ESTY,  b.  1827,  d.  July  2,  1881;  practised  in 
Boston. 

Principal  works:  Union  Congregational  Church,  Boston;  Har- 
vard Street  Baptist  Church,  Cambridge,  Mass.;  Grace  Church, 
Newton,  Mass.;  Emanuel  Church,  on  Newbury  Street,  Boston; 
Buildings  of  the  Colby  University,  Waterville,  Me.;  Massachu- 
setts State  Normal  Schools,  at  Framingham  and  Worcester,  and 
the  University  of  Rochester,  N.  Y. 

CARL  PFEIFFER,  b.  in  Germany,  d.  May,  1888;  practised  in 
New  York  City. 

Principal  works:  Fifth  Avenue  Presbyterian  Church,  New 
York;  Fifth  Avenue  Riding  School,  New  York;  and  many  pri- 
vate houses,  apartment  houses,  hotels,  etc. 

CHARLES  DEXTER  GAMBRILL,  b.  1832,  d.  September  13,  1880; 
practised  in  New  York,  first  in  partnership  with  Mr.  George  B. 
Post,  later  with  H.  H.  Richardson. 

JOHN  H.  STURGIS;  practised  in  Boston,  Mass.,  with  Mr. 
Charles  Brigham  as  Sturgis  &  Brigham. 

Principal  works:  Boston  Museum  of  Fine  Arts,  building  of  the 
Boston  Young  Men's  Christian  Association,  Church  of  the  Advent, 
residence  of  Mr.  F.  L.  Ames,  and  many  other  fine  residences  in 
Boston  and  vicinity. 

A.  B.  MULLETT,  b.  1834,  d.  October  20, 1890;  supervising  archi- 
tect to  the  Trea  ury  from  1865  to  1875.  Also  engineer  of  the 
District  of  Columbia  for  several  years.  The  Post-office  build- 
ings in  New  York,  Boston,  Cincinnati.  St.  Louis,  and  Chicago 
were  designed  by  him,  and  also  the  State,  War,  and  Navy  Build- 
ings in  Washington. 

HENRY  HOBSON  RICHARDSON,  b.  in  Louisiana  in  1838  or  1839, 
d.  in  Brookline,  Mass.,  April,  1886.  Graduated  at  Harvard  Uni- 
versity in  1859,  studied  seven  years  at  the  Ecole  des  Beaux- Arts 
in  Paris.  Was  associated  for  a  short  time  with  Charles  D.  Gam- 
brill  of  New  York. 

A  complete  list  of  the  works  executed  by  him,  arranged  in 
chronological  order,  may  be  found  in  the  thirteenth  edition  of 
this  book. 


1548  NOTED  AMERICAN  ARCHITECTS. 

Perhaps  the  best-known  examples  of  his  work  are: 

Trinity  Church  and  Brattle  Street  Church,  Boston;  City  Hall, 
Albany,  and  portions  of  the  New  York  State  Capitol;  the  Library 
and  Town  Hall,  at  North  Easton,  Mass.;  Sever  Hall  and  New 
Law  School,  Cambridge,  Mass.;  County  Court  House  and  Jail, 
Pittsburgh,  Pa.;  wholesale  warehouse  for  Marshall  Field  &  Co., 
Chicago;  Chamber  of  Commerce,  Cincinnati,  Ohio. 

THOMAS  WISEDELL,  b.  in  England  in  1846,  d.  in  New  York, 
July  31,  1884.  Educated  in  the  office  of  Mr.  R.  J.  Withers  of 
London.  Associated  with  Mr.  Kimball  of  New  York.  Princi- 
pal works:  Madison  Square  Theatre,  and  the  " Casino,"  both  in 
New  York  City 

JOSEPH  MORRILL  WELLS,  b  1853,  d.  in  New  York,  February, 
1890.  Mr.  Wells  was  a  junior  partner  in  the  firm  of  McKim, 
Mead  &  White,  architects,  of  New  York.  The  movement  of 
American  architects  towards  the  Italian  Renaissance,  which  com- 
menced about  the  year  1889,  was  undoubtedly  caused  more  by 
his  influence  than  that  of  any  other  single  individual.  Among 
the  buildings  of  the  firm,  more  especially  designed  by  him,  are: 
the  Villard  houses  on  Madison  Avenue,  New  York;  the 
"Memorial  Building"  in  New  Britain,  Conn.;  fagade  of 
the  Century  Club,  New  York,  and  a  fountain  in  Portland, 
Oregon. 

HENRY  O.  AVERT,  d.  1890;  studied  at  the«  School  of  Fine 
Arts  in  Paris.  Took  an  important  part  in  designing  the  houses 
of  W.  K.  Vanderbilt  and  Henry  G.  Marquand;  a  prominent 
member  of  the  architectural  League  of  New  York,  the  Archaeo- 
logical Institute,  and  the  Society  of  American  Artists. 

JOHN  WELLBORN  ROOT,  b.  in  Georgia,  January  10,  1850,  d. 
in  Chicago,  111.,  January  15,  1891.  Entered  into  partnership 
with  Daniel  H.  Burnham  in  1873,  which  continued  until  his 
death.  Mr.  Root  was  the  designer  of  the  firm.  They  designed 
and  executed  seventy-seven  public  buildings,  many  of  them  of 
the  first  class,  and  one  hundred  and  twenty  residences.  Of  their 
public  buildings  the  following  were  perhaps  the  most  important : 
Calumet  Club  House,  Art  Institute,  Academy  of  Fine  Arts, 
Montauk  Block,  Calumet  Building,  Rialto  Office  Building, 
Insurance  Exchange  Building,  Grannis  Block,  Phoenix  Build- 
ing, The  Rookery,  Masonic  Building,  Woman's  Temple,  First 
Regiment  Armory,  all  of  Chicago;  the  Mills  Block,  San  Fran- 
cisco; Midland  Hotel,  Board  of  Trade  Building,  American 
National  Bank  Building  of  Kansas  City.  Mr.  Root  was 


NOTED  AMERICAN  ARCHITECTS.  1549 

secreta^  of  the  American  Institute  of  Architects  at  the  time  of 
his  death. 

HERBERT  C.  BURDETT,  b.  in  Boston,  1855,  d.  in  Buffalo, 
April  10,  1891;  associated  with  J.  Herbert  Marling,  as  Marling 
&  Burdette,  and  practised  in  Buffalo,  N.  Y.  Principal  works: 
The  Saturn  Club  House  and  numerous  fine  residences  in 
Buffalo. 

GEORGE  WASHINGTOR  PERCY,  A. A.I. A.,  b.  at  Bath,  Me.  July  5, 
1847,  d.  during  1900.  Practiced  in  San  Francisco,  California, 
1876-1900;  from  1879  associated  with  Mr.  F.  F.  Hamilton. 
The  firm  designed  many  important  buildings  in  and  about  San 
Francisco  and  Los  Angeles,  also  at  Honolulu,  H.  I.  President 
of  the  Technical  Society  of  the  Pacific  Coast,  1898-1900. 

DANKMARK  ABLER,  F.A.I. A.,  b.  in  Langsfeld,  Saxe-Weimar, 
July  3,  1844.  Practised  architecture  in  Chicago  from  1869 
until  his  death,  April  16,  1900.  Was  for  many  years  asso- 
ciated with  Louis  II.  Sullivan,  Mr.  Adler  being  the  "  practical 
man"  of  the  firm;  secretary  A.I. A.  1891-92;  member  Board  of 
Directors  1890-93. 

EDWARD  C.  CABOT,  F.A.I. A.,  b.  in  Boston  April,  1818,  d. 
January,  1901.  Practised  in  Boston.  For  a  number  of  years 
associated  with  Mr.  F.  W.  Chandler.  Designed  the  Boston 
Athenaeum  in  1846,  the  Boston  Theatre  in  1852-53,  and  in 
association  with  Mr.  Chandler,  the  Johns  Hopkins  Hospital, 
Baltimore.  Became  a  member  of  the  A.I. A.  in  1857,  and  was 
president  of  the  Boston  Chapter  for  thirty-three  years. 

EDWARD  HALE  KENDALL,  F.A.I  A.,  b.  in  Boston,  July  30, 1842, 
d.  March  10,  1901.  Practised  in  New  York  from  about  1868 
until  his  death.  His  chief  works  are  perhaps  the  first  plans  of 
the  Equitable  Building,  the  Field  Building,  No.  1  Broadway, 
the  Methodist  Book  Concern,  the  Goelet  houses,  and  the 
Washington  Bridge,  of  which  he  was  the  consulting  architect. 
Was  vice-president  A. I. A.  in  1885,  a  director  for  many  years, 
and  president  in  1892  and  1893.  Was  president  of  the  New 
York  Chapter  from  1884-88. 

NAPOLEON  EUGENE,  H.  C.  LE  BRUN,  F.A.I. A.,  b.  in  Phila- 
delphia January  2,  1821,  d.  July  9,  1901.  Practised  in  Phila- 
delphia 1842-65,  when  he  removed  to  New  York.  Among  the 
prominent  buildings  which  he  designed  in  Philadelphia  are  the 
Cathedral,  the  Academy  of  Music,  the  old  Tabernacle  Presby- 
terian Church,  the  Girard  Estate  Building,  and  several  county 
buildings  and  prisons.  In  New  York  Citv,  in  connection  with 


1550  NOTED  AMERICAN   ARCHITECTS. 

his  son,  he  erected  many  dwellings  and  public  buildings, 
including  the  Masonic  Temple,  several  large  and  beautiful 
churches,  the  New  York  Foundling  Asylum,  the  Metropolitan 
Insurance  Building  on  Madison  Square,  the  Home  Life  Insur- 
ance Building,  and  several  municipal  edifices  Member  A. I. A. 
from  1868  until  his  death,  twice  president  of  the  New  York 
Chapter,  and  also  president  of  the  Willard  Architectural  Com- 
mission. 

EDWIN  CLARK,  F.A.I.A.,  b.  in  Philadelphia  August  15,  1822, 
d.  January  6,  1902.  Architect  of  the  United  States  Capitol 
from  1865  until  his  death. 

JAMES  BROWN  LORD,  F.A.I. A.,  b.  in  New  York  1859,  d.  June 
1,  1902.  Designed  the  Delmonico  Building,  New  York;  the 
Bloomingdale  Asylum  at  White  Plains;  the  Carnegie  Library 
in  East  Seventy-sixth  Street ;  and  the  Appellate  Court  Building 
on  Madison  Avenue  and  Twenty-fourth  Street. 

WALTER  COPE,  F.A.I.A.,  b.  in  Philadelphia  October  30,  1860, 
d.  November  3,  1902.  Associated  with  John  Stewardson  and 
E.  L.  Stewardson  from  1885  until  his  death. 

Among  the  notable  buildings  designed  by  this  firm  are  Den- 
bigh, Pembroke,  and  Rockefeller  Halls,  all  dormitories  of  Bryn 
Mawr  College;  the  Dormitories,  Law  School,  and  Medical 
Laboratories  of  the  University  of  Pennsvlvania ;  Blair  Han\ 
Stafford-Little  Hall,  and  Gymnasium  of  Princeton  University; 
the  Pennsylvania  Institution  for  the  Instruction  of  the  Blind, 
at  Overbrook,  Pa. ;  the  Washington  University  of  St.  Louis, 
Mo. ;  the  City  Hall,  at  Atlantic  City,  N.  J. ;  the  Harrison  Office 
Building  and  the  Harrison  stores  in  Philadelphia,  and  many 
fine  residences. 

HENRY  VAN  BRUNT,  F.A.I.A.,  b.  in  Boston,  Sept.  5,  1832, 
d.  April  6,  i903.  Student  of  Richard  M.  Hunt,  practised  in 
Boston,  under  the  firm  name  of  Ware  &  Van  Brunt,  until 
1882,  when  Mr.  Ware  accepted  the  chair  of  Architecture  at 
Columbia  College,  and  Mr.  Van  Brunt  formed  a  new  partner- 
ship with  Mr.  Frank  M.  Howe.  The  firm  of  Van  Brunt  &  Howe 
moved  to  Kansas  City  in  1887,  and  existed  until  the  death  of 
Van  Brunt.  President  of  the  American  Institute  of  Architects, 
1899,  and  a  writer  of  great  ability. 

Notable  buildings  designed  by  Ware  and  Van  Brunt:  Memo- 
rial Hall  of  Harvard  College;  First  Church  of  Boston;  St. 
Stephens  Church,  Lynn,  Mass.;  buildings  for  Wellesley  College. 
Of  Van  Brunt  &  Howe:  New  Coates  House;  the  Gibraltar 


NOTED  AMERICAN  ARCHITECTS.  1551 

Building;    Emery  -  Bird  -  Thayer  Building    Kansas    City    Star 
Building,  all  of  Kansas  City;   the  Union  Depot,  Denver. 

BRUCE  PRICE,  F.A.I. A.,  b.  in  Cumberland,  Md.,  1845,  d.  in 
Paris,  May,  1903.  An  architect  of  great  brilliance  and  origi- 
nality. His  chief  works  are  the  American  Surety  Company's 
Building,  N.  Y.;  St.  James  Building,  N.  Y.;  the  group  of 
buildings  near  Lake  wood,  N.  J.,  which  he  designed  for  Mr. 
George  J.  Gould  ;  Osborn  Hall  at  Yale  University,  and  a  pic- 
turesque hotel  in  Quebec  known  as  the  Chateau  Frontenac. 
Was  for  some  years  president  of  the  N.  Y.  Architectural  League. 


1552     SCHEDULE   OF   ARCHITECTS'    CHARGES. 


PROFESSIONAL  PRACTICE   OF  ARCHITECTS,   AND   SCHEDULE   OF 
USUAL  AND  PROPER  MINIMUM  CHARGES. 

(A.  I.  A.  Schedule,  revised  October,  1903.) 

The  architect's  professional  services  consist  in  making  the 
necessary  preliminary  studies,  working  drawings,  specifications, 
large-scale  and  full-size  details,  and  in  the  general  direction  and 
supervision  of  the  work,  for  which  the  minimum  charge  is  five 
per  cent,  upon  the  cost  of  the  work. 

For  new  buildings  costing  less  than  $10,000,  and  for  furniture, 
monuments,  decorative  and  cabinet  work,  it  is  usual  and  proper 
to  charge  a  special  fee  in  excess  of  the  above. 

For  alterations  and  additions  to  existing  buildings  the  fee  is 
ten  per  cent,  upon  the  cost  of  the  work. 

Consultation  fees  for  professional  advice  are  to  be  paid  in  pro- 
portion to  the  importance  of  the  questions  involved. 

None  of  the  charges  above  enumerated  covers  alterations  and 
additions  in  contracts,  drawings,  and  specifications,  nor  profes- 
sional or  legal  services  incidental  to  negotiations  for  site,  disputed 
party  walls,  right  of  light,  measurement  of  work,  or  failure  of 
contractors.  When  such  services  become  necessary,  they  shall 
be  charged  for  according  to  the  time  and  trouble  involved. 

Where  heating,  ventilating,  mechanical,  electrical,  and  sani- 
tary problems  in  a  building  are  of  such  a  nature  as  to  require  the 
assistance  of  a  specialist,  the  owner  is  to  pay  for  such  assistance. 
Chemical  and  mechanical  tests,  when  required,  are  to  be  paid 
for  by  the  owner. 

Necessary  travelling  expenses  are  to  be  paid  by  the  owner. 

Drawings  and  specifications,  as  instruments  of  service,  are 
the  property  of  the  architect. 

The  architect's  payments  are  due  as  his  work  progresses  in 
the  following  order:  Upon  completion  of  the  preliminary  sketches 
one-fifth  of  the  entire  fee;  upon  completion  of  working  draw- 
ings and  specifications,  two-fifths;  the  remaining  two-fifths 
being  due  from  time  to  time  in  proportion  to  the  amount  of 
work  done  by  the  architect  in  his  office  and  at  the  building. 

Until  an  actual  estimate  is  received,  the  charges  are  based 
upon  the  proposed  cost  of  the  work,  and  payments  are  received 
as  instalments  of  the  entire  fee,  which  is  based  upon  the  actual 
cost  to  the  owner  of  the  building  or  other  work,  when  completed, 
including  all  fixtures  necessary  to  render  it  fit  for  occupation. 


CONTRACT  BETWEEN  ARCHITECT  AND  OWNER.   1553 

The  architect  is  entitled  to  extra  compensation  for  furniture  or 
other  articles  purchased  under  his  direction. 

If  any  material  or  work  used  in  the  construction  of  the  build- 
ing be  already  upon  the  ground  or  come  into  the  owner's  posses- 
sion without  expense  to  him,  its  value  is  to  be  added  to  the  sum 
actually  expended  upon  the  building  before  the  architect's 
commission  is  computed. 

In  case  of  the  abandonment  or  suspension  of  the  work,  the 
basis  of  settlement  is  as  follows:  Preliminary  studies,  a  fee  in 
accordance  with  the  character  and  magnitude  of  the  work; 
preliminary  studies,  working  drawings,  and  specifications,  three- 
fifths  of  the  fee  for  complete  services. 

The  supervision  of  an  architect  (as  distinguished  from  the 
continuous  personal  superintendence  which  may  be  secured  by 
the  employment  of  a  clerk  of  the  works)  means  such  inspection 
by  the  architect  or  his  deputy  of  work  in  studios  and  shops,  or 
of  a  building  or  other  work  in  process  of  erection,  completion, 
or  alteration,  as  he  finds  necessary  to  ascertain  whether  it  is 
being  executed  in  conformity  with  the  drawings  and  specifica- 
tions or  directions.  He  is  to  act  in  constructive  emergencies, 
to  order  necessary  changes,  and  to  define  the  true  intent  and 
meaning  of  the  drawings  and  specifications,  and  he  has  author- 
ity to  stop  the  progress  of  the  work  and  order  its  removal  when 
not  in  accordance  with  them. 

On  buildings  where  the  constant  services  of  a  superintendent 
are  required,  a  clerk  of  the  works  shall  be  employed  by  the  ar- 
chitect at  the  owner's  expense. 


CONTRACT    BETWEEN   ARCHITECT   AND   OWNER. 

From ,  Architect, 

to ,  Owner. 

For  a  compensation  of 

the  architect  proposes  to  furnish  preliminary  sketches,  contract 
working  drawings  and  specifications,  detail  drawings  and  general 
superintendence  of  building  operations,  and,  also,  to  audit  all 

accounts,  for  a 

to  be  erected  for 

on.  . 

Terms  of  payment  to  be  as  follows: 

One  fifth  when  the  preliminary  sketches  are  completed;  three 
tenths  when  the  drawings  and  specifications  are  ready  for  letting 


1554  CONTRACT  BETWEEN  ARCHITECT  AND  OWNER. 

contracts;    thereafter  at  the  rate  of per  cent,  upon  each 

certificate  due  to  the  contractor 

If  work  upon  the  building  is  postponed  or  abandoned,  the 
compensation  for  the  work  done  by  the  architect  is  to  bear  such 
relation  to  the  compensation  for  the  entire  work  as  determined 
by  the  published  schedule  of  fees  of  the  American  Institute  of 
Architects. 

In  all  transactions  between  the  owner  and  contractor,  the 
architect  is  to  act  as  the  owner's  agent,  and  his  duties  and  liabili- 
ties in  this  connection  are  to  be  those  of  agent  only. 

A  representative  of  the  architect  will  make  visits  to  the  build- 
ing for  the  purpose  of  general  superintendence,  of  such  frequency 
and  duration  as,  in  the  architect's  judgment,  will  suffice,  or  may 
be  necessary  to  fully  instruct  contractors,  pass  upon  the  merits 
of  material  and  workmanship,  and  maintain  an  effective  working 
organization  of  the  several  contractors  engaged  upon  the  struc- 
ture. 

The  architect  will  demand  of  the  contractors  proper  correction 
and  remedy  of  all  defects  discovered  in  their  work,  and  will  assist 
the  owner  in  enforcing  the  terms  of  the  contracts;  but  the  archi- 
tect's superintendence  shall  not  include  liability  or  responsibility 
for  any  breach  of  contract  by  the  contractors. 

The  amount  of  the  architect's  compensation  is  to  be  reckoned 
upon  the  total  cost  of  the  building,  including  all  stationary 
fixtures. 

Drawings  and  specifications  are  instruments  of  service,  and  as 
such  are  to  remain  the  property  of  the  architect. 

,  Architect. 

Approved  and  accepted ,  190 

....  Owner. 


THE  UNIFORM  CONTRACT.  1555 


THE  UNIFORM  CONTRACT.* 

Form  of  Contract  Adopted  and  Recommended  for  General  Use  by 
the  American  Institute  of  Architects  and  the  National  Asso- 
ciation of  Builders.  Revised  1902. 

THIS  AGREEMENT,  made  the 

in   the   year   one   thousand   nine   hundred   and 

by  and  between 

party    of    the    first    part 

(hereinafter  designated  the  Contractor     ) ,  and 

party  of  the  second  part 

(hereinafter  designated  the  Owner  ), 

WITNESSETH  that  the  Contractor  ,  in  consideration  of  the 
agreements  herein  made  by  the  Owner  ,  agree  with  the  said 
Owner  as  follows : 

ARTICLE  I.  The  Contractor  shall  and  will  provide  all  the 
materials  and  perform  all  the  work  for  the 


as  shown  on  the  drawings  and  described  in  the  specifications. 

prepared   by Architect     , 

which  drawings  and  specifications  are  identified  by  the  signa- 
tures of  the  parties  hereto,  and  become  hereby  a  part  of  this 
contract. 

ART.  II.  It  is  understood  and  agreed  by  and  between  the 
parties  hereto  that  the  work  included  in  this  contract  is  to  be 

done  under  the  direction  of  the  said  Architect     ,  and  that 

decision  as  to  the  true  construction  and  meaning  of  the  draw- 
ings and  specifications  shall  be  final.  It  is  also  understood  and 
,  agreed  by  and  between  the  parties  hereto  that  such  additional 
drawings  and  explanations  as  may  be  necessary  to  detail  and 
illustrate  the  work  to  be  done  are  to  be  furnished  by  said  Archi- 
tect ,  and  they  agree  to  conform  to  and  abide  by  the  same  so 
far  as  they  may  be  consistent  with  the  purpose  and  intent  of 
the  original  drawings  and  specifications  referred  to  in  Art.  I. 

It  is  further  understood  and  agreed  by  the  parties  hereto  that 
any  and  all  drawings  and  specifications  prepared  for  the  purposes 

of  this  contract  by  the  said  Architect     are  and  remain 

property,  and  that  all  charges  for  the  use  of  the  same,  and  for 
the  services  of  said  Architect  are  to  be  paid  by  the  said 
Owner  . 

ART  III.  No  alterations  shall  be  made  in  the  work  except 
upon  written  order  of  the  Architect  ;  the  amount  to  be  paid  by 
the  Owner  or  allowed  by  the  Contractor  by  virtue  of  such  alter- 
ations to  be  stated  in  said  order.  Should  the  Owner  and  Con- 
tractor not  agree  as  to  amount  to  be  paid  or  allowed,  the  work 
shall  go  on  under  the  order  required  above,  and  in  case  of  failure 

*  Printed  here  by  permission  of  the  Secretary  of  the  Committee  and  the 
Inland  Publishing  Company,  the  licensees  for  its  exclusive  publication  and 
sale. 


1556  THE  UNIFORM  CONTRACT. 

to  agree,  the  determination  of  said  amount  shall  be  referred  to 
arbitration,  as  provided  for  in  Art.  XII  of  this  contract. 

ART.  IV.  The  Contractor  shall  provide  sufficient,  safe  and 
proper  facilities  at  all  times  for  the  inspection  of  the  work  by 

the   Architect      or authorized   representatives;    shall, 

within  twenty-four  hours  after  receiving  written  notice  from  the 
Architect  to  that  effect,  proceed  to  remove  from  the  grounds 

or    buildings   all   materials    condemned   by whether 

worked  or  unworked,  and  to  take  down  all  portions  of  the  work 
which  the  Architect  shall  by  like  written  notice  condemn  as 
unsound  or  improper,  or  as  in  any  way  failing  to  conform  to 
the  drawings  and  specifications,  and  shall  make  good  all  work 
damaged  or  destroyed  thereby. 

ART.  V.  Should  the  Contractor  at  any  time  refuse  or  neglect 
to  supply  a  sufficiency  of  properly  skilled  workmen,  or  of  mate- 
rials of  the  proper  quality,  or  fail  in  any  respect  to  prosecute 
the  work  with  promptness  and  diligence,  or  fail  in  the  perform 
ance  of  any  of  the  agreements  herein  contained,  such  refusal, 
neglect  or  failure  being  certified  by  the  Architect  ,  the  Owner 

shall  be  at  liberty,  after.  . days'  written  notice  to 

the  Contractor  ,  to  provide  any  such  labor  or  materials,  and  to 
deduct  the  cost  thereof  from  any  money  then  due  or  thereafter 
to  become  due  to  the  Contractor  under  this  contract;  and  if 
the  Architect  shall  certify  that  such  refusal,  neglect  or  failure 
is  sufficient  ground  for  such  action,  the  Owner  shall  also  be  at 
liberty  to  terminate  the  employment  of  the  Contractor  for  the 
said  work  and  to  enter  upon  the  premises  and  take  possession, 
for  the  purpose  of  completing  the  work  included  under  this 
contract,  of  all  materials,  tools  and  appliances  thereon,  and 
to  employ  any  other  person  or  persons  to  finish  the  work,  and 
to  provide  the  materials  therefor;  and  in  case  of  such  discon- 
tinuance of  the  employment  of  the  Contractor  

shall  not  be  entitled  to  receive  any  further  payment  under  this 
contract  until  the  said  work  shall  be  wholly  finished,  at  which 
time,  if  the  unpaid  balance  of  the  amount  to  be  paid  under  this 
contract  shall  exceed  the  expense  incurred  by  the  Owner  in 
finishing  the  work,  such  excess  shall  be  paid  by  the  Owner  to 
the  Contractor  ;  but  if  such  expense  shall  exceed  such  unpaid 
balance,  the  Contractor  shall  pay  the  difference  to  the  Owner  . 
The  expense  incurred  by  the  Owner  as  herein  provided,  either 
for  furnishing  materials  or  for  finishing  the  work,  and  any 
damage  incurred  through  such  default,  shall  be  audited  and 
certified  by  the  Architect  ,  whose  certificate  thereof  shall  be 
conclusive  upon  the  parties. 

ART.  VI.  The  Contractor  shall  complete  the  several  portions, 
and  the  whole  of  the  work  comprehended  in  this  agreement  by 
and  at  the  time  or  times  hereinafter  stated,  to  wit: 


ART.  VII.  Should  the  Contractor  be  delayed  in  the  prosecu- 
tion or  completion  of  the  work  by  the  act,  neglect  or  default 
of  the  Owner  ,  of  the  Architect  ",  or  of  any  other  contractor 


THE  UNIFORM  CONTRACT.  1557 

employed  by  the  Owner  upon  the  work,  or  by  any  damage 
caused  by  fire,  lightning,  earthquake,  cyclone  or  other  casualty 

for  which  the  Contractor  not  responsible,  or  by 

strikes  or  lockouts  caused  by  acts  of  employes,  then  the  time 
herein  fixed  for  the  completion  of  the  work  shall  be  extended 
for  a  period  equivalent  to  the  time  lost  by  reason  of  any  or  all 
the  causes  aforesaid,  which  extended  period  shall  be  deter- 
mined arid  fixed  by  the  Architect  ;  but  no  such  allowance 
shall  be  made  unless  a  claim  therefor  is  presented  in  writing 
to  the  Architect  within  forty-eight  hours  of  the  occurrence 
of  such  delay. 

ART.  VIII.  The  Owner  agree  to  provide  all  labor  and 
materials  essential  to  the  conduct  of  this  work  not  included 
in  this  contract  in  such  manner  as  not  to  delay  its  progress, 
and  in  the  event  of  failure  so  to  do,  thereby  causing  loss  to 
the  Contractor  ,  agree  that will  reimburse  the  Con- 
tractor for  such  loss;  and  the  Contractor  agree  that  if 

shall  delay  the  progress  of  the  work  so  as  to  cause  loss  for 

which  the  Owner  shall  become  liable,  then shall 

reimburse  the  Owner  for  such  loss.  Should  the  Owner  and 
Contractor  fail  to  agree  as  to  the  amount  of  loss  compre- 
hended in  this  Article,  the  determination  of  the  amount  shall 
be  referred  to  arbitration  as  provided  in  Art.  XII  of  this  con- 
tract. 

ART.  IX.  It  is  hereby  mutually  agreed  between  the  parties 
hereto  that  the  sum  to  be  paid  by  the  Owner  to  the  Con- 
tractor for  said  work  and  materials  shall  be 

subject  to  additions  and  deductions  as  hereinbefore  provided, 
and  that  such  sum  shall  be  paid  by  the  Owner  to  the  Con- 
tractor ,  in  current  funds,  and  only  upon  certificates  of  the 
Architect  ,  as  follows: 


The  final  payment  shall  be  made  within 

days  after  the  completion  of  the  work  included  in  this  contract, 
and  all  payments  shall  be  due  when  certificates  for  the  same 
are  issued. 

If  at  any  time  there  shall  be  evidence  of  any  lien  or  claim  for 
which,  if  established,  the  Owner  of  the  said  premises  might 
become  liable,  and  which  is  chargeable  to  the  Contractor  , 
the  Owner  shall  have  the  right  to  retain  out  of  any  payment 
then  due  or  thereafter  to  become  due  an  amount  sufficient  to 

completely  indemnify against  such  lien  or  claim. 

Should  there  prove  to  be  any  such  claim  after  all  payments 
are  made,  the  Contractor  shall  refund  to  the  Owner  all  moneys 
that  the  latter  may  be  compelled  to  pay  in  discharging  any 
lien  on  said  premises  made-  obligatory  in  consequence  of  the 
Contractor  default. 

ART  X.  It  is  further  mutually  agreed  between  the  parties 
hereto  that  no  certificate  given  or  payment  made  under  this 
contract,  except  the  final  certificate  or  final  payment,  shall  be 
conclusive  evidence  of  the  performance  of  this  contract,  either 


1558  ARCHITECTS'  LICENSE  LAW. 

wholly  or  in  part,  and  that  no  payment  shall  be  construed  to 
be  an  acceptance  of  defective  work  or  improper  materials. 

ART.  XI.  The  Owner     shall  during  the  progress  of  the  work 

maintain  insurance  on  said  work,  in own  name      and   in 

the  name  of  the  Contractor  ,  against  loss  or  damage  by  fire, 
lightning,  earthquake,  cyclone  or  other  casualty.  The  policies 
to  cover  all  work  incorporated  in  the  building,  and  all  materials 
for  the  same  in  or  about  the  premises,  and  shall  be  made  pay- 
able to  the  parties  hereto,  as  their  interest  may  appear. 

ART.  XII.  In  case  the  Owner  and  Contractor  fail  to  agree 
in  relation  to  matters  of  payment,  allowance  or  loss  referred  to 
in  Arts.  Ill  or  VIII  of  this  contract,  or  should  either  of  them 
dissent  from  the  decision  of  the  Architect  referred  to  in  Art. 
VII  of  this  contract,  which  dissent  shall  have  been  filed  in 
writing  with  the  Architect  within  ten  days  of  the  announce- 
ment of  such  decision,  then  the  matter  shall  be  referred  to  a 

Board  of  Arbitration  consisting  of 

in  hehalf  of  the  Owner     , 

and in  behalf  of  the  Contractor    , 

these  two  to  select  a  third.  The  decision  of  any  two  of  this 
Board  shall  be  final  and  binding  on  both  parties  hereto.  In 
event  of  the  death  or  inability  to  serve  of  the  party  named  in 
behalf  of  the  Owner  ,  then  the  Owner  shall  select  a  person  in 
his  place;  in  event  of  the  death  or  inability  to  serve  of  the 
party  named  in  behalf  of  the  Contractor  ,  then  the  Contractor 
shall  select  a  person  in  his  place;  in  event  of  the  death  or  in- 
ability to  serve  of  the  third  party,  then  the  remaining  arbi- 
trators snail  choose  a  person  in  his  place.  Each  party  hereto 
shall  pay  one-half  of  the  expense  of  such  reference. 

ART.  XIII.  The  said  parties  for  themselves,  their  heirs,  suc- 
cessors, executors,  administrators  and  assigns,  do  hereby  agree 
to  the  full  performance  of  the  covenants  herein  contained. 

IN  WITNESS  WHEREOF,  the  parties  to  these  presents  have 
hereunto  set  their  hands  and  seals,  the  day  and  year  first  above 
written. 

In  Presence  of 

ARCHITECTS'  LICENSE  LAW— STATE    OF  ILLINOIS. 

TO  PROVIDE  FOR  THE  LICENSING  OF  ARCHITECTS  AND  REGU- 
LATING THE  PRACTICE  OF  ARCHITECTURE  AS  A  PROFESSION. 

AN  ACT 

Enacted  by  the  Fortieth  General  Assembly  oi  the  Regular  Biennial 
Session,  Approved  June  3,  1897,  and  in  Force  July  1,  1897; 
with  Amendments  Adopted  by  the  Forty -first  General  Assem- 
bly and  Approved  April  19,  i899.  In  Force  July  1,  1899. 

APPOINTMENT  OF  A  STATE  BOARD  OF  EXAMINERS  OF  ARCHITECTS 

SECTION  1.  Be  it  enacted  by  the  people  of  the  State  of  Illinois, 
represented  in  General  Assembly:  That  within  thirty  days  after 
the  passage  ot  this  act  the  Governor  of  this  State  shall,  by  the 


ARCHITECTS'  LICENSE  LAW.  1559 

advice  and  consent  of  the  Senate,  appoint  a  State  Board  of 
Examiners  of  Architects,  to  be  composed  of  live  members,  one 
of  whom  shall  be  a  member  of  the  faculty  of  the  Illinois  State 
University,  and  the  other  four  shall  be  architects  residing  in  the 
State  of  Illinois,  who  have  been  engaged  in  the  practice  of 
architecture  at  least  ten  years.  Two  of  the  said  practicing 
architects  appointed  as  examiners  shall  be  designated  to  hold 
office  for  two  years  from  the  date  of  the  passage  of  this  act,  and 
the  other  two,  together  with  the  member  of  the  faculty  afore- 
said, shall  hold  office  for  four  years  from  the  passage  of  this 
act;  and  thereafter  upon  the  expiration  of  the  term  of  office  of 
the  person  so  appointed,  the  Governor  of  the  State  shall  ap- 
point a  successor  to  each  person  whose  term  of  office  shall 
expire,  to  hold  office  for  four  years,  and  said  person  so  ap- 
pointed shall  have  the  above  specified  qualifications.  In  case 
appointment  of  a  successor  is  not  made  before  the  expira- 
tion of  the  term  of  any  member,  such  member  shall  hold  office 
until  his  successor  is  appointed  arid  duly  qualified.  Any 
vacancy  occurring  in  membership  of  the  board  shall  be  filled 
by  the"  Governor  of  the  State  for  the  unexpired  term  of  such 
membership. 

[Sections  2  and  3  relate  to  the  organization  of  the  board, 
salaries,  meetings,  etc.] 

EXAMINATIONS FEES. 

SEC.  4.  Provisions  shall  be  made  by  the  board  hereby  con- 
stituted for  holding  examinations  at  least  twice  in  each  year,  of 
applicants  for  license  to  practice  architecture,  and  any  person 
over  twenty-one  years  of  age,  upon  payment  of  a  fee  of  fit'fceeu 
dollars  to  the  secretary  of  the  board,  shall  be  entitled  to  an 
examination  for  determining  his  or  her  qualifications.  All  ex- 
aminations shall  be  made  directly  by  said  board,  or  a  commit- 
tee of  two  members  delegated  by  the  board,  and  due  notice  of 
the  time  and  place  of  the  holding  of  such  examinations  shall  bo 
published,  as  in  the  case  provided  for  the  publication  of  the 
rules  and  regulations  thereof.  The  examination  shall  have 
special  reference  to  the  construction,  of  buildings,  and  a  test  of 
the  knowledge  of  the  candidate  of  the  strength  of  materials,  and 
of  his  or  her  abilitv  to  make  practical  application  of  such  knowl- 
edge in  the  ordinary  professional  work  of  an  architect,  and  in 
the  duties  of  a  supervisor  of  mechanical  work  on  buildings,  and 
should  also  seek  to  determine  his  or  her  knowledge  of  the  laws 
of  sanitation  as  applied  to  buildings.  If  the  result  of  the  exam- 
ination of  any  applicant  shall  be  satisfactory  to  a  majority  of 
the  board,  under  its  rules,  the  secretary  shall  upon  an  order  of 
the  board,  issue  to  the  applicant  a  certificate  to  that  effect, 
and  upon  payment  to  the  secretary  of  the  board  by  the  candi- 
date of  a  fee  of  twenty-five  dollars,  he  shall  thereupon 
issue  to  the  person  therein  named  a  license  to  practice  archi- 
tecture in  the  State,  in  accordance  with  the  provisions  of  this 
act,  which  license  shall  contain  the  full  name,  birth-place  and 
age  of  the  applicant,  and  be  signed  by  -the  president  and  secre- 


1560  ARCHITECTS'  LICENSE  LAW. 

tary,  and  sealed  with  the  seal  of  the  board.     If  an  applicant  fails 
to  pass  said  examination,  his  or  her  fee  shall  be  returned. 

All  papers  received  by  the  secretary  in  relation  to  applications 
for  license  shall  be  kept  on  file  in  his  office,  and  a  proper  index 
and  record  thereof  shall  be  kept  by  him. 

ARCHITECTS   WHO    ARE    ENTITLED    TO    LICENSE   WITHOUT  AN 
EXAMINATION. 

SEC.  5.  Any  person  who  shall,  by  affidavit,  show  to  the 
satisfaction  of  the  State  Board  of  Examiners  of  Architects  that 
he  or  she  was  engaged  in  the  practice  of  the  profession  of  archi- 
tecture on  the  date  of  the  passage  of  this  act  shall  be  entitled 
to  a  license  without  an  examination,  provided  such  application 
shall  bo  made  within  six  months  after  the  passage  of  this  act. 
Such  license,  when  granted,  shall  set  forth  the  fact  that  the 
person  to  whom  the  same  was  issued  was  practicing  architecture 
in  this  State  at  the  time  of  the  passage  of  this  act,  and  is  there- 
fore entitled  to  a  license  to  practice  architecture  without  an 
examination  by  the  board  of  examiners,  and  the  secretary  of  the 
Wj-d  shall,  upon  the  payment  to  him  of  the^fee  of  twenty- 
five  dollars,  issue  to  the  person  named  in  said  affidavit, 
a  license  to  practice  architecture  in  this  State,  in  accordance 
with  the  provisions  of  this  act.  In  the  case  of  a  co-partnership 
of  architects,  each  member  whose  name  appears  must  be 
licensed  to  practice  architecture.  No  stock  company  or  cor- 
poration shall  be  licensed  to  practice  architecture,  but  the 
same  may  employ  licensed  architects.  Each  licensed  archi- 
tect shall  have  his  or  her  license  recorded  in  the  office  of  the 
county  clerk  in  each  and  every  county  in  this  State  in  which 
the  holder  thereof  shall  practice,  and  he  or  she  shall  pay  to 
the  clerk  the  same  fee  that  is  charged  for  the  recording  of 
notarial  commissions.  A  failure  to  have  his  or  her  license  so 
recorded  shall  be  deemed  sufficient  cause  for  revocation  of 
such  license. 

COUNTY   CLERKS    TO    KEEP   RECORD    OF    LICENSES    RECORDED. 

SEC.  6.  Each  county  clerk  shall  keep  in  a  book,  provided  for 
the  purpose,  a  complete  list  of  all  licenses  recorded  by  him 
under  the  provisions  of  this  act,  together  with  the  date  of  the 
issuance  of  each  license. 

LICENSED    ARCHITECTS    TO    HAVE    A    SEAL. 

SEC.  7.  Every  licensed  architect  shall  have  a  seal,  the  im- 
pression of  which  must  contain  the  name  of  the  architect,  his 
or  her  place  of  business,  and  the  words,  " Licensed  Architect," 
"State  of  Illinois,"  with  which  he  shall  stamp  all  drawings 
and  specifications  issued  from  his  office,  for  use  in  this  State. 

PENALTY    FOR    PRACTICING    ARCHITECTURE    WITHOUT    A    LICENSE. 

SEC.  8.  After  six  months  from  the  passage  of  this  act  it 
shall  be  unlawful  and  it  shall  be  a  misdemeanor  punishable  by 
a  fine  of  not  less  than  $50  nor  more  than  $500  for  each  and 
every  week  during  which  said  offense  shall  continue,  for  any 


ARCHITECTS'  LICENSE  LAW.  1561 

person  to  practice  architecture  without  a  license  in  this  State, 
or  to  advertise,  or  put  out  any  sign  or  card,  or  other  device 
which  might  indicate  to  the  public  that  he  or  she  is  entitled  to 
practice  as  an  architect. 

PERSONS    WHO    ARE    TO    BE    REGARDED    AS    ARCHITECTS. 

SEC.  9.  Any  person  who  shall  be  engaged  in  the  planning 
or  supervision  of  the  erection,  enlargement,  or  alteration  of 
buildings  for  others,  and  to  be  constructed  by  other  persons 
than  himself,  shall  be  regarded  as  an  architect  within  the  pro- 
visions of  this  act,  and  shall  be  held  to  comply  with  the  same; 
but  nothing  contained  in  this  act  shall  prevent  the  draughts- 
men, students,  clerks  of  works  or  superintendents,  and  other 
employes  of  those  lawfully  practicing  as  architects,  under 
license  as  herein  provided  for,  from  acting  under  the  instruc- 
tion, control  or  supervision  of  their  employers;  or  shall  prevent 
the  employment  of  superintendents  of  buildings  paid  by  the 
owners  from  acting,  if  under  the  control  and  direction  of  a 
licensed  architect  who  has  prepared  the  drawing  and  specifica- 
tions for  the  building.  The  term  building  in  this  act  shall  be 
understood  to  be  a  structure,  consisting  of  foundations,  walls, 
and  roof,  with  or  without  the  other  parts;  but  nothing  con- 
tained in  this  act  shall  be  construed  to  prevent  any  person, 
mechanic  or  builder  from  making  plans  and  specifications  for, 
or  supervising  the  erection,  enlargement,  or  alteration  of  any 
building  that  is  to  be  constructed  by  himself  or  employes; 
nor  shall  a  civil  engineer  be  considered  as  an  architect  unless 
he  plans,  designs  and  supervises  the  erection  of  buildings,  in 
which  case  he  shall  be  subject  to  all  the  provisions  of  this  act, 
and  be  considered  as  an  architect. 

LICENSE    REVOKED. 

SEC.  10.  Architects'  licenses  issued  in  accordance  with  the 
provisions  of  this  act  shall  remain  in  full  force  until  revoked 
for  cause,  as  hereinafter  provided.  Any  license  so  granted 
may  be  revoked  by  unanimous  vote  of  the  State  Board  of 
Examiners  of  Architects  for  gross  incompetency,  or  reckless- 
ness in  the  construction  of  buildings,  or  for  dishonest  practices 
on  the  part  of  the  holder  thereof;  but  before  any  license  shall 
be  revoked  such  holder  shall  be  entitled  to  at  least  twenty 
days'  notice  of  the  charge  against  him,  and  of  the  time  and 
place  of  the  meeting  of  the  board  for  the  hearing  and  deter- 
mining of  such  charge.  And  on  the  cancellation  of  such 
license  it  shall  be  the  duty  of  the  secretary  of  the  board  to  give 
notice  of  such  cancellation  to  the  county  clerk  of  each  county 
in  the  State  in  which  the  license  has  been  recorded,  whereupon 
the  clerks  of  the  counties  shall  mark  the  license  recorded  in 
his  office  cancelled.  After  the  expiration  of  six  months  from 
the  revocation  of  a  license,  the  person  whose  license  was  revoked 
may  have  a  new  license  issued  to  him  by  the  secretary  upon 
certificate  of  the  Board  of  Examiners,  issued  by  them  upon 
satisfactory  evidence  of  proper  reasons  for  his  reinstatement, 
and  upon  payment  to  the  secretary  of  the  fee  of  five  dollars. 


1562  COLLEGES  AND  SCHOOLS  OF  ARCHITECTURE. 

For  the  purpose  of  carrying  out  the  provisions  of  this  act 
relating  to  the  revocation  of  licenses,  the  board  shall  have  the 
power  of  a  court  of  record,  sitting  in  the  county  in  which  their 
meeting  shall  be  held,  and  the  power  to  issue  subpoenas  and 
compel  the  attendance  and  testimony  of  witnesses.  Witnesses 
shall  be  entitled  to  the  same  fees  as  witnesses  in  a  court  of  record, 
to  be  paid  in  like  manner.  The  accused  shall  be  entitled  to 
the  subpoena  of  the  board  for  his  witnesses  and  to  be  heard  in 
person  or  by  counsel  in  open  public  trial. 

RENEWAL    OF    LICENSE. 

SEC.  11.  Every  licensed  architect  in  this  State  who  desires 
to  continue  the  practice  of  his  profession  shall  annually,  during 
the  time  he  shall  continue  in  such  practice,  pay  to  the  secretarv 
of  the  board  during  the  month  of  July  a  fee  of  iive  dollars  and 
the  secretary  shall  thereupon  issue  to  such  licensed  architect  a 
certificate  of  renewal  of  his  license  for  the  term  of  one  vear. 
Any  licensed  architect  who  shall  fail  to  have  his  license  renewed 
during  the  month  of  July  in  each  and  everv  year  shall  have  his 
license  revoked;  and  it  shall  be  the  duty  of  the  secretary  of  the 
board  to  give  notice  of  such  revocation  to  the  county  clerk  in 
each  county  in  the  State,  whereupon  the  clerks  of  the  counties 
shall  make  an  entry  of  such  revocation  accordingly. 

But  the  failure  to  renew  said  license  in  apt  time  shall  not 
deprive  such  architect  of  the  right  to  renewal  thereafter;  and 
the  secretary  of  the  board  shall  give  like  notice  of  such  renewal ; 
but  the  fee  to  be  paid  upon  the  renewal  of  license  after  the 
month  of  July  shall  be  ten  dollars,  to  cover  the  additional  ex- 
pense incurred  by  the  board  on  account  of  such  notices. 

REPORT  OF  PROCEEDINGS  TO  BE  FILED  WITH  THE  AUDITOR 
OF    PUBLIC    ACCOUNTS. 

SEC.  12.  Within  the  first  week  of  December,  after  the 
organization  of  the  board,  and  annually  thereafter,  the  secre- 
tary of  the  board  shall  file  with  the  Auditor  of  State  a  full 
report  of  the  proceedings  of  the  board,  and  a  complete  state- 
ment of  the  receipts  and  -expenditures  of  the  board,  attested 
bv  the  affidavits  of  the  president  and  secretary,  subject  to  the 
approval  of  the  State  Auditor. 

COLLEGES  AND   SCHOOLS  OF  ARCHITECTURE   IN 
THE   UNITED   STATES. 

Columbia  University,  New  York.—  School  of  Archi- 
tecture. Alfred  D.  F.  Hamlin,  Professor  in  charge.  Offers:  (1)  Full 
four-year  course  leading  to  degree  of  Bachelor  of  Science.  In 
the  fourth  year  the  student  may  elect  a  specialized  course  in 
Advanced  Architectural  Engineering,  in  place  of  the  usual 
course  in  Advanced  Design.  (2)  Advanced  courses  leading  to 
the  degrees  of  Master  of  Arts,  and  Doctor  of  Philosophy.  (3) 


COLLEGES  AXD  SCHOOLS  OF  ARCHITECTURE.   1563 

Special  or  elective  courses  for  students  not  candidates  for  a 
degree.  Tuition,  $200  per  year. 

Cornell  University,  Ithaca,  N.  Y. — College  of  Architec- 
ture. Prof.  John  V.  Van  Pelt  in  charge.  Prof.  Clarence  A.  Martin, 
Secretary.  Offers:  (1)  Three  courses  leading  to  the  degree  of 
Bachelor  of  Architecture  as  follows:  First,  the  regular  four-year 
course;  Second,  a  four-year  course  allowing  specialization  in 
Architectural  Design ;  Third,  a  four-year  course  allowing  special- 
ization in  Architectural  Engineering.  (2)  A  two-year  special 
course  in  Architecture,  leading  to  a  certificate.  (3)  A  regular 
two-year  course  in  Painting,  leading  to  a  certificate.  (4)  Special 
courses  in  Painting,  arranged  for  individual  cases  but  not  lead- 
ing to  a  certificate  or  degree.  Tuition,  $125  per  year. 

Harvard  University,  Lawrence  Scientific 
Scliool. — Department  of  Architecture.  Herbert  Langford 
Warren,  A.M.,  Nelson  Robinson,  Jr.,  Professor  of  Architecture, 
in  charge.  Offers:  (1)  Full  four-year  programme  of  courses  in 
Architecture  leading  to  the  degree  of  Bachelor  of  Science  in 
Architecture.  (2)  Competent  special  students  are  admitted  to 
take  a  partial  course.  A  certificate  will  be  given  to  such  stu- 
dents. Tuition,  $150  per  year. 

Lawrence  Scientific  Scliool. — Department  of  Land- 
scape Architecture.  Prof.  Frederick  Law  Olmstead,  A.B.,  in 
charge.  Offers:  (1)  Full  four-year  programme  of  courses  lead- 
ing to  the  degree  of  Bachelor  of  Science  in  Landscape  Architec- 
ture. (2)  Competent  special  students  are  admitted  to  take  a 
partial  course,  to  whom  a  certificate  will  be  given.  Tuition, 
$150  per  year. 

Massachusetts  Institute  of  Technology,  Boston, 
Mass. — Francis  W.  Chandler,  Professor  in  charge.  Offers: 
(1)  Three  courses  leading  to  the  degree  of  Bachelor  of  Science  : 
i First,  the  regular  four-year  course  in  Architecture;  Second, 
a  four-year  course  allowing  specialization  in  Architectural 
'  Engineering ;  Third,  a  four-year  course  allowing  specialization 
in  Landscape  Architecture.  (2)  Special  students  are  received 
on  the  basis  of  office  experience  or  college  graduation  and  prepa- 
ration in  Geometry  and  Drawing.  Graduate  courses  lead  to  the 
Master's  degree.  Tuition,  $250  per  year. 

University  of  Pennsylvania,  Philadelphia,  Pa. 
— Course  in  Architecture.  Warren  Powers  Laird,  Professor  in 
charge.  Offers:  (1)  Full  four-year  course  leading  to  the 
degree  of  B.S  in  Architecture.  (2)  Two-year  special  course 


1564  COLLEGES  AND  SCHOOLS  OF  ARCHITECTURE. 

leading  to  a  certificate  of  proficiency.  (3)  Five-year  or  gradu- 
ate course  leading  to  the  degree  of  M.S.  in  Architecture.  (4) 
Combined  six-year  course  in  Arts  and  Architecture  leading  to 
the  degree  of  A.B.  at  the  end  of  the  fourth  year  and  B.S.  in 
Architecture  at  the  end  of  the  sixth  year.  (5)  Course  in  Archi- 
tectural Engineering  leading  to  the  degree  of  B.S.  in  Architecture 
and  differentiated  from  the  regular  four-year  course  in  Archi- 
tecture by  the  substitution  in  the  last  year  of  specialized  work 
in  engineering  subjects  for  Architectural  Designing,  Drawing, 
etc.  Tuition  for  all  courses,  $150  per  year. 

University  of  Illinois,  Urbana,  111. —  Courses  in 
Architecture.  Nathan  Clifford  Ricker,  Professor  in  charge. 
Offers:  (1)  Full  four-year  course,  leading  to  degree  of  B.S.  in 
Architecture.  (2)  Full  four-year  course  leading  to  degree  of  B.S. 
in  Architectural  Engineering.  Tuition  is  free  to  residents  of  the 
State.  There  is  an  incidental  fee  of  $24  a  year. 

Ohio  State  University,  Columbus,  Ohio.— Course 
in  Architecture.  J.  N.  Bradford,  Professor  in  charge.  Offers: 
Full  four-year  course  leading  to  degree.  Tuition,  free. 

University  of  California,  Oakland,  Cal.— Has  re- 
cently established  a  Department  of  Architecture  with  John 
Galen  Howard,  Professor  in  charge. 

Syracuse  University,  Syracuse,  N.  Y.  —  College  of 
Fine  Arts.  F.  W.  Revels,  Professor  of  Architecture.  Offers: 
(1)  Full  four-year  course  leading  to  degree.  (2)  Two-year 
special  course  leading  to  certificate  of  proficiency.  Tuition, 
$120  per  year. 

Washington  University,  St.  Louis,  Mo.— Course  in 
Architecture.  Frederick  M.  Mann,  Professor  in  charge.  Offers: 
(1)  Four-year  course  leading  to  a  degree.  (2)  Special  course 
for  draughtsmen.  Tuition,  $150  per  year;  special  course, 
$100  per  year. 

Rose  Polytechnic  Institute,  Terre  Haute,  Ind.-~ 
Department  of  Architecture.  Malverd  A.  Howe,  C.E.,  director. 
Offers  a  full  four-year  course,  designed  to  give  a  thorough 
training  in  Architectural  Engineering  together  with  systematic 
instruction  in  Architectural  Design.  Tuition,  $100  per  year. 

Drexel  Institute,  Philadelphia,  Pa.— School  of 
Architecture.  Arthur  Truscott,  director.  Offers  a  two-year 
course  in  Architecture,  a  large  share  of  the  time  being  devoted 
to  purely  Architectural  work.  Tuition,  $60  a  year. 


TRAVELLING  SCHOLARSHIPS.  1565 

Pratt  Institute,  Brooklyn,  N.  Y. — Course  in  Archi- 
tecture. Walter  S.  Perry,  Director  of  Department  of  Fine  Arts. 
Offers:  Full  two-years'  course  leading  to  a  certificate  of  pro- 
ficiency. Tuition,  $45  per  year. 

Academy  of  Architecture  and  Industrial  Science, 
1742  Chouteau  Ave.,  St.  Louis,  Mo. — H.  Maack 
Principal.  This  is  a  private  school  founded  by  Mr.  Maack,  in 
1885,  and  designed  more  particularly  to  meet  the  wants  of  build- 
ing tradesmen,  offering  them  such  instruction  as  is  necessary 
to  attain  the  highest  proficiency  in  their  trade,  and  to  fully 
understand  the  plans  and  details  of  complicated  buildings. 
There  is  also  a  special  course  for  those  desiring  to  fit  them- 
selves for  positions  as  draughtsmen  in  architects'  offices.  Tui- 
tion for  the  regular  course  is  $50  for  a  three-months'  term,  or 
$300  for  the  full  course  of  eight  terms,  or  $100  for  the  year. 
There  are  several  special  courses  which  may  be  commenced  at  any 
time,  and  for  which  the  tuition  varies. 

The  Society  of  Beaux- Arts  Architects  of  New 
York  has  established  a  course  of  study  for  architectural  draughts- 
men, modelled  on  the  system  adopted  by  the  Ecole  des  Beaux- 
Arts,  Paris,  France.  The  course  is  divided  into  two  classes: 
Class  B,  into  which  any  one  of  either  sex  may  enter  without 
any  preliminary  examination;  Class  A,  which  the  student 
reaches  after  having  received  certain  awards  in  Class  B.  On 
completing  the  course,  which  is  not  limited  by  time,  the  Society 
awards  a  certificate  of  proficiency. 
Address 

CHAIRMAN,  Committee  on  Education, 

3  East  33d  St.,  New  York. 

Instruction  in  Architecture,  Architectural  Engineering,  and 
Drawing  is  also  given  by  the  International  Correspondence 
Schools,  Scran  ton,  Pa.,  and  by  the  American  School  of  Corre- 
spondence, at  Armour  Institute  of  Technology,  Chicago,  111. 

TRAVELLING  FELLOWSHIPS  AND  SCHOLARSHIPS. 

Kotch  Travelling  Scholarship.— C.  H.  Blackall,  Sec- 
retary, 1  Somerset  St.,  Boston,  Mass.  Candidates  must  be  under 
thirty  years  of  age,  must  have  worked  during  two  years  in 
Massachusetts  in  the  employ  of  an  architect  resident  in  Mas- 
sachusetts, and  will  be  required  to  pass  preliminary  examina- 
tions upon  the  following  subjects: 


1566  LIST  OF  VALUABLE  BOOKS  FOR  ARCHITECTS. 

I.  Construction,   Theory  and  Practice.      (Written    examina- 
tion.) 

II.  An    Elementary    Knowledge    of    the    French    Language. 
(Written  examination.) 

III.  History  of  Architecture.      (Written  examination.) 

IV.  Freehand  Drawing  from  the  Cast. 

Candidates  who  pass  in  these  preliminary  examinations  will 
be  asked  to  present  themselves  later  for  the  competition  in 
Design.  The  successful  candidate  in  each  yearly  examination 
receives  from  the  Trustees  of  the  Scholarship  annually,  for  two 
years,  $1,000  to  be  expended  in  foreign  travel  and  study,  pro- 
vided always  that  the  beneficiary  shows  such  fitness  and  dili- 
gence as  may  be  required  of  him. 

The  Boston  Society  of  Architects  has  offered  the  sum  of  $75 
as  a  second  prize. 

The  Society  of  Beaux-Arts  Architects,  Travel- 
ling Scholarship. — Lloyd  Warren,  Chairman  Com.  on  Edu- 
cation, 3  East  33d  St.,  New  York.  A  fund  of  $2,000  has  been 
provided  to  defray  the  expenses  of  this  prize,  which  will  be 
awarded  July,  1904,  and  the  recipient  will  spend  two  years  in 
travel  and  study  abroad.  The  award  will  be  based  on  the 
result  of  three  competitive  trials,  to  which  all  American 
draughtsmen  under  28  years  of  age  are  eligible.  The  four 
draughtsmen  holding  the  best  averages  next  to  the  final  winner 
of  the  scholarship  will  be  awarded  the  sum  of  $100  each. 

Columbia  University  Travelling-  Fellowships.— 
Four  travelling  fellowships  have  been  established,  open  to  all 
graduates  of  the  School  of  Architecture  under  30  years  of  age; 
they  are  awarded  in  May  of  each  year. 


LIST   OF  VALUABLE   BOOKS    FOR   ARCHITECTS, 
DRAUGHTSMEN,   AND   BUILDERS. 

[The  author  has  carefully  examined  nearly  all  of  the  books  named  below, 
and  can  recommend  them  as  containing  useful  information  on  the  subjects 
under  which  they  are  listed.  Name  and  address  of  publisher  given  at  end  of 
the  list.] 

ARCHITECTURE. 

Price 

Handbook  of  Architectural  Styles*     By  A.  Rosengarten.  . .  .  $2 . 50 

History  of  Architecture.1     By  Prof.  A.  D.  F.  Hamlin 2 . 00 

Vignola.    The  Five  Orders  of  Architecture.2     Edited  by  Ar- 
thur Lyman  Tuckerman 5.00 


LIST  OF  VALUABLE  BOOKS  FOR  ARCHITECTS.   1567 

Price 
Vignola.     American  edition  prepared  for  Bates  &  Guild 

Co $5.00 

The  American  Vignola.3     By  Prof.  William  R.  Ware 3  . 00 

Stepping-stone  to  Architecture*     By  Thomas  Mitchell 0 . 50 

A  Discussion  of  Composition,  especially  as  applied  to  Archi- 
tecture. By  John  V.  Van  Pelt 2.00 

Handbook  of  Ornament*     By  Meyer 3 . 60 1 

A   Dictionary  of  Architecture  and  Building.5     By  Russell 

Sturgis.     In  three  volumes,  per  volume 18 . 00 

BUILDING    CONSTRUCTION,    SUPERINTENDENCE,    AND    SPECIFI- 
CATIONS. 

(See  also  FOUNDATIONS  and  IRON  AND  STEEL  CONSTRUCTION.) 

A  Handbook  for  Superintendents  of  Construction,  Architects, 

Builders,  and  Building  Inspectors.*     By  H.  G.  Richey. 

16mo,  747  pages 4 .  00 

Cements,  Limes,  and  Plasters:  Their  Materials,  Manufacture, 

and  Properties.6  By  Edwin  C.  Eckel,  C.E.  8vo,  754  pp.  6.00 
Building  Construction  and  Superintendence.2  Part  I. 

Masonry  and  Plastering.     Part  II.  Carpenters'  Work. 

Part  III.  Trussed  Roofs  and  Roof-Trusses.     By  F.  E. 

Kidder.  Each  volume  so'd  sepa  atcly,  per  volume.  .  4. CO 

Building  Superintendence?  By  T.  M.  Clark 3 . 00 

Safe  Building?  By  Louis  De  Coppert  Berg.  Two  volumes, 

each 5 . 00 

Details  of  Building  Construction.*  By  Prof.  Clarence  A. 

Martin 2 . 00 

Inspectors'  Pocket-Book ,6  for  the  use  of  Inspectors  and  Super- 
intendents. By  Austin  T.  Byrne 3  . 00 

A  Practical  System  for  Writing  Specifications  for  Buildings.2 

By  W.  Frank  Bower 5.00 

CONCRETE.  PLAIN  AND  REINFORCED. 

Experimental  Researches  on  Reinforced  Concrete.13  By  Ar- 
mand  Considere.  Translated  by  Leon  Moisseiff,  C.E.  Author- 
ized American  Edition.  $2.00. 

A  Treatise  on  Concrete,  Plain  and  Reinforced.9  By  Frederick 
W.  Taylor,  M.E.,  and  Sanford  E.  Thompson,  Assoc.  M.  Am.  Soc. 
C.E.,  with  chapters  by  R.  Feret,  Wm.  B.  Fuller,  and  Spencer  B. 
Newberry.  8vo,  620  pp.  $5.00. 

Reinforced  Concrete.1*  By  Chas.  F.  Marsh,  Assoc.  M.  Inst.  C.E., 
Assoc.  M.  Inst.  M.  E.  4to,  7JX11,  530  pp.,  511  ill.  $7.00. 

Reinforced  Concrete.11     By  A.  W.  Buel  and  C.  S.  Hill.     $5.00. 


1568  LIST  OF  VALUABLE  BOOKS  FOR  ARCHITECTS. 

DRAWING.  Price. 

Architectural  Drawing .     ByC.  Franklin  Edminster $2.00 

[The    most  practical  and    complete   course  in   the  ele- 
ments of  Architectural  Drawing  now  published.] 
Architectural  Perspective  for  Beginners.'2'     By  F.  A.  Wright.  3.00 
Pen  Drawing.*     By  Charles  D.  Maginme 1 . 00 

ELECTRIC  WIRING. 

Vol.  13,  International  Library  of  Technology.1 
Practical  Lessons  in  Electricity* 

ESTIMATING. 

Estimating  Frame  and  Brick  Houses.9  By  Fred  T.  Hodg- 
son   1 .00 

FOUNDATIONS. 
Building  Construction  and  Superintendence.2     Part  I.     By 

F.  E.  Kidder 4.00 

A  Treatise  on  Masonry  Construction.^     By  Ira  O.  Baker.  ...    5 . 00 
A  Practical  Treatise  on  Foundations. °     By  W.  M.  Patton, 

CE.. 5.00 

FURNITURE  DESIGNING. 

Furniture   Designing   and  Drafting.2     By   Alvan   Crocker 

Nye 2.00 

HANDBOOKS. 

The  Civil  Engineers'  Pocket-Book*  By  John  C.  Trautwine, 
revised  by  John  C.  Trautwine,  Jr.,  and  John  C.  Traut- 
wine, 3d 5.00 

The  Mechanical  Engineers'  Pocket-Book*  By  William 

Kent 5 . 00 

Carnegie  Steel  Company's  Pocket  Companion 2 . 00 

Cambria  Steel.    Published  by  Cambria  Iron  Co 2 . 00 

Manual  of  Structural  Steel.  Compiled  by  Geo.  H.  Blakeley 
and  published  by  the  Passaic  Steel  Co. 

Steel  in  Construction.  Published  by  the  Pencoyd  Iron 
Works. 

Handbook.  Published  by  the  Dearborn  Foundry  Company, 
Chicago. 

Book  of  Standards.  Edited  by  Prof.  Reid  T.  Stewart, 

and  published  by  the  National  Tube  Works 1 . 00 

The  Building  Trades  Pocket-Book.  By  International 

Correspondence  Schools,  Scranton,  Pa 1.50 


LIST  OF  VALUABLE  BOOKS  FOR  ARCHITECTS.  1569 

FlREPROOFING.  Price. 

The  Fireproofing  of  Steel  Buildings*    By  J.  K.  Freitag. .  .$2.50 
[A  very  practical  and  valuable  work.] 

HEATING  AND  VENTILATION. 

Heating   and    Ventilation  of   Buildings*      By  Prof.  Rolla 

C.  Carpenter 3  .00 

Steam  Heating  for  Buildings*     By  Wm.  J.  Baldwin 2.50 

Vol.  32,  International  Library  of  Technology.1 

IRON  AND  STEEL  CONSTRUCTION — SKELETON  CONSTRUCTION. 

Architectural  Iron  and  Steel*    (many  useful  details).     By 

Wm.  H.  Birkmire 3 . 50 

Compound  Riveted  Girders*     By  Wm.  H.   Birkmire 2.00 

Skeleton  Construction  in  Buildings*  By  Wm.  H.  Birk- 
mire. ...  : 3 .00 

Architectural  Engineering*     By  Joseph  Kendall  Freitag.    3.50 
[The  best  discussion  of  the  engineering  problems  involved 
in  the  construction  of  high  buildings.] 

PAINTING. 

Rustless  Coatings:  *  Corrosion  and  Electrolysis  of  Iron  and 

Steel.  By  M.  P.  Wood.  432  pp 4.00 

The  Industrial  and  Artistic  Technology  of  Paints  and  Var- 
nish* By  Alvah  H.  Sabin,  378  pp 3 .00 

PLANNING  OF  CHURCHES 
Churches  and  Chapels*     By  F.  E.  Kidder 3.00 

PLANNING  OF  OFFICE  BUILDINGS. 
The  Planning  and  Construction  of  High  Office  Buildings* 

By  William  H.  Birkmire 3 . 50 

PLANNING  OF  SCHOOL  BUILDINGS. 
Modern    American    School    Buildings*     By    Warren    R.  ' 

Briggs 4.00 

School  Architecture.™     By  Edmund  M.  Wheelwright 5.00 

PLANNING  OF  THEATRES. 
The  Planning  and  Construction  of  American  Theatres.*     By 

William  H.  Birkmire.  .  .3.00 


1570  LIST  OF  VALUABLE  BOOKS  FOR  ARCHITECTS. 

PLUMBING  AND  SANITARY  ENGINEERING.  Price. 

Sanitary   Engineering   of  Buildings.     Vol.    I.     By   W.    P. 

Gerhard $5.00 

ROOF-TRUSSES. 

(See  also  Steel-Mill  Buildings.) 

Trussed  Roofs  and  Roof -Trusses.2     Being  the  third  volume 
of  Building  Construction  and  Superintendence.     By  F. 

E.  K.dder.     Sold  separately 4 . 00 

[A  complete  treatise  on  the  subject,  illustrated  by  many 

examples  of  roof  construction  in  wood  and  steel.] 
The  Design  of  Simple  Roof-Trusses  in  Wood  and  Steel.*     By 

Prof.  Malverd  A.  Howe 2 .00 

Graphics    for    Engineers,    Architects,    and    Builders.*     By 

Prof.  Chas.  E.  Greene. 
Part  I.     Roof-Trusses.     Diagrams  for  steady  load,  snow, 

and  wind 1 . 25 

Part  II.     Bridge  Trusses 2.50 

Part  III.     Arches  in  Wood,  Iron,  and  Stone 2 . 50 

[These  books  are  among  the  best  of  those  which  show  how 
stresses  may  be  determined  by  graphical  solution  ] 

STEEL-MILL  BUILDINGS. 

The  Design  of  Steel-Mill  Buildings.11     By  Milo  S.  Ketchum.  4 . 00 
[A  practical  and  useful  work,  containing  many  details  ] 

STONES  FOR  BUILDING  AND  DECORATION. 

Stones  for  Building  and  Decoration.*      By  Geo.  P.  Merrill.  .    5.00 
[The  most  complete  work  published  on  building  stones, 

marbles,  etc.] 
Much  practical  information  on  building  stones  is  contained  in 

Building  Construction  and  Superintendence.  Part  I. 
PUBLISHERS. — *  Published  abroad.  1  Longmans,  Green,  & 
Co.,  N.  Y.  2  Wm.  T.  Comstock,  N.  Y.  3  The  American  Archi- 
tect Co.,  Boston.  4  Bates  &  Guild  Co.,  Boston.  5  The  Macmil- 
lan  Co.,  N.  Y.  6  John  Wiley  &  Sons,  N.  Y.  'International 
Text-Book  Co. ,  Scranton,  Pa.  8  American  School  of  Corre- 
spondence at  Armour  Inst.  of  Technology,  Chicago.  9  David 
Williams  Co.,  N.  Y.  10  Rogers  &  Manson,  Boston.  u  Engineer- 
ing News  Publishing  Co.,  N.  Y.  12  Published  by  the  Author. 
13McGraw  Publishing  Co.,  N.  Y.  14  D.  Van  Nostrand  Co, 
N.  Y. 


TRADE  REFERENCES.  1571 

Trade  References. 

Because  they  are  somewhat  out  of  the  ordinary  line  of  building  con- 
struction and  equipment,  the  following  references  are  given  that  archi- 
tects and  builders  may  know  whom  to  consult  for  information  and  prices. 
All  names  have  been  inserted  without  the  knowledge  of  the  parties  inter- 
ested or  any  monetary  consideration.  Most  of  the  manufacturers  named 
issue  valuable  publications  along  the  line  of  their  especial  product,  which 
will  be  sent  gratis  on  application. 
Acetylene  Gas  Generators.* 

Davis  Acetylene  Co.,  Elkhart,  Ind. 

General  Acetylene  Co.,  New  York. 

Niagara  Falls  Acetylene  Gas  Generator  Co.,  Niagara  Falls,  N.  Y. 
Antifriction  Drawer  Slide. 

Grant  Pulley  &  Hardware  Co.  (Turner  Slide),  25  Warren  St.,  N.  Y. 
Artificial  Marble. 

Artificial  Marble  Co.,  St.  James  Building,  N.  Y. 

Mycenian  Marble  Co.,  524  W.  34th  St.,  N.  Y. 
Automatic  Fire  Apparatus,  Sprinklers,  etc. 

General  Fire  Extinguisher  Co.,  Providence,  R.  I. 

International  Sprinkler  Co.,  Philadelphia,  Pa. 

Niagara  Fire  Extinguisher  Co.,  Akron,  O. 
Bells. 

Meneely  Bell  Co.,  Troy,  N.  Y.,  and  177  Broadway,  N.  Y.  City. 
Blinds,  Venetian,  Rolling,  Sliding,  etc. 

Burlington  Venetian  Blind  Co.,  Burlington,  Vt. 

Jas.  Q.  Wilson  Mfg.  Co.,  3  W.  29th  St.,  N.  Y. 
Chain  Blocks. 

The  Yale  &  Towne  Mfg.  Co.,  9  Murray  St.,  N.  Y. 
Changeable  Directories,  for  Office  Buildings. 

U.  S.  Changeable  Sign  Co.,  150  Nassau  St.,  N.  Y. 
Chimney  Brick,  Perforated  Radial,  Manufacturers. 

National  Pyrogranite  Co.,  17  Battery  PI.,  N.  Y. 
Chimneys,  Self-sustaining  Steel. 

The  Wm.  B.  Pollock  Co.,  Youngstown,  O. 

The  Reeves  Bros.  Co.,  Alliance,  O. 

Walsh's  Holyoke  Steam  Boiler  Works,  Holyoke,  Mass- 
Chimneys,  Tall.— Radial  Brick  Systems,  see  also  p.  1229. 

Alphonse  Custodis  Chimney  Const.  Co.,  Bennett  Bldg.,  N.  Y. 

H.  R.  Heinicke,  160,  5th  Ave.,  N.  Y. 

Steinl  Improved  Chimney  Const.  Co.,  Birmingham,  Ala. 
Chimneys,  Tall. — Of  Reinforced  Concrete  (specialists). 

Weber  Steel-Concrete  Ohimriey  Co.,  Ashland  Bl'k,  Chicago,  111. 
Clocks,  Electric,  Programme,  and  Tower. 

Blodgett  Clock  Co.,  141  Franklin  St.,  Boston. 

Johnson  Service  Co.,  240  Fourth  Ave.,  N.  Y. 

The  Howard  Clock  Co.,  E.  Boston  and  New  York. 

Prentiss  Clock  Improvement  Co.,  304  Hudson  St.,  N.  Y. 
Clothes  Dryers. 

Chicago  Clothes  Dryer  Works,  346  Wabash  Ave.,  Chicago. 

Peck,  Williamson  Co.,  Cincinnati,  O. 

The  F.  M.  Watkins  Co.,  Cincinnati,  O. 
Conservatories  and  Horticultural  Buildings. 

Hitchings  &  Co.,  233  Mercer  St.    N.  Y. 

Lord  and  Burnham  Co.,  1133  Broadway,  N.  Y. 
Conveyors. 

Brown  Hoisting  Machinery  Co.,  Cleveland,  O. 

C.  W.  Hunt  Co.,  West  New  Brighton,  N.  Y. 

Lidgerwood  Mfg.  Co.,  New  York. 

Link-Belt  Machinery  Co.,  Chicago. 

Robbins  Conveying  Belt  Co.,  New  York. 

*  See  The  Buyers'  Reference  for  long  list  of  Manufacturers. 


1572  TRADE  REFERENCES. 

Cranes  ami  Hoists.*— See  also  Derricks. 

Brown  Hoisting  Machinery  Co.,  Cleveland,  O. 

General  Electric  Co.,  Schenectady,  N.  Y. 

Sprague  Electric  Co.,  New  York. 

Whiting  Foundry  Equipment  Co.,  Harvey,  111. 

Yale  &  Towne  Mfg.  Co.,  9  Murray  St.,  N.  Y. 
Creosoting  Works. 

American  Creosote  Works,  New  Orleans,  La. 

International  Creosoting  and  Construction  Co.,  Galveston,  Tex. 
Derricks.— See  also  Cranes  and  Hoists. 

American  Hoist  &  Derrick  Co.,  St.  Paul,  Minn. 
Domestic  Water  and  Light  Plants. — See  also  Pumps. 

Fairbanks,  Morse  &  Co.,  Monroe  St.,  Chicago. 

Electric  Blue  Printing;  Outfits,  for  making  blue  prints  by  means  of 
arc  lamps. 

General  Electric  Co.,  Schenectady,  N.  Y. 

J.  H.  Wagenhorst  &  Co.,  Mansfield,  O. 
Electric  Fans  and  Fan  Motors. 

General  Electric  Co.,  Schenectady,  N.  Y. 
Elevators.* 

Otis  Elevator  Co.,  principal  office  17  Battery  Place,  N.  Y. 

Reedy  Elevator  Co.,  New  York  &  Cincinnati,  O. 

Sprague  Elevator  Co.,  New  York. 

Standard  Plunger  Elevator  Co.,  New  York. 

Warner  Elevator  Mfg.  Co.,  Cincinnati,  O. 

Winslow  Elevator  and  Machinery  Co.,  Chicago. 
Fibre,  Hard,   in  Sheets.      For  insulating  under  columns,  etc. 

Delaware  Hard  Fibre  Co.,  Wilmington,  Del. 
Filters.* 

Albany  Filter  Co.,  New  York. 

Hygeia  Filter  Co.,  Detroit,  Mich. 

Wm.  B.  Scaife  &  Sons,  Pittsburg,  Pa. 

Fireproof  Doors  and  Shutters,  and    standard    fixtures    (underwriters' 
requirements). 

Coburn  Trolley  Track  Mfg.  Co.,  Holyoke,  Mass. 
Foundry  Equipment. 

Whiting  Foundry  Equipment  Co.,  Harvey,  111. 
Garbage  Furnaces. 

American  Process  Co.,  62  William  St.,  N.  Y. 

Morse-Boulger  Destroyer  Co.,  39  Cortlandt  St.,  N.  Y. 

Smith-Siemens  Garb.  Incin.  Furnaces,  141  Broadway,  N.  Y. 
Gasolene  Engines. 

De  La  Vergne  Machine  Co.,  E.  138th  St.,  N.  Y. 

Fairbanks,  Morse  &  Co.,  Monroe  St.,  Chicago. 
Hoists  (Pneumatic). — See  also  Cranes  and  Derricks. 

The  General  Pneumatic  Tool  Co.,  Montour  Falls,  N.  Y. 
Hot  Air  Pumping  Engines. 

Rider-Ericsson  Mfg.  Co.,  New  York,  Chicago,  and  Boston. 
Hydraulic  Rams. 

N.  O.  Nelson  Mfg.  Co.,  St.  Louis. 

U.  S.  Wind  Engine  &  Pump  Co.,  Batavia,  111. 
Ice   Machines. 

Remington  Machine  Co.,  Wilmington,  Del. 

The  Singer  Automatic  Ice  Machine  Co.,  Bridgeport,  Conn. 
Industrial  Railways  and  Equipment. 

Arthur  Koppel,  66  Broad  St.,  N.  Y. 

C.  W.  Hunt  Co.,  West  New  Brighton,  N.  Y. 

Wonham-Magor  Engineering  Co.,  29  Broadway,  N.  Y*, 
Insulating  Materials  for  Cold  Storage. 

Samuel  Cabot,  Boston. 

H.  W.  Johns-Manville  Co.,  100  William  St.,  N.  Y. 

Union  Fibre  Co.,  Winona,  Minn. 

Also  manufacturers  of  Mineral  Wool;  see  Buyers'  Reference. 

*  See  The  Buyers'  Reference  for  long  list  of  Manufacturers. 


TRADE  REFERENCES.  1573 

Jails  and  Jail   Cells. 

L.  Screiber  &  Sons  Co.,  Cincinnati,  O. 

The  Van  Dorn  Iron  Works  Co.,  Cleveland,  O.    • 
Laundry  Machinery. 

American  Laundry  Machinery  Co.,  42  Cortlaridt  St.,  N.  Y. 

Chicago  Clothes  Dryer  Works,  346  Wabash  Ave.,  Chicago. 

A.  T.  Hagen  Co.,  Chicago,  111. 

Steel  Roll  Mangle  Co.,  Chicago,  111. 

Troy  Laundry  Machinery  Co.,  Troy,  N.  Y. 
liihrary  Stacks. 

Art  Metal  Construction  Co.,  Jamestown,  N.  Y. 

Geo.  Stykeman,  280  Broadway,  N.  Y. 

J.  B.  &'J.  M.  Cornell,  26th  St.  &  llth  Ave.,  N.  Y. 

Library  Bureau,  530  Atlantic  Ave.,  Boston. 

Snead  Architectural  Iron  Works,  Louisville,  Ky. 

A.  B.  &  W.  T.  Westervelt,  102  Chambers  St.,  N.  Y. 
Lightning    Rods. 

Bacon  &  Co.,  Cleveland,  O. 

Bajohr  Lightning  Hod  Works,  St.  Louis,  Mo. 

Franklin  Lightning  Rod  Works,  St.  Louis,  Mo. 

E.  G.  Washburn  &  Co.,  New  York. 
Metal  Window  Frames  and  Sash. — See  p.  767. 
Parquet  Floors  and  Borders.* 

The  Interior  Hardwood  Co.,  Indianapolis,  Ind. 

S.  C.  Johnson  &  Son,  Racine,  Wis. 
Piling,  Concrete. 

Raymond  Concrete  Pile  Co.,  135  Adams  St.,  Chicago,  111. 

Simplex  Concrete  Piling  Co.,  915  Penn.  Building,  Philadelphia,  Pa. 

t  Crawford  Paving  Co.,  Home  Life  Building,  Washington,  D.  C. 

t  The  Foundation  Co.,  35  Nassau  St.,  N.  Y. 

t  The  Foundation  Co.,  McCague  Building,  Omaha,  Neb. 
Piling,  Sheet,  Interlocking  Steel. 

U.  S.  Steel  Piling  Co.,  135  Adams  St.,  Chicago,  111. 

Friestedt  Interlocking  Channel  Bar  Co.,  1408  Tribune  Bldg.,  Chicago,  III 
Pneumatic  Tools. 

Ingersoll-Sergeant  Drill  Co.,  The,  26  Cortlandt  St.,  N.  Y. 

Philadelphia  Pneumatic  Tool  Co.,  Philadelphia. 

Thos.  H.  Dallett  Co.,  Philadelphia,  Pa. 
Pumping  by  Compressed  Air. 

Ingersoll-Sergeant  Drill  Co.,  The,  26  Cortlandt  St.,  New  York 

Pneumatic  Engineering  Co.,  85  Cedar  St.,  N.  Y. 
Pumps  for  Domestic  Purposes.* 

The  American  Works,  Aurora,  111. 

The  Deming  Co.,  Salem,  O. 

Fairbanks,  Morse  &  Co.,  Monroe  St.,  Chicago. 

The  Goulds  Mfg.  Co.,  Seneca  Falls,  N.  Y. 

Rider-Ericsson  Mfg,  Co.  (Hot-Air),  New  York  and  Chicago. 
Refrigerators. — See  p.  1492. 
Revolving  Doors. 

Van  Kannel  Revolving  Door  Co.,  524  E.  134th  St.,  N.  Y. 
Rolling  Shutters   (Steel). 

Columbus  Steel  Rolling-Shutter  Co.,  Columbus,  O. 

Kinnear  Mfg.  Co.,  Columbus,  O. 

Rolling  Steel  Shutter  Works,  162  W.  27th  St.,  N.  Y 

Jas   G.  Wilson,  Mfg.  Co.,  3  W.  29th  St.,  N.  Y. 
Roofing  Tiles.*— See  p.  1430. 
Safes  and  Vaults.* 

Diebold  Safe  and  Lock  Co.,  Canton,  O. 

Hemng-Hall-Marvin  Safe  Co.,  Hamilton,  O. 

Victor  Safe  and  Lock  Co.,  Cincinnati,  O. 

*  See  The  Stivers'  Reference  for  long  list  of  Manufacturers, 
t  Licensed  by  the  Simplex  Concrete  Piling  Co. 


1574  TRADE  REFERENCES. 

Safety  Treads. 

American  Mason  Safety  Tread  Co.,  40  Water  St.,  Boston,  Mass. 

American  Pressed  Steel- Co.,  Witherspoon  Building,  Philadelphia. 

New  York  Belting  and  Packing  Co.,  New  York. 
Sash-lifting  Apparatus,  for  Monitor  windows,  greenhouses,  etc. 

The  G.  Drou ve  Co.,  Bridgeport,  Conn. 

Hitchinga  &  Co.,  233  Mercer  St.,  N.  Y. 

Lord  &  Burnham  Co.,  1133  Broadway,  N.  Y. 
Sash  Weights,  compressed  lead. 

Raymond  Lead  Co.,  Lake  &  Clinton  Sts.,  Chicago. 
Sewerage  Disposal  Apparatus. 

Newport  Foundry  and  Machine  Co.,  Newport,  R.  I. 
Snow  Guards. 

Folsom  Snow  Guard  Co.,  Roslinclale  (Boston),  Mass. 
Stand -pipes. 

The  Wm.  B.  Pollock  Co.,  Youngstown,  O. 

The  Reeves  Bros.  Co.,  Alliance,  O. 

Walsh's  Holyoke  Steam  Boiler  Works,  Holyoke,  Mass. 
Sun  Dials. 

E.  B.  Meyrowitz,  104  E.  23d  St.,  N.  Y. 
Swinging  Hose  Hacks,  for  use  in  connection  with  stand-pipes. 

H.  J.  M.  Howard,  915  E.  St.,  N.  W.,  Washington,  D.  C. 

Wirt  &  Knox  Mfg.  Co.,  22  N.  Fourth  St.,  Philadelphia,  Pa. 
Tall  Chimney  Construction. — See  p.  1229. 
Tanks,  Large   Wooden. 

W.  E.  Caldwell  Co.,  Louisville,  Ky. 

Flint  &  Walling  Mfg.  Co.,  Kendallville,  Ind. 

U.  S.  Wind  Engine  &  Pump  Co.,  Batavia,  111. 
Tanks,  Steel,  also  towers  for  supporting  Fame. 

Flint  &  Walling  Mfg.  Co.,  Kendallville,  Ind. 

Chicago  Bridge  and  Iron  Works.  105th  &  Troop  Sts.,  Chicago. 
Telephones,*  for  connecting  portions  of  large  buildings. 

De  Veau  Telephone  Mfg.  Co.,  27  Rose  St.,  N.  Y. 

Electric  Gas  Lighting  Co.,  113  Purchase  St.,  Boston. 

The  Simplex  Interior  Telephone  Co.,  19  E.  Third  St.,  Cincinnati. 
Thermostats    and  Temperature   Regulators.* 

Davis  &  Roesch  Temperature  Controlling  Co.,  136  Liberty  St.,  N.  Y. 

Howard  Thermostat  Co.,  Oswego,  N.  Y. 

Johnson  Electric  Service  Co.,  Milwaukee,  Wis. 

National  Regulator  Co.,  Chicago,  111. 
Tiles,  Hoofing — See  p.  1430. 
Tiles,  Rubber. 

Goodyear  Tire  &  Rubber  Co.,  Akron,  O. 

Gutta  Percha  &  Rubber  Mfg.  Co.,  New  York. 

Manhattan  Rubber  Mfg.  Co.,  New  York,  N.  Y. 

Mechanical  Rubber  Co.,  Chicago,  111. 

New  York  Belting  &  Packing  Co.,  New  York. 

Peerless  Rubber  Mfg.  Co.,  New  York,  N.  Y. 
Travelling  Cranes. — See  Cranes. 
Water  Proofing  for  Brick  and  Stone. 

Szerelmey  &  Co.,  Home  Life  Building,  Washington,  D.  C. 

Toch  Brothers,  470  West  Broadway,  N.  Y. 
AViiid   Mills. 

U.  S.  Wind  Engine  &  Pump  Co.,  Batavia,  111. 

Challenge  Wind  Mill  Co.,  Batavia,  111. 

Flint  &  Walling  Mfg.  Co.,  Kendallville,  Ind. 
Wire  Rope,  Wire  Rope   Tramways,  Transmission  of  Power  by. 

Broderick  &  Bascom  Rope  Co.,  St.  Louis,  Mo. 

A.  Leschen  &  Sons  Rope  Co.,t  St.  Louis,  Mo. 

John  A.  Roebling  Sons'  Co.,t  Trenton,  N.  J. 

The  Trenton  Iron  Co., f  Trenton,  N.  J. 

*  See  The  Buyers'  Reference  for  long  list  of  Manufacturers, 
t  Publish  valuable  pamphlets  on  these  subjects. 


GLOSSAEY 


CORINTHIAN      DORIC 
ABACUS. 


OF  TECHNICAL  TERMS,  ANCIENT  AND  MODERN,  USED  BY  ARCHITECTS, 
BUILDERS,  AND  DRAUGHTSMEN. 

(Compiled  by  the  author  from  various  sources.} 

Aaron's-Rod.— An  ornamental  figure  representing  a  rod  with  a  serpent 
twined  about  it.  It  is  sometimes  confounded  with  the  caduceus  of  Mercury. 
The  distinction  between  the  caduceus  and  the  Aaron's-rod  is  that  the  former 
has  two  serpents  twined  in  opposite  directions,  while  the  latter  nas  but  one. 

Abacus.— The  upper  member  of  the  capital  of  a  column.  It  is  sometimes 
equare  and  sometimes  curved,  forming  on  the  plan 
segments  of  a  circle  called  the  arch  of  the  abacus, 
and  is  commonly  decorated  with  a  rose  or  other  orna- 
ment in  the  centre,  having  the  angles,  called  horns 
of  the  abacus,  cut  off  in  the  direction  of  the  radius 
or  curve.  In  the  Tuscan  or  Doric,  it  is  a  square 
tablet ;  in  the  Ionic,  the  edges  are  moulded  ;  in  the 
Corinthian,  its  sides  are  concave  and  frequently 
enriched  with  carving.  In  Gothic  pillars  it  has  a 
great  variety  of  forms. 

Abbey. — A  term  for  the  church  and  other  build- 
ings used  by  conventual  bodies  presided  over  by  an 
abbot  or  abbess,  in  contradistinction  to  cathedral,  which  is  presided  over  by  a 
bishop  ;  and  priory,  the  head  of  which  was  a  prior  or  prioress. 

Abutment. — That  part  of  a  pier  from  which  the  arch  springs. 

Abuttals.— The  boundings  of  a  piece  of  land  on  other  land,  street,  river,  etc. 

Acanthus.— A  plant  found  in  the  south  of  Europe,  representations  of  whose 
leaves  are  employed  for  decorating  the  Corinthian  and 
Composite  capitals.    The  leaves  of  the  acanthus  are 
used  on  the  bell  of  the  capital,  and  distinguish  the  two 
rich  orders  from  the  three  others. 

Acroteria.— The  small  pedestals  placed  on  the  ex- 
tremities and  apex  of  a  pediment.  They  are  usually 
without  bases  or  plinths,  and  were  originally  intended 
to  receive  statues.  ACANTHUS. 

Aile,  Aisle. — The  wings;  inward  side  porticos  of  a  church;  the  inward 
lateral  corridors  which  enclose  the  choir,  the  presbytery,  and  the  body  of  the 
church  along  its  sides.  2.  Any  one  of  the  passages  in  a  church  or  hall  into  which 
the  pews  or  seats  open. 

Alcove.— The  original  and  strict  meaning  of  this  word,  which  is  derived  from 
the  Spanish  alcoba,  is  confined  to  that  part  of  a  bed-chamber  in  which  the  bed 
stands,  separated  from  the  other  parts  of  the  room  by  columns  or  pilasters.  It 
is  now  commonly  used  to  express  any  large  recess  in  a  room,  generally  sepa- 
rated by  an  arch. 

Alipterion,— In  ancient  Roman  architecture,  a  room  used  by  bathers  for 
anointing  themselves. 

1575 


1576  GLOSSARY. 

Almonry.— The  place  or  chamber  where  alms  were  distributed  to  the  poor  in 
churches,  or  other  ecclesiastical  building.  At  Bishopstone  Church,  Wiltshire, 
England,  it  is  a  sort  of  covered  porch  attached  to  the  south  transept,  but  not 
communicating  with  the  interior  of  the  church.  At  Worcester  Cathedral,  Eng- 
land, the  alms  are  said  to  have  been  distributed  on  stone  tables,  on  each  side, 
within  the  great  porch.  In  iarge  monastic  establishments,  as  at  Westminster, 
it  seems  to  have  been  a  separate  building  of  some  importance,  either  joining  the 
gate-house  or  near  it,  that  the  establishment  might  be  disturbed  as  little  as 
possible. 

Altar. — In  ancient  Roman  architecture,  a  place  on  which  offerings  or  sacri- 
fices were  made  to  the  gods.  In  Protestant  churches,  the  communion  table  is 
often  designated  as  the  Altar,  and  in  Roman  Catholic  churches  it  is  a  square 
table  placed  at  the  east  end  of  the  church  for  the  celebration  of  mass. 

Altar  of  Incense.— A  small  table  covered  with  plates  of  gold  on  which  was 
placed  the  smoking  censer  in  the  temple  at  Jerusalem. 

Altar-piece.— The  entire  decorations  of  an  altar  ;  a  painting  placed  behind  an 
altar. 

Altar-screen. — The  back  of  the  altar  from  which  the  canopy  was  suspended, 
and  separating  the  choir  from  the  lady  chapel  and  presbytery.  The  Altar-screen 
was  generally  of  stone,  and  composed  of  the  richest  tabernacle  work  of  niclies, 
finials,  and  pedestals,  supporting  statues  of  the  tutelary  saints. 

AltO-rilievo,— High  relief— a  sculpture,  the  figures  of  which  project  from 
the  surface  on  which  they  are  carved. 

Ainbo, — A  raised  platform,  a  pulpit,  a  reading-desk,  a  marble  pulpit— an  ob- 
long enclosure  in  ancient  churches,  resembling  in  its  uses  and  positions  the  mod- 
ern choir. 

Ambry, — A  cupboard  or  closet,  frequently  found  near  the  altar  in  ancient 
churches  to  hold  sacred  utensils. 

Ambulatory.— An  alley— a  gallery— a  cloister. 

Amphiprostylos.—  A  Grecian  temple  which  has  a  columned  portico  on  both 
ends. 

Amphitheatre.— A  double  theatre,  of  an  elliptical  form  on  the  plan,  for  the 
exhibition  of  the  ancient  gladiatorial  fights  and  other  shows.  Its  arena  or  pit,  in 
which  those  exhibitions  took  place,  was  encompassed  with  seats  rising  above 
each  other,  and  the  exterior  had  the  accommodation  of  porticos  or  arcades  for 
the  public. 

Amphora.— A  Grecian  vase  with  two  handles,  often  seen  on  medals. 

Ancones.— The  consoles  or  ornaments  cut  on  the  key-stones  of  arches  or  on 
the  sides  of  door-cases.  They  are  sometimes  made  use  of  to  support  busts  or 
other  figures. 

Angle-bar.— In  joinery,  an  upright  bar  at  the  angles  of  polygonal  windows  ; 
a  mullion. 

Angle-capital. — In  Greek  architecture,  those  Ionic  capitals  placed  on  the 
flank  columns  of  a  portico,  which  have  one  of  their  volutes  placed  horizontally 
at  an  angle  of  a  hundred  and  thirty-five  degrees  with  the  plane  of  the  frieze. 

Annulated  Columns.— Columns  clustered  together  by  rings  or  bands  ;  much 
used  in  English  architecture. 

Annular  Vault.— A  vault  rising  from  two  par- 
allel walls— the  vault  of  a  corridor.    Same  as  Barrel  Sg^  _^ 
Vault, 

Annulet.— A  small  square  moulding  used  to  sep- 
arate others.  The  fillet  which  separates  the  nut- 
ings  of  columns  is  sometimes  known  by  this  term. 


GLOSSARY. 


1577 


Anta,  Antae.— A  name  given  to  a  pilaster  when  attached  to  a  wall.  Vitruvius 
calls  pilasters  parastatce  when  insulated.  They  are  not  usually  diminished,  and 
in  all  Greek  examples  their  capitals  are  different  from  those  of  the  columns 
they  accompany. 

Antechamber.  —An  apartment  preceded  by  a  vestibule  and  from  which  is 
approached  another  room. 

Antechapel,— A  small  chapel  forming  the  entrance  to  another.  There  are 
examples  at  Merton  College,  Oxford,  and  at  King's  College,  Cambridge,  England, 
besides  several  others.  The  antechapel  to  the  lady-chapel  in  cathedrals  is 
generally  called  the  Presbytery. 

Antechoir.— The  part  under  the  rood  loft,  between  the  doors  of  the  choir 
and  the  outer  entrance  of  the  screen,  forming  a  sort  of  lobby.  It  is  also  called 
the  Fore-choir. 

Antefixa,— In  classical  architecture  (gargoyles,  in  Gothic  architecture),  the 

ornaments  of  lions''  and  other  heads  below  the  eaves  of  a 

temple,  through  channels  in  which,  usually  by  the  mouth,    ""  J$± 

the  water  is  carried  from  the  eaves.    By  some  this  term  is  /j£p 

applied  to  the  upright  ornaments  above  the  eaves  in  ancient    j  r    ^ ._JT~"  f^**' 
architecture,  which  hid  the  ends  of  the  Harmi  or  joint          ANTEFIXA 
tiles. 

Apophyge.— The  lowest  part  of  the  shaft  of  an  Ionic  or  Corinthian  column, 
or  the  highest  member  of  its  base  if  the  column  be  considered  as  a  whole.  The 
Apophyge  is  the  inverted  cavetto  or  concave  sweep,  on  the  upper  edge  of  which 
the  diminishing  shaft  rests. 

Apron. — A  plain  or  moulded  piece  of  finish  below  the  stool  of  a  window,  put 
on  to  cover  the  rough  edge  of  the  plastering. 

Apse.— The  semicircular  or  polygonal  termination  to  the  chancel  of  a  church. 

Apteral.— A  temple  without  columns  on  the  flanks  or  sides. 

Aqueduct.— An  artificial  canal  for  the  conveyance  of  water,  either  above  or 
under  ground.  The  Roman  aqueducts  are  mostly  of  the  former  construction. 

Arabesque. — A  building  after  the  manner  of  the  Arabs.  Ornaments  used  by 
the  same  people,  in  which  no  human  or  animal  figures  appear. 
Arabesque  is  sometimes  improperly  used  to  denote  a  species  of  or- 
naments  composed  of  capricious  fantastics  and  imaginary  repre- 
sentations of  animals  and  foliage  so  much  employed  by  the  Romans 
in  the  decorations  of  walls  and  ceilings. 

Arabian  Architecture.— A  style  of  architecture  the  rudiments 
of  which  appear  to  have  been  taken  from  surrounding  nations,  the 
Egyptians,  Syrians,  Chaldeans,  and  Persians.  The  best  preserved 
specimens  partake  chiefly  of  the  Grseco-Romati,  Byzantine,  and 
Egyptian.  It  is  supposed  that  they  constructed  many  of  their  finest 
buildings  from  the  ruins  of  ancient  cities. 

Araeostyle.— That  style  of  building  in  which  the  columns  are 
distant  from  one  another  from  four  to  five  diameters.  Strictly 
speaking,  the  term  should  be  limited  to  intercolumniation  of  four 
diameters,  which  is  only  suited  to  the  Tuscan  order. 

Araeosystylos.— That  style  of  building  in  which  four  columns 
are  used  in  the  space  of  eight  diameters  and  a  half  ;  the  central 
intercolumniation  being  three  diameters  and  a  half,  and  the  others  on  each 
side  being  only  half  a  diameter,  by  which  arrangement  coupled  columns  are 
introduced. 

Arbores.  —Large  bronze  candelabra,  in  the  shape  of  a  tree,  placed  on  the  floor 
of  ancient  churches,  so  as  to  appear  growing  out  of  it. 


ARABESQUE. 


1578 


GLOSSARY. 


Arcade,— A  range  of  arches,  supported  either 
on  columns  or  on  piers,  and  detached  or  attached 
to  the  wall. 

Arch.— In  building,  a  mechanical  arrange- 
ment of  building  materials  arranged  in  the  form 
of  a  curve,  which  preserves  a  given  form  when 
resisting  pressure,  and  enables  them,  supported 
by  piers  or  abutments,  to  carry  weights  and 
resist  pressure. 

Arch-buttress,— Sometimes  called   a  flying  ARCADE. 

buttress  ;  an  arch  springing  from  a  buttress  or  pier. 

Architrave. — That  part  of  an  entablature  which  rests  upon  the  capital  of  a 
column,  and  is  beneath  the  frieze. 

Architrave  Cornice. — An  entablature  consisting  of  an  architrave  and  cor- 
nice, without  the  intervention  of  the  frieze,  sometimes  introduced  when  incon- 
venient to  give  the  entablature  the  usual  height. 

Architrave  of  a  Door. — The  finished  work  surrounding  the  aperture  ;  the 
upper  part  of  the  lintel  is  called  the  traverse  ;  and  the  sides,  the  jambs. 

Archives. — A  repository  or  closet  for  the  preservation  of  writings  or  records. 

Archivolt. — A  collection  of  members  forming  the  inner  contour  of  an  arch, 
or  a  band  or  frame  adorned  with  mouldings  running  over  the  faces  or  the  arch- 
stones,  and  bearing  upon  the  imposts. 

Area. — The  superficial  contents  of  any  figure  ;  an  open  space  or  court  within 
a  building;  also,  an  uncovered  space  surrounding  the  foundation  walls  to  give 
light  to  the  basement. 

Arena. — The  plain  space  in  the  middle  of  the  amphitheatre  or  other  place  of 
public  resort. 

Arris.— The  meeting  of  two  surfaces  producing  an  angle. 

Arsenal. — A  public  storehouse  for  arms  and  ammunition. 

Artificer,  or  Artisan. — A  person  who  works  with  his  hands,  and  manufact- 
ures any  commodity  in  iron,  brass,  wood,  etc. 

Ashlar,  or  Ashler.— A  facing  made  of  squared  stones,  or  a  facing  made  of 
thin  slabs,  used  to  cover  walls  of  brick  or  rubble.  Coursed  ashlar  is  where  the 
stones  run  in  level  courses  all  around  the  building ;  random  asfdar,  where  the 
stones  are  of  different  heights,  but  level  beds.  2.  Common  freestones  of  small 
size,  as  they  come  from  the  quarry,  are  also  called  ashlar. 

Asphaltum. — A  kind  of  bituminous  stone,  principally  found  in  the  province 
of  Neufchatel.  Mixed  with  stone,  it  forms  an  excellent  cement,  incorruptible 
by  air  and  impenetrable  by  water. 

Astragal. -A  small  semicircular  moulding, 
sometimes  plain  and  sometimes  ornamented. 

Asymptote. — A  straight  line  which  continu- 
ally approaches  to  a  curve  without  touching  it. 

Atlases,  or  Atlantes.— Figures  or  half-figures 
of  men,  used  instead  of  columns  or  pilasters  to 
support  an  entablature  ;  called  also  Telamones. 

Atrium.— A  court  in  the  interior  division  of 
Roman  houses. 

Attached  Columns.  —  Those  which  project 
three-fourths  of  their  diameter  from  the  wall. 

Attic.—  A  low  story  above  an  entablature,  or 
above  a  cornice  which  limits  the  height  of  the 
main  part  of  an  elevation.  Although  the  term  is 


GLOSSARY.  1579 

evidently  derived  from  the  Greek,  we  find  nothing  exactly  answering  to  it  in 
Greek  architecture  ;  but  it  is  very  common  in  both  Roman  and  Italian  practice. 
What  are  otherwise  called  tholobates  in  St.  Peter's  and  St.  Paul's  Cathedrals 
are  frequently  termed  attics. 

Attic  Order. — A  term  used  to  denote  the  low  pilasters  employed  in  the 
decoration  of  an  attic  story. 

Attributes. — In  painting  and  sculpture,  symbols  given  to  figures  and  statues 
to  indicate  their  office  and  character. 

Auditory.— In  ancient  churches,  that  part  of  the  church  where  the  people 
usually  stood  to  be  instructed  in  the  Gospel,  now  called  the  nave. 

Aula.— A  court  or  hall  in  ancient  Roman  houses. 

Aviary.— A  large  apartment  for  breeding  birds. 

Azis.— The  spindle  or  centre  of  any  rotative  motion.  In  a  sphere,  an  imag- 
inary line  through  the  centre. 

Back-choir. — A  place  behind  the  altar  in  the  principal  choir,  in  which  there 
is,  or  was,  a  small  altar  standing  back  to  back  with  the  former. 

Backing  Of  a  Rafter  Or  Rib.— The  forming  of  an  upper  or  outer  surface, 
that  it  may  range  with  the  edges  of  the  ribs  or  rafters  on  either  side. 

Backing  of  a  Wall.— The  rough  inner  face  of  a  wall ;  earth  deposited  behind 
a  retaining  wall,  etc. 

Back  of  a  Window.  —That  piece  of  wainscoting  which  is  between  the  bottom 
of  the  sash  frame  and  the  floor. 

Balcony.— A  projection  from  the  face  of  a  wall,  supported  by  columns  or  con- 
soles, and  usually  surrounded  by  a  balustrade. 

Baldachin. — A  building  in  the  form  of  a  canopy,  supported  with  columns, 
and  serving  as  a  crown  or  covering  to  an  altar. 

Baluster. — A  small  pillar  or  column,  supporting  a  rail, 
of  various  forms,  used  in  balustrades. 

Baluster  Shaft.— The  shaft  dividing  a  window  in  Saxon 
architecture.  At  St.  Albans  are  some  of  these  shafts,  evi- 
dently out  of  the  old  Saxon  church,  which  have  been  fixed 
up  with  Norman  capitals. 

Balustrade. — A  series  of  balusters  connected  by  a  rail.. 

Band.— A  sort  of  flat  frieze  or  fascia  running  horizon- 
tally round  a  tower  or  other  parts  of  a  building,  particu- 
larly the  base  tables  in  perpendicular  work,  commonly  used 
with  the  long  shafts  characteristic  of  the  thirteenth  cen- 
tury. It  generally  has  a  bold,  projecting  moulding  above 
and  below,  and  is  carved  sometimes  with  foliages,  but  in  BALDACHIN. 

general  with  cusped  circles,  or  quatrefoils,  in  which  frequently  are  shields  of 
arms. 

Band  of  a  Column. — A  series  of  annulets  and  hollows  going  round  the  middle 
of  the  shafts  of  columns,  and  sometimes  of  the  entire  pier.  They  are  often  beau- 
tifully carved  with  foliages,  etc.,  as  at  Amiens.  In  several  cathedrals  there  are 
rings  of  bronze  apparently  covering  the  junction  of  the  frusta  of  the  columns. 
At  Worcester  and  Westminster  they  appear  to  have  been  gilt ;  they  are  there 
more  properly  called  Shaft-rings. 

Baptistery. — A  separate  building  to  contain  the  font,  for  the  rite  of  baptism. 
They  are  frequent  on  the  Continent ;  that  at  Rome,  near  St.  John  Lateran,  and 
those  at  Florence,  Pisa,  Pavia,  etc.,  are  all  well-known  examples.  The  only  ex- 
amples in  England  are  at  Cranbrook  and  Canterbury,  the  latter,  however,  is 
Bupposed  10  have  been  originally  part  of  the  treasury. 


1580 


GLOSSARY. 


Barbican.— An  outwork  for  the  defence  of  a  gate  or  drawbridge  :  also,  a  sort 
of  pent -house  or  construction  of  timber  to  shelter  warders  or  sentries  from 
arrows  or  other  missiles. 

Barge  Board.— See  Verge  Board. 

Bartizan. — A  small  turret,  corbelled  out  at  the  angle  of  a  wall  or  tower,  to  pro- 
tect a  warder  and  enable  him  to  see  around  him. 
They  generally  are  furnished  with  oylets  or  arrow- 
slits. 

Basement. — The  lower  part  of  a  building,  usu- 
ally in  part  below  the  grade  of  the  lot  or  street. 

Base  Mouldings.— The  mouldings  immediately 
above  the  plinth  of  a  wall,  pillar,  or  pedestal. 

Base  of  a  Column.  -That  part  which  is  between 
the  shaft  and  the  pedestal,  or,  if  there  be  no  pedes-  BARTIZAN. 

tal,  between  the  shaft  and  the  plinth.    The  Grecian  Doric  had  no  base,  and  the 
Tuscan  has  only  a  single  torus,  or  a  plinth. 

Basilica.— A  term  given  by  the  Greeks  and  Romans  to  the  public  buildings 
devoted  to  judicial  purposes. 

Bas-relief.— See  Basso-rilievo. 

Basse-cour.— A  court  separated  from  the  principal  one,  and  destined  for 
stables,  etc. 

Basso-rilievo,  or  Bas-relief.— -The  representations  of  figures  projected  from 
a  background  without  being  detached  from  it.  It  is  divided  into  three  parts  : 
Alto-rilievo,  when  the  figure  projects  more  than  one-half  ;  Mezzo-rilievo,  that  in 
which  the  figure  projects  one-half  ;  and  Basso-rilievo,  when  the  projection  of  the 
figure  is  less  than  one-half,  as  in  coins. 

Bat. — A  part  of  a  brick. 

Batten.  —Small  scantlings,  or  small  strips  of  boards,  used  for  various  purposes. 
2.  Small  strips  put  over  the  joints  of  sheathing  to  keep  out  the  weather. 

Batten-door. — A  door  made  of  sheathing,  secured  by  strips  of  board,  put 
crossways,  and  nailed  with  clinched  nails. 

Batter.— A  term  used  by  bricklayers,  carpenters,  etc.,  to  signify  a  wall,  piece 
of  timber,  or  other  material,  which  does  not  stand  upright,  but  inclines  from  you 
when  you  stand  before  it ;  but  when,  on  the  contrary,  it  leans  toward  you,  it  is 
said  to  overhang. 

Battlement. — A  parapet  with  a  series  of  notches  in  it,  from  which  arrows  may 
be  shot,  or  other  instruments  of  defence 
hurled  on  besiegers.  The  raised  portions 
are  called  merlons  ;  and  the  notches,  em- 
brasures or  crenelles.  The  former  were 
intended  to  cover  the  soldier  while  dis- 
charging his  weapon  through  the  latter. 
Their  use  is  of  great  antiquity;  they  are 
found  in  the  sculptures  of  Nineveh,  in  the 
tombs  of  Egypt,  and  on  the  famous  Fran- 
cois vase,  where  there  is  a  delineation  of 
the  siege  of  Troy.  In  ecclesiastical  architecture  the  early  battlements  have  small 
shallow  embrasures  at  some  distance  apart,  In  the  Decorated  period  they  are 
closer  together,  and  deeper,  and  the  mouldings  on  the  top  of  the  merlon  and  bot- 
tom of  the  embrasure  are  richer.  During  this  period,  and  the  early  part  of  the 
Perpendicular,  the  sides  or  cheeks  of  the  embrasures  are  perfectly  square  and 
plain.  In  later  times  the  monldinirs  were  continued  round  the  sides,  as  well  as 
at  top  and  bottom,  mitring  at  the  angles,  as  over  the  doorway  of  Magdalene  Col- 


BATTLEMENT. 


GLOSSARY.  1581 

lege,  Oxford,  England.  The  battlements  of  the  Decorated  and  later  periods  are 
often  richly  ornamented  by  panelling,  as  in  the  last  example.  In  castellated 
work  the  merlons  are  often  pierced  by  narrow  arrow-slits.  (See  Oylet.)  In  South. 
Italy  some  battlements  are  found  strongly  resembling  those  of  old  Rome  and 
Pompeii ;  in  the  Continental  ecclesiastical  architecture,  the  parapets  are  very 
rarely  embattled. 

Bay.— Any  division  or  compartment  of  an  arcade,  roof,  etc.  Thus  each  space, 
from  pillar  to  pillar,  in  a  cathedral,  is  called  a  bay,  or  severy. 

Bay  Window.— Any  window  projecting  outward  from  the  wall  of  a  buijding, 
either  square  or  polygonal  on  plan,  and  commencing  from  the  ground.  If  they 
are  carried  on  projecting  corbels,  they  are  called  Oriel  windows.  Their  use  seems 
to  have  been  confined  to  the  later  periods.  In  the  Tudor  and  Elizabethan  styles 
they  are  often  semicircular  in  plan,  in  which  case  some  think  it  more  correct  to 
call  them  Bow  Windows. 

Baza&r. — A  kind  of  Eastern  mart,  of  Arabic  origin. 

Bead.— A  circular  moulding.  When  several  are  joined,  it  is  called  Reeding  r 
when  flush  with  the  surface,  it  is  called  Quirk-bead  ;  and  when  raised,  Cock-bead. 

Beam. — A  piece  of  timber,  iron,  stone,  or  other  material,  placed  horizontally, 
or  nearly  so,  to  support  a  load  over  an  opening,  or  from  post  to  post. 

Bearing.— The  portion  of  a  beam,  truss,  etc.,  that  rests  on  the  supports. 

Bearing  Wall,  or  Partition.— A  wall  which  supports  the  floors  and  roofs  in 
a  building. 

Beaufet,  or  Buffet.— A  small  cupboard,  or  cabinet,  to  contain  china.  It  may 
either  be  built  into  a  wall,  or  be  a  separate  piece  of  furniture. 

Bed. — Iu  bricklaying  and  masonry,  the  horizontal  surfaces  on  which  the  stones 
or  bricks  of  walls  lie  in  courses. 

Bed  of  a  Slate.— The  lower  side. 

Bed  Mouldings.— Those  mouldings  in  all  the  orders  between  the  corona  and 
frieze. 

Belfry.— Properly  speaking,  a  detached  tower  or  campanile  containing  bells, 
as  at  Evesham,  England,  but  more  generally  applied  to  the  ringing-room  or  loft 
of  the  tower  of  a  church.  See  Tower. 

Bell-cot,  Bell-gable,  or  Bell-turret.— The  place  where  one  or  more  bells 
are  hung  in  chapels,  or  small  churches  which  have  no  towers.  Bell-cots  are 
sometimes  double,  as  at  Northborough  and  Coxwell,  England  ;  a  very  common 
form  in  France  and  Switzerland  admits  of  three  bells.  In  these  countries,  al=o, 
they  are  frequently  of  wood,  and  attached  to  the  ridge.  Those  which  stand  on , 
the  gable,  dividing  the  nave  from  the  chancel,  are  generally  called  Sanctus  Bells.  ( 
A  very  curious  and,  it  is  believed,  unique  example  at  Cleves  Abbey,  England,  juts 
out  from  the  wall.  In  later  times  bell-turrets  were  much  ornamented  ;  these  are 
often  called  Fleches. 

Bell  of  a  Capital.— In  Gothic  work,  immediately  above  the  necking  is  a  deep, 
hollow  curve  ;  this  is  called  the  bell  of  a  capital .  It  is  often  enriched  with  foli- 
ages. It  is  also  applied  to  the  body  of  the  Corinthian  and  Composite  capitals. 

Belt.— A  course  of  stones  or  brick  projecting  from  a  brick  or  stone  wall,  gen- 
erally placed  in  a  line  with  the  sills  of  the  windows  ;  it  is  either  moulded,  fluted, 
plane,  or  enriched  with  patras  at  regular  intervals.  Sometimes  called  Stone 
String. 

Belvedere,  or  Look-out.— A  turret  or  lantern  raised  above  the  roof  of  an 
observatory  for  the  purpose  of  enjoying  a  fino  prospect. 

Bema.— The  semicircular  recess,  or  hexedra,  in  the  basilica,  where  the  judges 
sat,  and  where  in  after-times  the  altar  was  placed.  It  generally  is  roofed  with  a 
haJLf-dome  or  concha.  The  seats  of  the  priests  were  against  the  wall,  looking 


1582  GLOSSARY, 

into  the  body  of  the  church,  that  of  the  bishop  beinsj  In  the  centre.  The  bema  5a 
generally  ascended  by  steps,  and  railed  off  by  cancelli. 

Bench  Table. — The  stone  seat  which  runs  round  the  walls  of  large  churches, 
and  sometimes  round  the  piers  ;  it  very  generally  is  placed  in  the  porches. 

Bevel.— An  instrument  for  taking  angles.  One  side  of  a  solid  body  is  said  to 
be  bevelled  with  respect  to  another,  when  the  angle  contained  between  those  two 
sides  is  greater  or  less  than  a  right  angle. 

Bezantee, — A  name  given  to  an  ornamented  moulding  much  used  in  the  Nor- 
man period,  resembling  bezants,  coins  struck  in  Byzantium. 

Billet.— A  species  of  ornamented  moulding  much  used  in  Norman,  and  some- 
times in  Early  English  work,  like  short  pieces  of  stick  cut  off  and  arranged  alter- 
nately. 

Blocking,  or  Blocking-course.— In  masonry,  a  course  of  stones  placed  on 
the  top  of  a  cornice  crowning  the  walls. 

Bond. — In  bricklaying  and  masonry,  that  connection  between  bricks  or  stones 
formed  by  lapping  them  upon  one  another  in  carrying  up  the  work,  so  as  to  form 
an  inseparable  mass  of  building,  by  preventing  the  vertical  joints  falling  over 
each  other.  In  brickwork  there  are  several  kinds  of  bond.  In  common  brick 
walls  in  every  sixth  or  seventh  course  the  bricks  are  laid  crossways  of  the  wall, 
called  Headers.  In  face  work,  the  back  of  the  face  brick  are  clipped  so  as  to 
get  in  a  diagonal  course  of  headers  behind.  In  Old  English  bond,  every  alternate 
course  is  a  header  course.  In  Flemish  bond,  a  header  and  stretcher  alternate 
in  each  course. 

Bond-stones.— Stones  running  through  the  thickness  of  the  wall  at  right 
angles  to  its  face,  in  order  to  bind  it  together. 

Bond-timbers.— Timbers  placed  in  a  horizontal  direction  in  the  walls  of  a 
brick  building  in  tiers,  and  to  which  the  battens,  laths,  etc.,  are  secured.  In  rub- 
ble work,  walls  are  better  plugged  for  this  purpose. 

Border.— Useful  ornamental  pieces  around  the  edge  of  anything. 

Boss.— An  ornament,  generally  carved,  forming  the  key-stone  at  the  intersec- 
tion of  the  ribs  of  a  groined  vault.  Early  Norman  vaults  have  no  bosses.  The 
carving  is  generally  foliage,  and  resembles  that  of  the  period  in  capitals,  etc. 
Sometimes  they  have  human  heads,  as  at  Notre  Dame  at  Paris,  and  sometimes 
grotesque  figures.  In  Later  Gothic  vaulting  there  are  bosses  at  every  intersection. 

Boutell.— The  mediaeval  term  for  a  round  moulding,  or  torus.  When  it  follows 
a  curve,  as  round  a  bench  end,  it  is  called  a  Roving  Boutell. 

Bow. — Any  projecting  part  of  a  building  in  the  form  of  an  arc  of  a  circle.  A 
bow,  however,  is  sometimes  polygonal. 

Bow  Window. — A  v/indow  placed  in  the  bow  of  a  building. 

Brace. — In  carpentry,  an  inclined  piece  of  timber,  used  in  trussed  partitions, 
or  in  framed  roofs,  in  order  to  form  a  triangle,  and  thereby  stiffen  the  framing. 
When  a  brace  is  used  by  way  of  support  to  a  rafter,  it  is  called  a  strut.  Braces 
in  partitions  and  span-roofs  are,  or  always  should  be,  disposed  in  pairs,  and 
introduced  in  opposite  directions. 

Brace  Mould.— [{]  Two  ressaunts  or  ogees  united  together  like  a  brace  in 
printing,  sometimes  with  a  small  bead  between  them. 

Bracket.— A  projecting  ornament  carrying  a  cornice.  Those  which  support 
vaulting  shafts  or  cross  springers  of  a  roof  are  more  generally  called  Corbels. 

Break. — Any  projection  from  the  general  surface  of  a  building. 

Breaking  Joint.— The  arrangement  of  stones  or  bricks  so  as  not  to  allow  two 
joints  to  come  immediately  over  each  other.  See  Band. 

Breast  of  a  Window.— The  masonry  forming  the  back  of  the  recess  and  the 
parapet  under  the  window-sill. 


GLOSSARY. 


1583 


Bressummer.— A  lintel,  beam,  or  iron  tie,  intended  to  carry  an  external 
wall  and  itself  supported  by  piers  or  posts  ;  used  principally  over  shop  win- 
dows. This  term  is  now  seldom  used,  the  word  beam,  or  girder,  taking  its  place. 

Bridging.— A  method  of  stiffening  floor  joist  and  partition  studs,  by  cutting 
pieces  in  between.    Cross  bridging  of  floor  joist  is  illus- 
trated in  cut. 

Bulwark.— In  ancient  fortification,  nearly  the  same  as 
Bastion  in  modern. 

Burse,  or  Bourse.— A  public  edifice  for  the  assembly  of 
merchant  traders  ;  an  exchange. 

Bust.— In  sculpture,  that  portion  of  the  human  figure 
which  comprises  the  head,  neck,  and  shoulders. 

Buttery.— A  store-room  for  provisions. 

Butt-joint.— Where  the  ends  of  two  pieces  of  timber 
or  moulding  butt  together.  CROSS-BRIDGING. 

Buttress.— Masonry  projecting  from  a  wall,  and  intended  to  strengthen  the 
same  against  the  thrust  of  a  roof  or  vault.  Buttresses  are 
no  doubt  derived  from  the  classic  pilasters  which  serve  to 
strengthen  walls  where  there  is  a  pressure  of  a  girder  or  roof- 
timber.  In  very  early  work  they  have  little  projection,  and,  in 
fact,  are  "  strippilasters."  In  Norman  work  they  are  wider, 
with  very  little  projection,  and  generally  stop  under  a  cornice 
or  corbel  table.  Early  English  buttresses  project  considerably, 
sometimes  with  deep  sloping  weatherings  in  several  stages, 
and  sometimes  with  gabled  heads.  Sometimes  they  are  cham- 
fered, and  sometimes  the  angles  have  jamb  shafts.  At  Wells 
and  Salisbury,  England,  they  are  richly  ornamented  with  can- 
opies and  statues.  In  the  Decorated  period  they  became  richly 
panelled  in  stages,  and  often  finish  with  niches  and  statues  and 
elegantly  carved  and  crocketed  gabelts,  as  at  York,  England. 
In  the  Perpendicular  period  the  weatherings  became  waved,  BUTTRESS 
and  they  frequently  terminate  with  niches  and  pinnacles. 

Buttress,  Flying.— A  detached  buttress  or  pier  of  masonry  at  some  distance 
from  a  wall,  and  connected  therewith  by  an  arch  or  por- 
tion of  an  arch,  so  as  to  discharge  the  thrust  of  a  roof  or 
vault  on  some  strong  point. 

Buttress  Shafts.— Slender  columns  at  the  angle  of 
buttresses,  chiefly  used  in  the  Early  English  period. 

Byzantine  Architecture.— A  style  developed  in  the 
Byzantine  Empire.  The  capitals  of  the  pillars  are  of 
endless  variety  and  full  of  invention  ;  some  are  founded 
on  the  Greek  Corinthian,  some  resemble  the  Norman 
and  the  Lombard  style,  and  so  varied  that  no  two  sides 
of  the  same  capital  are  alike.  They  are  comprised  under 
the  style  Romanesque,  which  comprehends  the  round- 
arch  style.  Byzantine  architecture  reached  its  height  in 
the  Church  of  St.  Sophia  at  Constantinople.  FLYING  BUTTRESS. 


Cabinet.— A  highly  ornamented  kind  of  buffet  or  chest  of  drawers  set  apart 
for  the  preservation  of  things  of  value. 

Cabling. — The  flutes  of  columns  are  said  to  be  cabled  when  they  are  partly 
occupied  by  solid  convex  masses,  or  appear  to  be  refilled  with  cylinders  aftet 
they  had  been  formed. 


1584  GLOSSARY. 

Caduceus.— Mercury's  rod,  a  wand  entwined  by  two  serpents  and  surmounted 
by  two  wings.    The  rod  represents  power  ;  the  serpents,  wisdom  ;  and 
the  wings,  diligence  and  activity. 

Caisson. — A  panel  sunk  below  the  surface  in  flat  or  vaulted  ceil-^ 
ings.    See  Cassoon. 

Caisson.— In  bridge  building,  a  chest  or  vessel  in  which  the  piers 
of  a  bridge  are  built,  gradually  sinking  as  the  work  advances  till  its 
bottom  comes  in  contact  with  the  bed  of  the  river,  and  then  the  sides 
are  disengaged,  being  so  constructed  as  to  allow  of  their  being  thus 
detached  without  injury  to  its  floor  or  bottom. 

Caliber,  or  Caliper.— The  diameter  of  any  round  body  ;  the  width 
of  the  mouth  of  a  piece  of  ordnance. 

Camber. — In  carpentry,  the  convexity  of  a  beam  upon  the  surface, 
in  order  to  prevent  its  becoming  concave  by  its  own  weight,  or  by  the 
burden  it  may  have  to  sustain. 

Campanile.— A  name  given  in  Italy  to  the  bell-tower  of  a  town-hall  or  church. 
In  that  country  this  is  almost  always  detached  from  the  latter. 

Candelabrum. — Stand  or  support  on  which  the  ancients  placed  their  lamps. 
Candelabra  were  made  in  a  variety  of  shapes  and  with  much  taste  and  elegance. 
The  term  is  also  used  to  denote  a  tall  ornamental  candlestick  with  several  arms, 
or  a  bracket  with  arms  for  candles. 

Canopy. — The  upper  part  or  cover  of  a  niche,  or  the  projection  or  ornament 
over  an  altar,  seat,  or  tomb.  The  word  is  supposed  to  be  derived  from  c<>no- 
pseum,  tlie  gauze  covering  over  a  bed  to  keep  off  the  gnats  ;  a  mosquito  curtain. 
Early  English  canopies  are  generally  simple,  with  trefoiled  or  cinque-foiled  head-  •, 
but  in  the  later  styles  they  are  very  rich,  and  divided  into  compartments  with 
pendants,  knots,  pinnacles,  etc.  The  triangular  arrangement  over  an  Early  Eng- 
lish and  Decorated  doorway  is  often  called  a  canopy.  The  triangular  canopies 
in  the  North  of  Italy  are  peculiar.  Those  in  England  are  generally  part  of  the 
arrangement  of  the  arch  mouldings  of  the  door,  and  form,  as  it  were,  the  hood- 
moulds  to  them,  as  at  York.  The  former  are  above  and  independent  of  the  door 
moulding:?,  and  frequently  support  an  arch  with  a  tympanum,  above  which  is  a 
triangular  canopy,  as  in  the  Duomo  at  Florence.  Sometimes  the  canopy  and 
arch  project  from  the  wall,  and  are  carried  on  small  jamb  shafts,  as  at  San  Pietro 
Martiro  at  Verona.  Canopies  are  often  used  over  windows,  as  at  York  Minster 
over  the  great  west  window,  and  lower  ties  in  the  towers.  These  are  triangular, 
while  the  upper  windows  in  the  towers  have  ogee  canopies. 

Capital.— The  upper  part  of  a  column,  pilaster,  pier,  etc.  Capitals  have  been 
used  in  every  style  down  to  the  present  time.  That  mostly  used  by  the  Egyp- 
tians was  bell-shaped,  with  or  without  ornaments.  The  Persians  used  the  double- 
headed  bell,  forming  a  kind  of  bracket  capital.  The  Assyrians  apparently  made 
use  of  the  Ionic  and  Corinthian,  which  were  developed  by  the  Greeks,  Romans, 
and  Italians  into  their  present  well-known  forms.  The  Doric  was  apparently  an 
invention  or  adaptation  by  the  Greeks,  and  was  altered  by  the  Romans  and 
Italians.  But  in  all  these  examples,  both  ancient  and  modern,  the  capitals  of  au 
order  are  all  of  the  same  form  throughout  the  same  building,  so  that  if  one  be 
seen  the  form  of  all  the  others  is  known.  The  Romanesque  architects  altered 
all  this,  and  in  the  carving  of  their  capitals  often  introduced  such  figures  and 
emblems  as  helped  to  tell  the  story  of  their  building.  Another  form  was  intro- 
duced by  them  in  the  curtain  capital,  rude  at  first,  but  afterward  highly  deco- 
rated. It  evidently  took  its  origin  from  the  cutting  off  of  the  lower  angles  of  a 
square  block,  and  then  rounding  them  off.  The  process  may  be  distinctly  seen, 
iii  its  gever^l  stages,  in  Mayence  Cathedral.  But  this  form  of  capital  was  more 


GLOSSARY.  1585 

fully  developed  by  the  Normans,  with  whom  it  became  a  marked  feature.  In 
the  early  English  capitals  a  peculiar  flower  of  three  or  more  lobes  was  used 
spreading  from  the  necking  upward  in  most  graceful  forms.  In  Decorated  and 
Perpendicular  styles  this  was  abandoned  in  favor  of  more  realistic  forms  of 
crumpled  leaves,  enclosing  the  bell  like  a  wreath.  In  each  style  bold  abacus 
mouldings  were  always  used,  whether  with  or  without  foliage. 

Caravansary.— A  huge,  square  building,  or  inn,  in  the  East,  for  the  recep- 
tion of  travellers  and  lodging  of  caravans. 

Carriage, — The  timber  or  iron  joist  which  supports  the  steps  of  a  wooden  stair. 

Carton,  or  Cartoon, — A  design  made  on  strong  paper,  to  be  transferred  on 
the  fresh  plaster  wall  to  be  afterward  painted  in  fresco ;  also,  a  colored  design 
for  working  in  mosaic  tapestry. 

Cartouche.— An  ornament  which  like  an  escutcheon,  a  shield  or  an  oval 
or  oblong  panel  has  the  central  part  plain,  and  usually  slightly  convex,  to  re- 
ceive an  inscription,  armorial  bearings,  or  an  ornamental  or  significant  piece 
of  painting  or  sculpture.  Frequently  used  in  French  Renaissance  and  Modern 
Architecture. 

Caryatides.— Human  female  figures  used  as  piers,  columns,   or  supports. 
Caryatic  is  applied  to  the  human  figure  generally,  when  used  in 
the  manner  of  caryatides. 

Cased. — Covered  with  other  materials,  generally  of  a  better 
quality. 

Casement.— A  glass  frame  which  is  made  to  open  by  turning  on 
hinges  affixed  to  its  vertical  edges. 

Cassoon,  or  Caisson. — A  deep  panel  or  coffer  in  a  soffit  or  ceil- 
ing. This  term  is  sometimes  written  in  the  French  form,  caisson  / 
sometimes  derived  directly  from  the  Italian  cassone,  the  augmenta- 
tive of  cosset,  a  chest  or  coffer. 

Cast. — A  term  used  in  sculpture  for  the  impression  of  any  figure 
taken  in  plaster  of  Paris,  wax,  or  other  substances. 

Catacombs. — Subterranean  places  for  burying  the  dead.  Those 
of  Egypt,  and  near  Rome,  are  believed  to  be  the  most  important.  CARYATID. 

Catafalco.—  An  ornamental  scaffold  used  in  funeral  solemnities. 

Cathedral. — The  principal  church,  where  the  bishop  has  his  seat  as  diocesan. 

Cauliculus. — The  inner  scroll  of  the  Corinthian  capital.  It  is  not  uncommon, 
however,  to  apply  this  term  to  the  larger  scrolls  or  volutes  also. 

Causeway. — A  raised  or  paved  way. 

CavettO.  —  A  concave  ornamental  moulding,  opposed  in  effect  to  the  ovolo— 
the  quadrant  of  a  circle. 

Ceiling.— That  covering  of  a  room  which  hides  the  joists  of  the  floor  above, 
or  the  rafters  of  the  roof.  Most  European  churches  have  either  open  roofs,  or 
are  groined  in  stone.  At  Peterborough  and  St.  Albans,  England,  there  are  verj 
old  flat  ceilings  of  boards  curiously  painted.  In  later  times  the  boarded  ceilings, 
and,  in  fact,  some  of  those  of  plaster,  have  moulded  ribs,  locked  with  bosses  at 
the  intersection,  and  are  sometimes  elaborately  carved.  In  many  English  churches 
there  are  ceilings  formed  of  oak  ribs,  filled  in  at  the  spandrels  with  narrow,  tiiln 
pieces  of  board,  in  exact  imitation  of  stone  groining.  In  the  Elizabethan  and 
subsequent  periods  the  ceilings  are  enriched  with  most  elaborate  ornaments  in 
stucco.  2.  Matched  and  beaded  boards,  planed  and  smoothed,  used  for  wain, 
scoting.  In  the  New  England  States  it  is  called  sheathing. 

Cenotaph.- An  honorary  tomb  or  monument,  distinguished  from  monuments 
in  being  empty,  the  individual  it  is  to  memorialize  having  received  interment 
elsewhere. 


1586  ,  GLOSSARY, 

Centaur.— A  poetical  imaginary  being  of  heathen  mythology,  half-man  and 
half  horse. 

Centring.— In  building,  the  frames  on  which  an  arch  is  turned. 

Chamfer,  Champfer,  or  Chaumfer.—  When  the  edge  or  arris  of  any  work  is 
cut-off  at  an  angle  of  45°  in  a  small  degree,  it  is  said  to  be;  chamfered  ;  if  to  a 
large  scale,  it  is  said  to  be  a  canted  corner.  The  chamfer  is  much  used  in  mediae- 
val work,  and  is  sometimes  plain,  sometimes  hollowed  out,  and  sometimes 
moulded. 

Chamfer  Stop.— Chamfers  sometimes  simply  ran  into  the  arris  by  a  plane 
face  ;  more  commonly  they  are  first  stopped  by  some  ornament,  as  by  a  bead  ; 
they  are  sometimes  terminated  by  trefoils,  or  cinque-foils,  double  or  single,  and 
in  general  form  very  pleasing  features  in  mediaeval  architecture. 

Chancel.  -A  place  separated  from  the  rest  of  a  church  by  a  screen.  The  word 
is  now  generally  used  to  signify  the  portion  of  an  Episcopal  or  Catholic  church 
containing  the  altar  and  communion  table. 

Chantry.— A  small  chapel,  generally  built  out  from  a  church.  They  generally 
contain  a  founder's  tomb,  and  are  often  endowed  places  where  masses  might  be 
said  for  his  soul.  The  officiator,  or  mass  priest,  being  often  unconnected  with 
the  parochial  clergy  ;  the  chantry  has  generally  an  entrance  from  the  outside. 

Chapel.— A  small,  detached  building  used  as  a  substitute  for  a  church  in  a 
large  parish  ;  an  apartment  in  any  large  building,  a  palace,  a  nobleman \s  house,  a 
hospital  or  prison,  used  for  public  worship  ;  or  an  attached  building  running  out 
of  and  forming  part  of  a  large  church,  generally  dedicated  to  different  saints, 
each  having  its  own  altar,  piscina,  etc.,  and  screened  off  from  the  body  of  the 
building. 

Chapter  House. — The  chamber  in  which  the  chapter  or  heads  of  the  monastic 
bodies  assembled  to  transact  business.  They  are  of  various  forms  ;  some  arc 
oblong  apartments,  some  octagonal,  and  some  circular. 

Chaptrel.— In  Gothic  architecture,  the  capital  of  a  pier  or  column  which  re- 
ceives an  arch. 

Charnel  House.— A  place  for  depositing  the  bones  which  might  be 
thrown  up  in  digging  graves.  Sometimes  it  was  a  portion  of  the 
crypt :  sometimes  it  was  a  separate  building  in  the  church-yard  ; 
sometimes  chantry  chapels  were  attached  to  these  buildings.  M. 
Viollct-le-Duc  has  given  two  very  curious  examples  of  ossvaires — 
one  from  Fleurance,  the  other  from  Faouet. 

Cherub— Gothic.— A  representation  of  an  infant's  head  joined  to 
two  wings,  used  in  the  churches  on  key-stones  of  arches  and  corbels.  CHAPTREL 

Chevron— Gothic.— An  ornament  turning  this  and  that  way,  like  a 
zigzag,  or  letter  Z. 

Chiaro-oscuro. — The  effects  of  light  and 
shade  in  a  picture. 

Choir.— That  part  of  a  church  or  monastery 
where  the  breviary  service,  or  "horae,"  is 
chanted.  , 

Church.— A  building  for  the  performance  of 
public  worship.  The  first  churches  were  built  on  CHEVRON. 

the  plan  of  the  ancient  basilicas,  and  afterward 

on  the  plan  of  a  cross  :  a  church  is  said  to  be  in  Greek  cross  when  the  length  of 
the  transverse  is  equal  to  that  of  the  nave  ;  in  Latin  cross,  when  the  nave  is 
longer  than  the  transverse  part ;  in  rotundo,  when  it  is  a  perfect  circle  ;  simple, 
when  it  has  only  a  nave  and  choir  ;  with  aisles,  when  it  has  a  row  of  porticos  in 
form  of  vaulted  galleries,  with  chapels  in  its  circumference. 


GLOSSARY. 


1587 


Ciborium.— A  tabernacle  or  vaulted  canopy  supported  on  shafts  standing  over 

the  high  altar. 

Cincture,— A  ring,  list,  or  fillet  at  the  top  and  bottom  of  a 
column,  serving  to  divide  the  shaft  of  the  column  from  its 
capital  and  base. 

Cinque-foil. — A  sinking  or  perforation,  like  a  flower,  of 
five  points  or  leaves,  as  a  quatre-foil  is  of  four.  The  points 
are  sometimes  in  a  circle,  and  sometimes  form  the  cusping  of 
a  head. 

Civic  Crown.— A  garland  of  oak-leaves  and  acorns,  given 

as  honorary  distinction  among  the  Romans  to  such  as  had  preserved  the  life 
of  a  fellow-citizen. 

Clere-story,  Clear-story.— When  the  middle  of  the  nave  of  a  church  rises 
above  the  aisles  and  is  pierced  with 
windows,  the  upper  story  is  thus 
called.  Sometimes  these  windows 
are  very  small,  being  mere  quatre- 
foils,  or  spherical  triangles.  In  large 
buildings,  however,  they  are  impor- 
tant objects,  both  for  beauty  and 
utility.  The  window  of  the  clere- 
stories of  Norman  work,  even  in  large 
churches,  are  of  less  importance  than 
in  the  later  styles.  In  Early  English 
they  became  larger  ;  and  in  the  Deco- 
rated they  are  more  important  still, 
being  lengthened  as  the  triforium 
diminishes.  In  Perpendicular  work 
the  latter  often  disappears  altogether, 
and  in  many  later  churches  the  clere- 
stories are  close  ranges  of  windows. 
The  word  clere-story  is  also  used  to 
denote  a  similar  method  of  lighting 
other  buildings  besides  churches,  es- 
pecially factories,  depots,  ehcds,  etc. 

Cloister.— An  enclosed  square,  like 
the  atrium  of  a  Roman  h«rase,  with  a 
walk  or  ambulatory  around,  sheltered 
by  a  roof,  generally  groined,  and  by 
tracery  windows,  which  were  more 
or  less  glazed. 

Close.— The  precinct  6f  a  cathedral 
or  abbey.  Sometimes  the  walls  are 
traceable,  but  now  generally  the 
boundary  is  only  known  by  tradi- 
tion. 

Close  String,  or  Box  String.— A 

method  of  finishing  the  outer  edge  of  buttress  .supporting  clew-story  ;  C,  vaulted 

.     roof  of  aisle  ;  D  D,  pier  dividing  nave  from 

stairs,  by  building  up  a  sort  of  curb  aisle  .  E)  vaulted  roof  of  nave, 
string  on  which  the    balusters    set, 
and  the  treads  and  risers  stop  against  it. 

Clustered. — In  architecture,  the  coalition  of  several  members  which  penetrate 
each  other. 


Bath  Abbey. 

FLYING   BUTTRESS    AND   CLERE-STOKY. 

A,   buttress    with  pinnacle ;    B,  flying 


1588 


GLOSSARY* 


Clustered  Column, — Several  slender  pillars  attached  to  each  other  so  as  to 
form  one.    The  term  is  used  in  Roman  architecture  to  denote  two 
or  four  columns  which  appear  to  intersect  each  other  at  the  angle  of 
a  building  to  answer  at  each  return. 

Coat. — A  thickness  or  covering  of  paint,  plaster,  or  other  work, 
done  at  one  time.  The  first  coat  of  plastering  is  called  the  scratch 
coat,  the  second  coat  (when  there  are  three  coats)  is  called  the  brown 
coat,  and  the  last  coat  is  variously  known  as  the  slipped  coat,  skim 
coat,  or  white  coat.  It  varies  in  composition  in  different  localities. 
Coffer.— A  deep  panel  in  a  ceiling. 

Coffer  Dam. — A  frame  used  in  the  building  of  a  bridge  in  deep 
water,  similar  to  a  caisson. 

Collar  Beam. — A  beam  above  the  lower  ends  of  the  rafters,  and 
spiked  to  them. 

Colonnade.— A  row  of  columns.    The  colonnade  is  termed,  accord- 
ing to  the  number  of  columns  which  support  the  entablature  :  Tetra-     COLUMNJ 
style,  when  there  are  four  ;  hexastyle,  when  six;  octostyle,  when 
eight,  etc.    When  in  front  of  a  building  they  are  termed  porticos  ;  when  surround- 
ing a  building,  peristyle  ;  and  when  double  or  more,  polystyle. 

Colosseum,  or  Coliseum.-  The  immense  amphitheatre  built  at  Rome  by  Fla- 
vius  Vespasian,  A.D.  72,  after  his  return  from  his  victories  over  the  Jews.    It 
would  contain  ninety  thousand   persons  sitting,   and  twenty  thousand  more 
standing.    The  name  is  now  employed 
to  denote  an  unusually  lar^e  audience 
building,   generally  of    a    temporary 
nature. 

Colossus. — The  name  of  a  brazen 
statue  which  was  erected  at  the 
entrance  of  the  harbor  at  Rhodes, 
one  hundred  and  five  feet  in  height. 
Vessels  could  sail  between  its  legs. 

Column.  —  A  round  pillar.  The 
parts  are  the  base,  on  which  it  rests ; 
its  body,  called  the  shaft  ;  and  the 
head,  called  the  capital.  The  capital 
finishes  with  a  horizontal  table,  called 
the  abacus,  and  the  base  commonly 
stands  on  another,  called  the  plinth. 
Columns  may  be  either  insulated  or 
attached.  They  are  said  to  be  at- 
tached or  engaged  when  they  form 
part  of  a  wall,  projecting  one-half  or 
more,  but  not  the  whole,  of  their 
substance. 

Common. — A  line,  angle,  surface, 
etc.,  which  belongs  equally  to  several 
objects.    Common  centring  is  a  cen- 
tring without    trusses,   having  a  tie 
beam'at  bottom.    Common  joists  are  SECTION  OP  COLUMN  AND  ENTABLATURE. 
the  beams  in  naked  flooring  to  which  (Divided  according  to  the  Tuscan  Order.) 
the  joists  are  fixed.    Common  rafters 
in  a  roof  are  those  to  which  the  laths  are  attached. 
Composite  Arch.— Is  the  pointed  or  lancet  arch. 


GLOSSARY.  1589 

Composite  Order.— The  most  elaborate  of  the  orders  of  classical  architecture. 

Concrete.— A  mass  composed  of  broken  stone,  sand,  and  hydraulic  cement, 
which  makes  a  sort  of  artificial  stone,  much  used  for  foundations  ;  a  finer  variety 
is  sometimes  used  in  blocks  for  building  houses. 

Conduit.— A  Jong  narrow  passage  between  two  walls  or  underground  for 
secret  communication  between  different  apartments  :  also,  acanal  or  pipe  for  the 
conveyance  of  water, 

Confessional.-  The  seat  where  a  priest  or  confessor  sits  to  hear  confessions. 

Conge.— Another  name  for  the  echinus  or  quarter  round. 

Conservatory. —A  building  for  the  protection  and  rearing  of  tender  plants, 
often  attached  to  a  house  as  an  apartment.  Also,  a  public  place  of  instruction, 
designed  to  preserve  and  perfect  the  knowledge  of  some  branch  of  learning  or 
the  fine  arts  ;  as,  a  conservatory  of  music. 

Consistory.— The  judicial  hall  of  the  College  of  Cardinals  at  Rome. 

Consol,  or  Console.— A  bracket  or  truss,  generally  with  scrolls  or  volutes  at  the 
two  ends,  of  unequal  size  and  contrasted,  but  con- 
nected by  a  flowing  line  from  the  back  of  the  upper  one 
to  the  inner  convolving  face  of  the  lower. 

Coping.— The  capping  or  covering  of  a  wall.  This 
is  of  stone,  weathered  to  throw  off  the  wet.  Jn  Nor- 
man times,  as  far  as  can  be  judged  from  the  little  there 
is  left,  it  was  generally  plain  and  flat,  and  projected 
over  the  wall  with  a  throating  to  form  a  drip  After- 
ward it  assumed  a  torus  or  bowtell  at  the  top,  and  be-  CONSOLES. 
came  deeper,  and  in  the  Decorated  period  there  were 

generally  several  sets-off.  The  copings  in  the  Perpendicular  period  assumed 
something  of  the  wavy  section  of  the  buttress  caps,  and  mitred  round  the  sides 
of  the  embrasure,  as  well  as  the  top  and  bottom. 

Corbel.— The  name,  in  medieval  architecture,  for  apiece  of  stone  iuttingoutof 
a  wall  to  carry  any  superincumbent  weight.  A  piece  of  timber  projecting  in  the 
game  way  was  called  a  tassel  or  a  bragger.  Thus,  the  carved  ornaments  from 
which  the  vaulting  shafts  spring  at  Lincoln  are  corbels.  Norman  corbels  are 
generally  plain  Jn  the  Early  English  period  they  are  sometimes  elaborately 
carved  They  sometimes  end  with  a  point,  apparently  growing  into  the  wall, 
or  forming  a  knot,  and  often  are  supported  by  angles  and  other  figures.  In 
the  later  periods  tlie  foliage  or  ornaments  resemble  those  in  the  capitals.  In 
modern  architecture,  a  short  piece  of  stone  or  wood  projecting  from  a  wall  to 
form  a  support,  generally  ornamented. 

Corbel  Out.— To  build  out  one  or  more  courses  of  brick  or  stone  from  the 
face  of  a  wall,  to  form  a  support  for  timbers. 

Corbel  Table.— A  projecting  cornice  or  parapet,  supported  by  a  range  of 
corbels  a  short  distance  apart,  which  carry  a  moulding,  above  which  is  a  plain 
piece  of  projecting  wall  forming  a  parapet,  and  covered  by  a  coping.  Sometimes 
small  arches  are  thrown  across  from  corbel  to  corbel,  to  carry  the  projection. 
Cornice. — The  projection  at  the  top  of  a  wall  finished  by  a  blocking-course, 
common  in  classic  architecture.  In  Norman  times,  the  wall  finished  with  a  cor- 
bel table,  which  carried  a  portion  of  plain  projecting  work,  which  was  finished 
by  a  coping,  and  the  whole  formed  a  parapet.  In  Early  English  times  the  para- 
pet was  much  the  same,  but  the  work  was  executed  in  a  much  better  way,  espe- 
cially the  small  arches  connecting  the  corbels.  In  the  Decorated  period  the  cor- 
bel table  was  nearly  abandoned,  and  a  large  hollow, with  one  or  two  subordinate 
mouldings,  substituted ;  this  is  sometimes  filled  with  the  ball  flowers,  and  some- 
times with  running  foliages.  In  the  Perpendicular  style  the  parapet  frequently 


1590  GLOSSARY. 

did  not  project  beyond  the  wall-line  below  ;  the  moulding  then  became  a  string 
(though  often  improperly  called  a  cornice),  and  was  .ornamented  by  a  quatre-foil, 
or  small  rosettes,  set  at  equal  intervals  immediately  under  the  battlements.  In 
many  French  examples  the  moulded  string  is  very  bold,  and  enriched  with  foli- 
age ornaments. 

Corona. — The  brow  of  the  cornice  which  projects  over  the  bed  mouldings  to 
throw  off  Che  water. 

Corridor,— A  long  gallery  or  passage  in  a  mansion  connecting  various  apart- 
ments and  running  round  a  quadrangle.  Any  long  passage-way  in  a  building. 

Countersink,— To  make  a  cavity  for  the  reception  of  a  plate  of  iron,  or  the 
hea.1  of  a  screw  or  bolt,  so  that  it  shall  not  project  beyond  the  face  of  the  work. 

Coupled  Columns. — Columns  arranged  in  pairs. 

Course. — A  continued  layer  of  bricks  or  stones  in  buildings  ;  the  term  is  also 
applicable  to  slates,  shingles,  etc. 

Court,— An  open  area  behind  a  house,  or  in  the  centre  of  a  building  and  the 
wings.  Courts  admit  of  the  most  elegant  ornamentations,  such  as  arcades, 
etc 

Cove— Coving.— The  moulding  called  the  cavetto,  or  the  scotia  inverted,  on  a 
large  ^cale,  and  not  as  a  mere  moulding  in  the  composition  of  a  cornice,  is  called 
a  cove  or  a  coving. 

Cove-bracketing.  —The  wooden  skeleton  mould  or  framing  of  a  cove,  applied 
chiefly  to  the  bracketing  of  a  cove  ceiling 

Cove  Ceiling.— A  ceiling  springing  from  the  walls  with  a  curve. 

Coved  and  Flat  Ceiling  —A  ceiling  in  which  the  section  is  the  quadrant  of 
a  circle,  rising  from  the  walls  and  intersecting  in  a  flat  surface. 

Cradling  —Timber  work  for  sustaining  the  lath  and  plaster  of  vaulted 
ceilings, 

Cresting,— An  ornamental  finish  in  the  wall  or  ridge  of  a  building,  which  is 
common  on  the  Continent  of  Europe  An  example  occurs  at  Exeter  Cathedral, 
the  ridge  of  which  is  ornamented  with  a  range  of  small  fleurs-de-lis  in  lead. 

Crocket—  An  ornament  running  up  the  sides  of  gablets,  hood -moulds,  pinna- 
c.es  spires  :  generally,  a  winding  stem  like  a  creeping  plant, 
with  flowers  or  leaves  projecting  at  intervals,  and  terminat- 
ing ID  a  finial 

Cross  -This  religious  symbol  is  almost  always  placed  on 
the  ends  of  gables,  the  summit  of  spires,  and  other  conspicu- 
ous piaces  of  old  churches      in  early  times  it  was  generally 
very  piam  often  a  simple  cross  in  a  circle.    Sometimes  they 
take  the  lorm  or  a  light  cross,  crosslet,  or  a  cross  in  a  square, 
In  the  Decorated  and  later  styles  they  became  richly  floriated, 
and  assumed  an  endless  variety  of  forms.    Of  memorial 
crosses  the  finest  examples  are  the  Eleanor  crosses,  erected 
•by  Edward  I.    Of  these  a  few  yet  remain,  one  of  which  has 
recently  been  reerected  at  Charing  Cross.    Preaching  crosses  were  often  setup 
bv  the  wayside  as  stations  for  preaching  ;  ihe  most  noted  is  that  in  front  of  St. 
Pau)  s,  England.    The  finest  remaining  sepulchral  crosses  are  toe  old  elaborately 
carved  examples  found  in  Ireland. 

Cross-aisle.— An  old  name  for  a  transept. 

Cross-springer.— The  transverse  ribs  of  a  vault, 

Cross -vaulting  —  A  common  name  given  to  groins  and  cylindrical  vaults. 

Crown  —In  architecture  the  uppermost  member  of  the  cornice-  called  also 
Corona  and  Larmier 

Crypt,  _A  vaulted  apartment  of  greater  or  less  size,  usually  under  the  choir. 


GLOSSARY.  1591 

Cupola.—  A  small  room,  either  circular  or  polygonal,  standing  on  the  top  of  a 
dome  By  some  it  is  called  a  Lantern. 

Curb  Boot,  or  Mansard  Roof,  -A  roof  formed  of  four  contiguous  planes,  each 
two  having  an  external  inclination 

Curtail  Step.  -The  first  step  in  a  stair,  which  is  generally  finished  in  the  form 
of  a  scroll. 

Cusp.—  The  point,  where  the  foliations  of  tracery  intersect.  The  earliest  ex- 
ample in  England  of  a  plain  cusp  is  probably  that  at  Pythagoras  School,  at,  Cam- 
bridge .  of  an  ornamental  cusp  at  Ely  Cathedral,  where  a  small  roll,  witha  rosette 
at  the  end.  is  formed  at  the  termination  of  a  cusp.  In  the  later  styles  the  termi- 
nations of  the  cusps  were  more  richly  decorated  ;  they  also  sometimes  terminate 
not  only  in  learves  or  foliages,  but  in  rosettes,  heads,  and  other  fanciful  orna- 
ments 

Cyclostyle.—  A  structure  composed  ot  a  circular  range  of  columns  without  a 
core  is  cyclostylar  ,  with  a  core.,  the  range  would  be  a  peristyle,  This  Is  the  spe- 
cies of  edifice  called  by  Vitruvms  monopterai 

Cyma.,—  The  name  of  a  moulding  of  very  frequent  use     It  is  a  simple,  waved 
line,  concave  at  one  end  and  convex  at  the  other,  like  an  r-  ------  -  .....  -  ----  <, 

Italic/,    When  the  concave  part  is  uppermost  it  is  called   "\ 
a  cyma  recta  ,  but  if  the  convexity  appear  above,  and  the 


concavity  below  it  is  then  a  cyma  reversa.  CYMA  RECTA. 

Cymatium,—  When  the  crowning  moulding  of  an  en 
tablature  is  of  the  cyma  form,  it  is  termed  the  Cyma 
tium 

Cyrtostyle  -A  circular  projecting  portico.    Such  are        CYMA  REVERSA. 
those  of  the  transept  entrances  to  St   Paul's  Cathedral.  London 

Dado,  or  Die  —The  vertical  face  of  an  insulated  pedestal  between  the  base  and 
cornice,  or  surbase.  It  is  extended  also  to  the  similar  part  of  ail  istereobates  which 
are  arranged  like  pedestals  in  Roman  and  Italian  architecture 

Dais  —A  part  of  the  floor  at  the  end  of  a  mediaeval  hall,  raised  a  step  above 
the  rest  of  the  floor.  On  this  the  lord  of  the  mansion  dined  with  his  friends 
at  the  great  table,  apart  from  the  retainers  and  servants.  In  mediaeval  nails 
there  was  generally  a  deep  recessed  bay  window  at  one  or  at  each  end  of  [he  dais. 
supposed  to  be  for  retirement,  or  greater  privacy  than  the  open  hall  could  afford. 
In  France  the  word  is  understood  as  a  canopv  or  hanging  over  a  seat;  probably 
the  name  was  given  from  the  fact  thac  the  seats  of  great  men  were  then  sur- 
mounted by  such  an  ornament 

Darby.—  A  flat  tool  used  by  plasterers  in  working,  especially  on  ceilings  It  is 
generally  about  seven  inches  wide  and  forty  -two  inches  Jong  with  two  handles  on 
the  back. 

Decastyle,—  A  portico  of  ten  columns  in  front 

Decorated  Style.—  The  second  stage  of  the  Pointed  or  Gothic  style  of  archi- 
tecture, considered  the  most  complete  and  perfect  development  of  Gothic  archi 
tecture,  the  best  examples  of  which  are  found  in  England 

Derni-me  tope.  —  The  half  of  a  metope,  which  is  found  at  the  retiring  or  pro 
jecting  angles  of  a  Doric  frieze. 

Dentil,—  The  cogged  or  toothed  member  common  in  the  bed-mould  of  a  Corin- 
thian entablature,  is  said  to  be  dentilled.  and  each  cog  or  tooth  is  called  a  dentil. 

Depressed  Arches,  or  Drop  Arches  —Those  of  less  pitch  than  the  equilateral 

Design,—  The  plans  elevations,  sections  and  whatever  other  drawings  may 
be  necessary  for  an  edifice,  exhibit  the  design  the  term  plan  navmg  a  restricted 
application  to  a  technical  portion  of  the  design 

Detail,—  As  used  by  architects,  detail  means  the  smaller  parts  into  which  a 


1592  GLOSSARY. 

composition  may  be  divided.  It  is  applied  generally  to  mouldings  and  other 
enrichments,  and  again  to  their  minutiae. 

Diameter.— The  line  in  a  circle  passing  through  its  centre,  or  thickest  part, 
which  gives  the  measure  proportioning  the  intercoluruniation  in  .some  of  the 
orders. 

Diameters.— The  diameters  of  the  lower  and  upper  ends  of  the  shaft  of  a 
column  are  called  its  inferior  and  superior  diameters,  respectively  ;  the  former  is 
the  greatest,  the  latter  the  least  diameter  of  the  shaft. 

Diaper.— A  method  of  decorating  a  wall,  panel,  stained  glass,  or  any  plain  sur- 
face, by  covering  it  with  a  continuous  design  of  flowers,  rosettes,  etc..  either  in 
squares  or  lozenges,  or  some  geometrical  form  resembling  the  pattern  of  a  dia- 
pered table-cloth,  from  which,  in  fact,  the  name  is  supposed  b>"  Home  to  have 
been  derived. 

Diastyle. — A  spacious  intercolumniation,  to  which  three  diameters  are  as- 
signed. 

Dipteros. — A  double-winged  temple.  The  Greeks  are  said  to  have  constructed 
temples  with  two  ranges  of  columns  all  around,  which  were  called  dipteroi.  A 
portico  projecting  two  columns  and  their  interspaces  is  of  dipterai  or  pseudo- 
dipteral  arrangement. 

Discharging  Arch.— An  arch  over  the  opening  of  a  door  or  window,  to  dis- 
charge or  relieve  the  superincumbent  weight  from  pressing  on  the  lintel. 

Distemper. — Term  applied  to  painting  with  colors  mixed  with  size  or  other 
glutinous  substance.  All  the  cartoons  of  the  ancients,  previous  to  the  year  1410, 
are  said  to  be  done  in  distemper. 

Distyle. — A  portico  of  two  columns.  This  is  not  generally  applied  to  the 
mere  porch  with  two  columns,  but  to  describe  a  portico  with  two  columns  in 
antis. 

Ditriglyph.— An  intercolumniation  in  the  Doric  order,  of  two  triglyphs. 

Dodecastyle.— A  portico  of  twelve  columns  in  front.  The  lower  one  of  the 
west  front  of  St.  Paul's  Cathedral,  London,  is  of  twelve  columns,  but  they  are 
coupled,  making  the  arrangement  pseudo-dodecastyle.  The  Chamber  of  Depu- 
ties in  Paris  has  a  true  dodecastyle. 

Dog-tooth.— A  favorite  enrichment  used  from  the  latter  part  of  the  Norman 
period  to  the  early  part  of  the  Decorated.  Jt  is  in  the  form  of  a  four  Jeaved 
flower,  the  centre  of  which  projects,  and  probably  was  named  from  its  resem- 
blance to  the  dog-toothed  violet. 

Dome. — A  cupola  or  inverted  cup  on  a  building.  The  application  of  this  term 
to  its  generally  received  purpose  is  from  the  Italian  custom  of  calling  an  archi- 
episcopal  church,  by  way  of  eminence,  II  Duomo,  the  temple  ;  for  to  one  of  that 
rank,  the  Cathedral  of  Florence,  the  cupola  was  first  applied  in  modern  practice. 
The  Italians  themselves  never  call  a  cupola  a  dome  ;  it  is  on  this  side  of  the  Alps 
the  application  has  arisen,  from  the  circumstance,  it  would  appear,  that  the  Ital- 
ians use  the  term  with  reference  to  those  structures  whose  most  distinguishing 
feature  is  the  cupola,  tholus,  or  (as  we  now  call  it)  dome. 

Domestic  Architecture.— That  branch  which  relates  to  private  buildings. 

Donjon. — The  principal  tower  of  a  castle,  generally  containing  the  prison. 

Door  Frame. — The  surrounding  case  into  and  out  of  which  the  door  shuts  and 
opens.  It  consists  of  two  upright  pieces,  called  jambs,  and  a  head,  generally  fixed 
together  by  morticesand  tenons,  and  wrought,  rebated,  and  beaded. 

Doric  Order.— The  oldest  of  the  three  orders  of  Grecian  architecture. 

Dormer  Window.— A  window  belonging  to  a  room  in  a  roof,  which  conse- 
quently projects  from  it  with  a  valley  gutter  on  each  side.  They  are  said  not  to 
be  earlier  than  the  fourteenth  century.  In  Germany  there  are  often  several  rows 


GLOSSARY,  1593 

of  dormers,  one  above  the  other  In  Italian  Gothic  they  are  very  rare  •  in  fact, 
the  former  have  an  unusually  stsep  root,  while  in  the  latter  country,  where  the 
Italian  tile  is  used,  the  roofs  are  rather  flat. 

Dormitory,  —A  room,  suite  of  rooms,  or  building  used  to  sleep  in.  The  name 
•was  first  applied  to  the  pJace  where  the  monks  slept  at  night.-  Jt  was  sometimes 
one  Jong  room  like  a  barrack,  and  sometimes  divided  into  a  succession  of  small 
chambers  or  cells.  The  dormitory  was  generally  on  the  first  floor,  and  connected 
with  the  church,  so  that  it  was  not  necessary  to  go  out- of  doors  to  attend  the 
nocturnal  services,  in  the  large  houses  of  the  Perpendicular  period,  and  also  in 
some  of  the  Elizabethan,  the  entire  upper  story  in  the  roof  formed  one  large 
apartment,  said  to  have  been  a  place  for  exercise  in  wet  weather,  and  also  foi  a 
dormitory  for  the  retainers  of  the  nousehold,  or  those  of  visitors. 

Double  Vault.— Formed  by  a  duplicate  wall  ;  wine  cellars  are  sometimes  so 
formed. 

Dovetailing.— In  carpentry  and  joinery,  the  method  of  fastening  boards  or 
other  timbers  together,  by  Jetting  one  piece  Into  another  in  the  form  of  the 
expanded  tail  of  a  dove. 

Dowel. — 1.  A  pin  Jet  into  two  pieces  of  wood  or  stone,  where  they  are  joined 
together.  2.  A  piece  of  wood  driven  into  a  wall  so  that,  other  pieces  may  be 
nailed  to  it.  This  is  also  called  plugging. 

Draw-bridge-  —  A  bridge  made  to  draw  up  or  let  down,  much  used  in  forti- 
fied places.  In  navigable  rivers,  the  arch  over  the  deepest  channel  is  made  to 
draw  or  revolve,  in  order  to  let  the  masts  of  ships  pass  through. 

Drawing-room. -A  room  appropriated  for  the  reception  of  company;  a 
room  to  which  company  withdraws  from  the  dining  room. 

Dresser.— A  cupboard  or  set  of  shelves  to  receive  dishes  and  cooking  utensils. 

Dressing.— Is  the  operation  of  squaring  and  smoothing  stones  for  building  ; 
also  applied  to  smoothing  lumber. 

Dressing-room. —An  apartment  appropriated  for  dressing  the  person. 

Drip.— A  name  given  to  the  member  of  a  cornice  which  has  a  projection 
beyond  the  other  parts  for  throwing  off  water  by  small  portions,  drop  by  drop. 
Jt  is  also  called  Larmier. 

Drip-stone.— The  label  moulding  which  serves  on  a  canopy  for  an  opening, 
and  to  throw  off  tne  rain.  ]t  is  also  called  Weather  Moulding. 

Drop-scene.— A  curtain  suspended  by  pulleys,  which  descends  cr  drops  in 
front  of  the  stage  in  a  theatre. 

Drum.— The  upright  part  of  a  cupoJa  over  a  dome  ;  also,  the  solid  part  or  vase 
of  the  Corinthian  and  Composite  capitals. 

Dry-rot.— A  rapid  decay  of  timber,  by  which  its  substance  is  converted  into 
a  dry  powder,  which  issues  from  minute  cavities  resembling  the  borings  of 
worms. 

Dungeon.— The  prison  in  a  castle  keep,  so  called  because  the  Norrnan  name 
for  the  latter  is  donjon,  and  the  dungeons,  or  prisons,  are  generally  in  its  lowest 
story. 

Dwarf  Wall.— The  walls  enclosing  courts  above  which  are  railings  of  iron  ; 
low  walls,  in  general,  receive  this  name. 

Eaves.— In  slating  and  shingling,  the  margin  or  iower  part  of  the  slating 
hanging  over  the  wall,  to  throw  the  water  off  from  the  masonry  or  brickwork. 

Echinus.— A  moulding  of  eccentric  curve,  gener- 
ally cut  (when  it  is  carved)  into  the  forms  of  eggs 
and  anchors  alternating,  whence  the  moulding  is 
called  by  the  name  of  the  more  conspicuous.  It  is 
the  same  as  Ovolo.  ECHINUS. 


1594  GLOSSARY. 

Edifice.— Is  synonymous  with  the  terms  building,  fabric,  erection,  but  is 
more  strictly  applicable  to  architecture  distinguished  for  size,  dignity,  and 
grandeur. 

Efflorescence.— In  architecture,  the  formation  of  a  whitish  loose  powder,  or 
crust,  on  the  surface  of  stone  or  brick  walls. 

Egyptian  Architecture.— The  earli3st  civilization  and  cultivation  of  the 
arts  was  in  Upper  Egypt.  The  most  remarkable  and  most  ancient  monuments 
of  the  Egyptians,  with  the  exception  of  the  pyramids,  are  nearly  all  included  in 
Upper  Egypt.  The  buildings  of  Egypt  are  characterized  by  solidity  and  mas- 
eiveness  of  construction,  originality  of  conception,  and  boldness  of  form.  The 
walls,  the  pillars,  and  the  most  sacred  places  of  their  religious  buildings  were 
ornamented  with  hieroglyphics  and  symbolical  figures,  while  the  ceilings  of  the 
porticos  exhibited  zodiacs  and  celestial  planispheres.  The  temples  of  Egypt 
were  generally  without  roofs,  and,  consequently,  the  interior  colonnades  had  no 
pediments,  supporting  merely  an  entablature,  composed  of  only  architrave,  frieze, 
and  cornice,  formed  of  immense  blocks  united  without  cement  and  ornamented 
with  hieroglyphics. 

Element.— The  outline  of  the  design  of  a  Decorated  window,  on  which  the 
centres  for  the  tracery  are  formed.  These  centres  will  all  be  found  to  fall  on 
points  which,  in  some  way  or  other,  will  be  equimultiples  of  parts  of  the  open- 
ings. To  draw  tracery  well,  or  understand  even  the  principles  of  its  composition, 
much  attention  should  be  given  to  the  study  of  the  element. 

Elevation. — The  front  facade,  as  the  French  term  it,  of  a  structure  ;  a  geo- 
metrical drawing  of  the  external  upright  parts  of  a  building. 

Embattlement, — An  indented  parapet  ;  battlement. 

Emblazon.— To  adorn  with  figures  of  heraldry,  or  ensigns  armorial. 

Embossing.— Sculpture  in  rilievo,  the  figures  standing  partly  out  from  the 
plane. 

Embrasure.— The  opening  in  a  battlement  between  the  two  raised  solid  por- 
tions or  merlons,  sometimes  called  a  crenelle. 

Encaustic. — Pertaining  to  the  art  of  burning  in  colors,  applied  to  painting  on 
glass,  porcelain,  or  tiles,  where  colors  are  fixed  by  heat  ;  hence,  encaustic  tiles, 
brick,  etc. 

Engaged  Columns. — Are  those  attached  to,  or  built  into  walls  or  piers,  a  por- 
tion being  concealed. 

Enrichment.— The  addition  of  ornament,  carving,  etc.,  to  plain  work  ;  decora- 
tion ;  embellishment. 

Ensemble. — Means  the  whole  work  or  composition  considered  together,  and 
not  in  parts. 

Entablature.— The  assemblage  of  parts  supported  by  the  column.  It  con- 
sists of  three  parts  :  the  architrave,  frieze,  and  cornice. 

Entail.— In  Gothic  architecture,  delicate  carving. 

Entasis. — The  swelling  of  a  column,  etc.  In  mediaeval  architecture,  some 
spires,  particularly  those  called  "broach  spires,"  have  a  slight  swelling  in  the 
sides,  but  no  more  than  to  make  them  look  straight  ;  for,  from  a  particular 
"deceptio  visus,"  that  which  is  quite  straight,  when  viewed  at  a  height,  looks 
hollow. 

Entry.— A  hall  without  stairs  or  vestibule. 

Epistyle.— This  term  may  with  propriety  be  applied  to  tht  whole  entablature, 
with  which  it  is  synonymous  ;  but  it  is  restricted  in  use  to  the  architrave,  or 
lowest  member  of  the  entablature. 

Escutcheon.— (Her.)  The  field  or  ground  on  which  a  coat-of-arms  is  repre- 
eented.  (Arch.)  The  shields  used  on  tombs,  in  the  spandrels  of  doors,  or  in 


GLOSSARY.  1595 

string-courses  ;  also,  the  ornamented  plates  from  the  centre  of  which  door  rings, 
knockers,  etc.,  are  suspended,  or  which  protect  the  wood  of  the  key-hole  from 
the  wear  of  the  key.  In  mediaeval  times  these  were  often  worked  in  a  very 
beautiful  manner. 

Etching.— A  mode  of  engraving  on  glass  or  metal  (generally  copper)  by  means 
of  lines,  eaten  in  or  corroded  by  means  of  some  strong  acid, 

Eustyle,— A  species  of  intercolumniation  to  which  a  proportion  of  two  diam- 
eters and  a  quarter  is  assigned.  This  term,  together  with  the  others  of  similar 
import — pycnostyle,  systyle,  diastyle,  and  araeostyle— referring  to  the  distances 
of  columns  from  one  another  in  composition,  is  from  Vitrnvius,  who  assigns  to 
each  the  space  it  is  to  express.  It  will  be  seen,  however,  by  reference  to  them 
individually,  that  the  words  themselves,  though  perhaps  sufficiently  applicable, 
convey  no  idea  of  an  exactly  defined  space,  and,  by  reference  to  the  columnar 
structures  of  the  ancients,  that  no  attention  was  paid  by  them  to  such  limita- 
tions. It  follows,  then,  that  the  proportions  assigned  to  each  are  purely  conven- 
tional, and  may  or  may  not  be  attended  to  without  vitiating  the  power  of  apply- 
ing the  terms.  Eustyle  means  the  best  or  most  beautiful  arrangement  ;  but,  as 
the  effect  of  a  columnar  composition  depends  on  many  things  besides  the  diam- 
eter of  the  columns,  the  same  proportioned  intercolumniation  would  look  well 
or  ill  according  to  those  other  circumstances,  so  that  the  limitation  of  Eustyle  to 
two  diameters  and  a  quarter  is  absurd. 

Extrados. — The  exterior  or  convex  curve  forming  the  upper  line  of  the  arch 
stones  ;  the  term  is  opposed  to  the  intrados,  or  concave  side. 

Eye  of  a  Dome. — The  aperture  at  its  summit. 

Eye  of  a  Volute. — The  circle  in  its  centre. 

Facade,  or  Face.— The  whole  exterior  side  of  a  building  that  can  be  seen  at 
one  view  ;  strictly  speaking,  the  principal  front. 

Face  Mould.— The  pattern  for  marking  the  plank  or  board  out  of  which  orna- 
mental hand-railings  for  stairs  and  other  works  are  cut. 

Fan  Tracery.— The  very  complicated  mode  of  roofing  used  in  the  Perpendicu- 
lar style,  in  which  the  vault  is  covered  by  ribs  and  veins  of  tracery. 

Fascia.— A  flat,  broad  member  in  the  entablature  of  columns  or  other  parts  of 
buildings,  but  of  small  projection.  The  architraves  in  some  of  the  orders  are 
composed  of  three  bands,  or  fasciae  :  the  Tuscan  and  the  Doric  ought  to  have  only 
one.  Ornamental  projections  from  the  walls  of  brick  buildings  over  any  of  the 
windows,  except  the  uppermost,  are  called  Fasciae. 

Fenestral.— A  frame,  or  "  chassis,"  on  which  oiled  paper  or  thin  cloth  was 
strained  to  keep  out  wind  and  rain  when  the  windows  were  not  glazed. 

Festoon. — An  ornament  of  carved  work,  representing  a  wreath  or  garland  of 
flowers  or  leaves,  or  both,  interwoven  with  each 
other.    It  is  thickest  in  the  middle,  and  small 
at  each  extremity,  where  it  is  tied,  a  part  often 
hanging  down  below  the  knot. 

Fillet.— A  narrow  vertical  band  or  listel    of 
frequent  use  in  congeries  <,f  mouldings,  to  sepa- 
rate and  combine  them,  and  also  to  give  breadth  FESTOON. 
and  firmness  to  the  upper  edge  of  a  crowning 

cyma  or  cavetto,  as  in  an  external  cornice.  The  narrow  slips  or  breadth  between 
the  flutes  of  Corinthian  and  Ionic  columns  are  also  called  fillets.  In  medieeval 
work  the  filiet  is  a  small,  flat,  projecting  square,  chiefly  used  to  separate  hollows 
and  rounds,  and  often  found  in  the  outer  parts  of  shafts  and  boutel  <.  In  this 
situation  the  centre  fillet  has  been  termed  a  keel,  and  the  two  side  ones,  wings ; 
but,  apparently,  this  is  not  an  ancient  usage. 


1596  GLOSSARY. 

Finial.— The  flower,  or  bunch  of  flowers,  with  which  a  spire,  pinnacle,  gablet, 
canopy,  etc.,  generally  terminates.  Where  there  are 
crockets,  the  finial  generally  bears  as  close  a  resem- 
blance as  possible  to  them  in  point  of  design.  They 
are  found  in  early  work  where  there  are  no  crockets. 
The  simplest  form  more  resembles  a  bud  about  to 
burst  than  an  open  flower.  They  soon  became  more 
elaborate,  as  at  Lincoln,  and  still  more,  as  at  West- 
minster and  the  Hotel  Cluny  at  Paris.  Many  per- 
pendicular finials  are  like  four  crockets  bound  to- 
gether. Almost  every  known  example  of  a  finial  has  PINIALS 
a  sort  of  necking  separating  it  from  the  parts  below. 

Fish-joint.— A  splice  where  the  pieces  are  joined  butt  end  to  end,  and  are  con- 
nected by  pieces)  of  wood  or  iron  placed  on  each  side  and  firmly  bolted  to  the 
timbers,  or  pier.es  joined.  (See  Chapter  XXIX.) 

Flags.— Flat  stones,  from  1  to  3  inches  thick,  for  floors. 

Flamboyant.— A  name  applied  to  the  Third  Pointed  style  in  France,  which 
seems  to  have  been  developed  from  the  Second,  as  the  English  Perpendicular 
was  from  the  Decorated.  The  great  characteristic  is,  that  tbe  element  of  the 
tracery  flows  upward  in  long  wavy  divisions  like  flames  of  fire.  In  most  cases, 
also,  every  division  has  only  one  cusp  on  each  side,  however  long  the  division 
may  be.  cThe  mouldings  seem  to  be  as  much  inferior  to  those  of  the  preceding 
period  as  the  Perpendicular  mouldings  were  to  the  Early  English,  a  fact  which 
seems  to  show  that  the  decadence  of  Gothic  architecture  was  not  confined  to  one 
country. 

Flange.— A  projecting  edge,  rib,  or  rim.  Flanges  are  often  cast  on  the  top  or 
bottom  of  iron  columns,  to  fasten  them  to  those  above  or  below  ;  the  top  and 
bottom  of  I-beams  and  channels  are  called  the  flange. 

Flashings.— Pieces  of  lead,  tin,  or  copper,  let  into  the  joints  of  a  wall  so  as 
to  lap  over  gutters  or  other  pieces  ;  also,  pieces  worked  in  the  slates  or  shingles 
around  dormers,  chimneys,  and  any  rising  part,  to  prevent  leaking. 

Flatting.— Painting  finished  without  leaving  a  gloss  on  the  surface. 

Fleche.— A  general  term  in  French  architecture  for  a  spire,  but  more  particu- 
larly used  for  the  small,  slender  erection  rising  from  the  intersection  of  the  nave 
and  transepts  in  cathedrals  and  large  churches,  and  carrying  the  sanctus  bell. 

Flight.— A  run  of  steps  or  stairs  from  one  landing  to  another. 

Floating. — The  equal  spreading  of  plaster  or  stucco  on  the  surface  of  walls, 
by  means  of  a  board  called  a  float ;  as  a  rule,  only  rough  plastering  is  floated. 

Floriated.— Having  florid  ornaments,  as  in  Gothic  pillars. 

Fleur-de-lis.— The  royal  insignia  of  France,  much  used  in  decoration. 

Flue.— The  space  or  passage  in  a  chimney  through  which  the  smoke  ascends. 
Each  passage  is  called  a  flue,  while  all  together  make  the  chimney. 

Flush.— The  continued  surface,  in  the  same  plane,  of  two  contiguous  masses. 

Flute.— A  concave  channel.  Columns  whose  shafts  are  channelled  are  said 
to  be  fluted,  and  the  flutes  are  collectively  called  Flutings. 

Flying  Buttress.— An  arched  buttress  used  when  extra  strength  was  required 
for  the  upper  part  of  the  wall  of  the  nave,  elc.,  to  resist  the  outward  thrust  of  a 
vaulted  ceiling.  The  flying  buttress  generally  rests  on  the  wall  and  buttress  of 
the  aisle. 

Foils.— The  small  arcs  in  the  tracery  of  Gothic  windows,  panels,  etc. 

Foliage. — An  ornamental  distribution  of  leaves  on  various  parts  of  buildings. 

Foliation.— The  use  of  small  arcs  or  foils  in  forming  tracery. 

Font,— The  vessel  used  in  the  rite  of  baptism.    The  earliest  extant  is  supposed 


GLOSSARY.  1597 

to  be  that  in  miichConstantine  is  said  to  have  been  baptized  ;  tins  is  a  porphyry 
labrum  from  a  Roman  bath.  Those  in  the  baptisteries  in  Italy  are  all  large,  and 
were  intended  for  immersion  ;  as  time  went  on,  they  seem  to  have  become 
smaller.  Fonts  are  sometimes  mere  plain  hollow  cylinders,  generally  a  little 
smaller  below  than  above  ;  others  are  massive  squares,  supported  on  a  thick  stem, 
round  which  sometimes  there  are  smaller  shafts.  In  the  Early  English  this  form 
is  still  pursued,  and  the  shafts  are  detached  ;  sometimes,  however,  they  are  hex- 
agonal and  octagonal,  and  in  this  and  the  later  styles  assume  the  form  of  a  vessel 
on  a  stem.  Norman  fonts  have  frequently  curious  carvings  on  them,  approach- 
ing the  grotesque  ;  in  later  times  the  foliages,  etc.,  partook  absolutely  of  the 
character  of  those  used  in  other  architectural  details  of  their  respective  periods. 
The  font  in  European  churches  is  usually  placed  close  to  a  pillar  near  the  en- 
trance, generally  that  nearest  but  one  to  the  tower  in  the  south  arcade  ;  or,  in 
large  buildings,  in  the  middle  of  the  nave,  opposite  the  entrance  porch,  and 
sometimes  in  a  separate  building.  In  Protestant  churches  in  this  country,  the 
font  is  generally  ^placed  inside  the  communion  rail,  or  on  the  steps  of  the 
chancel. 

Footings. — The  spreading  courses  at  the  base  or  foundation  of  a  wall.  When 
a  layer  of  different  material  from  that  of  the  wall  (as  a  bed  of  concrete)  is  used, 
it  is  called  the  Footing. 

Foundation. — That  part  of  a  building  or  wall  which  is  below  the  surface  of 
the  ground. 

Foxtail  Wedging.— Is  a  peculiar  mode  of  mortising,  in  which  the  end  of  the 
tenon  is  notched  beyond  the  mortise,  and  is  split  and  a  wedge  inserted,  which, 
being  forcibly  driven  in,  enlarges  the  tenon  and  renders  the  joint  firm  and  im- 
movable. 

Frame. — The  name  given  to  the  wood-work  of  windows,  doors,  etc.  ;  and  in 
carpentry,  to  the  timber  works  supporting  floors,  roofs,  etc. 

Framing. — The  rough  timber  work  of  a  house,  including  the  flooring,  roofing, 
partitioning,  ceiling,  and  beams  thereof. 

Freestone.— Stone  which  can  be  used  for  mouldings,  tracery,  and  other  work 
required  to  be  executed  with  the  chisel.  The  oolitic  and  sandstones  are  thot*e 
generally  included  by  this  term. 

Fresco.— The  method  of  painting  on  a  wall  while  the  plastering  is  wet.  The 
color  penetrates  through  the  material,  which,  therefore,  will  bear  rubbing  or  clean- 
ing to  almost  any  extent.  The  transparency,  the  chiaro-oscuro,  and  lucidity,  as 
well  as  force,  which  can  be  obtained  by  this  method,  cannot  be  conceived  unless 
the  frescos  of  Fra  Angelico  or  Raffaelle  are  studied.  The  word,  however,  is 
often  applied  improperly  to  painting  on  the  surface  in  distemper  or  body  color, 
mixed  with  size  or  white  of  egg,  which  gives  an  opaque  effect. 

Fret.— An  ornament  consisting  of  small  fillets  inter- 
secting each  other  at  right  angles. 

Frieze.— That  portion  of  an  entablature  between  the 
cornice  above  and  architrave  below.  It  derives  its 
name  from  being  the  recipient  of  the  sculptured  en- 
richments either  of  foliage  or  figures  which  may  be 
relevant  to  the  object  of  the  sculpture.  The  frieze  is  also  called  the  ZoOphorus. 

Frigidarium.— An  apartment  in  the  Roman  bath,  supplied  with  cold  water. 

Furniture.— A  name  given  to  the  metal  trimmings  of  doors,  windows,  and 
other  similar  parts  of  a  house.  In  this  country  the  word  "hardware"  is  more 
generally  used  to  denote  the  same  thing. 

Furr  ings.  -Flat  piece?  of  timber  used  to  bring  an  irregular  framing  to  an  even 
surface. 


1598  GLOSSARY. 

Gable.— When  a  roof  is  not  hipped  or  returned  on  itself  at  the  ends,  its  ends 
are  stopped  by  carrying  up  the  walls  under  them  in  the  triangular  form  of  the 
roof  itself.  This  is  called  the  gable,  or,  in  the  case  of  the  ornamental  and  orna- 
mented gable,  the  pediment.  Of  necessity,  gables  follow  the  angles  of  the  slope 
of  the  roof,  and  differ  in  the  various  styles.  In  Norman  work  they  are  generally 
about  half-pitch  ;  in  Early  English,  seldom  less  than  equilateral,  and  often  more. 
In  Decorated  work  they  become  lower,  and  still  more  so  in  the  Perpendicular 
style.  In  all  important  buildings  they  are  finished  with  copings  or  parapets.  In 
the  Later  Gothic  style*  gables  are  often  surmounted  with  battlements,  or  enriched 
with  crockets  ;  they  are  also  often  panelled  or  perforated,  sometimes  very  richly. 
The  gables  in  ecclesiastical  buildings  are  mostly  terminated  with  a  cross  ;  in 
others,  by  a  finial  or  pinnacle.  In  later  times  the  parapets  or  copings  were  broken 
into  a  sort  of  steps,  called  corbie  steps.  In  buildings  of  less  pretension  the  tiles 
or  other  roof  covering  passed  over  the  front  of  the  wall,  which  then,  of  course, 
had  no  coping.  In  this  case,  the  outer  pair  of  rafters  were  concealed  by  moulded 
or  carved  verge  boards. 

Gable  Window,— A  term  sometimes  applied  to  the  large  window  under  a 
gable,  but  more  properly  to  the  windows  in  the  gable  itself. 

Gabled  Towers,— Those  which  are  finished  with  gables  instead  of  parapets. 
Many  of  the  German  Romanesque  towers  are  gabled. 

Gablets. — Triangular  terminations  to  buttresses,  much  in  use  in  the  Early 
English  and  Decorated  periods,  after  which  the  buttresses  generally  terminate  in 
pinnacles.  The  Early  English  gablets  are  generally  plain,  and  very  sharp  in 
pitch.  In  the  Decorated  period  they  are  often  enriched  with  panelling  and 
crockets.  They  are  sometimes  finished  with  small  crosses,  but  oftener  with 
finials. 

Gain.— A  bevelled  shoulder  on  the  end  of  a  mortised  brace,  for  the  purpose  of 
giving  additional  resistance  to  the  shoulder. 

Gallery. — Any  long  passage  looking  down  into  another  part  of  a  building,  or 
into  the  court  outside.  In  like  manner,  any  stage  erected  to  carry  a  rood  or  an 
organ,  or  to  receive  spectators,  was  latterly  called  a  gallery,  though  originally  a 
loft.  In  later  times  the  name  was  given  to  any  very  long  rooms,  particularly 
those  intended  for  purposes  of  state,  or  for  the  exhibition  of  pictures. 

Gambrel  Roof.— A  roof  with  two  pitches,  similar  to  a  mansard  or  curb  roof. 

Gargoyle,  or  Gurgoyle.— The  carved  termination 
to  a  spout  which  conveyed  away  the  water  from  the 
gutters,  supposed  to  be  called  so  from  the  gurgling 
noise  made  by  the  water  passing  through  it.  Gar- 
goyles are  mostly  grotesque  figures. 

Gate-house.— A  building  forming  the  entrance  to 
a  town,  the  door  of  an  abbey,  or  the  enceinte  of  a 
castle  or  other  important  edifice.  They  generally  had 
a  large  gateway  protected  by  a  gate,  and  also  a  port- 
cullis, over  which  were  battlemented  parapets  with 
holes  (machicolations)  for  throwing  down  darts, 
melted  lead,  or  hot  sand  on  the  besiegers.  Gate- 
houses always  had  a  lodge,' with  apartments  for  the 
porter,  and  guard-rooms  for  the  soldiers  ;  and,  gener- 
ally, rooms  over  for  the  officers,  and  often  places  for  prisoners  beneath.  The  name 
is  now  commonly  applied  to  the  gate-keeper's  lodge  on  large  estates. 

Gauge,— 1.  To  mix  plaster  of  Paris  with  common  plaster  to  make  it  set  quick, 
called  gauged  mortar.  2.  A  tool  used  by  carpenters,  to  strike  a  line  parallel  to  tha 
edge  of  a  board. 


GLOSSARY.  1599 

Girder.— A  large  timber  or  iron  beam,  either  single  or  built  up,  used  to  sup- 
port joists  or  walls  over  an  opening. 

Glyph,— A  vertical  channel  in  a  frieze. 

Gothic  Style.— The  name  of  Gothic  was  given  to  the  various  Mediaeval  styles 
at  a  period  in  the  sixteenth  century  when  a  great  classic  revival  was  going  on, 
and  everything  not  classic  was  considered  barbarian,  or  Gothic.  The  term  was 
thus  originally  intended  as  one  of  stigma,  and,  although  it  conveys  a  false  idea  of 
the  character  of  the  Mediaeval  styles,  it  has  long  been  used  to  distinguish  them 
from  the  Grecian  and  Roman.  The  true  principle  of  Gothic  architecture  is  the 
vertical  division,  relation  and  subordination  of  the  different  parts,  distinct  and 
yet  at  unity  with  each  other,  and  while  this  principle  was  adhered  to,  Gothic 
architecture  may  be  said  to  have  retained  its  vitality. 

Grange.— A  word  derived  from  the  French,  signifying  a  large  barn  or  granary. 
Granges  were  usually  long  buildings  with  high  wooden  roofs,  sometimes  divided 
by  posts  or  columns  into  a  sort  of  nave  and  aisles,  with>valls  strongly  buttressed. 
In  England  the  term  was  applied  not  only  to  the  barns,  but  to  the  whole  of  the 
buildings  which  formed  the  detached  farms  belonging  to  the  monasteries  ;  in 
most  cases  there  was  a  chapel  either  included  among  these  or  standing  apart  as  a 
separate  edifice. 

Grillage. — A  framework  of  beams  laid  longitudinally  and  crossed  by  similar 
beams  notched  upon  them,  used  to  sustain  walls  to  prevent  irregular  settiDg. 

Grille. — The  iron-work  forming  the  enclosure  screen  to  a  chapel,  or  the  pro- 
tecting railing  to  a  tomb  or  shrine;  more  commonly  found  in  France  than  in 
England.  They  are  of  wrought  iron,  ornamented  by  the  swage  and  punch,  and 
put  together  either  by  rivets  or  clips.  In  modern  times  grilles  are  used  exten- 
sively for  protecting  the  lower  windows  in  city  houses,  also  the  glass  opening  in 
outside  doors. 

Groin. — By  some  described  as  the  line  of  intersection  of  two  vaults  where  they 
cross  each  other,  which  others  call  the  groin  point  ;  by  others  the  curved  section 
or  spandrel  of  such  vaulting  is  called  a  groin,  and  by  others  the  whole  system  of 
vaulting  is  so  named. 

Groin  Arch.— The  cross-rib  in  the  later  styles 
of  groining,  passing  at  right  angles  from  wall  to 
wall,  and  dividing  the  vault  into  bays  or  travees. 

Groin  Ceiling.— A  ceiling  to  a  building  com- 
posed of  oak  ribs,  the  spandrels  of  which  are  filled 
in  with  narrow,  thin  slips  of  wood.  There  are 
several  in  England  ;  one  at  the  Early  English 
church  at  Warmington,  and  one  at  Winchester 
Cathedral,  exactly  resembling  those  of  stone. 

Groin  Centring.— In  groining  without  ribs, 
the  whole  surface  is  supported  by  centring  during 
the  erection  of  the  vaulting.  In  ribbed  work  the 
stone  ribs  only  are  supported  by  timber  ribs  dur-  GROINED  VAULTING. 

ing  the  progress  of  the  work,  any  light  stuff  being  used  while  filling  in  the  span- 
drels. 

Groin  Point.— The  name  given  by  workmen  to  the  arris  or  line  of"  intersec- 
tion of  one  vault  with  another  where  there  are  no  ribs. 

Groin  Rib. — The  rib  which  conceals  the  groin  point  or  joints,  where  the  span- 
drels intersect. 

Groined  Vaulting.— The  system  of  covering  a  building  with  stone  vaults 
which  cross  and  intersect  each  other,  as  opposed  to  the  barrel  vaulting,  or  series 
of  arches  placed  side  by  side.  The  earliest  groins  are  plain,  without  any  ribs, 


1600  GLOSSARY. 

except  occasionally  a  sort  of  wide  band  from  wall  to  wall,  to  strengthen  the  con- 
struction. In  later  Norman  times  ribs  were  added  on  the  line  of  intersection  of 
Che  spandrels,  crossing  each  other,  and  having  a  boss  as  a  key  common  to  both  ; 
these  ribs  the  French  anthors  call  nerfs  en  ogive.  Their  introduction,  however, 
caused  an  entire  change  in  the  system  of  vaulting  ;  instead  of  arches  of  uniform 
thickness  an,d  great  weight,  these  ribs  were  first  put  up  as  the  main  construction, 
and  spandrels  of  the  lightest  and  thinnest  possible  material  placed  upon  them,  the 
haunches  only  being  loaded  sufficiently  to  counterbalance  the  pressure  from  the 
crown.  Shortly  after,  half -ribs  against  the  walls  (formerets)  were  introduced  to 
carry  the  spandrels  without  cutting  into  the  walling,  and  to  add  to  the  appearance. 
The  work  was  now  not  treated  as  continued  vaulting,  but  as  divided  into  bays, 
and  it  was  formed  by  keeping  up  the  ogive,  or  intersecting  ribs  and  their  bosses  ; 
a  sort  of  construction  having  some  affinity  to  the  dome  was  formed,  which  added 
much  to  the  strength  of  the  groining.  Of  course,  the  top  of  the  soffit  or  ridge  of 
the  vault  was  not  horizontal,  but  rose  from  the  level  of  the  top  of  the  formeret-rib 
to  the  boss  and  fell  again  ;  but  this  could  not  be  perceived  from  below.  As  this 
system  of  construction  got  more  into  use,  and  as  the  vaults  were  required  to  be  of 
greater  span  and  of  higher  pitch,  the  spandrels  became  larger,  and  required  more 
support .  To  give  this,  another  set  of  ribs  was  introduced,  passing  from  the  spring- 
ers of  the  ogive  ribs;  and  going  to  about  half-way  between  these  and  the  ogive, 
and  meeting  on  the  ridge  of  the  vault ;  these  intermediate  ribs  are  called  by  the 
French  tiercerons>  and  began  to  come  into  use  in  the  transition  from  Early 
English  to  Decorated.  About  the  same  period  a  system  of  vaulting  came  into 
use  called  hexpartite,  from  the  fact  that  every  bay  is  divided  into  six  compart- 
ments instead  of  four.  It  was  invented  to  cover  the  naves  of  churches  of  unu- 
sual width.  The  filling  of  the  spandrels  in  this  style  is  very  peculiar,  and,  where 
the  different  compartments  meet  at  the  ridge,  some  pieces  of  harder  stone  have 
been  used,  which  give  rather  a  pleasing  effect.  The  arches  against  the  wall, 
being  of  smaller  span  than  the  main  arche?,  cause  the  centre  springers  to  be  per- 
pendicular and  parallel  for  some  height,  and  the  spandrels  themselves  are  very 
hollow.  As  styles  progressed,  and  the  desire  for  greater  richness  increased, 
another  series  of  ribs,  called  liernes,  was  introduced  ;  these  passed  crossvvays 
from  the  ogives  to  the  tiercerons,  and  thence  to  the  doubleaux,  dividing  the 
spandrels  nearly  horizontally.  These  various  systems  increased  in  the  Perpen- 
dicular period,  so  that  the  vaults  were  quite  a  net-work  of  ribs,  and  led  at  last  to 
the  Tudor,  or,  as  it  is  called  by  many,  fan-tracery  vaulting.  In  this  system  the 
Tibs  are  no  part  of  the  real  construction,  but  are  merely  carved  upon  the  vous- 
eolrs,  which  form  the  actual  vaulting.  Fan  Tracery  is  so  called  because  the  ribs 
radiate  from  the  springers,  and  spread  out  like  the  sticks  of  a  fan.  These  later 
methods  are  not  strictly  groins,  for  the  pendentives  are  not  square  on  plan,  but 
circular,  and  there  is,  therefore,  no  arris  intersection  or  groin  point. 

Groins,  Welsh,  or  TTnderpitch.— When  the  main  longitudinal  vault  of  any 
groining  is  hisrher  than  the  cross  or  transverse  vaults  which  run  from  the  windows, 
the  system  of  vaulting  is  called  underpitch  groining,  or,  as  termed  by  the  work- 
men, Welsh  groining.  A  very  fine  example  is  at  St.  George's  Chapel,  Windsor, 
England. 

Groove.— In  joinery,  a  term  used  to  signify  a  sunk  channel  whose  section  is 
rectangular.  It  is  usually  employed  on  the  edge  of  a  moulding,  stile,  or  rail, 
etc.,  into  which  a  tongue  corresponding  to  its  section,  and  in  the  substance  of 
the  wood  to  which  it  is  joined,  is  inserted. 

Grotesque.— A  singular  and  fantastic  style  of  ornament  found  in  ancient 
buildings. 

Grotto,— An  artificial  cavern. 


GLOSSARY.  1601 

Ground  Floor.  —The  floor  of  a  building  on  a  level,  or  nearly  so,  with  the 

ground. 

Ground  Joist.— Joist  that  is  blocked  up  from  the  ground. 

Grounds.— Pieces  of  wood  embedded  in  the  plastering  of  walls  to  which 
skirting  and  other  joiner's  work  is  attached.  They  are  also  used  to  stop  the 
plastering  around  door  and  window  openings. 

Grouped  Columns.— Three,  four,  or  more  columns  put  together  on  the  same 
pedestal.  When  two  are  placed  together,  they  are  said  to  be  coupled. 

Grout.— Mortar  made  so  thin  by  the  addition  of 
water  that  it  will  run  into  all  the  joints  and  cavities 
of  the  mason-work,  and  fill  it  up  solid. 

Guilloche,  or  Guillochos. — An  interlaced  orna- 
ment like  net-work,  used  most  frequently  to  enrich 
the  torus. 

Guttfle. — The  small  cylindrical  drops  used  to  en- 
rch  the  mu tales  and  regulae  of  the  Doric  entabla- 
ture are  so  called. 

Gutter.— The  channel   for  carrying    off    rain-water,     g, ,„.„., 

The  mediaeval  gutters  differed  little  from  others,  except 
that  they  are  often  hollows  sunk  in  the  top  of  stone 
cornices,  in  which  case  they  are  generally  called  chan- 
nels in  English,  and  cheneaux  in  French. 

Gymnasium,— A  building  classed  in  the  first  jank  by  the  Greeks  ;  it  was  in 
them  they  instructed  the  youth  in  all  the  arts  of  peace  and  war  ;  a  building  for 
athletic  exercises. 

Hall.— 1.  The  principal  apartment  in  the  large  dwellings  of  the  Middle  Ages, 
used  for  the  purposes  of  receptions,  feasts  etc.  In  the  Norman  castle  the  hall 
was  generally  in  the  keep  above  the  ground  floor,  where  the  retainers  lived,  the 
basement  being  devoted  to  stores  and  dungeons  for  confining  prisoners.  Later 
halls— indeed,  some  Norman  halls  (not  in  castles)— are  generally  on  the  ground 
floor,  as  at  Westminster,  approached  by  a  porch  either  at  the  end,  as  in  this  last 
example,  or  at  the  side,  as  at  Guildhall,  London,  having  at  one  end  a  raised  dais 
or  estrade.  The  roofs  are  generally  open  and  more  or  less  ornamented.  In 
the  middle  of  these  was  an  opening  to  let  out  the  smoke,  though  in  later  times 
the  halls  have  large  chimney-places  with  funnels  or  chimney-shafts  for  this 
purpose.  At  this  period  there  were  usually  two  deeply  recessed  bay  windows  at 
each  end  of  the  dais,  and  doors  leading  into  the  withdrawing-rooms,  or  the 
ladies1  apartments  ;  they  are  also  generally  wainscoted  with  oak,  in  small  panels, 
to  the  height  of  five  or  six  feet,  the  panels  often  being  enriched.  Westminster 
Hall  was  originally  divided  into  three  parts,  like  a  nave  and  side  aisles,  as  are 
some  on  the  Continent  of  Europe.  2.  A  room  or  passage-way  at  the  entrance 
of  a  house,  or  suite  of  chambers.  3.  A  place  of  public  assembly,  as  a  town-hall, 
a  music-hall. 

Halving.— The  junction  of  two  pieces  of  timber,  by  letting  one  into  the 
other. 

Hammer  Beam.— A  beam  in  a  Gothic  roof,  not  extending  to  the  opposite 
side  ;  a  beam  at  the  foot  of  a  rafter. 

Hanging  Buttress. — A  buttress  not  rising  from  the  ground,  but  supported 
on  a  corbel,  applied  chiefly  as  a  decoration  and  used  only  in  the  Decorated  and 
Perpendicular  style. 

Hanging  Stile.— Of  a  door,  is  that  to  which  the  hinges  are  fixed. 

Hangings,— Tapestry ;   originally  invented  to  hide  the  coarseness  of  the 


1602 


GLOSSARY. 


walls  of  a  chamber.    Different  materials  were  employed  for  this  pnrpose,  some 
of  them  exceedingly  costly  and  beautifully  worked  in  figures,  gold  and  silk. 

Hatching. — Drawing  parallel  lines  close  together  for  the  purpose  of  indicat- 
ing a  section  of  anything.  The  lines  are  generally  drawn  at  an  angle  of  456 
with  a  horizontal. 

Haunches.— The  sides  of  an  arch,  about  half-way  from  the  springing  to  the 
crown. 

Headers. — In  masonry,  are  stones  or  bricks  extending  over  the  thickness  of  a 
wall.  In  carpentry,  the  large  beam  into  which  the  common  joists  are  framed  in 
framing  openings  for  stairs,  chimneys,  etc. 

Heading  Courses.— Courses  of  a  wall  in  which  the  stone  or  brick  are  afl 
headers. 

Head-way. — Clear  space  or  height  under  an  arch,  or  over  a  stairway,  and  the 
like. 

Heel.— Of  a  rafter,  the  end  or  foot  that  rests  upon  the  wall  plate. 

Height.— Of  an  arch,  a  line  drawn  from  the  middle  of  the  chord  to  the  in- 
trados. 

Helix.— A  small  volute  or  twist  like  a  stalk,  representing  the  twisted  tops  of 
the  acanthus,  placed  under  the  abacus  of  the  Corinthian  capital. 

Hermes. — A  rough  quadrangular  stone  or  pillar,  having  a  head,  usually  of 
Hermes  or  Mercury,  sculptured  on  the  top,  without  arms  or 
body,  placed  by  the  Greeks  in  front  of  buildings. 

Herring-bone  Work. — Bricks,  tile,  or  other  materials  ar- 
ranged diagonally  in  building. 

Hexastyle.— A  portico  of  six  columns  in  front  is  of  this 
description. 

High  Altar. — The  principal  altar  in  a  cathedral  or  church. 
Where  there  is  a  second,  it  is  generally  at  the  end  of  the  choir 
or  chancel,  not  in  the  lady  chapel. 

Hip-knob.— The  finial  on  the  hip  of  a  roof,  or  between  the 
barge  boards  of  a  gable. 

Hip-roof.— A  roof  which  rises  by  equally  inclined  planes 
from  all  four  sides  of  the  building. 

Hippodrome.— A  place  appropriated  by  the  ancients  for 
equestrian  exercises. 

Hips.— Those  pieces  of  timber  placed  in  an  inclined  position 
at  the  corners  or  angles  of  a  hip-roof. 

Hood-mould.— A  word  used  to  signify  the  drip-stone  for 
label  over  a  window  or  door  opening,  whether  inside  or  HERMES. 

out. 

Hotel  de  Ville.— The  town-hall,  or  guild-hall,  in  France,  Germany,  and 
Northern  Italy.  The  building,  in  general,  serves  for  the  admini  stration  of  justice, 
the  receipt  of  town  dues,  the  regulation  of  markets,  the  residence  of  magistrates, 
barracks  for  police,  prisons,  and  all  other  fiscal  purposes.  As  may  be  imagined, 
they  differ  very  much  in  different  towns,  but  they  have  almost  invariably 
attached  to  them,  or  closely  adjacent,  a  large  clock-tower  containing  one  or 
more  bells,  for  calling  the  people  together  on  special  occasions. 

Hotel  Dieu.— The  name  for  a  hospital  in  mediaeval  times.  In  England  there 
are  but  few  remains  of  these  buildings,  one  of  which  is  at  Dover  ;  in  France 
there  are  many.  The  most  celebrated  is  the  one  at  Angers,  described  by  Parker. 
They  do  not  seem  to  differ  much  in  arrangement  of  plan  from  those  in  modem 
days,  the  accommodation  for  the  chaplain,  medicine,  nurses,  stores,  etc.,  being 
much  the  same  in  all  ages,  except  that  in  some  of  the  earlier,  instead  of  the  sick 


GLOSSARY.  1603 

being  placeu  in  long  wards  like  galleries,  as  is  now  done,  they  occupied  large 
buildings,  with  naves  and  side  aisles,  like  churches. 

Housing.— The  space  taken  out  of  one  solid  to  admit  the  insertion  of  another, 
The  base  on  a  stair  is  generally  housed  into  the  treads  and  risers  ;  a  niche  for  a 
etatue. 

Hypsethros.— A  temple  open  to  the  air,  or  uncovered.  The  term  may  be  the 
more  easily  understood  by  supposing  the  roof  removed  from  over  the  nave  of  a 
church  in  which  columns  or  piers  go  up  from  the  floor  to  the  ceiling,  leaving  the 
aisles  still  covered. 

Hypogea. — Constructions  under  the  surface  of  the  earth,  or  in  the  sides  of  a 
hill  or  mountain. 

Ichnography.— A  horizontal  section  of  a  building  or  other  object,  showing  its 
true  dimensions  according  to  a  geometric  scale  ,  a  ground  plan. 

Impluvium. — The  centra?  part  of  an  ancient  Roman  court,  which  was  un- 
covered. ; 

Impost. — A  term  in  classic  architecture  for  the  horizontal  mouldings  of  piers 
or  pilasters,  from  the  top  of  which  spring  the  archivoits  or  mouldings  which  go 
round  the  arch. 

In  Antis.— When  there  are  two  columns  between  the  antse  of  the  lateral  walls 
and  the  cella. 

Incise.— To  cut  in  ;  to  carve  :  to  engrave. 

Indented.— Toothed  together. 

Inlaying.  —Inserting  pieces  of  ivory,  metal,  or  choice  woods,  or  the  like,  into 
a  groundwork  of  some  other  material,  for  ornamentation. 

Insulated.— Detached  from  another  building.  A  church  is  insulated,  when 
not  contiguous  to  any  other  edifice.  A  column  is  said  to  be  insulated,  when 
standing  free  from  the  wall ,  thus,  the  columns  of  peripteral  temples  were  insu- 
lated. 

Intaglio.— A  sculpture  or  carving  in  which,  the  figures  are  sunk  below  the  gen- 
eral  surface,  such  as  a  seal  the  impression  of  which  in  wax  is  in  bas-relief  ; 
opposed  to  Cameo. 

Intercolumniation.— Tie  distance  from  column  to  column,  the  clear  space 
between  columns. 

Interlaced  Arches.— Arches  where  one  passes  over  two  openings,  and  they 
consequently  cut  or  intersect  each  other. 

Intrados.— Of  an  arch,  tne  inner  or  concave  curve  of  the  arch  stones. 

Inverted  Arches.— Those  whose  key  stone  or  brick  is  the  lowest  in  the 
arch. 

Ionic  Order, — One  of  the  orders  of  Classical  architecture. 

Iron  Work.— In  mediaeval  architecture,  as  an  ornament,  is  chiefly  confined  to 
the  hinges,  etc.,  01  doors  and  ol  church  chests,  etc.  In  some  instances  not  only 
do  the  hinges  become  a  mass  of  scroll  work,  but  the  surface  of  the  doors  is 
covered  by  similar  ornaments.  In  almost  all  styles  the  smaller  and  less  important 
doors  had  merely  plain  strap  hinges,  terminating  in  a  few  bent  scrolls,  and  lat- 
terly in  fleurs-de-lis.  Escutcheon  and  ring  handles,  and  the  other  furniture,  par- 
took more  or  less  of  the  character  of  the  time,,  On  the  Continent  of  Europe  the 
knockers  are  very  elaborate.  At  all  periods  doors  have  been  ornamented  with 
nails  having  projecting  heads,  sometimes  square,  sometimes  polygonal,  and 
sometimes  ornamented  with  roses,  etc.  The  iron  work  of  windows  is  generally 
plain,  and  the  ornament  confined  to  simple  fleur-de-lis  heads  to  the  stanchions. 
The  iron  work  of  screens  enclosing  tombs  ana  chapels  is  noticed  under 


1604  GLOSSARY. 

Jack.— An  Instrument  for  raising  heavy  loads,  either  by  a  crank,  siren  and 
pinion,  or  by  hydraulic  power,  and  in  all  cases  worked  by  hand. 

Jack  Kafter.— A  short  rafter,  used  especially  in  hip-roofs. 

Jamb.— The  side-post  or  lining  of  a  doorway  or  other  aperture.  The  jambs  of 
a  window  outside  the  frame  are  called  Reveals. 

Jamb-shafts. — Small  shafts  to  doors  and  windows  with  caps  and  bases  ;  when 
In  the  inside  arris  of  the  jamb  of  a  window  they  are  sometimes  called  Escon- 
Bons. 

Joggle.— A  joint  between  two  bodies  so  constructed  by  means  of  jogs  or 
notches  as  to  prevent  their  sliding  past  each  other. 

Joinery.— That  branch  in  building  confined  to  the  nicer  and  more  ornamental 
parts  of  carpentry. 

Joist.— A  small  timber  to  which  the  boards  of  a  floor  or  the  laths  of  ceiling 
are  nailed.  It  rests  on  the  wal!  or  on  girders. 

Keep.— The  inmost  and  strongest  part  of  a  mediaeval  castle,  answering  to  the 
citadel  of  modern  times.  The  arrangement  is  said  to  have  originated  with  Gun- 
dolf,  the  celebrated  Bishop  of  Rochester.  The  Norman  keep  is  generally  a  very 
massive  square  tower,  the  basement  or  stories  partly  below  ground  being  used 
for  stores  and  prisons.  The  main  story  is  generally  a  great  deal  above  ground 
level,  with  a  projecting  entrance,  approached  by  a  flight  of  steps  and  drawbridge. 
This  floor  is  generally  supposed  to  have  been  the  guard-room  or  place  for  the 
soldiery  ;  above  this  was  the  hall,  which  generally  extended  over  the  whole  area 
of  the  building,  and  is  sometimes  separated  by  columns ;  above  this  are  other 
apartments  for  the  residents.  There  are  winding  staircases  in  the  angles  of  the 
buildings,  and  passages  and  small  chambers  in  the  thickness  of  the  walls.  The 
keep  was  intended  for  the  last  refuge,  in  case  the  outworks  were  scaled  and  the 
other  buildings  stormed.  There  is  generally  a  well  in  a  mediaeval  keep,  ingen- 
iously concealed  in  the  thickness  of  a  wall,  or  in  a  pillar.  The  most  celebrated 
of  Norman  times  are  the  White  Tower  in  London,  the  castles  at  Rochester, 
Arundel,  and  Newcastle,  Castle  Hedingham,  etc.  The  keep  was  often  circular. 

Key-stone. — The  stone  placed  in  the  centre  of  the  top  of  an  arch.  The  char- 
acter of  the  key-stone  varies  in  different  orders.  Tn  the  Tuscan  and  Doric  it  is 
only  a  simple  stone  projecting  beyond  the  rest ;  in  the  Ionic  it  is  adorned  with 
mouldings  in  the  manner  of  a  console  ;  in  the  Co'riuthian  and  Composite  it  is  a 
rich-sculptured  console. 

King-post.— The  middle  post  of  a  trussed  piece  of  framing  for  supporting  the 
tie-beam  at  the  middle  and  the  lower  ends  of  the  struts. 

Knee. — A  piece  of  timber  naturally  or  artificially  bent  to  receive  another  to 
relieve  a  weight  or  strain. 

Knob,  Knot.— The  bunch  of  flowers  carved  on  a  corbel,  or  on  a  Boss. 

Kremlin. — The  Russian  name  for  the  citadel  of  a  town  or  city. 

Label.— Gothic  :  the  drip  or  hood-moulding  of  an  arch,  when  it  is  returned  to 
the  square. 

Label  Terminations.— Carvings  on  which  the  labels  terminate  near  the 
springing  of  the  windows.  In  Norman  Times  those  were  frequently  grotesque 
heads  of  fish,  birds,  etc.,  and  sometimes  stiff  foliage.  In  the  Early  English  and 
Decorated  periods  they  are  often  elegant  knots  of  flowers,  or  heads  of  kings, 
queens,  bishops,  and  other  persons  supposed  to  be  the  founders  of  churches. 
In  the  Perpendicular  period  they  are  often  finished  with  a  short  square,  mitred 
return  or  knee,  and  the  foliages  are  generally  leaves  of  square  or  octagonal 


GLOSSARY.  1605 

Lacunar.— A  panelled  or  coffered  ceiling  or  soffit.  The  panels  or  cassoons  of 
a  ceiling  are  by  Vitruvius  called  lacunaria. 

Lady-chapel.  —  A  small  chapel  dedicated  to  the 
Virgin  Mary,  generally  found  in  ancient  cathedrals, 

Lancet. — A  high  and  narrow  window  pointed  like 
a  lancet,  often  called  a  Jancet  window. 

Landing1. — A  platform  in  a  flight  of  stairs  between 
two  stories  ;  the  terminating  of  a  stair. 

Lantern.— A  turret  raised  above  a  roof  or  tower 
and  very  much  pierced,  the  better  to  transmit  light. 

In  modern  practice  this  term  is  generally  applied  to     LACUNARS  IN  CEILINO. 
any  raised  part  in  a  roof  or  ceiling  containing  vertical 

windows,  but  covered  in  horizontally.  The  name  was  also  often  applied  to  the 
louver  or  femerell  on  a  roof  to  carry  off  the  smoke  ;  sometimes,  too,  to  the  open 
constructions  at  the  top  of  towers,  as  at  Ely  Cathedral,  probably  because  lights 
were  placed  in  them  at  night  to  serve  as  beacons. 

Lanterns  of  the  Dead.— Curious  small  slender  towers,  found  chiefly  in  the 
centre  and  west  of  France,  having  apertures  at  the  top,  where  a  light  was  ex- 
hibited at  night  to  mark  the  place  of  a  cemetery.  Some  have  supposed  that  the 
round  towers  in  Ireland  may  have  served  for  this  purpose. 

Lath.— A  slip  of  wood  used  in  slating,  tiling,  and  plastering. 

Lattice.— Any  work  of  wood  or  metal  made  by  crossing  laths,  rods,  or  bars, 
and  forming  a  net-work.  2.  A  reticulated  window,  made  of  laths  or  slips  of  iront 
separated  by  glass  windows,  and  only  used  where  air  rather  than  light  is  to  be 
admitted,  as  in  cellars  and  dairies. 

Lavaho.— The  lavatory  for  washing  hands,  generally  erected  jn  cloisters  of 
monasteries.  A  very  curious  one  at  Fontenay,  surrounding  a  pillar,  is  given  by 
Viollet  le-Duc.  In  general,  it  is  a  sort  of  trough,  and  iu  some  places  has  an 
almry  for  towels,  etc. 

Lavatory.— A  place  for  washing  the  person. 

Lean-to.— A  small  building  whose  rafters  pitch  or  lean  against  another  build- 
ing, or  against  a  wall. 

Lectern. — The  reading-desk  in  the  choir  of  churches. 

Ledge,  or  Lodgement, — A  projection  from  a  plane,  as  slips  on  the  side  of 
window  and  door  frames  to  keep  them  steady  in  their  places. 

Ledgers. — The  horizontal  pieces  fastened  to  the  standard  poles  or  timbers  of 
scaffolding  raised  around  buildings  during  their  erection.  Those  which  rest  on 
the  ledgers  are  called  putlogs,  and  on  these  the  boards  are  laid. 

Lewis.— An  iron  clamp  dovetailed  into  a  large  stone  to  lift  it  by. 

Lich-gate.— A  covered  gate  at  the  entrance  of  a  cemetery,  under  the  shelter 
of  which  the  mourners  rested  with  the  corpse,  while  the  procession  of  the  clergy 
came  to  meet  them.  There  are  several  examples  in  England. 

Light, — A  division  or  space  in  a  sash  for  a  single  pane  of  glass  ;  also  a  pane 
of  glas?. 

Linen  Scroll.— An  ornament  formerly  used  for  filling  panels,  and  so  called 
from  its  resemblance  to  tue  convolutions  of  a  folded  napkin. 

Lining.— Covering  for  the  interior,  as  casing  is  covering 
the  exterior  surface  of  a  building  ;  also,  such  as  linings  of  a 
door  for  windows,  shutters,  and  similar  work. 

Lintel,— The  horizontal  piece  which  covers  the  opening  of 
a  door  or  window.  LINEN  SCROLL. 

Lip  Mould.— A  moulding  of  the  Perpendicular  period  like  a  hanging  lip. 

List,  or  Listel,— A  little  square  moulding,  to  crown  a  larger;  also  termed  a  fillet. 


1606 


GLOSSARY. 


Lithograph,— A  print  from  a  drawing  on  stone. 

Lobby, — An  open  space  surrounding  a  range  of  chambers,  or  seats  in  a  theatre; 
a  small  hall  or  waiting  room. 

Lodge,— A  small  house  in  a  park. 

Loft,— The  highest  room  in  a  house,  particularly  if  in  the  roof  ;  also,  a  gallery 
raised  up  in  a  church  to  contain  the  rood,  the  organ,  or  singers. 

Loggia.— An  outside  gallery  or  portico  'above  the  ground,  and  contained 
within  the  building. 

Loop-hole,— An  opening  in  the  wall  of  a  building,  very  narrow  on  the  outside, 
and  splayed  within,  from  which  arrows  or  darts  might  be  discharged  on  an 
enemy.  They  are  often  in  the  form  of  a  cross,  and  generally  have  round  holes 
at  the  ends. 

Lombard  Architecture.— A  name  given  to  the  round-arched  architecture  of 
Italy,  introduced  by  the  conquering  Goths  and  Ostrogoths,  and  which  super- 
seded the  Romanesque.  Jt  reigned  between  the  eighth  and  twelfth  centuries, 
during  the  time  that  the  Saxon  and  Norman  styles  were  in  vogue  in  Eng- 
land, and  corresponded  with  them  in  its  development  into  the  Continental 
Gothic. 

Lotus. — A  plant  of  great  celebrity  amongst  the  ancients,  the  leaves  and 
blossoms  of  which  generally'  form  the  capitals  of  Egyptian  columns. 

Louver,— A  kind  of  vertical  window;  frequently  in  the  peaks  of  gables,  and  in 
the  top  of .  towers,  and  provided  with  horizontal  slats  which 
permit  ventilation  and  exclude  rain. 

Lozenge  Moulding,— A  kind  of  moulding  used  in  Norman 
architecture,  of  many  different  forms,  all  of  which  are  char- 
acterized by  lozenge- shaped  ornaments. 

Lunette.— The  French  term 
for  the  circular  opening  in  the 
groining  of  the  lower  stories  of 
towers,  through  which  the  bells 
are  drawn  up. 

LOZENGE  MOULDING.        tOUVER  WINDOW. 

Machicolation.— A  parapet 

or  gallery  projecting  from  the  upper  part  of  the  wall  of  a  house  or  fortification, 
supported  by  brackets  or  corbels,  and  perforated  in  the  lower  part  so  that 
the  defenders  of  the  building  might  throw  down  darts,  stones,  and  sometimes 
hot  sand,  molten  lead,  etc.,  upon  their  assailants  below. 

Man-hole,— A  hole  through  which  a  man  may  creep  into  a  drain,  cesspool, 
Bteam-boiler,  etc. 

Manor-house. — The  residence  of  the  suzerain  or  lord  of  the  manor  ;  in  France 
the  central  tower  or  keep  of  a  castle  is  often  called  the  manoir. 

Mansard  Roof.— Curb  roof,  invented  by  Frai^ois  Mansard,  a  distinguished 
French  architect,  who  died  in  1666. 

Mansion. — A  residence  of  considerable  size  and  pretension. 

Mantel.— The  work  over  a  fireplace  in  front  of  a  chimney  ;  especially,  a  shelf, 
usually  ornamented,  above  the  fireplace. 

Marquetry,— Inlaid  work  of  fine  hard  pieces  of  wood 
of  different  colors,-  also  of  shells,  ivory,  and  the  like. 

Mausoleum.— A  magnificent  tomb  or  sumptuous  sepul- 
chral monument. 

Medallion,  —  Any  circular  tablet  on  which  are  em- 
bossed figures  or  busts. 

Mediaeval  Architecture.— The  architecture  of  Bng-    -  MACHICOLATION; 


GLOSSARY. 


1607 


land,  France,  Germany,  etc.,  during  the  Middle  Ages,  including  the  Norman  and 
Early  Gothic  styles.  It  comprises  also  the  Romanesque,  Byzantine  and  Saracenic, 
Lombard,  and  other  styles. 

Members.— The  different  parts  of  a  building,  the  different  parts  of  an  entab- 
lature, the  different  mouldings  of  a  cornice,  etc. 

Merlon.— That  part  of  a  parapet  which  lies  between  two  embrasures. 

Metope.— The  square  recess  between  the  triglyphs  in  a  Doric  frieze.  It  is 
sometimes  occupied  by  sculptures.  p  __,_  _  \ 

Mezzanine. — A  low  story  between  two  lofty  ones. 
It  is  called  by  the  French  entresol,  or  inter-story. 

Mezzo-rilievo. — Or  mean  relief,  in  comparison 
with  alto-rilievo,  or  high  relief. 

Minaret.— Turkish  :  a  circular  turret  rising  by  dif- 
ferent stages  or  divisions,  each  of  which  has  a  balcony. 

Minster.— Probably  a  corruption  of  monasterium— 
the  large  church  attached  to  any  ecclesiastical  fraternity. 
If  the  latter  be  presided  over  by  a  bishop,  it  is  generally  METOPE. 

called  a  Cathedral ;  if  by  an  abbot,  an  Abbey  ;  if  by  a  prior,  a  Priory. 

Minute.— The  sixtieth  part  of  the  lower  diameter  of  a  column  ;  it 
is  the  measure  used  by  architects  to  determine  the  proportions  of  an 
order. 

Miserere.— A  seat  in  a  stall  of  a  large  church  made  to  turn  up 
and  afford  support  to  a  person  in  a  position  between  sitting  and 
(standing.  The  under  side  is  generally  carved  with  some  ornament, 
and  very  often  with  grotesque  figures  and  caricatures  of  different 
persons. 

Mitre.— A  moulding  returned  upon  itself  at  right  angles  is  said  to 
mitre.  In  joinery,  the  ends  of  any  two  pieces  of  wood  of  correspond- 
ing form,  cut  off  at  45°,  necessarily  abut  upon  one  another  so  as  to 
form  a  right  angle,  and  are  *aid  to  mitre. 

Modilllon. — So  called  because  of  its  arrangement  in  regulated  distances  ;  the 
enriched  block  or  horizontal  bracket  generally  found 
under   the    cornice   of   the    Corinthian   entablature. 
Less  ornamented,  it  is  sometimes  used  in  the  Ionic. 

Module. — This  is  a  term  which  has  been  generally 
used  by  architects  in  determining  the  relative  propor- 
tions of  the  various  parts  of  a  columnar  ordinance. 
The  semi-diameter  of  the  column  at  its  base  is  the 
module,  which  being  divided  into  thirty  parts  called  minutes,  any  part  of  the 
composition  is  said  to  be  of  so  many  modules  and  minutes,  or  minutes  alone,  in 
height,  breadth,  or  projection.  The  whole  diameter  is  now  generally  preferred 
as  a  module,  it  being  a  better  rule  of  proportion  than  its  half. 

Monastery.— A  set  of  buildings  adapted  for  the  reception  of  any  of  the 
various  orders  of  monks,  the  different  parts  of  which  are  described  in  the  separate 
article,  Abbey. 

Monotriglyph.— The  intercolumniations  of  the  Doric  order  are  determined 
by  the  number  of  triglyphs  which  intervene,  instead  of  the  number  of  diameters 
of  the  column,  as  in  other  cases ;  and  this  term  designates  the  ordinary  inter- 
columniation  of  one  triglyph. 

Monument.— A  name  given  to  a  tomb,  particularly  to  those  fine  structures 
recessed  in  the  walls  of  mediaeval  churches. 

•   Mosaic.— Pictorial  representations,  or  ornaments,  formed  of  small  pieces  of 
stone,  marble,  or  enamel  of  various  colors.    In  Roman  houses  the  floors  are  often 
3 


MINARET. 


MODILLION. 


1608 


GLOSSARY. 


entirely  of  mosaic,  the  pieces  being  cubical.    The  best  examples  of  mosaic  work 
are  found  in  St.  Mark's,  at  Venice. 

Mosque. — A  Mahometan  temple,  or  place  of  worship. 

Moulding.— When  any  work  is  wrought  into  long  regular  channels  or  projec- 
tions, forming  curves  or  rounds,  hollows,  etc.,  it  is 
said  to  be  moulded,  and  each  separate  member  is 
called  a  moulding.  In  mediaeval  architecture  the 
principal  mouldings  are  those  of  the  arches,  doors, 
windows,  piers,  etc.  In  the  Early  English  style,  the 
mouldings,  for  some  time,  formed  groups  set  back 
in  squares,  and  frequently  very  deeply  undercut. 
The  scroll  moulding  is  also  common.  Small  fillets 
now  become  very  frequent  in  the  keel  moulding, 
from  its  resemblance  in  section  to  the  bottom  of  a 
ship  ;  sometimes,  also,  it  has  a  peculiar  hollow  on 
each  side,  like  two  wings.  Later  in  the  Decorated 
style  the  mouldings  are  more  varied  in  design, 
though  hollows  and  rounds  still  prevail.  The  under- 
cutting is  not  so  deep,  fillets  abound,  ogees  are  more 


MOULDINGS. 

«,  astragal ;  ft,  ogee  ; 
<?,  cymatium  ;  d,  cavet- 
to :  e,  scotia,  or  case- 
ment ;  /,  apophyges  ; 
g,  ovolb,  or  quarter 
round ;  h,  torus ;  it 
reeding ;  ,;',  band. 


frequent,  and  the  wave  mould,  double  ogee,  or  double  ressaunt,  is  often  seen. 
In  many  places  the  strings  and  labels  are  a  round,  the  lower  half  of  which  is  cut 
off  by  a  plain  chamfer.  The  mouldings  in  the  later  styles  in  some  degree  resem- 
ble those  of  the  Decorated,  flattened  and  extended  ;  they  run  more  into  one 
another,  having  fewer  fillets,  and  being,  as  it  were,  less  grouped.  One  of  the 
principal  features  of  the  change  is  the  substitution  of  one,  or  perhaps  two  (sel- 
dom more),  very  large  hollows  in  the  set  of  mouldings.  These  hollows  are 
neither  circular  nor  elliptical,  but  obovate,  like  an  egg  cut  across,  so  that  one 
half  is  larger  than  the  other.  The  brace  mould  also  has  a  small  bead,  where  the 
two  ogees  meet.  Another  sort  of  moulding,  which  has  been  called  a  lip  mould, 
is  common  in  parapets,  bases,  and  weatherings. 

Mouldings,  Ornamented.— The  Saxon  and  early  Norman  mouldings  do  not 
seem  to  have  been  much  enriched,  but  the  complete  and  later  styles  of  Norman 
are  remarkable  for  a  profusion  of  ornamentation,  the  most  usual  of  which  is 
what  is  called  the  zigzag.  This  seems  to  be  to  Norman  architecture  what  the 
meander  or  fret  was  to  the  Grecian  ;  but  it  was  probably  derived  from  the 
Saxons,  as  it  is  very  frequently  found  in  their  pottery.  Bezants,  quatrefoils, 
lozenges,  crescents,  billets,  heads  of  nails,  are  very  common  ornaments.  Besides 
these,  battlements,  cables  ;  large  ropes  round  which  smaller  ropes  are  turned,  or, 
as  our  sailors  say,  "  wormed'1 ;  scallops,  pellets,  chains,  a  sort  of  conical  barrels, 
quaint  stiff  foliages,  beaks  of  birds,  heads  of  fishes,  ornaments  of  almost  every  con- 
ceivable kind,  are  sculptured  in  Norman  mouldings  ;  and  they  are  used  in  such 
profusion  as  has  been  attempted  in  no  other  style.  The  decorations  on  Early 
English  mouldings  are  chiefly  the  dog-tooth,  which  is  one  of  the  great  charac- 
teristics of  this  style,  though  it  is  to  be  found  in  the  Transition  Norman.  It  is 
generally  placed  in  a  deep  hollow  between  two  projecting  mouldings,  the  dark 
shadow  in  the  hollow  contrasting  in  a  very  beautiful  way  with  the  light  in  these 
mouldings.  In  this  period  and  in  the  next  the  tympanum  over  doorways,  par- 
ticularly if  they  are  double  doors,  is  highly  ornamented.  Those  of  the  Decorated 
period  resemble  the  former,  except  that  the  foliage  is  more  natural  and  the  dog- 
tooth gives  way  to  the  ball  -flower.  Some  of  the  hollows,  also,  are  ornamented  with 
rosettes  set  at  intervals,  which  are  sometimes  connected  by  a  running  tendril,  as 
the  ball-flowers  are  frequently.  Some  very  pleasing  leaf-like  ornaments  in  the 
labels  of  windows  are  often  found  in  Continental  architecture.  In  the  Perpen- 


GLOSSARY.  1609 

dicukr  period  the  mouldings  are  ornamented  very  frequently  by  square  four- 
leaved  flowers  set  at  intervals,  but  the  two  characteristic  ornaments  of  the  time 
are  running  patterns  of  vine  leaves,  tendrils,  and  grapes  in  the  hollows,  which 
by  old  writers  are  called  "  vignettes  in  casements,"  and  upright  stiff  leaves, 
generally  called  the  Tudor  leaf.  On  the  Continent  mouldings  partook  much  of 
the  same  character. 

Mullion,  Munion.— The  perpendicular  pieces  of  stone,  sometimes  like  col- 
umns, sometimes  like  slender  piers,  which  divide  the  bays  or  lights  of  windows 
or  screen-work  from  each  other.  In  all  styles,  in  less  important  work,  the  mull- 
ions  are  often  simply  plain  chamfered,  and  more  commonly  have  a  very  flat  hol- 
low on  each.  side.  Jn  larger  buildings  there  is  often  a  bead  or  boutell  on  the  edge, 
and  often  a  single  very  small  column  with  a  capital.  As  tracer}1"  grew  richer,  the 
windows  were  divided  by  a  larger  order  of  mullion,  between  which  came  a  lesser 
or  subordinate  set  of  mullions,  which  ran  into  each  other,  The  term  is  also 
applied  to  a  wood  or  iron  division  between  two  windows. 

Multifoil.— A  leaf  ornament  consisting  of  more  than  five  divisions,  applied  to 
foils  in  windows, 

Mutule.  — The  rectangular  impending  block  under  the  corona  of  the  Doric 
cornice,  from  which  guttae,  or  drops,  depend.  Mutuie  is  equivalent  to  modillion, 
but  the  latter  term  is  applied  more  particularly  to  enriched  blocks  or  brackets, 
euch  as  those  of  Ionic  and  Corinthian  entablatures. 

Narthex.— The  long  arcaded  porch  forming  the  entrance  into  the  Christian 
basilica.  Sometimes  there  was  an  inner  narthex,  or  lobby,  before  entering  the 
church  When  this  was  the  case,  the  former  was  called  exo-narthex.  and  the 
latter  eso  narthex.  In  the  Byzantine  churches  this  inner  narthex  forms  part  of 
the  solid  structure  of  the  church,  being  marked  off  by  a  wall  or  row  of  columns, 
whereas  in  the  Latin  churches  it  was  usually  formed  only  by  a  wooden  or  other 
temporary  screen. 

Natural  Beds. -In  stratified  rocks,  is  the  surface  of  a  stone  as  it  lies  in  the 
quarry  If  not  laid  in  walis  in  their  natural  bed  the  laminae  separate. 

Have-— The  central  part  between  the  arches  of  a  church,  wnich  formerly  was 
separated  from  a  chancel  or  choir  by  a  screen.  It  is  so  called  from  its  fancied 
resemblance  to  a  ship.  In  the  nave  were  generally  placed  the  pulpit  and  font. 
In  continental  Europe  it  often  also  contains  a  high  altar  but  this  is  of  rare 
occurrence  in  England 

Necking  —The  annulec  or  round,  or  series  of  horizontal  mouldings,  which 
separates  the  capital  of  a  column  from  the  plain  part  or  shaft. 

Newel.— In  mediaeval  architecture,  the  circular  ends  of  a  winding  staircase 
which  stand  ever  each  other,  and  form  a  sort  of  cylindrical  column. 

Newel  Post,  — The  post,  plain  or  ornamented,  placed  at  the  first,  or  lowest 
step  to  receive  or  start  the  hand-rail  upon. 

Niche.  — A  recess  sunk  in  a  wall  generally  for  the  reception  of  a  statue. 
Niches  sometimes  terminate  by  a  simple  label  but  more  commonly  by  a  can- 
opy and  with  a  bracket  or  corbel  for  the  figure,  in  which  case  they  are  often 
called  tabernacles 

Norman  Style.  —Was  that  species  of  Romanesque  which  was  practised  by  the 
Normans,  and  which  was  introduced  and  fully  developed  in  England  after  they 
had  established  themselves  in  it.  The  chief  features  of  this  style  are  plainness 
nnd  m:issiveness  The  arches,  windows,  and  doorways  were  semicircular,  the 
pillars  were  very  massive,  and  often  buiit  up  of  smab  stones  laid  like  brickwork. 

Nosings. -The  rounded  and  projecting  edges  of  the  treads  of  a  stair,  or  the 
edge  of  a  landing. 


1610  GLOSSARY. 

Obelisk.— Lofty  pillars  of  stone,  of  a  rectangular  form,  diminishing  toward  the 
top,  and  generally  ornamented  with  inscriptions  and  hieroglyphics  among  the 
ancient  Egyptians. 

Observatory.— A  building  erected  on  an  derated  spot  of  ground  for  making 
astronomical  observations. 

Octostyle.— A  portico  of  eight  columns  in  front. 

Offsets. — When  the  face  of  a  wall  is  not  one  continued  surface,  but  sets  in  by 
horizontal  jogs,  as  the  wall  grows  higher  and  thinner,  the  jogs  are  called  off- 
sets. 

Ogee. — The  name  applied  to  a  moulding,  partly  a  hollow  and  partly  a  round, 
and  derived  no  doubt  from  its  resemblance  to  an  O  placed  over  a  G.  It  is  rarely 
found  in  Norman  work,  and  is  not  very  common  in  Early  English.  It  is  of  fre- 
quent use  in  Decorated  work,  where  it  becomes  sometimes  double,  and  is  called  a 
wave  moulding  ;  and  later  still,  two  waves  are  connected  with  a  small  bead, 
which  is  then  called  a  brace  moulding.  In  ancient  MSS.  it  is  called  a  Ressaunt. 

Orchestra.— In  ancient  theatres,  where  the  chorus  used  to  dance  ;  in  modern 
theatres,  where  the  musicians  sit. 

Order. — A  column  with  its  entablature  and  stylobate  is  so  called.  The  term  is 
the  result  of  the  dogmatic  laws  deduced  from  the  writings  of  Yitruvius,  and  has 
been  exclusively  applied  to  those  arrangements  which  they  were  thought  to 
warrant. 

Oriel  Window.— Gothic  :  a  projecting  angular  window,  commonly  of  a  tri- 
agonal  or  pentagonal  form,  and  divided  by  mullions  and  transoms  into  different 
bays  and  compartments. 

Orthography.— A  geometrical  elevation  of  a  building  or  other  object  in  which 
it  is  represented  as  it  actually  exists  or  may  exist,  and  not  perspectively,  or  as  it 
would  appear. 

Orthostyle.— A  columnar  arrangement  in  which  the  columns  are  placed  in  a 
straight  line. 

Ovolo. — Same  as  Echinus. 

Pagoda.— A  name  given  to  temples  in  India  and  China. 

Palace. — The  dwelling  of  a  king,  prince,  or  bishop. 

Pale.— A  fence  picket,  sharpened  at  the  upper  end. 

Pane.— Probably  a  diminutive  of  panneau,  a  term  applied  to  the  different 
pieces  of  glass  in  a  window  ;  same  as  Light. 

Panel.— Properly  a  piece  of  wood  framed  within  four  other  pieces  of  wood,  as 
in  the  styles  and  rails  of  a  door,  filling  up  the  aperture,  but  often  applied  both  to 
the  whole  square  frame  and  the  sinking  itself  ;  also  to  the  ranges  of  sunken  com- 
partments in  wainscoting,  cornices,  corbel  tables,  groined  vaults,  ceilings,  etc. 

Pantograph,  or  Pentagraph.— An  instrument  for  copying  on  the  same,  or  an 
enlarged  or  reduced  scale. 

Pantry. — An  apartment  or  closet  in  which  bread  and  other  provisions  are 
kept. 

Papier-mache.— A  hard  substance  made  of  a  pulp  from  rags  or  paper  mixed 
with  size  or  glue,  and  moulded  into  any  desired  shape.  Much  used  for  architect- 
ural ornaments. 

Parapet.— A  dwarf  wall  along  the  edge  of  a  roof,  or  round  a  terrace  walk,  etc., 
to  prevent  persons  from  falling  over,  and  as  a  protection  to  the  defenders  in  case 
of  a  siege.  Parapets  are  either  plain,  embattled,  perforated,  or  panelled.  The 
las^t  two  are  found  in  all  styles  except  the  Norman.  Plain  parapets  are  simply 
portions  of  the  wall  generally  overhanging  a  little,  with  coping  at  tho  top  and 
corbel  table  below.  Embattled  parapets  are  sometimes  panelled,  but  ofteuer 


GLOSSARY.  1611 

pierced  for  the  discharge  of  arrows,  etc.  Perforated  parapets  are  pierced  in  various 
devices— as  circles,  trefoils,  quatrefoils,  and  other  designs— go  that  the  light  is 
seen  through.  Panelled  parapets  are  those  ornamented  by  a  series  of  panels, 
either  oblong  or  square,  and  more  or  less  enriched,  but  are  not  perforated.  These 
are  common  in  the  Decorated  and  Perpendicular  periods. 

Pargeting,— A  species  of  plastering  decorated  by  impressing  patterns  on  it 
when  wet.  These  seem  generally  to  have  been  made  by  sticking  a  number  of 
pins  in  aboard  in  certain  lines  or  curves,  and  then  pressing  on  the  wet  plaster  in 
various  directions,  so  as  to  form  geometrical  figures.  Sometimes  these  devices 
are  in  relief,  and  in  the  time  of  Elizabeth  represent  figures,  birds,  foliages,  etc. 
2.  Rough  plastering,  commonly  adopted  for  the  interior  surface  of  chimneys. 

Parlor.— A  room  in  a  house  which  the  family  usually  occupy  for  society  and 
conversation,  and  for  receiving  visitors.  2.  The  apartment  in  a  monastery  or 
nunnery  where  the  inmates  are  permitted  to  meet  and  converse  with  each  other, 
or  with  visitors  and  friends  from  without. 

Parochial.— Belonging  or  relating  to  a  parish. 

Parquetry,  or  Marquetry.— A  kind  of  inlaid  floor  composed  of  small  pieces 
of  wood  either  square  or  triangular,  which  are  capable  of  forming,  by  their  dis- 
position, various  combinations  of  figures  ;  this  description  of  joinery  is  very 
suitable  for  the  floors  of  libraries,  halls,  and  public  apartments. 

Party  Walls.— Partitions  of  brick  or  stone  between  buildings  on  two  ad- 
joining properties. 

Patera.— A  circular  ornament  resembling  a  dish,  often  worked  in  relief  on 
friezes,  etc. 

Pavement.— Tessellated,  a  pavement  of  mosaic  work, 
used  by  the  ancients,  made  of  square  pieces  of  stone,  etc., 
called  Tessera. 

Pavilion.— A  turret  or  small  insulated  building,  and 
comprised  beneath  a  single  roof  ;  also,  the  projecting 
part  in  front  of  a  building  which  marks  the  centre,  and 
which  sometimes  flanks  a  corner,  when  it  is  termed  an 
angular  pavilion. 

Pedestal.— The  square  support  of  a  column,  statue, 
etc. ;  and  the  base  or  lower  part  of  an  order  of  columns  :  it  consists  of  a  plinth 
for  a  base,  the  die,  and  a  talon  crowned  for  a  cornice.  When  the  height  and 
width  are  equal,  it  is  termed  a  square  pedestal  •  one  which  supports  two  columns, 
a  double  pedestal  ;  and  if  it  supports  a  row  of  columns  without  any  break,  it  is 
a  continued  pedestal. 

Pediment.— A  low  triangular  crowning,  ornamented,  in  front  of  a  building,  and 
over  doors  and  windows.  Pediments  are  sometimes  made  in  the  form  of  a  seg- 
ment ;  the  space  enclosed  within  the  triangle  is  called  the  tympanum.  Also,  the 
gable  ends  of  classic  buildings,  where  the  horizontal  cornice  is  carried  across  the 
front,  forming  a  triangle  with  the  end  of  the  roof. 

Pendent.— A  name  given  to  an  elongated  boss,  either  moulded  or  foliated, 
such  as  hang  down  from  the  intersection  of  groins,  especially  in  fan  tracery,  or 
at  the  end  of  hammer  beams.  Sometimes  long  corbels,  under  the  wall  pieces, 
have  been  so  called.  The  name  has  also  been  given  to  the  large  masses  depend- 
ing from  enriched  ceilings,  in  the  later  works  of  the  Pointed  style. 

Pendent  Posts.— A  name  given  to  those  timbers  which  hang  down  the  side  of 
a  wall  from  the  plate  in  hammer  beam  trusses,  and  which  receive  the  hammer 
braces. 

Pendentive.— A  name  given  to  an  arch  which  cuts  off,  as  it  wore,  the  cornera 
of  a  square  building  internally,  so  that  the  superstructure  may  become  an  octagon 


1612  GLOSSARY. 

or  a  dome.  In  mediaeval  architecture  these  arches,  when  under  a  spire  in  the 
interior  of  a  tower,  are  called  Squinches. 

Pendent! ve  Bracketing1,  or  Cove  Bracketing.— Springing  from  the  rec- 
tangular walls  of  an  apartment  upward  to  the  ceiling,  and  forming  the  horizon 
tal  part  of  the  ceiling  into  a  circle  or  ellipse. 

Pen t as tyle.— Having  five  columns  in  front. 

Pent-roof. — A  roof  with  a  slope  on  one  side  only. 

Perch. — A  measure  used  in  measuring  stone  work,  being  24f  cu.  ft.  and  IGf 
cu.  ft.,  according  to  locality  and  custom. 

Periptery.— An  edifice  or  temple  surrounded  by  a  peristyle. 

Peristyle. — A  range  of  columns  encircling  an  edifice,  such  as  that  which  sur- 
rounds the  cylindrical  drum  under  the  cupola  of  St.  Paul's.  The  columns  of  a 
Greek  peripteral  temple  form  a  peristyle  also,  the  former  being  a  circular,  and 
the  latter  a  quadrilateral  peristyle. 

Perpendicular  Style.— The  third  and  last  of  the  Pointed  or  Gothic  styles  ; 
also  called  the  Florid  style. 

Perspective  Drawing,— The  art  of  making  such  a  representation  of  an  ob- 
ject upon  a  plane  surface  as  shall  present  precisely  the  same  appearance  that  the 
object  itself  would  to  the  eye  situated  at  a  particular  point. 

Pews. — A  word  of  uncertain  origin,  signifying  fixed  seats  in  churches,  com- 
posed of  wood  framing,  mostly  with  ornamented  ends.  They  seem  to  have  come 
into  general  use  early  in  the  reign  of  Henry  VI.  and  to  have  been  rented  and 
"well  paid  for"  before  the  Reformation.  Some  bench  ends  are  certainly  of  a 
decorated  character,  and  some  have  been  considered  to  be  of  the  Early  English 
period.  They  are  sometimes  of  plain  oak  board,  two  and  a  half  to  three  inches 
thick,  chamfered,  and  with  a  necking  and  finial,  generally  called  a  poppy  head  ; 
others  arc  plainly  panelled  with  bold  cappings  ;  in  others  the  panels  are  orna- 
mented with  tracery  or  with  the  linen  pattern,  and  sometimes  with  running 
foliages.  The  divisions  are  filled  in  with  thin  chamfered  boarding,  sometimes 
reaching  to  the  floor,  and  sometimes  only  from  the  capping  to  the  seat. 

Picket.— A  narrow  board,  often  pointed,  used  in  making  fences  ;  a  pale  or 
paling. 

Pier-glass. — A  mirror  hanging  between  windows. 

Piers, — The  solid  parts  of  a  wrall  between  windows,  and  between  voids  gener- 
ally. The  term  is  also  applied  to  masses  of  brick- work  or  masonry  which  are 
insulated  to  form  supports  to  gates  or  to  cany  arches,  posts,  girders,  etc. 

Pilasters.— Are  flat  square  columns,  attached  to  a  wall,  behind  a  column,  or 
along  the  side  of  a  building,  and  projecting  from  the  wall  about  a  fourth  or  a 
sixth  part  of  their  breadth.  The  Greeks  had  a  slightly  different  design  for  the 
capitals  of  pilasters,  and  made  them  tiic  same  width  at  top  as  at  bottom,  but  the 
Romans  gave  them  the  same  capitals  as  the  columns,  and  made  them  of 
diminished  width  at  the  top,  similar  to  the  columns. 

Pile.— A  large  stake  or  trunk  of  a  tree,  driven  into  soft  ground,  as  at  the  bottom 
of  a  river,  or  in  made  land,  for  the  support  of  a  building.  (See  p.  134.) 

Pillar,  or  Pyller. — A  word  generally  used  to  express  the  round  or  polygonal 
piers,  or  those  surrounded  with  clustered  columns,  which  carry  the  main  arches 
of  a  building.  Saxon  and  Early  Norman  pillars  are  generally  stout  cylindrical 
shafts  built  up  of  small  stones.  Sometimes,  however,  they  are  quite  square,  some- 
times with  other  squares  breaking  out  of  them  (this  is  more  common  in  French 
and  German  work),  sometimes  with  angular  shafts,  and  sometimes  they  are  plain 
octagons.  In  Romanesque  Norman  work  the  pillar  is  sometimes  square,  with 
two  or  more  semicircular  or  half-columns  attached.  In  the  Early  English  period 
the  pillars  become  loftier  and  lighter,  and  in  most  important  buildings  are  a  series 


GLOSSARY.  1613 

of  clustered  columns,  frequently  of  marble,  placed  side  by  side,  sometimes  set  at 
intervals  round  a  circular  centre,  and  sometimes  almost  touching  each  other. 
These  shafts  are  often  wholly  detached  from  the  central  pillar,  though  grouped 
round  it,  in  which  case  they  are  almost  always  of  Purbeck  or  Bethersden  marbles. 
In  Decorated  work  the  shafts  on  plan  are  very  often  placed  round  a  square  set 
auglewise,  or  a  lozenge,  the  long  way  down  the  nave  ;  the  centre  or  core  itself  is 
often  worked  into  hollows  or  other  mouldings,  to  show  between  the  shafts,  and 
to  form  part  of  the  composition.  Jn  this  and  the  latter  part  of  the  previous  style 
there  is  generally  a  fillet  on  the  outer  part  of  the  shaft,  forming  what  has  been 
called  a  keel  moulding.  They  are  also  often,  as  it  were,  tied  together  by  bands 
formed  of  rings  of  stone  and  sometimes  of  metal.  The  small  pillars  at  the  jambs 
of  doors  and  windows,  and  in  arcades,  and  also  those  slender  columns  attached 
to  pillars,  or  standing  detached,  are  generally  called  shafts. 

Pin. — A  cylindrical  piece  of  wood,  iron,  or  steel,  used  to  hold  two  or  more  pieces 
together,  by  passing  through  a  hole  in  each  of  them,  as  in  a  mortise  and  tenon 
joint,  or  a  pin  joint  of  a  trussv 

Pinnacle. — An  ornament  originally  forming  the  cap  or  cro\vn  of  a  buttress  or 
gmall  turret,  but  afterward  used  on  parapets  at  the  corners  of 
towers  and  in  many  other  situations.  It  was  a  weight  to  counter- 
act the  thrust  of  the  groining  of  roofs,  particularly  where  there 
were  flying  buttresses  ;  it  stopped  the  tendency  to  slip  of  the  stone 
copings  of  the  gables,  and  counterpoised  the  thrust  of  spires  ;  it 
formed  the  piers  to  steady  the  elegant  perforated  parapets  of 
Jater  periods  ;  and  in  France,  especially,  served  to  counterbalance 
the  weight  of  overhanging  corbel  tables,  huge  gargoyles,  etc.  In 
the  Early  English  period  the  smaller  buttresses  frequently  finished 
with  gablets,  and  the  more  important  with  pinnacles  supported 
with  clustered  shafts.  At  this  period  the  pinnacles  were  often 
supported  on  these  shafts  alone,  and  were  open  below ;  and  in 
larger  work  in  this  and  the  subsequent  periods  they  frequently  form 
niches  and  contain  statues.  In  France,  pinnacles,  like  spires, 
seem  to  have  been  in  use  earlier  than  in  England.  There  are  small 
pinnacles  at  the  angles  of  the  tower  in  the  Abbey  of  Saintes.  At 
Roullet  there  are  pinnacles  in  a  similar  position,  each  composed  of 
four  small  shafts,  with  caps  and  bases  surmounted  with  small  ] 
pyramidal  spires.  In  all  these  examples  the  towers  have  semicircular  headed 
windows. 

Pitch  of  a  Roof.  —  The  proportion  obtained  by  dividing  the  span  by  the 
height ;  thus,  we  speak  of  its  being  one-half,  one-third,  one-fourth.  When  the 
length  of  the  rafters  is  equal  to  the  breadth  of  the  building  it  is  denominated 
Gothic. 

Pitching-piece,—  A  horizontal  timber,  with  one  of  its  ends  wedged  into  the 
wall  at  the  top  of  a  flight  of  stairs,  to  support  the  upper  end  of  the  rough  strings. 

Place.— An  open  piece  of  ground  surrounded  by  buildings,  generally  decorated 
with  a  statue,  column,  or  other  ornament. 

Plan,— A  horizontal  geometrical  section  of  the  walls  of  a  building  ;  or  indi- 
cations, ona  horizontal  plane,  of  the  relative  positions  of  the  walls  and  partitions, 
with  the  various  openings,  such  as  windows  and  doors,  recesses  and  projections, 
chimneys  and  chimney-breasts*,  columns,  pilasters,  etc.  This  term  is  often  in- 
correctly used  in  the  sense  of  Design. 

Planceer. — Is  sometimes  used  in  the  same  sense  as  soffit,  but  is  more  correctly 
applied  to  the  soffit  of  the  corona  in  a  cornice. 

Plastering.— A  mixture  of  lime,  hair,  and  sand,  to  cover  lath- work  between 


1G14  GLOSSARY. 


timbers  or  rough  walling,  used  from  the  earliest  times,  and  very  common  in 
Roman  work.  In  the  Middle  Ages,  too,  it  was  used  not  only  in  private,  but  in 
public  constructions.  On  the  inside  face  of  old  ruhble  walls  it  was  not  only  used 
for  purposes  of  cleanliness,  rough  work  holding  dirt  and  dust,  but  as  a  ground 
for  distemper  painting  (tempera,  or,  as  it  is  often  improperly  called,  fresco  ,  a 
species  of  ornament  often  used  in  the  Middle  Ages.  At  St.  Albans  Abbey,  Eng- 
land, the  Norman  work  is  plastered,  and  covered  with  lines  imitating  the  joints 
of  stone.  The  same  thing  is  found  in  English  Perpendicular  work.  On  the  out- 
side of  rubble  walls,  and  often  of  wood  framing,  it  was  used  as  roughcast ; 
when  ornamented  in  patterns  outside,  it  is  called  pargeting. 

Plate.— The  piece  of  timber  in  a  building  which  supports  the  end  of  the  rafters. 

Plinth.— The  square  block  at  the  base  of  a  column  or  pedestal.  In  a  wall,  the 
term  plinth  is  applied  to  the  projecting  base  or  water  table,  generally  at  the  level 
of  the  first  floor. 

Plumb,—  Perpendicular  ;  that  is,  standing  according  to  a  plumb  line,  as,  the 
post  of  a  house  or  wall  is  plumb. 

Plumbing.— The  lead  and  iron  pipes  and  other  apparatus  employed  in  con 
veying  water,  and  for  toilet  purposes  in  a  building  ;  originally  the  art  of  casting 
and  working  in  lead. 

Ply.— Used  to  denote  the  number  of  thicknesses  of  roofing  paper  >  as  three  ply, 
four  ply,  etc. 

Podium.— A  continued  pedestal  ;  a  projection  from  a  wall,  forming  a  kind  of 
gallery. 

Polytriglyph. — An  intercolumniation  in  the  Doric  order  of  more  than  two 
triglyphs. 

Poppy  Heads.— Probably  from  the  French  poupee ;  the  finials  or  other  orna- 
ments which  terminate  the  tops  of  bench  ends,  either  to  pews  or 
stalls.  They  are  sometimes  small  human  heads,  sometimes  richly 
carved  images,  knots  of  foliage,  or  finials,  and  sometimes  fleurs- 
de-lis  simply  cut  out  of  the  thickness  of  the  bench  end  and  cham- 
fered. 

Porch.— A  covered  erection  forming  a  shelter  to  the  entrance 
door  of  a  large  building.  The  earliest  known  are  the  long  arcaded 
porches  in  front  of  the  early  Christian  basilicas,  called  Narthex. 
In  later  times  they  assume  two  forms— one,  the  projecting  erection 
covering  the  entrance  at  the  west  front  of  cathedrals,  and  divided 
into  three  or  more  doorways,  etc.  ;  and  the  other,  a  kind  of  covered  rOpPT  HEAD 
chambers  open  at  the  ends,  and  having  small  windows  at  the  sides 
as  a  protection  from  rain. 

Mortal.— A  name  given  to  the  deeply  recessed  and  richly  decorated  entrance 
doors  to  the  cathedrals  in  Continental  Europe. 

Portcullis.— A  strong-framed  grating  of  oak,  the  lower  points  shod  with  iron,, 
and  sometimes  entirely  made  of  metal,  hung  so  as  to  slide  up  and  down  in  grooves 
with  counterbalances,  and  intended  to  protect  the  gateways  of  castles,  etc. 

Portico.— An  open  space  before  the  door  or  other  entrance  to  any  building, 
fronted  with  columns.  A~portico  is  distinguished  as  prostyle  or  in  antis  accord- 
ing as  it  projects  from  or  recedes  within  the  building,  and  is  further  designated 
by  the  number  of  columns  its  front  may  consist  of. 

Post.— Square  timbers  set  on  end.  The  term  is  especially  applied  to  those 
which  support  the  corners  of  a  building,  and  are  framed  into  bressummers  or 
crossbeams  under  the  walls. 

Posticum.— A  portico  behind  a  temple. 

Presbytery.— A  wordapplied  to  various  parts  of  large  churches  in  a  very 


GLOSSARY.  ;        1615 

biguous  way.  Some  consider  it  to  be  the  choir  itself  ;  others,  what  Is  now  named 
the  sacrarium.  Traditionally,  however,  it  seems  to  be  applied  to  the  vacant 
space  between  the  back  of  the  high  altar  and  the  entrance  to  the  lady-chapel,  as 
at  Lincoln  and  Chichester  ;  in  other  words,  the  back-  or  retro-choir. 

Priming.— The  laying  on  of  the  first  shade  of  color,  in  oil  paint,  and  generally 
consisting  mostly  of  oil,  to  protect  and  fill  the  wood. 

Priory.— A  monastic  establishment,  generally  in  connection  with  an  abbey, 
and  presided  over  by  a  prior,  who  was  a  subordinate  to  the  abbot,  and  held  much 
the  same  relation  to  that  dignitary  as  a  dean  does  to  a  bishop. 

Profile.— The  outline  ;  the  contour  of  apart,  or  the  parts  composing  an  order, 
as  of  abase,  cornice,  etc.  ;  also,  the  perpendicular  section.  It  is  in  the  just  pro- 
portion of  their  profiles  that  the  chief  beauties  of  the  different  orders  of  archi- 
tecture depend.  The  ancients  were  most  careful  of  the  profiles  of  their  mould- 
Ings. 

Proscenium,— The  front  part  of  the  stage  of  ancient  theatres,  on  which  the 
actors  performed. 

Prostyle. — A  portico  in  which  the  columns  project  from  the  building  to  which 
it  is  attached. 

Protractor.— A  mathematical  instrument  for  laying  down  and  measuring  angles 
on  paper,  used  in  drawing  or  plotting. 

Pseudo-dipteral. — False  double-winged.  When  the  inner  row  of  columns 
of  a  dipteral  arrangement  is  omitted  and  the  space  from  the  wall  of  the  building 
to  the  columns  is  preserved,  it  is  pseudo-dipteral. 

Puddle.— To  settle  loose  dirt  by  turning  on  water,  so  as  to  render  it  firm  and 
solid. 

Pugging.— A  coarse  kind  of  mortar  laid  on  the  boarding,  between  floor  joists, 
to  prevent  the  passage  of  sound  ;  also  called  deafening. 

Pulpit.— A  raised  platform  with  enclosed  front,  whence  sermons,  homilies,  etc, > 
were  delivered.  Pulpits  were  probably  derived  in  their  modern  form  from  the 
ambones  in  the  early  Christian  church.  There  are  many  old  pulpits  of  stone, 
though  the  majority  are  of  wood.  Those  in  the  churches  are  generally  hexagonal 
or  octagonal ;  and  some  stand  on  stone  bases,  and  others  on  slender  wooden 
stems,  like  columns.  The  designs  vary  according  to  the  periods  in  which  they 
were  erected,  having  panelling,  tracery,  cuspings,  crockets,  and  other  ornaments 
then  in  use.  Some  are  extremely  rich,  and  ornamented  with  color  and  gilding. 
A  few  also  have  fine  canopies  or  sounding  boards.  Their  usual  place  is  in  the 
nave,  mostly  on  the  north  side,  against  the  second  pier  from  the  chancel  arch. 
Pulpits  for  addressing  the  people  in  the  open  air  were  common  in  the  Mediaeval 
period,  and  stood  near  a  road  or  cross.  Thus,  there  was  one  at  Spitalfields,  and 
one  at  St.  Paul's,  London.  External  pulpits  still  remain  at  Magdalen  College, 
Oxford,  and  at  Shrewsbury,  England. 

Purlins.— Those  pieces  of  timbers  which  support  the  rafters  to  prevent  them 
from  sinking. 

Putlog. — Horizontal  pieces  for  supporting  the  floor  of  a  scaffold,  one  end 
being  inserted  into  putlog  holes,  left  for  that  purpose  in  the  masonry. 

Putty  in  Plastering. — Lump  lime  slacked  with  water  to  the  consistency  of 
cream,  and  then  left  to  harden  by  evaporation  till  it  becomes  like  soft  putty.  It 
is  then  mixed  with  plaster  of  Paris,  or  sand,  for  the  finishing  coat. 

Puzzolana.— A  grayish  earth  used  for  building  under  water. 
Pyramid.— A  solid,  having  one  of  its  sides,  called  a  base,  a  plane  figure,  and 
the  other  sides  triangles,  these  points  joining  in  one  point  at  the  top,  called  the 
vertex.    Pyramids  are  called  triangular,  square,  etc.,  according  to  the  form  of 
their  bases. 


1616  GLOSSARY. 

Pyx. — In  Roman  Catholic  churches,  the  box  in  which  the  host,  or  consecrated 
wafer,  is  kept. 

Quadrangle. — A  square  or  quadrangular  court  surrounded  by  buildings,  as 
was  often  done  formerly  in  monasteries,  colleges,  etc. 

Quarry.— A  pane  of  glass  cut  in  a  diamond  or  lozenge  form. 

Quarry-face. — Ashlar  as  it  comes  from  the  quarry,  squared  off  for  the  joints 
only,  with  .split  face.  In  distinction  from  Rock-face,  in  that  the  latter  may  be 
weather-worn,  while  Quarry-face  should  be  fresh  split.  The  terms  are  often 
used  indiscriminately. 

Quatrefoil.— Any  small  panel  or  perforation  in  the  form  of  a  four  leaved  flower. 
Sometimes  used  alone,  sometimes  in  circles  and  over  the  aisle  windows,  but  more 
frequently  in  square  panels.  They  are  generally  cusped,  and  the  cusps  are  often 
feathered. 

Queen  Truss.— A  truss  framed  with  two  vertical  tie-posts,  in  distinction  from 
the  king-post,  which  has  but  one.  The  upright  ties  are  called  Queen-posts. 

Quirk  Mouldings. — The  convex  part  of  Grecian  mouldings  when  they  recede 
at  the  top,  forming  a  reentrant  angle,  with  the  surface  which  covers  the  mould- 
ings. 

Quoins.— Large  squared  stones  at  the  angles  of  buildings,  buttresses,  etc., 
generally  used  to  stop  the  rubble  or  rough  stone  work,  and  that  the  angles  may 
be  true  and  stronger.  Saxon  quoin  stones  are  said  to  have  been  composed  of 
one  long  and  one  short  stone  alternately.  Early  quoins  are  generally  roughly 
axed ;  in  later  times  they  had  a  draught  tooled  by  the  chisel  round  the  outside 
edges,  and  later  still  were  worked  fine  from  the  saw. 

Rafters.— The  joist  to  which  the  roof  boarding  Is  nailed.  Principal  rafters 
are  the  upper  timbers  in  a  truss,  having  the  same  inclination  as  the  common 
rafters. 

Rail.— A  piece  of  timber  or  metal  extending  from  one  post  to  another,  as  in 
fences,  balustrades,  staircases,  etc.  In  framing  and  panelling,  the  horizontal 
pieces  are  called  rails,  and  the  perpendicular,  stiles. 

Raking. — Mouldings  whose  arrises  are  inclined  to  the  horizon. 

Ramp. — A  concavity  on  the  upper  side  of  hand  railings  formed  over  risers, 
made  by  a  sudden  rise  of  the  steps  above.  Any  concave  bend  or  slope  in  the  cap 
or  upper  member  of  any  piece  of  ascending  or  descending  workmanship. 

Rampant. — A  term  applied  to  an  arch  whose  abutments  spring  from  an 
inclined  plane. 

Random  Work. — A  term  used  by  stone-masons  for  stones  fitted  together  at 
r-tndom  without  any  attempt  at  laying  them  in  courses.  Random  Coursed  Work 
js  a  like  term  applied  to  work  coursed  iu  horizontal  beds,  but  the  stones  are  of 
any  height,  and  fitted  to  one  another. 

Range  Work. — Ashlar  laid  in  horizontal  courses  ;  same  as  coursed  ashlar. 

Rebate. — A  groove  ou  the  edges  of  a  board. 

Recess. — A  depth  of  some  inches  in  the  thickness  of  a  wall,  as  a  niche,  etc. 

Refectory, — The  hall  of  a  monastery,  convent,  etc.,  where  the  religious  took 
their  chief  meals  together.  It  much  resembled  the  great  halls  of  mansions,  cas- 
tles, etc.,  except  that  there  frequently  was  a  sort  of  ambo,  approached  by  steps, 
from  which  to  read  the  Legenda  Sanctorum,  etc.,  during  meals. 

Reglet.— A  flat,  narrow  moulding,  used  to  separate  from  each  other  the  parta 
or  members  of  compartments  and  panels,  to  form  frets,  knots,  etc. 

Renaissance  (a  new  birth).— A  name  given  to  the  revival  of  Roman  architect- 
tire  which  sprang  into  existence  in  Italy  as  early  as  the  beginning  of  the  fifteenth 


GLOSSARY.  1617 

century,  and  reached  its  zenith  in  that  country  at  the  close  of  the  century.    There 
are  several  divisions  of  this  style  as  developed  in  different  localities  ;  viz., 

The  Florentine  Renaissance,  of  which  the  Pitti  Palace,  by  Brunelleschi,  is  one 
of  the  best  examples. 

The  Venetian  Renaissance,  characterized  by  its  elegance  and  richness. 
The  Roman  Renaissance,  which  originated  in  Rome,  under  the  architects 
known  as  Bronte,  Vignola,  and  Michael  Angelo.    Of  this  style  the  Farnese  Palace, 
St.  Peter's,  and  the  modern  Capitol  at  Rome  are  the  best  examples. 

The  French  Renaissance,  introduced  into  France  in  the  latter  part  of  the  fif- 
teenth century,  by  Italian  architects,  where  it  nourished  until  the  middle  of  the 
seventeenth  century.  The  Renaissance  style  was  introduced  into  Germany  about 
the  middle  of  the  sixteenth  century,  and  into  England  about  the  same  time  by 
John  of  Padua^  architect  to  Henry  VIII.  This  style  in  England  is  generally 
known  under  the  name  of  Elizabethan. 

Rendering, — In  drawing,  finishing  a  perspective  drawing  in  ink  or  color,  to 
bring  out  the  spirit  and  effect  of  the  design.  2.  The  first  coat  of  plaster  on  brick 
or  stone  work. 

Reredos,  Dorsal,  or  Dossel.— The  screen  or  ot'her  ornamental  work  at  the  back 
of  an  altar.  In  some  large  English  cathedrals,  as  Winchester,  Durham,  St.  Albans, 
etc.,  this  is  a  mass  of  splendid  tabernacle  work,  reaching  nearly  to  the  groining. 
In  smaller  churches  there  are  sometimes  ranges  of  arcades  or  panellings  behind 
the  altars  ;  but,  in  general,  the  walls  at  the  back  and  sides  of  them  were  of  plain 
masonry,  and  adorned  with  hangings  or  paraments.  In  the  large  churches  of 
Continental  Europe  the  high  altar  usually  stands  under  a  sort  of  canopy  or  cibo- 
rinm,  and  the  sacrarium  is  hung  round  at  the  back  and  sides  with  curtains  on 
movable  rods. 

Reticulated  Work.— That  in  which  the  courses  are  arranged  in  a  form  like 
the  meshes  of  a  net.  The  stones  or  bricks  are  square  and  placed  lozenge- 
wise. 

Return.— The  continuation  of  a  moulding,  projection,  etc.,  in  an  opposite 
direction. 

Return  Head. — One  that  appears  both  on  the  face  and  edge  of  a  work. 
Reveal.  -The  two  vertical  sides  of  an  aperture,  between  the  front  of  a  wall 
and  the  window  or  door  frame. 

Rib.— A  moulding  or  projecting  piece  upon  the  interior  of  a  vault,  or  used  to 
form  tracery  and  the  like.  The  earliest  groining  had  no  ribs.  In  early  Norman 
times  plain  flat  arches  crossed  each  other,  forming  ogive  ribs.  These  by  degrees 
became  narrower,  had  greater  projection,  and  were  chamfered.  In  later  Nor- 
man work  the  ribs  were  often  formed  of  a  large  roll  placed  upon  the  flat  band, 
and  then  of  two  rolls  side  by  side  with  a  smaller  roll  or  a  fillet  between  them, 
much  like  the  lower  member.  Sometimes  they  are  enriched  with  zigzags  and 
other  Norman  decorations,  and  about  this  time  bosses  became  of  very  general 
use.  As  styles  progressed,  the  mouldings  were  more  undercut,  richer,  and  more 
elaborate,  and  had  the  dog-tooth  or  ball-flower  or  other  characteristic  ornament 
in  the  hollows.  In  all  instances  the  mouldings  are  of  similar  contours  to  those 
of  arches,  etc.,  of  the  respective  periods.  Later,  wooden  roofs  are  often  formed 
into  cants  or  polygonal  barrel  vaults,  and  in  these  the  ribs  are  generally  a  cluster 
of  rounds,  and  form  square  or  stellar  panels,  with  carved  bosses  or  shields  at  the 
intersections. 

Ridge.— The  top  of  a  roof  which  rises  to  an  acute  angle. 

Ridge-pole.— The  highest  horizontal  timber  in  a  roof,  extending  f-om  top  to 
top  of  the  several  pairs  of  rafters  of  the  trusses,  for  supporting  the  heads  of  the 
jack  rafters. 


1618  GLOSS  ART. 

Rilievo,  or  Relief.-~The  projection  of  an  architectural  ornament. 

Rise.— The  distance  through  which  anything  rises,  as  the  rise  of  a  stair,  01 

inclined  plane. 

Riser. — The  vertical  board  under  the  tread  in  stairs. 

Rococo  Style.— A  name  given  to  that  variety  of  the  Renaissance  which  was  in 
vogue  during  the  seventeenth  and  the  latter  part  of  the  sixteenth  centurj'. 

Romanesque  Style. — The  term  Romanesque  embraces  all  those  styles  of 
architecture  which  prevailed  between  the  destruction  of  the  Roman  Empire  and 
the  beginning  of  Gothic  architecture.  In  it  are  included  the  Early  Roman  Chris- 
tian  architecture,  Byzantine,  Mahometan,  and  the  later  Romanesque  architect- 
ure proper,  which  was  developed  in  Italy,  France,  England,  and  Germany. 
This  later  Romanesque,  which  was  quite  different  from  the  preceding,  came 
into  vogue  during  the  tenth  century,  and  reached  its  height  during  the  twelfth 
century,  and  in  the  thirteenth  century]  gave  way  to  the  Pointed  or  Gothic  style. 
In  England,  Romanesque  architecture  is  known  under  the  name  of  the  Saxon, 
Korman,  and  Lombard  styles,  according  to  the  different  political  periods. 

Rood. — A  name  applied  to  a  crucifix,  particularly  to  those  which  were  placed 
fn  the  rood-loft  or  chancel  screens.  These  generally  had  not  only  the  image  of 
the  crucified  Saviour,  but  also  those  of  St.  John  and  the  Virgin  Mary  standing 
one  on  each  side.  Sometimes  other  saints  and  angels  are  by  them,  and  the  top 
of  the  screen  is  set  with  candlesticks  or  other  decoration. 

Rood-loft,  Rood-screen,  Rood-beam,  Tube  Gallery,  etc.— The  arrangement 
to  carry  the  crucifix  or  rood,  and  to  screen  off  the  chancel  from  the  rest  of  the 
church  during  the  breviary  services,  and  as  a  place  whence  to  read  certain  parts  of 
those  services.  Sometimes  the  crucifix  is  carried  simply  on  a  strong  transverse 
beam,  with  or  without  a  low  screen,  with  folding-doors  below  but  forming  no  part 
of  such  support.  In  European  churches  the  general  construction  of  wooden 
screens  is  close  panelling  beneath,  about  3  feet  to  3  feet  6  inches  high,  on 
which  stands  screen  work  composed  of  slender  turned  balusters  or  regular 
wooden  mullions,  supporting  tracery  more  or  less  rich,  with  cornices,  cresting, 
etc.,  and  often  painted  in  brilliant  colors  and  gilded.  These  not  only  enclose  the 
chancels,  but  also  chapels,  chantries,  and  sometimes  even  tombs.  In  English 
mansions,  and  some  private  houses,  the  great  halls  were  screened  off  by  a  low 
passage  at  the  end  opposite  to  the  dais,  over  which  was  a  gallery  for  the  use  of 
minstrels  or  spectators.  These  screens  Avere  sometimes  close  and  sometimes 
glazed. 

Rood-tower.— A  name  given  by  some  writers  to  I:Q  central  tower,  or  that  over 
the  intersection  of  the  nave  and  chancel  with  the  transv,A  '1- 

Roof.— The  covering  or  upper  part  of  any  building. 

Roofing.— The  material  put  on  a  roof  to  make  it  water-tight. 

Rose  Window.— A  name  given  to  a  circular  window  with  radiating  tracery ; 
called  also  wheel  window. 

Rostrum.— An  elevated  platform  from  which  a  speaker  addresses  an  audience. 

Rotunda.— A  building  which  is  round  both  within  and  without.  2.  A  circular 
room  under  a  dome  in  large  buildings  is  also  called  the  rotunda. 

Roughcast.— A  sort  of  external  plastering  in  which  small  sharp  stones  are 
mixed,  and  which,  when  wet,  is  forcibly  thrown  or  cast  from  a  trowel  against 
the  wall,  to  which  it  forms  a  coating  of  pleasing  appearance.  Roughcast  work 
has  been  used  in  Europe  for  several  centuries,  where  it  was  much  used  in  timber 
houses,  and  when  well  executed  the  work  is  sound  and  durable.  The  mortar  for 
roughcast  work  should  always  have  cement  mixed  with  it. 

Rubble  Work. —Masonry  of  rough,  undressed  stones.  When  only  the 
roughest  irregularities  are  knocked  off,  it  is  called  scabbled  rubble,  and  whea  the 


GLOSSARY.  1619 

stones  in  each  course  are  rudely  dressed  to  nearly  a  uniform  height,  ranged 
rubble. 

Rudenture,— The  figure  of  a  rope  or  staff,  which  is  frequently  used  to  fill  up 
the  flutings  of  columns,  the  convexity  of  which  contrasts  with  the  concavity  of 
the  flutings,  and  serves  to  strengthen  the  edges.  Sometimes,  instead  of  a  convex 
shape,  the  flutings  are  filled  with  a  flat  surface  ;  sometimes  they  are  ornament- 
ally carved,  and  sometimes  on  pilasters,  etc.  Euderitures  are  used  in  relief 
without  flutings,  as  their  use  is  to  give  greater  solidity  to  the  lower  part  of  the 
shaft,  and  secure  the  edges.  They  are  generally  only  used  in  columns  which  rise 
from  the  ground  and  are  not  to  reach  above  one-third  of  the  height  of  the 
shaft. 

Rustic  or  Rock  Work. — A  mode  of  building  in  imitation  of  nature.  This  term 
is  applied  to  those  courses  of  stone  work  the  face  of  which  is  jagged  or  picked 
so  as  to  present  a  rough  surface.  That  work  is  also  called  rustic  in  which  the 
horizontal  and  vertical  channels  are  cut  in  the  joinings  of  stones,  so  that  when 
placed  together  an  angular  channel  is  formed  at  each  joint.  Frosted  rustic  work 
has  the  margins  of  the  stones  reduced  to  a  plane  parallel  to  the  plane  of  the 
wall,  the  intermediate  parts  having  an  irregular  surface.  Vermiculated  rustic 
work  has  these  intermediate  parts  so  worked  as  to  have  the  appearance  of  having 
been  eaten  by  worms.  Rustic  chamfered  work,  in  which  the  face  of  the  stones 
is  smooth,  and  parallel  to  the  face  of  the  wall,  and  the  angles  bevelled  to  an 
angle  of  one  hundred  and  thirty-five  degrees  with  the  face  so  that  two  stones 
coming  together  on  the  wall,  the  bevelling  will  form  an  internal  right  angle. 

Sacristy.  —A  small  chamber  attached  to  churches,  where  the  chalices,  vest- 
ment?;  books,  etc.,  were  kept  by  the  officer  called  the  sacristan.  In  the  early 
Christian  basilicas  there  were  two  semicircular  recesses  or  apsides,  one  on  each 
side  of  the  altar.  One  of  these  served  as  a  sacristy,  and  the  other  as  the  biblio- 
theca  or  library.  Some  have  supposed  the  sacristy  to  have  been  the  place  where 
the  vestments  were  kept,  and  the  vestry  that  where  the  priests  put  them  on  ;  but 
we  find  from  Durandus  that  the  sacrarium  was  used  for  both  these  purposes. 
Sometimes  the  place  where  the  altar  stands  enclosed  by  the  rails  has  been  called 
eacrarium. 

Saddle  Bars.— Narrow  horizontal  iron  bars  passing  from  mullion  to  mullion, 
and  often  through  the  whole  window,  from  side  to  side,  to  steady  the  stone  work, 
and  to  form  stays,  to  which  the  lead  work  is  secured.  When  the  bays  of  the 
windows  are  wide,  the  lead  lights  are  further  strengthened  by  upright  bars 
passing  through  eyes  forged  on  the  saddle  bars,  and  called  stanchions.  When 
saddle  bars  pass  right  through  the  mullions  in  one  piece,  and  are  secured  to  the 
jambs,  they  have  sometimes  been  called  stay  bars. 

Sagging. — The  bending  of  a  body  in  the  middle  by  its  own  weight,  or  the  load 
upon  it. 

Salient.— A  projection. 

Salon.— A  spacious  and  elegant  apartment  for  the  reception  of  company,  or 
for  state  purposes,  or  for  the  reception  of  paintings,  and  usually  extending 
through  two  stories  of  the  house.  It  may  be  square,  oblong,  polygonal,  or 
circular. 

Sanctuary.— That  part  of  a  church  where  the  altar  is  placed  ;  also,  the  most 
sacred  or  retired  part  of  a  temple.  2.  A  place  for  divine  worship  ;  a  church. 

Sanctus  Bell-cot,  or  Turret.— A  turret  or  enclosure  to  hold  the  small  bell 
sonnded  at  various  parts  of  the  service,  particularly  where  the  words  "  Sanctus,1' 
etc.,  are  read.  This  differs  but  little  from  the  common  bell-cot,  except  that  it  is 
generally  on  the  lop  of  the  arch  dividing  the  nave  from  the  chancel.  Sometime^ 


1620  GLOSSARY. 

however,  the  bell  seems  to  have  been  placed  in  a  cot  outside  the  wall.    In  Eng. 
land  sanctus  bells  have  also  been  placed  over  the  gables  of  porches.    In  Conti- 
nental  Europe  they  run  up  into  a  sort  of  email  slender  spire,  called  Jlfo/te  in  • 
France,  and  guglio  in  Italy. 

Saracenic  Architecture.— That  Eastern  style  employed  by  the  Saracens,  and 
which  distributed  itself  over  the  world  with  the  religion  of  Mahomet.  It  is  a 
modification  and  combination  of  the  various  styles  of  the  countries  which  they 
conquered. 

Sarcophagus.— A  tomb  or  coffin  made  of  stone,  and  intended  to  contain  the 
body. 

Sash. — The  framework  which  holds  the  glass  in  a  window. 

Scagliola.— An  imitation  of  colored  marbles  in  plaster  work,  made  by  a  com- 
bination of  gypsum,  glue,  isinglass,  and  coloring  matter,  and  finished  with  a 
high  polish,  invented  between  1600  and  1649. 

Scabble.— To  dress  off  the  rougher  projections  of  stones  for  rubble  masonry 
with  a  stone  axe  or  scabbling  hammer. 

Scantling1.— The  dimensions  of  a  piece  of  timber  in  breadth  and  thickness ; 
also,  studding  for  a  partition,  when  under  five  inches  square. 

Scarfing.— The  joining  and  bolting  of  two  pieces  of  timber  together  trans- 
versely, so  thcit  the  two  appear  as  one. 

Sconce.— A  fixed  hanging  or  projecting  candlestick. 

Scotia. — A  concave  moulding,  most  commonly  used  in  bases,  which  projects  a 
deep  shadow  on  itself,  and  is  thereby  a  most  effective  moulding  under  the  eye, 
as  in  a  base.  It  is  like  a  reversed  ovolo,  or,  rather,  what  the  mould  of  an  ovolo 
would  present. 

Scratch  Coat.— The  first  coat  of  plaster,  which  is  scratched  to  afford  a  bond 
for  the  second  coat. 

Screeds. — Long  narrow  strips  of  plaster  put  on  horizontally  along  a  wall,  and 
caref ally  faced  out  of  wind,  to  serve  as  guides  for  plastering  the  wide  intervals 
between  them. 

Screen.— Any  construction  subdividing  one  part  of  a  building  from  another,  a3 
a  choir,  chantry,  chapel,  etc.  The  earliest  screens  are  the  low  marble  podia 
shutting  off  the  chorus  cantantium  in  the  Roman  basilicas,  and  the  perforated 
cancelli  enclosing  the  bema,  altar,  and  seats  of  the  bishops  and  presbyters.  The 
chief  screens  in  a  church  are  those  which  enclose  the  choir  or  the  place  where 
the  breviary  services  are  recited.  In  Continental  Europe  this  is  done  not  only  by 
doors  and  screen  work,  but  also,  when  these  are  of  open  work,  by  curtains,  the 
laity  having  no  part  in  these  services.  In  England  screens  were  of  two  kinds: 
one,  of  open  wood-work,  generally  called  rood-screens  or  jubes,  and  which  the 
French  call  grilles,  dotures  du  chmur ;  the  other,  massive  enclosures  of  stone 
work  enriched  with  niches,  tabernacles,  canopies,  pinnacles,  statues,  crestings, 
etc.,  as  at,  Canterbury,  York,  Gloucester,  and  many  other  places. 

Scribing.— Fitting  wood-work  to  an  irregular  eurface. 

Section. — A  drawing  showing  the  internal  heights  of  the  various  parts  of  a 
building.  It  supposes  the  building  to  be  cut  through  entirely,  so  as  to  exhibit 
the  walls,  the  heights  of  the  internal  doors  and  other  aoertures,  the  heights  of 
the  stories,  thicknesses  of  the  floors,  etc.  It  is  one  of  the  t,pec.'es  of  drawings 
necessary  to  the  exhibition  of  a  Design. 

Sedilia. — Seats  used  by  the  celebrants  during  the  pauses  in  the  mass.  They 
are  generally  three  in  number — for  the  priest,  deacon,  and  sub-deacon— and 
are  in  England  almost  always  a  species  of  niches  cut  into  the  south  walls  of 
churches,  separated  by  shafts  or  by  a  species  of  mullions,  and  crowned  with  can- 
opies, pinnacles,  and  other  enrichments  more  or  less  elaborate.  The  piscina  and 


GLOSSARY.  1621 

ambry  sometimes  are  attached  to  them.  In  Continental  Europe  the  sedilia  are 
often  movable  seats ;  a  single  stone  seat  has  rarely  been  found. 

Set-off. — The  horizontal  line  shown  where  a  wall  is  reduced  in  thickness,  and, 
consequently,  the  part  of  the  thicker  portion  appears  projecting  before  the  thin- 
ner. In  plinths  this  is  generally  simply  chamfered.  In  other  parts  of  work  the 
set-off  is  generally  concealed  by  a  projecting  string.  Where,  as  in  parapets,  the 
upper  part  projects  before  the  lower,  the  break  is  generally  hid  by  a  corbel  table. 
The  portions  of  buttress  caps  which  recede  one  behind  another  are  also  called 
eet-offs. 

Shaft. — In  Classical  architecture  that  part  of  a  column  between  the  necking 
and  the  apophyge  at  the  top  of  the  base.  In  later  times  the  term  is  applied  to 
slender  columns  either  standing  alone  or  in  connection  with  pillars,  buttresses, 
jambs,  vaulting,  etc. 

Shed  Hoof,  or  Lean-to. — A  roof  with  only  one  set  of  rafters,  falling  from  a 
higher  to  a  lower  wall,  like  an  aisle  roof. 

Shore.— A  piece  of  timber  placed  in  an  oblique  direction  to  support  a  building 
or  wall  temporarily  while  it  is  being  repaired  or  altered. 

Shrine. — A  sort  of  ark  or  chest  to  hold  relics.  It  is  sometimes  merely  a 
small  box,  generally  with  a  raised  top  like  a  roof ;  sometimes  an  actual  model  of 
churches  ;  sometimes  a  large  construction,  like  that  of  Edward  the  Confessor  at 
Westminster,  of  St.  Genevieve  at  Paris,  etc.  Many  are  covered  with  jewels  in 
the  richest  way  ;  that  of  San  Carlo  Borromeo,  at  Milan,  is  of  beaten  silver. 

Sills.— Are  the  timbers  on  the  ground  which  support  the  posts  and  superstruct- 
ure of  a  timber  building.  The  term  is  most  frequently  applied  to  those  pieces 
of  timber  or  stone  at  the  bottom  of  doors  or  windows. 

Skewback. — The  inclined  stone  from  which  an  arch  springs. 

Skirting's. — The  narrow  boards  which  form  a  plinth  around  the  margin  of  a 
floor,  now  generally  called  the  base. 

Sleeper.— A  piece  of  timber  laid  on  the  ground  to  receive  floor  joists. 

Soffit.— The  lower  horizontal  face  of  anything,  as,  for  example,  of  an  entab- 
lature resting  on  and  lying  open  between  the  columns  or  the  under  face  of  an 
arch  where  its  thickness  is  seen. 

Sound  Board. — The  covering  of  a  pulpit  to  deflect  the  sound  into  a  church. 

Spall.— Bad  or  broken  brick  :  stone  chips. 

Span.— The  distance  between  the  supports  of  a  beam,  girder,  arch,  truss,  etc. 

Spandrel,  or  Spandril. — The  space  between  any  arch  or  curved  brace  and  the 
level  label,  beams,  etc.,  over  the  same.  The  spandrels  over  doorways  in  Perpen- 
dicular works  are  generally  richly  decorated. 

Specification.— Architect's.  The  designation  of  the  kind,  quality,  and  quantity 
of  work  and  material  to  go  in  a  building,  in  conjunction  with  the  working  draw- 
ings. 

Spire. — A  sharply  pointed  pyramid  or  large  pinnacle,  generally  octagonal  in 
England,  and  forming  a  finish  to  the  tops  of  towers.  Timber  spires  are  very 
common  in  England.  Some  are  covered  with  lead  in  flat  sheets,  others  with  the 
•ame  metal  in  narrow  strips  laid  diagonally.  Very  many  are  covered  with 
Bhingles.  In  Continental  Europe  there  are  some  elegant  examples  of  spires  of 
open  timber  work  covered  with  lead. 

Splayed.— The  jamb  of  a  door,  or  anything  else  of  which  one  side  makes  an 
oblique  angle  with  the  other. 

Springer.— The  stone  from  which  an  arch  springs  :  in  some  cases  this  is  a 
capital,  or  impost ;  in  other  cases  the  mouldings  continue  down  the  pier.  The 
Jowest  stone  of  the  gable  is  sometimes  called  a  springer. 

Squinches.— Small  arches  or  corbelled  set-offs  running  diagonally  and,  as  it 


1622  GLOSSARY, 

were,  cutting  off  the  corners  of  the  interior  of  towers,  to  bring  them  from  the 
square  to  the  octagon,  etc.,  to  carry  the  spire. 

Squint.— An  oblique  opening  in  the  wall  of  a  church ;  especially,  in  medieval 
architecture,  an  opening  so  placed  as  to  afford  a  view  of  the  high  altar  from  the 
transept  or  aisles. 

Staging". — A  structure  of  posts  and  boards  for  supporting  workmen  and 
material  in  building. 

Stall,— A  fixed  seat  in  the  choir  for  the  use  of  the  clergy.  In  early  Christian 
times  the  thronus  cathedra,  or  seat  of  the  bishop,  \vas  in  the  centre  of  the  apsis 
or  bema  behind  the  altar,  and  against  the  wall ;  those  of  the  presbyters  also  were 
against  the  wall,  branching  off  from  side  to  side  around  the  semicircle.  In  later 
times  the  stalls  occupied  both  sides  of  the  choir,  return  seats  being  placed  at  the 
ends  for  the  prior,  dean,  precentor,  chancellor,  or  other  officers.  In  general,  in 
cathedrals,  each,  stall  is  surmounted  by  tabernacle  work,  and  rich  canopies, 
generally  of  oak. 

Stanchion.— A  word  derived  from  the  French  etan$on,  a  wooden  post,  applied 
to  the  upright  iron  bars  which  pass  through  the  eyes  of  the  saddle  bars  or  hori- 
zontal irons  to  steady  the  lead  lights.  The  French  call  the  latter  traverses,  the 
stanchions  montants,  and  the  whole  arrangement  armature.  Stanchions  fre- 
quently finish  with  ornamental  heads  forged  out  of  the  iron. 

Steeple. — A  general  name  for  the  whole  arrangement  of  tower,  belfry,  spire, 
etc. 

Stereobate.— A  basement,  distinguished  from  the  nearly  equivalent  term  sty- 
lobate  by  the  absence  of  columns. 

Stile.—  Trie  upright  piece  in  framing  or  panelling. 

Stilted.— Anything  raised  above  its  usual  level.  An  arch  is  stilted  when  its 
centre  is  raised  above  the  line  from  which  the  arch  appears  to  spring. 

Stoop. — A  seat  before  the  door  ;  often  a  porch  with  a  balustrade  and  seats  on 
the  sides. 

Stoup.— A  basin  for  holy  water  at  the  entrance  of  Roman  Catholic  churches, 
into  which  all  who  enter  dip  their  fingers  and  cross  themselves. 

Straight  Arch.— A  form  of  arch  in  which  the  intrados  is  straight,  but  with 
Us  joints  radiating  as  in  a  common  arch. 

Strap.— An  iron  plate  for  connecting  two  or  more  timbers,  to  which  it  is 
screwed  by  bolts.  It  generally  passes  around  one  of  the  timbers. 

Stretcher. — A  brick  or  block  of  masonry  laid  lengthwise  of  a  wall. 

String  Board. — A  board  placed  next  to  the  well-hole  in  wooden  stairs,  termi- 
nating the  ends  of  the  steps.  The  string  piece  is  the  piece  of  board  put  under 
the  treads  and  risers  for  a  support,  and  forming  the  support  of  the  stair. 

String-course. — A  narrow,  vertically  faced  and  slightly  projecting  course  in 
an  elevation.  If  window-sills  are  made  continuous,  they  form  a  string-course  : 
but  if  this  course  is  made  thicker  or  deeper  than  ordinary  window-sills,  or  covers 
a  set-off  in  the  wall,  it  becomes  a  blocking-course.  Also,  horizontal  mouldings 
running  under  windows,  separating  the  walls  from  the  plain  part  of  the  parapets, 
dividing  towers  into  stories  or  stages,  etc.  Their  section  is  much  the  same  as 
the  labels  of  the  respective  periods  ;  in  fact,  these  last,  after  passing  round  the 
windows,  frequently  run  on  horizontally  and  form  strings.  Like  labels,  they  are 
often  decorated  with  foliages,  ball-flowers,  etc. 

Studs,  or  Studding. — The  small  timbers  used  in  partitions  and  outside  wrooden 
walls,  to  which  the  laths  and  boards  are  nailed 

Style.— The  term  style  in  architecture  has  obtained  a  conventional  meaning 
beyond  its  simpler  one,  which  applies  only  to  columns  and  columnar  arrange- 
ments. It  is  now  used  to  signify  the  differences  in  the  mouldings,  general  out- 


GLOSSARY.  1623 

lines,  ornaments,  and  other  details  which  exist  between  the  works  of  various 
nations,  and  also  those  differences  which  are  found  to  exist  between  the  works 
of  any  nation  at  different  times. 

Stylobate.— A  basement  to  columns.  Stylobate  is  synonymous  with  pedestal, 
but  is  applied  to  a  continued  and  unbroken  substructure  or  basement  to  columns, 
while  the  latter  term  is  confined  to  insulated  supports.  The  Greek  temples  gen- 
erally had  three  or  more  steps  all  around  the  temple,  the  base  of  the  column 
resting  on  the  top  step  ;  this  was  the  Stylobate. 

Subsellium.— A  name  sometimes  given  to  the  seat  in  the  stalls  of  churches  ; 
same  as  miserere. 

Summer, — A  girder  or  main-beam  of  a  floor  ;  if  supported  on  two-story  posts 
and  open  below,  it  is  called  a  Brace-summer. 

Surbase.— A  cornice  or  series  of  mouldings  on  the  top  of  the  base  of  a  pedes- 
tal, podium,  etc.;  a  moulding  above  the  base. 

Surface.— To  make  plane  and  smooth. 

Systyle. — An  intercolumniation  to  which  two  diameters  are  assigned. 

Tabernacle. — A  species  of  niche  or  recess  in  which  an  image  may  be  placed. 
They  are  generally  highly  ornamented  and  often  surmounted  with  crocketed 
gables.  The  word  tabernacle  is  also  often  used  to  denote  the  receptacle  for  relicB, 
which  was  often  made  in  the  form  of  a  small  house  or  church. 

Tabernacle  Work.— The  rich  ornamental  tracery  forming  the  canopy,  etc., 
to  a  tabernacle,  is  called  tabernacle  work  ;  it  is  common  in  the  stalls  and  screens 
of  cathedrals,  and  in  them  is  generally  open  or  pierced  through. 

Tail  Trimmer.— A  trimmer  next  to  the  wall,  into  which  the  ends  of  joists  are 
fastened  to  avoid  flues. 

Tamp. — To  pound  the  earth  down  around  a  wall  after  it  has  been  thrown  in. 

Tapestry.— A  kind  of  woven  hangings  of  wool  or  silk,  ornamented  with  figures, 
and  used  formerly  to  cover  and  adorn  the  walls  of  rooms.  They  were  often  of 
the  most  costly  materials  and  beautifully  embroidered. 

Temple.— An  edifice  destined,  in  the  earliest  times,  for  the  public  exercise  of 
religious  worship. 

Templet,  or  Template. — A  mould  used  by  masons  for  cutting  or  setting 
work.  2.  A  short  piece  of  timber  sometimes  laid  under  a  girder. 

Terminal.— Figures  of  which  the  upper  parts  only,  or  perhaps  the  head  and 
shoulders  alone,  are  carved,  the  rest  running  into 
a  parallelepiped,  and  sometimes  into  a  diminishing 
pedestal,  with  feet  indicated  below,  or  even  with- 
out them,  are  called  terminal  figures. 

Terra-cotta.— Baked  clay  of  a  fine  quality. 
Much  used  for  bas-reliefs  for  adorning  the  friezes 
of  temples.  In  modern  times  employed  for  archi- 
tectural ornaments,  statues,  vases,  etc. 

Tessellated  Pavements.— Those  formed  of 
tesserae,  or,  as  some  write  it,  tessellae,  or  small 
cubes  from  half  an  inch  to  an  inch  square,  like 
dice,  of  pottery,  stone,  marble,  enamel,  etc. 

Tetrastyle.  —  A  portico  of  four  columns  in 
front. 

Tholobate.— That  on  which  a  dome  or  cupola 
rests.  This  is  a  term  not  in  general  use,  but  it  is  ANCIENT  TERMINI. 

not  the  less  of  useful  application.  What  is  generally  termed  the  attic  above  the 
peristyle  and  under  the  cupola  of  St.  Paul's,  London,  would  be  correctly  desig- 


1624  GLOSSARY. 

nated  the  tholobate.  A  tholobate  of  a  different  description,  and  one  to  which 
no  other  name  can  well  be  applied,  is  the  circular  substructure  to  the  cupola  ol 
the  University  College,  London. 

Throat. — A  channel  or  groove  made  on  the  under-side  of  a  string-course, 
coping,  etc.,  to  prevent  water  from  running  inward  toward  the  walls. 

Tie.— A  timber,  rod,  chain,  etc.,  binding  two  bodies  together,  which  have  a 
tendency  to  separate  or  diverge  from  each  other.  The  tie-beam  connects  the 
bottom  of  a  pair  of  principal  rafters,  and  prevents  them  from  bursting  out  the 
wall. 

Tiles. — Flat  pieces  of  clay  burned  in  kilns,  to  cover  roofs  in  place  of  slates 
or  lead.  2.  Also,  flat  pieces  of  burned  clay,  either  plain  or  ornamented,  glazed 
or  unglazed,  used  for  floors,  wainscoting,  and  about  fireplaces,  etc.  3.  Small 
square  pieces  of  marble  are  also  called  tile. 

Tongue.— The  part  of  a  board  left  projecting,  to  be  inserted  into  a  groove. 

Tooth  Ornament. — One  of  the  peculiar  marks  of  the  Early  English  period  of 
Gothic  architecture,  generally  inserted  in  the  hollow  mouldings  of  doorways, 
Windows,  etc. 

Torso.— Amutilated  statue  of  which  nothing  remains  but  the  trunk.  Columns 
With  twisted  shafts  have  also  this  term.  Of  this  kind  there  are  several  varieties. 

Torus. — A  protuberance  or  swelling,  a  moulding  whose  form  is  convex, 
and  generally  nearly  approaches  a  semicircle.  It  is 

most  frequently  used  in  bases,  and  is  generally  the    /"I""]  *\ 

lowest  moulding  in  a  base.  \\_.  •  J 

Tower. — An  elevated  building  originally  designed  TORUS. 

for  purposes  of  defence.    Those  buildings  are  of  the 

remotest  antiquity,  and  are,  indeed,  mentioned  in  the  earliest  Scriptures.  In 
mediaeval  times  they  were  generally  attached  to  churches,  to  cemeteries,  to  cas- 
tles, or  used  as  bell-towers  in  public  places  of  large  cities.  In  churches,  the 
towers  of  the  Saxon  period  were  generally  square.  Norman  towers  were  also 
generally  square.  Many  were  entirely  without  buttresses  ;  others  had  broad, 
flat,  shallow  projections  which  served  for  this  purpose.  The  lower  windows  were 
very  narrow,  with  extremely  wide  splays  inside,  probably  intended  to  be  de- 
fended by  archers.  The  upper  windows,  like  those  of  the  preceding  style,  were 
generally  separated  into  two  lights,  but  by  a  shaft  or  short  column,  and  not  by  a 
baluster.  Early  English  towers  were  generally  taller,  and  of  more  elegant  pro- 
portions. They  almost  always  had  large  projecting  buttresses,  and  frequently 
stone  staircases.  The  lower  windows,  as  in  the  former  style,  were  frequently 
mere  arrow-slits  ;  the  upper  were  in  couplets  or  triplets,  and  sometimes  the 
tower  top  had  an  arcade  all  round.  The  spires  were  generally  broach  spires ; 
but  sometimes  the  tower  tops  finished  with  corbel  courses  and  plain  parapets, 
and  (rarely)  with  pinnacles.  There  are  a  few  Early  English  towers  which  break 
into  the  octagon  from  the  square  toward  the  top,  and  still  fewer  which  finish 
with  two  gables.  Both  these  methods  of  termination,  however,  are  common 
in  Continental  Europe.  At  Vendome,  Chartres,  and  Senlis  the  towers  have 
octagonal  upper  stages  surrounded  with  pinnacles,  from  which  elegant  spires 
arise.  In  the  North  of  Italy,  and  in  Rome,  they  are  generally  tall  square  shafts 
in  four  to  six  stages,  without  buttresses,  with  couplets  or  triplets  of  semicircular 
windows  in  each  stage,  generally  crenellated  at  top,  and  covered  with  a  low 
pyramidal  roof.  The  well-known  leaning  tower  at  Pisa  is  cylindrical,  in  five 
Stories  of  arcaded  colonnades.  In  Ireland  there  are  in  some  of  the  churchyards 
very  curious  round  towers. 

Tracery. — The  ornamental  filling  in  of  the  heads  of  windows,  panels,  circular 
Windows,  etc.,  which  has  given  such  characteristic  beauty  to  the  architecture  of 


GLOSSAKY.  1625 

the  fourteenth  century.  Like  almost  everything  connected  with  mediaeval  aichi- 
tecture,  this  elegant  and  sometimes  fairy-like  decoration  seems  to  have  sprung 
from  the  smallest  beginnings.  The  circular-headed  window  of  the  Normans 
gradually  gave  way  to  the  narrow-pointed  lancets  of  the  Early  English  period, 
and,  as  less  light  was  afforded  by  the  latter  system  than  by  the  former,  it  was 
necessary  to  have  a  greater  number  of  windows  ;  and  it  was  found  convenient  to 
group  them  together  in  couplets,  triplets,  etc.  When  these  couplets  were 
assembled  under  one  label,  a  sort  of  vacant  space  or  spandrel  was  formed  over 
the  lancets  and  under  the  label.  To  relieve  this,  the  first  attempts  were  simply  to 
perforate  this  flat  spandrel,  first  by  a  simple  lozenge-shaped  or  circular  opening, 
and  afterward  by  a  quatrefoil.  By  piercing  the  whole  of  the  vacant  spaces  in 
the  window  head,  carrying  mouldings  around  the  tracery,  and  adding  cusps  to  it, 
the  formation  of  tracery  was  complete,  and  its  earliest  result  was  the  beautiful 
geometrical  work  such  as  is  found  at  Westminster  Abbey. 

Transept,— That  portion  of  a  church  which  passes  transversely  between  the 
nave  and  choir  at  right  angles,  and  so  forms  a  cross  on  the  plan. 

Transom.— The  horizontal  construction  which  divides  a  window  into  heights 
or  stages.  Transoms  are  sometimes  simple  pieces  of  mullions  placed  trans- 
versely [as  cross-bars,  and  in  later  times  are  richly  decorated  with  cuspings, 
etc. 

Traverse. — To  plane  in  a  direction  across  the  grain  of  the  wood,  as  to  traverse 
a  floor  by  planing  across  the  boards. 

Tread.— The  horizontal  part  of  a  step  of  a  stair. 

Trefoil.— A  cusping  the  outline  of  which  is  derived  from  a  three-leaved  flower 
or  leaf,  as  the  quatrefoil  and  cinque-foil  are  from  those  with  four  and  five. 

Trellis.— Lattice-work  of  metal  or  wood  for  vines  to  run  on. 

Trestle.— A  movable  frame  or  support  for  anything ;  when  made  of  a  cross 
piece  with  four  legs  it  is  called  by  carpenters  a  horse. 

Triforium.— The  arcaded  story  between  the  lower  range  of  piers  and  arches 
and  the  clere-story.  The  name  has  been  supposed  to  be  derived  from  ires  and 
fores— three  doors,  or  openings— that  being  a  frequent  number  of  arches  in  each 
bay. 

Triglyph.— The  vertically  channelled  tablets  of  the  Doric  frieze  are  called 
triglyphs,  because  of  the  three  angular  channels  in  them— two  perfect  and  one 
divided — the  two  chamfered  angles  or  hemiglyphs  being  reckoned  as  one.  The 
square  sunk  spaces  between  the  triglyphs  on  a  frieze  are  called  metopes. 

Trim.— Of  a  door,  sometimes  used  to  denote  the  locks,  knobs,  and  hinges. 

Trimmer.— The  beam  or  floor  joist  into  which  a  header  is  framed. 

Trimmer  Arch.— An  arch  built  in  front  of  a  fireplace,  in  the  thicknc  ^s  of  the 
floor,  between  two  trimmers.  The  bottom  of  the  arch  starting  from  the  chimney 
and  the  top  pressing  against  the  header. 

Tuck-pointing.— Marking  the  joints  of  brickwork  with  a  narrow  parallel 
ridge  of  fine  putty. 

Tudor  Style. — The  architecture  which  prevailed  in  England  during  the  reign 
of  the  Tudors  ;  its  period  is  generally  restricted  to  the  end  of  the  reign  of  Henry 
VIII. 

Turret.— A  small  tower,  especially  at  the  angles  of  larger  buildings,  sometimes 
overhanging  and  built  on  corbels,  and  sometimes  rising  from  the  ground. 

Tuscan  Order.— The  plainest  of  the  five  orders  of  Classic  architecture. 

Tympanum.— The  triangular  recessed  space  enclosed  by  the  cornice  which 
bounds  a  pediment.  The  Greeks  often  placed  sculptures  representing  subjects 
connected  with  the  purposes  of  the  edifice  in  the  tympana  of  temples,  as  at  the 
Parthenon  and  JSgina. 


1626 


GLOSSARY. 


Under-CroKr.—  A  vaulted  chamber  under  ground. 

Upset.— To  thicken,  and  shorten  as  by  hammering  a  heated  bar  of  iron  on  the 
end. 

Vagina,— The  upper  part  of  the  shaft  of  a  terminus,  from  which  the  bust  or 
figure  seems  to  rise. 

Valley. — The  internal  angle  formed  by  two  inclined  sides  of  a  roof. 

Valley  Rafters.— Those  which  are  disposed  in  the  internal  angle  of  a  roof  to 
form  the  valleys. 

Vane,— The  weathercock  on  a  steeple.  In  early  times  it  seems  to  have  been 
of  various  forms,  as  dragons,  etc. ;  but  in  the  Tudor  period  the  favorite  design 
was  a  beast  or  bird  sitting  on  a  slender  pedestal,  and  carrying  an  upright  rod, 
on  which  a  thin  plate  of  metal  is  hung  like  a  flag,  ornamented  in  various 
ways. 

Vault.— An  arched  ceiling  or  roof.  A  vault  is,  indeed,  a  laterally  conjoined 
series  of  arches.  The  arch  of  a  bridge  is,  strictly  speaking,  a  vault.  Intersect- 
ing vaults  are  said  to  be  groined.  See  Groined  Vaulting  for  fuller  description  of 
vaults. 

Verge.— The  edge  of  the  tiling,  slate  or  shingles,  projecting  over  the  gable  of  a 
roof,  that  on  the  horizontal  portion  being  called  eaves. 

Verge  Board.— Often  corrupted  into  Barge  Board  ;  the  board  under  the  verge 
of  gables,  sometimes  moulded,  and  often  very  richly  carved,  perforated,  and 
cusped,  and  frequently  having  pendants,  and  sometimes  finials,  at  the  apex. 

Vermiculated,— Stones,  etc.,  worked  so  as  to  have  the  appearance  of  having 
been  worked  by  worms. 

Vestibule. — An  anti-hall,  lobby,  or  porch. 

Vestry. — A  room  adjoining  a  church,  where  the  vest- 
ments of  the  minister  are  kept  and  parish  meetings  held. 
In  American  Protestant  churches,  the  Sunday-school 
room  is  often  called  the  vestry. 

Viaduct.— A  structure  of  considerable  magnitude, 
and  usually  of  masonry,  for  carrying  a  railway  across  a 
valley. 

Vignette,— A  running  ornament,  representing,  as  its  name  imports,  a  little 
vine,  with  branches,  leaves,  and  grapes.  It  is  common  in  the  Tudor  period, 
and  runs  or  roves  in  a  large  hollow  or  casement.  It  is  also  called  Trayle. 

Villa. — A  country  house  for  the  retreat  of  the  rich. 

Volute. — The  convolved  or  spiral  ornament  which  forms  the  characteristic  of 
the  Ionic  capital.  Volute,  scroll,  helix,  and  cauliculus  are  used  indifferently  for 
the  angular  horns  of  the  Corinthian  capital. 

Voussoir.— One  of  the  wedge-like  stones  which  form  an  arch  ;  the  middle  one 
is  called  the  key-stone. 

Wainscot.— The  wooden  lining  of  walls,  generally  in  panels. 

Wall  Plates.— Pieces  of  timber  which  are  placed  on  top  of  brick  or  stone 
walls  so  as  to  form  the  support  to  the  roof  of  a  building. 

Warped, — Twisted  out  of  shape  by  seasoning. 

Water  Table.— A  slight  projection  of  the  lower  masonry  or  brickwork  on  the 
outside  of  a  wall  a  few  feet  above  the  ground  as  a  protection  against  rain. 

Weather  Boarding,— Boards  lapped  over  each  other  to  prevent  rain,  etc., 
from  passing  through. 

Weathering.— A  slight  fall  on  the  top  of  cornices,  window-sills,  etc.,  to  throw 
off  the  rain. 


VERMICULATED. 


GLOSSABY.  1627 

Wicket.— A  email  door  opening  in  a  larger.  They  are  common  in  mediaeval 
doors,  and  were  intended  to  admit  single  persons,  and  guard  against  sudden 
surprises. 

Wind. — A  turn,  a  bend.  A  wall  is  out  of  wind  when  it  is  a  perfectly  flat 
surface. 

"Wing.— A  side  building  less  than  the  main  building. 

Withes.— The  partition  between  two  chimney  flues  in  the  same  stack. 


ARCHITECTURAL  TERMS  AS  DEFINED  IN 
VARIOUS  BUILDING  LAWS, 

COMPILED  BY  THE  AMERICAN  ARCHITECT  AND  BUILDING 
NEWS,  PAGE  150,  VOL.  XXXIII. 

(Republished  by  permission  of  Tickuor  &  Co.) 


TERMS  DEFINED. 

[The  following  terms  chance  to  be  defined  in  sundry  building  codes— which  are 
mentioned  in  each  case.  The  fact  that  other  codes  are  not  mentioned  is  not 
necessarily  a  proof  that  the  term  is  not  also  elsewhere  in  use  as  defined.] 

Adjoining  Owner.— The  owner  of  the  premises  adjoining  those  on  which 
work  is  doing  or  to  be  done.  [District  of  Columbia.] 

Alteration. — Any  change  or  addition  except  necessary  repairs  in,  to,  or  upon 
any  building  affecting  an  external,  party,  or  partition  wall,  chimney,  floor,  or 
stairway,  and  "  to  alter  "  means  to  make  such  change  or  addition.  [Boston  and 
Denver.] 

Appendages. — Dormer-windows,  cornices,  mouldings,  bay-windows,  towers, 
spires,  ventilators,  etc.  [Chicago;  Minneapolis.] 

Areas. — Sub-surface  excavations  adjacent  to  the  building-line  for  lighting  or 
ventilation  of  cellars  or  basements.  [District  of  Columbia.] 

Attic  Story.— A  story  situated  either  in  whole  or  in  part  in  the  roof.  [Denver 
and  District  of  Columbia.] 

Base. — "  The  base  of  a  brick  wall"  means  the  course  immediately  above  the 
foundation  wall.  [  Cincinnati  and  Cleveland.] 

Basement  Story.— One  whose  floor  is  12"  or  more  below  the  sidewalk,  and 
whose  height  does  not  exceed  12'  in  the  clear ;  all  such  stories  that  exceed 
12'  high  shall  be  considered  as  first  stories.  [Chicago,  Louisville.] 

A  story  whose  floor  is  12"  or  more  below  the  grade  of  sidewalk.     [Milwaukee.] 

A  story  whose  floor  is  3'  or  more  below  the  sidewalk,  and  whose  height  does 
not  exceed  II7  in  the  clear ;  all  such  stories  that  exceed  11'  high  shall  be  con. 
sidered  as  first  stories.  [Minneapolis.] 

A  story  suitable  for  habitation,  partially  below  the  level  of  the  adjoining  street 
or  ground. »  [District  of  Columbia  and  Denver. "\ 

(See  Cellar.) 

Bay-window. — A  first-floor  projection  for  a  window  other  than  a  tower-pro- 
jection or  show-window.  [District  of  Columbia.] 

Any  projection  for  a  window  other  than  a  show-window.     [Denver.] 

i  And  below  the  first  floor  of  joists.    [District  of  Columbia.] 

1628 


LEGAL  DEFINITIONS   OF  ARCHITECTUKAL   TEBMS.  1629 

Bearing  Walls.— Those  on  which  beams,  trusses,  or  girders  rest.  [New  York 
and  San  Francisco. } 

Brick  Building. — A  building  the  walls  of  which  are  built  of  brick,  stone, 
iron,  or  other  substantial  and  incombustible  materials.  [Boston,  Denver,  and 
Kansas  City} 

Building. — Any  construction  within  the  scope  and  purview  of  these  regula- 
tions. [District  of  Columbia.} 

Building  Line.— The  line  of  demarcation  between  public  and  private  space. 
[District  of  Columbia.} 

Building  Owner.— The  owner  of  premises  on  which  work  is  doing  or  to  be 
done.  [District  of  Columbia.} 

Business  buildings  shall  embrace  all  buildings  used  principally  for  business 
purposes,  thus  including,  among  others,  hotels,  theatres,  and  office-buildings. 
[Chicago,  Louisville,  Milwaukee,  and  Minneapolis} 

Cellar. — Basement  or  lower  story  of  any  building,  of  which  one-half  or  more 
of  the  height  from  the  floor  to  the  ceiling  is  below  the  level  of  the  street5 
adjoining.2  [Boston,  Denver,  and  Kansas  City.} 

Portion  of  building  below  first  floor  of  joists,  if  partially  or  entirely  below  the 
level  of  the  adjoining  parking,  street,  or  ground,  and  not  suitable  for  habitation. 
I  District  of  Columbia.] 

Cement-mortar.— A  proper  proportion  of  cement  and  sand  without  the  ad- 
mixture of  lime.  [Kansas  City.} 

Division  Wall.— One  that  separates  part  of  any  building  from  another  part 
of  the  same  building.  [Cincinnati  and  Cleveland.} 

Floor- bearing  walls  extending  through  buildings  from  front  to  rear,  and  sepa- 
rating stores  and  tenements  in  buildings  or  blocks  owned  by  the  same  parly. 
{Minneapolis .] 

(See  Partition-wall.) 

Dwelling-house  Class.— All  buildings  except  public  buildings  and  buildings 
of  the  warehouse  class.  {Cincinnati  and  Cleveland.} 

Shall  not  apply  to  buildings  accommodating  more  than  three  families.  [San 
Francisco.} 

External  Wall.— Every  outer  wall  or  vertical  enclosure  of  a  building  other 
than  a  party-wall.  [Boston,  Cincinnati,  Cleveland,  Denver,  District  of  Columbia, 
Kansas  City,  and  Providence.} 

First  Story.— The  story  the  floor  of  which  is  at  or  first  above  the  level  of  the 
sidewalk  or  adjoining  ground,  the  other  stories  to  be  numbered  in  regular  suc- 
cession, counting  upward.  [Denver  and  District  of  Columbia.} 

Footing  Course.— A  projecting  course  or  courses  under  base  of  foundation 
wall.  [Cincinnati and  Cleveland .} 

Foundation.— That  portion  of  wall  below  level  of  street  curb,3  and,  where  the 
wall  is  not  on  a  street,  that  portion  of  wall  below  the  level  of  the  highest  ground 
next  to  the  wall.  [Boston,  Kansas  City,  New  York,  and  Providence.} 

Portion  of  exterior  wall  below  surface  of  adjoining  earth  or  pavement,  and 
portion  of  partition  or  party  wall  below  level  of  basement  or  cellar  floor. 
[District  of  Columbia  and  Denver.} 

Foundation,  Basement,  or  Cellar  Walls.— That  part  of  walls  of  building  that 
are  below  the  floor  or  joists,  which  are  on  or  next  above  the  grade  line.  \ Detroit.} 

i  Ground.    [Providence.] 

*  And  not  suitable  for  habitation.     [Denver.} 

*  "And  serve  as  supports  for  piers,  columns,  girders,  beams,  or  other  walls.1* 
INew  York.} 


1G30  LEGAL  DEFINITIONS  OF  ARCHITECTURAL  TERMS. 

Portion  of  the  wall  below  the  level  of  street  curb,  in  fronf  of  the  central  line  ot 
building.  [San  Francisco.] 

Incombustible  scantling  partition.— One  plastered  on  both  sides  upon  iron 
lath  or  wire  cloth,  and  filled  in  with  brickwork  8"  high  from  floor,  provided  the 
build  Jig  is  not  over  80'  high.  [  Chicago,"] 

Incombustible  Roofing.— Covered  with  not  less  than  three  (3)  thicknesses 
roofing-felt,  and  good  coat  of  tar  and  gravel,  or  with  tin,  corrugated-iron,  or  other 
fire-resisting  material  with  standing-seam  or  lap-joint.  [Denver.] 

Lengths.— Walls  are  deemed  to  be  divided  into  distinct  lengths  by  return 
walls,  and  the  length  of  every  wall  is  measured  from  the  centre  of  one  return 
wall  to  the  centre  of  another,  provided  that  such  return  walls  are  external  or 
party  cross-walls  of  the  thickness  herein  required,  and  bonded  into  the  walls  so 
deemed  to  be  divided.  [Cincinnati  and  Cleveland.] 

Inflammable  Material. — Dry  goods,  clothing,  millinery,  and  the  like  in 
stores,  flyings  or  goods  in  factories,  or  other  substance  readily  ignited  by  drop- 
pings or  flyings  from  electric  lights.  [Minneapolis.'] 

Lodging-house.— A  building  in  which  persons  are  temporarily  accommodated 
with  sleeping  1  apartments,  and  includes  hotels.  [Boston  and  Kansas  City.] 

Any  building  or  portion  thereof  in  which  persons  are  lodged  for  hire  for  less 
than  a  week  at  one  time.  [District  of  Columbia  and  Providence.'} 

Any  building  or  portion  thereof  in  which  persons  are  lodged  for  hire  tempo- 
rarily, and  includes  hotels.  [Denver.] 

Mansard  Boof.— One  formed  with  an  upper  and  under  set  of  rafters,  the 
upper  set  more  inclined  to  the  horizon  than  the  lower  set.  [Denver  and  District 
of  Columbia.] 

Oriel  Window.— A  projection  for  a  window  above  the  first  floor.  [District 
of  Columbia.] 

Partition.— An  interior  division  constructed  of  iron,  glass,  wrood,  lath  and 
plaster,  or  other  destructible  natures.  [District  of  Columbia.] 

Partition- wall.— Any  interior  wall  of  masonry  in  a  building.  [Boston, 
Kansas  City,  and  Providence.] 

An  interior  wall  of  non-combustible  material.    [District  of  Columbia.] 

Any  interior  division  constructed  of  iron,  glass,  wood,  lath  and  plaster,  or 
any  combination  of  those  materials.  [Denver.] 

(See  Division  Wall.) 

Party-wall.— Every  wall  used,  or  built,  in  order  to  be  used,  as  a  separation 
of  two  or  more  buildings.3  [Boston,  Cincinnati,  Cleveland^  Denver^  Kansas 
City,  and  Providence.] 

A  wall  built  upon  dividing  line  between  adjoining  premises  for  their  common 
use.  [District  of  Columbia.] 

Parking. — The  space  between  the  sidewalk  and  the  building  line.  [District 
of  Columbia.] 

Parking  Line.— The  line  separating  parking  and  sidewalk.  [District  of 
Columbia.'] 

Public  Building. — Every  building  used  as  church,  chapel,  or  other  place  of 
public  worship  ;  also  every  building  used  as  a  college,  school,  public  hall, 
hospital,  theatre,  public  concert-room,  public  ball-room,  public  lecture-room,  or 
for  any  public  assemblage.  [Boston,  Chicago,  Cincinnati,  Cleveland,  Denver, 
Kansas  City,  and  Minneapolis.] 

Such  buildings  as  shall  be  owned  and  occupied  for  public  purposes  for  this 

*  Staying  apartment?.     [Kansas  City."] 

2 To  be  used  jointly  by  separate  buildings.     [Cincinnati  and  Cleveland.] 


LEGAL   DEFINITIONS   OF  ARCHITECTURAL  TERMS.  1631 

State,  the  United  States,  the  corporation  of  the  City  of  Brooklyn,  or  other 
public  schools  within  said  city.  [Brooklyn.] 

Public  Hall.— Every  theatre,  opera-house,  hali,  church,  school,  or  other  build- 
ing intended  to  be  used  for  public  assemblage.  [Milwaukee  and  Louisville.] 

Return  Wall.— No  wall  subdividing  any  building  shall  be  deemed  a  return 
wall,  as  before  mentioned,  unless  it  is  two-thirds  the  height  of  the  external  or 
party-walls.  [Cincinnati  and  Cleveland.] 

Shed.— A  skeleton  structure  for  storage  or  shelter.     [District  of  Columbia.} 

Open  structure,  enclosed  only  on  one  side  and  end,  and  erected  on  the 
ground.  [San  Francisco~\ 

Open  or  closed  board  structure.     [Denver.]  i 

Show-window.— A  store- window  in  which  goods  are  displayed  for  sale  or 
advertisement.  [District  of  Columbia  and  Denver.] 

Square  thereof.— The  square  or  level  of  the  walls  before  commencing  the 
pitch  for  roof.  [District  of  Columbia.] 

Standard  Depth  for  Foundations.— For  brick  and  stone  buildings,  14' 
below  curb  line.  [San  Francisco.] 

Standard  Depth  of  Cellars.— 16',  measured  down  from  sidewalk  grade  at 
property  line.  [Memphis.] 

Standard  Iron  Door.— Made  of  No.  12  plate-iron,  frame  or  continuous 
12"  x  2"  x  f '  angle -iron,  firmly  riveted.  Two  panel  doors,  to  have  proper  cross- 
bars, one  panel  on  either  side,  fastened  together  with  hooks  or  proper  bolts  top 
and  bottom,  and  with  not  less  than  two  lever -bars.  All  doors  hung  on  iron 
frames  of  §'  x  4"  iron,  securely  bolted  together  through  wall,  swung  on  three 
hinges,  fitting  close  to  frame  all  around  ;  sill  between  doors,  iron,  brick,  or  stone, 
to  rise  not  less  than  two  (2)  inches  above  floor  on  each  side  of  opening.  Lintel 
over  door,  brick,  iron,  or  stone.  Floors  of  basement,  when  doors  are  to  swing, 
stone  or  cement,  in  no  case  wood.  [Denver.] 

Standard  Skylight.— Constructed  of  wrought-iron  frames,  with  hammered 
or  desk-light  glass  not  less  than  i"  thick  ;  not  larger  than  10'  by  12',  except  by 
special  permission  of  the  Inspector.  [Denver] 

Storehouse. -(See  Warehouse  Class.) 

Street.— All  streets,  avenues,  and  public  alleys.     [Minneapolis .] 

Tenement-house.— A  building  which,  or  any  portion  of  which,  is  to  be  occu- 
pied, or  is  occupied,  as  a  dwelling  by  more  than  three  l  families  living  independ- 
ently of  one  another,  and  doing  their  cooking  upon  the  premises.  [Boston, 
Denver  i  and  Kansas  City.] 

Or  by  more  than  two  families2  above  the  second  floor,  so  living  and  cooking. 
[Boston  and  Kansas  City.] 

Building  which  shall  contain  more  than  two  rooms  in  front  on  each  floor,  or 
which  shall  be  built  with  a  passage  or  arched  way  between  distinct  parts  of  the 
samo  building,  or  which  building  shall  be  intended  for  the  separate  accommoda- 
tion of  different  families  or  occupants.  [Charleston.] 

Theatre. — Public  hall  containing  movable  scenery  or  fixed  scenery  which 
is  not  made  of  metal,  plaster,  or  other  incombustible  material.  [Chicago,  Louis- 
mile,  and  Milwaukee.'] 

Thickness  of  a  Wall.— The  minimum  thickness  of  such  wall.3  [Boston, 
Cincinnati,  Cleveland,  Kansas  City,  Milwaukee,  and  Providence.] 

1  Two  instead  of  three.     [District  of  Columbia  and  Minneapolis.] 
•Upon  one  floor,  but  having  a  common  right  in  the  halls,  stairways,  yards, 
etc.    [Providence.] 
8  As  applied  to  solid  walla .     [Minneapolis  and  Providence.} 


1632  LEGAL   DEFINITIONS   OF  ARCHITECTTJKAL  TERMS. 

Tinned  Covered  Fire-door. -Wood  doors  or  shutters,  double  thickness  of 
wood,  cross  or  diagonal  construction,  covered  on  both  sides  and  all  edges  with 
sheet-tin,  joints  securely  clinched  and  nailed.  [Denver.] 

Tower  Projection.— A  projection  designed  for  an  ornamental  door-entrance, 
for  ornamental  windows,  or  for  buttresses.  [District  of  Columbia.] 

Vault,  -An  underground  construction  beneath  parking  or  sidewalk  [District 
of  Columbia.] 

Veneered  Building. —Frame  structure,  the  walls  covered  above  the  sill  by  a 
4'  wall  of  brick,  instead  of  clapboards.  F  Common  understanding  in  Chicago, 
Milwaukee,  and  Minneapolis,  but  not  defined  by  law.] 

Warehouse  Class.— Buildings  used  for  the  storage  of  merchandise,  manufac 
tories  in  which  machinery  is  operated,  breweries,  and  distilleries  [Cincinnati 
and  /S7.  Louis.] 

Width  of  buildings  shall  be  computed  by  the  way  the  beams  are  placed  ;  the 
lengthwise  of  the  beams  shall  be  considered  and  taken  to  be  the  widthwise  of 
the  building  [New  York  and  San  Francisco.} 

Wholesale  Store,  or  storehouse,  shall  embrace  all  buildings  used  (or  in- 
tended to  be  used)  exclusively  for  purpose  of  mercantile  business  or  storage  of 
goods,  r Chicago \  Louisville,  and  Milwaukee] 

Wooden  Building.— A  wooden  or  frame  v  building,  [Boston*  Kansas  City, 
and  Minneapolis.] 

Any  building  of  which  an  external  or  party  wall  is  constructed  in  whole  or  in 
part  of  wood.  [Denver  and  District  of  Columbia.] 

Having  more  wood  on  the  outside  than  thar,  required  for  the  door  and  window 
frames,  doors,  shutters,  sash  porticos,  and  wooden  steps,  and  all  frame  buildings 
or  sheds,  although  the  sides  and  ends  are  proposed  to  be  covered  with  corrugated 
iron  or  other  metal,  shall  be  deemed  a  wooden  building  under  this  la\v.  [  Charles- 
ton and  Nashville,  j 

i  Or  Tcneered.    [Minneapolis.^ 


INDEX. 


The  numbers  refer  to  paffes.  See  also  Glossary,  pp.  1575,  etc.,  and 
Table  of  Contents.  For  address  of  Manufacturers,  see  Trade  References, 
p.  1570. 


A — Avenues. 


A.  I.  A.  Schedule  of  charges,  1552. 

Acetylene  gas,  1285. 

Adamant,  1391. 

Adhesion     between     concrete     and 

steel,  tests  on,  866. 
Adhesive  strength  of  sulphur,  lead, 
and  cement ,  for  anchoring  bolts, 
1507. 

Aggregate,  concrete,  854. 
coarser  aggregate,  854. 
•  size  of  aggregate,  856. 
Air, 

composition    and    properties    of, 

1113. 

saturated,  1115. 
specific  heat  of,  1117. 
weight  and  volume  of,  1116. 
Air-lift  process  of  raising  water,  1249. 
Alarms,  automatic  fire,  849. 
Alhambra,  the,  1529. 
Ampere,  definition  of,  1306. 
Anchoring  bolts  in  stone,  1507. 
Anchors,   box,    for   wooden   beams, 

714. 

wall,  for  steel  beams,  553. 
Ancient  measures  and  weights,  36. 
Angles  and  tees,  clips  for  fastening, 

to  beams  and  channels,  811. 
Angles,   bulb,    size    and   properties, 

312. 

measured  by  a  2-ft.  rule,  73. 
measured  by  chords,  72,  88. 
steel,  size  and  properties,  300. 
strength  of,  as  beams,  524,  528. 
tensile  strength  of,  tables,  349. 
3"    and    under,    list   of  extras, 

1456. 

Angular  measure,  31. 
Anticondensation     lining    for     iron 

roofs,  1442. 

Apostles,  the  symbols  for,  1524. 
Arc  lamps,  1314;    space  illuminated 

by,  1297. 

Arch  floor  system,  Roebling,  774. 
Arch  girders  of  cast  iron,  262. 
Arched  trusses,  932. . 

wooden  ribs,  with  steel  ties,  911. 


Arches, 

brick,  251.     See  also  Brick  arches. 

centers  for,  252. 

concrete-steel,  262. 

definition  of   terms,  249. 

depth  of  keystone,  253. 

for   fire-proof   floors,   see   Hollow 
tile  arches. 

inverted,  in  foundations,  183. 

stability  of,  how  found,  256. 
Arches    in    fire-proof    construction, 
747-770. 

brick,  747. 

terra-cotta,  see  Terra-cotta  arches. 

tile,  see  Tile  arches. 
Architects'   charges,  A.  I.  A.  sched- 
ule, 1552. 

license  law,  State  of  Illinois,  1558. 
Architects,  noted,  list  of,   1540. 
Architects  of  noted  public  and  semi- 
public  buildings,   1537;    of  tall 
9ffice  buildings,  1531. 
Architectural  terra-cotta,  weight  and 

strength,  228. 
Architecture, 

colleges  and  schools  of,  1562. 

the  Five  Orders  of,  1497. 
Arcs,  circular,  length  of,  56. 
Areas  of  circles,  tables  of,  44. 

of  square  and  round  bars,  1350. 
Arithmetic, 

cube  root,  5,  8. 

signs  and  characters,  3. 

square  root,  4,  8. 

table  of  squares,  cubes,  etc.,  8. 
Art  Institutes,  Architects  of,  1539. 
Asbestos  building  felts,  1402. 
Asbestos  pipe  coverings,  1166. 
Asphaltum  as  a  varnish,  1409. 
Ashlar,  1347. 

walls  faced  with,  189. 
Asphalt,  Asphaltum,  1448. 
Asphalt   roofing,    specifications   for, 

etc.,  1436. 

Auditorium  Building,  Chicago,  1536. 
Automatic  fire-alarms,  849. 
Automatic  sprinklers,  850. 
Avenues  of  the  city  of  New  York, 
1475. 

1633 


1634 


INDEX. 


B— Breaking. 


Baltimore   fire,    test   of   reinforced- 
concrete  construction  in,-  8810. 
Barrel,  dimensions  of,  1474. 
Bars,  necessity  for  longitudinal,  in 

reinforcement,  773. 
Bars,  flat,  tensile  strength  of,  347; 

weight  of,  1353. 

Base  price  of  structural  steel,  1451. 
Bath-tubs,  dimensions  of,  1471. 
Baths,  plunge.  1283. 
Beam     connections,      to     compute 
strength  pf?  369;  standard,  545. 
Beam,  definition  of,  497. 
Waite's  concrete,  794. 
Beams, 

built-up  wooden,  579. 
compound  wooden,  579. 
continuous,  608. 
cylindrical  strength  of,  571. 
flitch-plate,  584. 
inclined  strength  of,  506. 
rectangular,  relative  strength  of, 

570. 

stone,  strength  of,  573. 
strength  of,  general  principles,497. 
strut,  of  steel,  511;   of  wood,  568. 
supporting  brick  walls,  542. 
tie,  of  steel,  512;  of  wood,  569. 
trussed,  586. 
with  concentrated  loads,  503,  505, 

514. 

Beams  and  channels,  clips  for  fas- 
tening tees  and  angles  to,  811. 
Beams   and   girders,   protection   of, 

795. 

Beams  in  reinforced-concrete  con- 
construction,  see  under  Rein- 
forced concrete. 

Beams,  Cast  Iron,  strength  of,  for- 
mulas, 555. 

Beams,  I-,  see  Beams,  steel. 
Beams,  Steel  (see  also  Steel  beams), 
buckling  strength  of,  508. 
deepest  beams  most  economical, 

507. 

deflection  of,  510,  595,  601. 
economical  shapes,  507. 
lateral  strength  of,  509. 
maximum  safe  load  for,  507. 
size  and  properties  of,  296. 
strength  of 

formulas  and  examples,  500. 
tables,  515. 
Beams,  Wooden, 

stiffness  of,  595;    tables,  603. 
strength    of,    formulas,    533;     ta- 
bles, 574. 

with  concentrated  loads,  567. 
Bearing  plates,  proportions  of,  398. 
Bearing  power  of  soils  and  rock,  137. 
Bearing  resistance  of  rivets,  371. 
Bedsteads,  dimensions  of,  1470. 
Bells,  dimensions,  tone  and  weight 

of,  1522. 

the  largest  in  the  world,  1523. 
Belly-rod  trusses,  587. 


Belting,  Belts,  notes  on,  1514:  trans- 
mitting power,  of  1513. 
Bending,  see  Deflection. 
Bending  moments, 

in  beams  in  reinforced-concrete 

construction,  881a. 
in  beams,  rules  for,  266. 

determined  graphically,  270. 
in  slabs,  88 la. 
in  pins,  377,  379. 
Bent  glass,  cost  of,  1418. 
Berger's    Economy     studding    and 

furring,  825. 

spacing  of  studding,  825. 
Berger's  multiplex  steel  plate.  792. 
Bevels  of  hip  and  jack  rafters,  97. 
Billiard-tables,  dimensions  of,  1471. 
Bitumen,  1448. 
Blackboards,  height  of,  1475. 
Blocks,  chain,  1516. 
Blue-prints,   directions  for  making, 

1510. 

Board,  Sackett's  wall,  832. 
Board  measure,  definition  of,  1395; 

tables  of.  1396. 
Boards,  plaster,  832. 
Boiler  tubes,  dimensions  and  data, 

1204. 

Boilers,  hot-water,  1170. 
Boilers,  steam, 
classes  of,  1133. 
fire-box,  1137. 
horizontal  tubular,  1133;    setting 

of,  1136. 

rating  (horse-power)  of,  1145. 
requirements  of,  1143. 
sectional  cast  iron,  1137;    setting 

and  covering  of,  1145. 
size  required  to  supply  radiation, 

1145. 

trimmings  for,  1146. 
Boiling-point  of  water,  1110. 
Bolsters,  see  Columns. 
Bolt-heads,  dimensions  and  propor- 
tions of,  1631. 
Bolts,  expansion,  1370. 

strength  of,  in  wooden  trusses  and 

girders,  382. 
weight  of,  1363. 
Bond  hoop  iron,  216. 
Bond-stones  in  piers,  216. 
Boneblack  as  an  ingredient  of  car- 
bon paints,  1409. 
Books,  for  Architects,  builders,  and 

draughtsmen.  1566. 
Bowling  alleys,  1474. 
Bowstring  truss,  the, 

description  and  examples,  931. 
stress  diagrams,  1003. 
Box  anchors  for  wooden  beams,  714. 
Box   girders,    of   steel   beams,    safe 

loads,  537. 
of  steel  plates  and  angles,    618, 

644. 

Braces,  see  Struts. 
Bracing  of  tall  buildings,  1082.     See 

also  Wind  bracing. 
Breaking  strain,  498. 


INDEX. 


1635 


Breadth — Cast  iron. 


Breadth  of  beams  in  reinforced-con- 

crete  construction,  88 If. 
Breast  walls,  210. 

Brick,  Bricks  (see  also  Brickwork), 
crushing  strength  of,  218,  229. 
glazed  and  enamelled,  1380. 
kinds  of,  clay,  1376. 
quantity  required  for  setting  boil- 
ers   1138. 
sand-lime,  1379. 
size  and  weight  of,  1378. 
space  required  for  piling,  1386. 
Brick  arches,  250. 

in    fire-proof    floor    construction, 

747. 

Brick  chimneys  (see  also  Chimneys), 
construction    of,    thickness    of 
walls,  etc.,  1224. 

tall,  examples  of,  1226. 
Brick  footings,  181. 
Brick  partitions,  814. 
Brick  piers, 

bond-stones  in,  216. 
effect  of  bond  on  strength  of,  216. 
strength  by  actual  tests,  219,  222. 
strength  of,  213,  214. 
Brick  stairs  and  stairways,  842. 
Brick  walls, 

general  rule  for,  188. 
thickness  of,  186. 
Brickwork, 
cost  of,  1385. 
crushing  height  of,  217. 
efflorescence  on,  1508. 
grouting  of,  216. 

in  fire-proofing  of  buildings,  730. 
measurement  of,  1382. 
municipal  requirements,  214. 
strength  of,  213,  214,  216. 
supported  by  girders,  542. 
Bridges,  longest  in  the  world,  1519. 

notable,  1521. 

Bridging  of  floor  beams,  678. 
Broken-stone  concrete,  elastic  prop- 
erties of,  881. 

Brooklyn  Bridge,  the,  1519. 
Brooklyn  regulations  for  reinforced- 

C9ncrete  columns,  881/1. 
Buckling  resistance  of  web  plates, 

624,  642. 

Building  Laws,  relating  to  • 
floor  loads,  minimum,  654. 
footings,     proportioning    to    live 

loads,  140. 

masonry,  maximum  loads,  214. 
pile  foundations,  147. 
plumbing,  1262. 
soils,  maximum  load  on,  138. 
steel  columns,  460. 
wind  bracing,  1083. 
wooden  beams,  safe  loads  for,  573. 
Building  papers,  kinds  of,  quantity 
in  a  roll,  weight,  cost,  etc. ,1401. 
Building  stones,  see  Stones. 
Buildings, 

cost  of,  per  cubic  foot,  1457. 
cost  of,  per  square  foot,  1467. 
depreciation  of,  1468. 


Buildings — continued . 
exposition,  cost  of,  1467. 
fire-proofing  of,  see  Fire-proofing 

of  buildings. 

government,  cost  of,  1468. 
iron,  cost  of,  1467. 
limiting    areas   for   non-fireproof, 

728 
limiting  heights  for  non-fireproof, 

729. 
notable  American,  description  of, 

1533. 

noted,  Architects  of,  1537. 
noted   European,    dimensions   of, 

1530. 

steel  mill,  shop  cost  of,  1543. 
tallest,  height  of,  1531. 
wear  and  tear  of,  1469. 
Built-up  beams,  wooden,  579. 
Bulb    angles,    size    and    properties, 

312. 

Bureaus,  dimensions  of,  1470. 
Burning  off  old  paint,  1407. 
Buttresses,  stability  of,  242. 


Cables,  see  Ropes. 

Caisson  foundations,  172. 

Calendar,  the  old  and  new,  31. 

Candle  foot,  1296. 

Candle  power,  how  measured,  1295. 

of  lamps,  1295,  1313. 
Cantilever  beam,  definition,  497. 
Cantilever  foundations,  174. 
Cantilever  trusses, 

advantages     and    disadvantages, 
939. 


example  of,  940. 
principle  of,  936. 


stress  diagrams,  1014. 
Canvas,  roofing,  707. 
Capacity  of 

churches    and    theatres,    to   esti- 
mate, 1478;   examples  of,  1479. 

freight  cars,  1474. 

hot-air  pipes  and  registers,  1200. 

library  stacks,  1495. 

pipes  and  cylinders,  1258. 

sewer-pipes,  1281. 

single-acting      cylinder      pumps, 
1247. 

tanks,  cylindrical,  1256,  1259. 

tanks,  rectangular,  1261. 

wheelbarrows,  wagons,  and  scrap- 
ers, 1372. 

Carriages,  dimensions  of,  1473. 
Cars,  dimensions  of,  1473. 
Castings,  weight  and  shrinkage  of, 

1357. 
Cast  iron, 

in  fire-proofing  of  buildings,   736. 

rules  for  estimating  weight,  1367. 

specifications  for,  327. 

strength  of,  327. 
Cast-iron  arch  girders,  262, 


1636 


INDEX. 


Cast  iron — Cocks. 


Cast-iron  columns,  see  Columns. 
Cast-iron     columns     in     reinforced 

concrete  construction,  88 II. 
Cast-iron  stairs  and  stairways,  841, 

842. 

Cathedrals,  the  English,  dimensions 
of,  1527. 

European,  1529. 

Ceiling     (wood),     thicknesses     and 
widths,     1399;      quantity     re- 
quired, 1400. 
Ceiling  joists,  maximum  span,  table, 

671. 
Ceilings,  flat  vs.  panelled,  761. 

protection  from  stains  in,  753. 

removal  of  smoke  and  dirt  from, 
1407. 

suspended,  809. 
Cellar  drainer,  Climax,  1282. 
Cement,  Cements, 

cost  of,  197. 

leading  brands  of,  192,  196. 

natural  rock,  192. 

Portland,  194,  197. 

proportions  of,  for  mortar,  193, 199. 

Puzzolan,  slag,  195. 

quantities    required    for    mortar, 
concrete,  etc.,  193,  199. 

Silica-Portland,  194. 

stainless,  196. 

water  required  for  mixing,  198. 
Cement  and  sand  mortar,  734. 
Cement  in  reinforced-concrete  con- 
struction, 852. 

constancy  of  volume,  853. 

fineness,  853. 

specific  gravity,  853. 

sulphuric  acid  and  magnesia,  854. 

tensile  strength,  853. 

time  of  setting,  853. 
Cement-block  walls,  190. 
Cement-coated  nails,  1365. 
Cement  floors,  752. 
Cement  mortars, 

freezing  of,  193,  199. 

proportions  of,  193,  199. 

quantities   required   for  masonry 

and  plastering,  199. 
Cement  stairs,  842,  843. 
Cement  trim,  840 
Cement  wall  plaster,  1391. 
Centers  for  arches,  253. 
Centre  of  gravity,  236. 

examples  of,  236. 

of  compound  sections,  239. 

to  find,  237,  239. 
Chain  blocks,  1516. 
Chains,  weight  and  strength  of,  358. 
Chairs   and  desks  for  schools,  sizes 

of,  1475. 
Chairs    and    seats,    dimensions    of, 

1470. 
Channel  columns, 

details,  437. 

strength  of,  tables,  466,  472. 
Channels  (standard  steel), 

size  and  properties  of,  298. 

strength  of,  as  beams,  519,  521. 


Channels,  small, 

extras,  on  (price),  1456. 
size  and  properties  of,  300. 
strength  of,  522. 
Charges  and  professional  practice  of 

Architects,  1552. 

Check   formulae   for  reinforced-con- 
crete beams,  878. 
Check  valves,  1157. 
Chenoweth  concrete  piles,  881n. 
Chicago,    fire-proofing   of   buildings 

in,  727. 
Chimneys,  1220. 

brick,  construction  of,  1224. 
draught  in,  1221. 
fire-brick  lining,  1225. 
foundations  for,  146. 
object  of,  1220. 
radial  block,  1229. 
reinforced  concrete,  1229. 
self-sustaining  steel,  1230. 
size  of,  for  fire-places,   1224;    for 
house  heaters,  1222;   for  power 
plants,  1222. 
stability  of,  1224. 
tall,   examples  of,    1226;     list    of 

1227. 

theory  of,  1221. 
thickness  of  walls,  1225. 
Chords,  table  of,  88. 
Churches,  capacity  of  several  large 

1479. 
to  estimate  seating  capacity  of, 

1478. 
Cinder   concrete   as   a   fire-proofing 

material,  734,  855. 
corrosion  in,  734,  882d. 
Circles,  areas  and  circumferences  of, 

tables,  44. 

Circuit-breakers,  1313. 
Circular  arcs,  length  of,  etc.,  56. 
Circular  measure,  31. 
Circular  sectors,  area  of,  62. 
Circumferences  of  circles,  tables,  44. 

of  round  bars,  1350. 
Cisterns    and    tanks,    capacity     of, 

1259. 

City  Hall,  Philadelphia,  1535. 
Clapboards,  dimensions  of,  1399. 
Classical  mouldings,  1496. 
Classical  Orders,  the,  1497. 
Clay, 

bearing  power  of,  137. 
foundations  on,  144. 
Clay  tile  stairs  and  stairways,  842. 
Clevises,  336;  dimensions  of,  344. 
Climax  cellar  drainer,  1282. 
Clips  for  fastening  tees  and  angles 

to  beams  and  channels,  811. 
Clock  dials,   rules  for,   and  dimen- 
sions of  some  large,  1494. 
Coach  screws,  1370. 
Coal,  Coals, 

value  of,  in  heat  units,  1109. 
weight  of,  1341,  1342. 
Coal   burned    per   hour   in    tnbular 

boilers,  1146. 
Cocks,  1158. 


INDEX. 


1637 


Coefficient — Concrete. 


Coefficient   of  strength,  definitions, 

498. 

Coin,  weight  of,  30. 
Cold-air  supply  for  furnace  heating, 

1177,  1181.  1184. 
Colleges  of  Architecture,  1562. 
Colored  paints    1404. 
Color  of  illuminants,  1299. 
Colors  of  iron  caused  by  heat,  1119. 
Columbian  floor  system,  786. 

safe  loads  for,  790. 
Column,  Columns, 

Base  plates,  or  stools, 
bedding  of,  403. 
proportions  for,  399. 
weight  of,  1360. 

Cast  iron;    advantages  and  disad- 
vantages, 414. 
base  plates  for,  399. 
brackets  on,  403. 
connections  of,  418. 
connections  to,  405. 
eccentric  loading  of,  421. 
H-shaped,  427. 
maximum  length  of,  416. 
prominent    buildings    used    in, 

494. 

shapes  of,  416. 
strength  of,  formulas,  420. 
strength  of  (tables)  round,  424; 
square  and  rectangular,  425. 
weight  of,  1358. 

Gas-  or  steam-pipe  columns,  465. 
I-beam,  strength  of,  as  columns, 

471. 

Monumental,  height  of,  1525. 
Schedule  of,  462. 
Sheets,  460. 
Steel, 

advantages  and  disadvantages, 

429. 

building  laws,  relating  to,  460. 
channel  columns, 
details,  of  437. 
latticing  of,  439. 
strength  of,  tables,  466,  472. 
connection  of,  431. 
cost  of,  1453. 
eccentric  loads  on,  456. 
forms  of,  428. 
formulas  for,  452. 
formulas    for,    comparison    of, 

495. 

Gray  column,  448. 
strength  of,  489. 
Larimer  column,  445. 

strength  of,  486 
length  of,  maximum,  451. 
loads,    method    of    computing, 

459. 
number   and  spacing  of  rivets, 

432. 
Nurick  columns,  448. 

strength  of,  488. 
Phoanix  column, 
details,  etc.,  440. 
strength  of,  484. 
plate  and  angle  columns,  440. 


Column,  steel — continued. 

strength  of,  formulas,  452. 

strength  of,  tables,  463. 

used  in  some  prominent  office 

buildings,  494. 
Z-bar  columns  and  details,  433; 

strength  of,  tables  4,75. 
Wooden, 

caps  and  bolsters  for,  414. 
eccentric  loading  of,  413. 
strength  of,  408. 

Column    and    girder    protection    in 
fire-proofing  of  buildings,  739- 
744. 
necessity  for,  740. 

tests,  740. 

Columns  in  reinforced-concrete  con- 
struction, see  under  Reinforced 
concrete. 

Comparison  of  the  Metric  and  Eng- 
lish systems  of  weights  and 
measures.  34. 

Comparison  of  thermometers,  1118. 
Composite  Order,  the,  1504. 
Composition      and      resolution      of 

forces,  231. 

Composition  flooring,  838. 
Compound  wooden  girders,  579. 
Compression  rods  in  reinforced-con- 

ceret  beams,  88 1/. 
Concentrated  loads,   factors  for  re- 
ducing to  equivalent  distributed 
load,  567. 
Concrete,  Concretes,  200. 

aggregates,  relative  merits,  201. 
cost  of,  203,  205. 
examples  of,  205. 
footings  of,  180.  \ 
freezing  of,  202. 
hooped  strength  of,  222. 
materials  required  for,  203,  205. 
mixing  of,  202. 
natural  cement,  201. 
Portland  cement,  202. 
strength  of,  214,  226. 
weight  of,  205. 

Concrete   and   steel   tests  on  adhe- 
sion between,  866. 
Concrete  beam,  Waite's,  794. 
Concrete  column  protection  in  fire- 
proofing  of  buildings,  742. 
Concrete  floors,  reinforced,  771. 
advantages  of  reinforced  concrete, 

771. 

Berger's  multiplex  steel  plate,  792. 
Columbian  system,  786. 
composition  of  the  concrete,  772. 
disadvantages,  772. 
dovetail  corrugated  sheets  (ferro- 

inclave),  790. 
expanded  metal,  778. 
flat  reinforced  floors,  777. 
forms  of  reinforcement,  772. 
load  tests,  809. 
lock-woven  fabric,  780. 
Merrick  system  of  floor  construc- 
tion, 795. 
necessity  for  longitudinal  bars, 773. 


1638 


INDEX. 


Concrete — Corrugated . 


Concrete  floors — continued 

patented  systems  of  flat  floor  con- 
struction, 784. 
protection  of  girders  and   beams, 

795. 

Roebling  arch  floor  system,  774. 
Roebling  flat  construction,  784. 
sectional  systems,  disadvantages 

of,  794. 

segmental  concrete  arches,  773. 
steel-wire  reinforcement,  782. 
Thacher  floor  unit,  793. 
Waite's  concrete  beam,  794. 
welded  metal  fabric,  779. 
Concrete  in  section  work: 
inspection,  882. 
finish,  882m. 
floor  finish,  882m. 
forms,  882/. 
load  tests,  882p. 
mixing,  882. 

charging  the  mixers,  882k. 
wet  mixture,  882k. 
pouring,  882fc. 
ramming,  8821. 
removing  forms,  882n. 
Concrete  in  fire-proof  building  con- 
struction, 733. 
cinder,  734. 
slag,  733. 
stone,  733 

Concrete  in  reinforced-concrete  con- 
struction, 852. 
aggregate,  854. 
coarser,  854. 
size  of,  856. 
cement,  852. 
cinders,  852. 

corrosion  in  cinder  concrete,  882d. 
elastic  properties  of  broken-stone 

concrete,  881. 
finish,  882m. 

fire  protection,  881n  to  8812. 
footings,  881m. 
forms.  882 f. 

removing,  882n. 
gravel,  855. 
inspection,  882n. 
load  tests,  882p. 
mixing,  882ft. 

charging  the  mixers,  882%. 
non-conductivity.  881  w. 
proportion  of  materials  in,  856. 
protection        against      corrosion, 

882d. 

pouring,  882k. 
ramming,  8821. 
sand,  854. 
stone,  855. 
strength  of,  858. 

thickness    required    for   fire   pro- 
tection, 882. 
wet  mixture,  882fc. 
working  stresses,  859. 
Concrete  mixers,  882ft. 
charging,  882fc. 
McKelvey,  882ft. 
paddle,  882.?. 


Concrete  mixers — continued 
Ransome,  882ft. 
Smith,  882?. 
Concrete  mixing,  882ft. 

charging  the  mixers,  882&. 
pouring,  882k. 
wet  mixture,  882/c. 
Concrete  partitions,  817. 
Concrete  piles,  881n. 
Chenoweth,  881n. 
connections,  8810. 
corrugated,  88 In. 
loads,  8810. 
Concrete  protection  of  girders  and   . 

beams,  795. 

Concrete-steel,  see  Reinforced  con- 
crete. 

Concrete-steel  beams,  855 
Concrete-steel  columns,  239. 
Concrete-steel  floors,  see  Reinforced 

concrete  floors. 

Concrete-steel  foundations.  158. 
Conductors,  proportion  to  roof  sur- 
face, 1481. 
Conduit  systems  of  electric  wiring, 

1334. 
Cones,   surface  of,   64;    volume  of, 

67. 

Congressional  Library,  the,  descrip- 
tion and  capacity  of,  1534;   di- 
mensions of  stacks,  1496. 
Connections  for  steel  beams,  545. 
of  steel  columns,  431,  434,  436, 

438,  442,  446. 
to  cast-iron  columns,  405. 
Constancy  of  volume  of  cement  in 

concrete  erection,  853. 
Construction,  forms  of,  in  fire-proof 

buildings,  739. 
Construction,      reinforced-concrete, 

see  Reinforced  concrete 
Construction,    types   of   reinforced- 
concrete,  88lp. 
Faber,  88  U 
Hennebique,  864. 
Kahn  hollow-tile,  881r. 
Merrick,  88 It. 

fire  protection  of,  8826. 
Mill,  881p. 
mushroom,  881r. 
skeleton,  881<?. 
system,  "M,"  88 Ir. 
Consumption  of  water,  1274. 
Continuous    girders,    strength    and 

stiffness  of,  608. 
Contract    between     Architect     and 

Owner,  1553. 
Contract,     the     Uniform,     between 

owner  and  builder,  1555. 
Conversion    tables,    metric-English, 

34. 

Corinthian  Order,  the,  1502. 
Corrosion    in    reinforced    concrete, 

protection  against,  882d. 
in  cinder  concrete,  882d. 
thickness    of    concrete    required, 

882. 
Corrugated  concrete  piles,  88 In. 


INDEX. 


1639 


Corrugated — Dimensions. 


Corrugated    iron    and    steel   sheets, 

1437. 

Corrugated  roofing,  1439. 
Corrugated     sheets,     dovetail,     see 

Dovetail  corrugated  sheets. 
Corrugated  sheets  for  ceilings,  1443. 
Corrugated  siding,  1412. 
Cosecants,  table  of,  123a. 
Cosines,  table  of,  103. 
Cost  of 

bending  glass,  1418. 
brickwork,  how  estimated,  1382, 
builder's  work,  of  different  kinds 
per  cubic  foot  of  building,  1466 
building  papers,  felts,  and  quilts, 

1401. 
buildings  per  cubic  foot,  1457. 

per  square  foot,  1467. 
carpenter's  work,  1400. 
concrete,  203,  205. 
curbing,  1376. 

drafting  structural  steel,  1454. 
electric-light  wiring  and  installa- 

tions, 1339. 
enamelled  brick,  1381. 
erecting  structural  steel,  1453. 
excavating  and  quarrying,  1372 
Exposition      buildings      (Chicago 

and  St.  Louis),  1467. 
fire-proof  construction,  729. 
floor  and  mantel  tiles,  1447. 
galvanized  iron  sheets,  1443. 
glass,  plate,    1420;    rolled,   1419; 

sheet,  1417. 
ravel  roofing,  1435. 
lathing,  1393. 
merchant  steel,  1454. 
mills  and  factories,  723. 
mineral  wool,  1450. 
mortar  colors,  1386. 
pile  driving,  157. 
piles,  158. 

plasterers'  work,  1393. 
pumping  by  air-lift  process,  1250. 
rock  asphalt,  1449. 
ro9fing  tile,  1429. 
shingles  and  shingling,  1426 
slates  and  slate  roofs,  1428. 
steel  roof  trusses,  1453. 
stonework,  rough  and  cut,  1375. 
structural  steel  for  buildings,  data 

for  estimating,  1451. 
tin  roofing,  1432. 
Translucent  Fabric,  1424. 
U.  S.  Government  buildings,  1468. 
Cotangents,  table    of,  112. 
Counter-braces      in     wooden     roof 

trusses,  887,  894. 
Counter-flashings,  1427. 
Courses  in  Architecture,  1562. 
Covering  of  steam-pipes,  1166. 
Creosote  stain,  1405. 
Cross  bridging,  679. 
Cross  strain,  see  Beams. 
Crushing  height  of  bricks  and  tone, 

217. 

Crushing  loads  for  wood  ands  met- 
als, 407.     See  also  Columns. 


g 
l 


Crushing  of  timber  perpendicular  to 
the  grain,  414. 

Crushing  strength,  see  Strength. 

Cube  root,  5;  table  of,  8. 

Cubes,  table  of,  8. 

Cubic  measure,  28. 

Cummings  system  of  reinforced- 
concrete  beams,  870. 

Cup  bar  in  reinforced-concrete  con- 
struction, 864. 

Curbing,  cost  of,  1376. 

Curtain  walls,  190. 

Cutler  mail  chutes,  1491. 

Cycloid,  to  describe  a,  87. 

Cylinders,  capacity  of,  1258. 

Cylindrical  beams,  strength  of,  571; 
stiffness  of,  601. 


De  Man  undulated  bar  in  reinforced- 
concrete  construction,  864. 
Dead  load,  definition  of,  132. 
Deadening    qualities    of    fire-proof 

partitions,  833. 
Decimal  equivalents  for  fractions  of 

an  inch,  26. 
Deck  beams,  size  and  properties  of, 

312. 

strength  of,  table,  518. 
Deep-well  pumps,  1245. 
Deep  wells,  1244 
Definition  of,  see  Term  in  question, 

also  Glossary. 

Definitions  of  terms  used  in  mechan- 
ics, 130. 
Deflection  of  steel  beams,  510. 

wooden  beams,  595. 
Deflection  to  crack  plastering,  596. 
Deformed    bars    in    reinforced-con- 
crete construction,  861. 
Dense  tiling,  its  value  in  fire-proof- 
ing of  buildings.  731. 
Depreciation  of  buildings,  1468. 
Description    of    notable    American 

buildings,  1533. 
Design   in   reinforced   concrete,   see 

under  Reinforced  concrete. 
Details  of 

columns,  see  Columns, 
steel  roof  trusses,  1064. 
wooden  roof  trusses,  1051. 
Devices  for  detecting  and  checking 

fires,  849. 

automatic  alarms,  849. 
automatic  sprinklers,  850. 
stand-pipes  and  hose  reels,  850. 
Dials,  clock,  diameter  of,  1494. 
Diamond  bar  in  reinforced-concrete 

construction,  863. 
Differential  pulleys,  1516. 
Diffusion  of  light  through  windows, 

1300. 
Dimensions  of   (see  also  Article  in 

question), 
barrels,  1474. 


1640 


INDEX. 


Dimensions — Electric. 


Dimensions — continued, 
bells,  1522. 
billiard-tables,  1471. 
bowling  alleys,  1474. 
bricks,    clay,    1378;     enamelled, 

1381. 
carriages,   cars  and  locomotives, 

1473. 

chairs  and  desks  for  schools,  1475. 
chimneys,  for  fire-places,  1224. 
for  house  heaters,  1222. 
for  power  plants,  1222. 
for  ranges,  1224. 
clevis  nuts,  344. 
clock  dials,  1494. 
domes,    principal    in    the    world, 

1526. 

elevator  hatchways,  1490. 
elevators,  1486. 
English  cathedrals,  the,  1527. 
eye-bars,  table,  343. 
fire-engines  and  wagons,  1473. 
furniture,  1470. 

Grand  Opera  House,  Paris,  1530. 
hods  for  brick  and  mortar,  1387. 
horse  stalls,  1474. 
library  stacks,  1495. 
Madison  Square  Garden,  1536. 
noted  European  buildings,  1529. 
nuts  and  bolt-heads,  1361: 
obelisks,  still  existing,  1528. 
opera  chairs,  1478. 
Patent  Office  drawings,  1474. 
plumbing  fixtures,  1471. 
rivets,  373,  374. 
schoolrooms,  1475. 
eleeve-nuts,  346. 
steel  eye-bars,  343. 
steel  structural  shapes,  296. 
theatres  and  opera  houses,  1480. 
turnbuckles,  345. 
U.  S.  Government  buildings,  1533. 
upset  screw-ends,  341. 
Washington        Monument,      the, 

1535, 

Disc  valves,  1156. 
Discharge  of  wnter,  1234. 
Domes,  height  of,  1525;  diameter  of, 

1526. 
Door  and  window  frames,  painting 

of,  1405. 

Door  and  window  protection  in  fire- 
proofing  of  buildings,  844. 
metal-covered  wood  doors,  846. 
sheet-metal   window   frames   and 

sash,  847. 
material,  848. 

steel  fire  doors  and  shutters,  846. 
tin-covered  wood  doors  and  shut- 
ters, 844,  845. 
water  curtains,  848. 
wire-glass  sash,  847,  848. 
Door- jamb  and  trim;  metal-covered, 

839. 
Doors,     trim,     and    other    Interior 

finish,  fire-proof,  728. 
Doric  Order,  the,  1499. 
Double  partitions,  823. 


Dovetail  corrugated  sheets  (ferroin- 
clave),  790. 

advantages,  791. 

carrying  capacity,  789. 

long-span  construction,  788. 
Down  spouts,  proportioning  to  roof 

surface,  1481. 
Drafting  structural  steel,   cost   of, 

1454. 

Drain-pipes,  capacity  and  descrip- 
tion of,  1279. 
Draught  in  aspirating  flues,  1213. 

in  chimneys,  1221. 
Driers,  1404. 

Drums  and  pulleys,  1513. 
Drying  by  steam,  1117. 
Duplex  joist  and  wall  hangers,  681, 

713,  716. 

Duplex  post  caps,  721. 
Durability  of 

asphalt  roofing,  1436. 

gravel  roofing,  1435. 

iron  in  masonry,  191. 

ready  roofings,  1437. 

tin  roofing,  1432. 
Duvinage  post  caps,  720. 
Dynamos,  1309. 


E 

Eccentric  loads, 

on  steel  columns,  456. 
on  wooden  columns,  413. 
upon     reinforced  -  concrete     col- 
umns, SSll. 
Edison    3-wire    system    of    wiring, 

1317. 

Efflorescence  on  brickwork,  1508. 
Egyptian     style     of     Architecture, 

1504. 

Elastic  cement,  1427. 
Elastic   properties   of  broken-stone 

concrete,  881. 
Elasticity,  moduli  of,  in  reinforced- 

concrete  construction,  881. 
Elasticity,  modulus  of,  133;    table, 

597. 

Electric  elevators,  see  Elevators. 
Electric  lighting,  1311. 
circuit-breakers,  1313. 
fuses  and  cut-outs,  1311. 
lamps,    arc,    1314;    incandescent, 

1313. 

switches,  1332. 
systems    of,    1311;     comparative 

cost  of,  1312. 
Electric-light  wiring, 

carrying  capacity  of  wire,    1321, 

1326. 

centre  of  distribution,  1323. 
conduit  system,  1334. 
cost  of,  1339. 
distributing  centres,  1323. 
drop  of  potential,  1322. 
Edison  3-wire  system,  1317. 


INDEX. 


1641 


Electric — Fire-extinguishing. 


Electric-light — continued. 

example  of,  1329. 

methods     of    connecting    lamps, 
1315. 

National  Electrical  Code,  1335. 

resistance  of  copper  wire,  1327. 

specifications  for,  1338. 

switches.  1332. 

wire  calculations,  1323. 

wire    gauges     (for    copper    wire), 
1320. 

wiring  tables,  1328. 
Electricity,  1305. 

definitions,  1305. 

dynamo-electric  machines,  1309. 

electrical  currents,  kinds  of,  1310. 

electrical  equations,  1308. 

electrical  units,  1308. 

electromotive  force,  1306. 

flow  of,  1306. 

heating  effects  of,  1308. 

resistance  to,  1307. 
Electroplated  trim,  839. 
Elevators, 

data  as   to  size  and   number  re- 
quired, 1486. 

makers  of  (see  Trade  references), 
1570. 

notes  on,  1482. 

relation  of  hatchway  to  car  plat- 
form, 1490. 

specifications  for,  1484. 

with  push-button  control,  1489. 
Ellipse,  to  describe  an,  81. 
Ellipsoids,  63. 
Enamelled  brick,  1380;  cost  and  size 

of,  1381. 

Enamelled  tiles,  1445. 
Enamels  (paint),  1405. 
End-construction  flat  arches,  757. 

See  also  Flat  arches. 
Engines,  hot-air,  1246. 
English  catherdals,  the,  dimensions 

of,  1527. 

Equalization  of  pipe  areas,  1203. 
Equilibrium,  definition  of,  130. 
Erecting   structural   steel,    cost   of, 

1453. 
Erection,     reinforced-concrete,     see 

under  Reinforced  concrete. 
Escurial,  the,  1529. 
Estimating,    see    Cost   or   Measure- 
ment. 
Examples  of 

arches,  254. 

caisson  foundations,  174. 

concrete  foundations,  205. 

pile  foundations,  156. 

steel-beam  footings,  169. 
Excavating,  Excavations, 

data  for  estimating  cost  of,  1372. 

measurement  of,  1371. 

to  compute  volume  of  irregular, 

69. 
Expanded-metal  floor  construction, 

778. 

Expanded-metal  lath,  828, 
Expansion  bolts,  1370. 


Expansion  of  solids  for  1°  tempera- 
ture, 1120. 

Expansion  tank,  for  hot-water  heat- 
ing, 1169. 
Exposition   buildings,   Chicago  and 

St.  Louis,  cost  of,  1468. 
Exterior   woodwork,    repainting  of, 

1407. 

Extras  on  merchant  steel,  1455. 
Extras,    to    be    added    to    price    of 

beams  and  channels,  1452. 
Eye-bars, 

description  and  data,  336. 
dimensions  of  (table),  343. 
steel  for,  specifications,  334. 
strength  of,  331. 

Eye-beams,      see      I-beams;       also 
Beams,  steel. 


Faber  reinforced-concrete  construc- 
tion, 881*. 

Fabric     for     reinforcement,     lock- 
woven,  780. 
welded  metal,  779. 
Factor  of  safety  for 
beams,  498. 
masonry,  213. 
wood  in  compression,  408. 
wood  in  tension,  322. 
Factors  of  safety  defined,  132. 
Fan  and  Fink  trusses, 
cambering  of,  920. 
depth  of,  920. 

description  and  examples,  918. 
stress  diagrams,  984. 
stresses  in,  tables,  958. 
with  pin  joints,  923. 
with  wooden  rafters   and  struts, 

910. 

Fan  systems  of  ventilation,  1215. 
Fans  for  moving  air,  1218;   capacity 

of,  1219. 

Feet  converted  into  metres,  36a. 
Fellowships,  travelling,  1565. 
Felts,  dry,  1401;  saturated,  1402. 
Ferroinclave  stairs    and   stairways, 
843.     See  also  Dovetail  corru- 
gated sheets. 
Fibre  stress,  see  Modulus  of  rupture, 

498. 

Filling-blocks,  terra-cotta,  752. 
Filters,  1281. 
Finish  of  concrete  surfaces,  882m. 

floor  finish,  882m. 
Fink    trusses,    see    Fan    and    Fink 

trusses. 

Fire,  temperature  of,  1109;  to  de- 
termine by  fusion  of  metals. 
1110. 

Fire  alarms,  automatic,  849. 
Fire-box  boilers,  1137. 
Fire-bricks,  1377. 
Fire  engines,  dimensions  of,  1473. 
Fire-extinguishing  devices,  849. 


1642 


INDEX. 


Fire-proof— Flat. 


Fire-proof,  Fire-proofing, 
definition  of  726. 
definitions,  municipal,  727. 
of  steel  and  iron  in  slow-burning 

construction,  712. 

Fire-proof  construction,  when  to  be 
employed,  728.     See  also  Fire- 
proofing  of  buildings, 
cost  of,  729. 
Fire-proof  doors  and  windows,  see 

Door  and  window  protection. 
Fire-proof  flooring,  837. 
Fire-proof  floors,  745-805. 
load  tests,  805. 

proposed  standard  test  for,  745. 
requirements,  745. 
steel  framing  for,  799. 
tables  for  floor  beams,  802. 
tie-rods,  802. 
trusses,  798. 
types  of,  747. 

brick  arches,  747. 
composition  systems, 

concrete    floors,    see    Concrete 

floors. 

flat  reinforced  floors, 
sectional  systems,  794. 
segmental     concrete    arches, 

773. 

Terra-cotta  floors,  749.  See 
also  Terra-cotta  arches ; 
Tile  arches. 

flat  end  construction,  757. 
flat  side  construction,  756. 
Guastavino  tile-arch  system, 

770. 

segmental  terra-cotta  arches, 
see  Segmental  terra-cotta. 
Fire-proof  paint,  739. 
Fire-proof  stairs,  841. 
Fire-proof  wood,  736. 
disadvantages,  737. 
test,  737. 

Fire-proofing  of  buildings,  726-850. 
arches,  see  Arches, 
column  and  girder  protection,  739, 

795. 

concrete,  742. 
necessity  for,  740. 
plaster,  743. 
terra-cotta,  740. 
definitions,  726. 

municipal,  727. 
divisions  of  the  subject,  730. 
doors  and  windows,  844-848. 
extinguishing  devices,  849. 
flooring,  837. 

floors,    see   Concrete  floors,   rein- 
forced;   Fire-proof  floors, 
furring,  metal,  837. 

of  outside  walls,  837. 
forms  of  construction,  739-744. 
interior  finish,  see  Interior  finish, 
materials     of     construction,     see 

Materials  of  construction, 
metallic  furniture  and  fittings,841. 
partitions,     see    Partitions,     fire- 
proof. 


Fire-proofing — continued, 
protecting  devices,  844. 
recesses  for  pipes,  744. 
roof  coverings,  844. 
roofs,  see  Fire:proof  roofs, 
stairs,  and  stairways,  841. 
suspended  ceilings,  809. 
Fire    protection    in    reinforced-coii- 
crete    construction,    see    under 
Reinforced  concrete. 
Fire     tests     of     reinforced-concrete 

construction,  881.V. 
loss  of  strength,  88iy. 

tables  of  tests,  ^881*,  88 ly. 
Fire  tests  on  partitions,  813. 
Fire  Underwriters'   requirements  in 
reinforced  -  concrete      construc- 
tion, 882. 

Fire  streams,  1251. 
Fittings  and  furniture,  metallic,  841. 
Fitting    for    steam    and    hot-water 

piping,  1153. 
Five  Orders,  the,  1497. 
Flag-poles,  rule  for  diameter  of,  1475. 
Flashings,  1427. 
Flat   arches,    756-769. 

arches  of  same  depth  as  beams, 

762. 

depth,  span,  and  weight,  762. 
end  construction,  757. 
flat  vs.  panelled  ceilings,  761. 
form  of  skewbacks,  758. 
Herculean  arch,  765. 
advantages,  766. 
span,  766. 
strength,  766. 
weight,  766. 
Johnson  long  span  construction, 

766. 

advantages,  768. 
span,  767. 
strength,  768. 
weight,  767. 
keys,  760. 

raised  skewbacks,  760. 
reinforced  tile  arches,  765. 
safe    loads    for    end-construction 

arches,  762. 
side  construction,  756. 
thickness  of    web,  758. 
Flat  bars, 

list  of  extras,  steel,  1455. 
strength  of,  as  beams,  table,  523. 
tensile  strength  of,  table,  347. 
weight  of,  1354. 
Flat    floor    construction,    patented, 

784. 

Berger's  multiplex  steel  plate,  792 
Columbian  system,  786. 

safe  loads  for,  790. 
dovetail  corrugated  sheets  (ferro- 

inclave),  790. 
Roebling  system,  784. 
Thacher  floor  unit,  793. 
\Yaite's  concrete  beam,  794. 
Flat  reinforced  floors,  777. 
Flat  roofs,  fire-proof,  806. 
Flat  vs.  panelled  ceilings,  761. 


INDEX. 


1643 


Flitch-plate — Fuses . 


Flitch-plate  girders,  584. 

Floor  beams,  tables  for,  802. 

Floor    construction,    fire-proof,    see 

Fire-proof  floors. 
Floor    construction,    types    of    fire- 

pnx>f,  747. 
Floor  joists,  wooden. 

framing  of,  679. 

maximum  span  of,  tables,  671. 

weight  of,  653. 
Floor  tiling,  1443. 
Floor  unit,  Thacher,  793. 
Floor-wax,  1406. 
Flooring,  fire-proof,  837. 

Composition,  838. 
Flooring,  wood, 

cost  of  laying,  1400. 

dimensions  of,  1399. 

quantity  required,  1400. 
Floors  and  walls,  concrete,  finish  of, 

882m. 

Floors,    fire-proof,    727,    728.     See 
also  Fire-proof  floors. 

concrete,  see  Reinforced  concrete 
floors, 

flat  reinforced,  777. 

mill,  692. 

minimum  strength  of,  as  required 
by  building  laws,  and  as  re- 
commended by  author,  654. 

solid  or  mill,  strength  of,  667. 
Floors,  varnishing  of,  1406. 

waxing  of,  1406. 

wooden,  see  Wooden  floors. 
Flow  of  water  in  pipes,  1232. 
Flues,   for   ventilation,   shapes   and 
materials  of,  1213;  sizeof,1211. 
Fluid  measure,  28. 
Footings, 

brick,  181. 

computing  width  of,  example,  139. 

concrete,  180. 

concrete-steel,  158. 

inverted  arches,  183. 

load  on,  method  of  computing, 
139. 

object  of,  178. 

offsets,  of  179. 

proportioning  to  soil  and  load,139. 

reinforced  concrete,  881m. 
economy  of,  881m. 

steel  beam,  161. 

timber,  170. 

Force,  definition  of,  130. 
Force  of  the  wind,  1510. 
Forces, 

composition  and  resolution  of, 231. 

in  and  on  a  truss,  967. 

moments  of,  233. 

polygon  of,  233. 

principle  of  the  lever,  235. 

supporting,  how  found,  274. 
Formula      for      reinforced-concrete 

columns,  New  York,  881/. 
Formulas     for     reinforced-concrete 
beams,  872. 

check  formulae,  878.  » 

tables,  873-77. 


Formulas  for  strength  of 
steel  beams,  500. 
steel    columns    and    struts,    452; 

comparison    of,  495. 
Formulas    for    tee    beams    in    rein- 
forced -  concrete     construction, 
879. 
Forms,  concrete,  882/. 

removing,  882n. 
Foundations,  135. 

actual  loads  on  piles,  156. 
bearing  power  of  soils  and  rock, 

135. 

caisson,  172 
cantilever,  174. 
example  of  footings,  141. 
for  chimneys,  146. 
for  temporary  buildings,  171. 
masonry  wells  for,  171. 
municipal   laws,   governing  loads 

on  soils,  138. 
municipal     requirements     as     to 

footings,  140. 
object  of,  135. 
on  clay,  144. 

on  loam  and  made  land,  145. 
on  rock,  144. 
on  sand  and  gravel,  145. 
pile,  147. 

proportioning  the  footings,  139. 
spread  with    reinforced  concrete, 

158. 

spread  with  steel  beams,  161. 
testing  of  soils,  136. 
timber  footings,  170. 
Foundation  walls,  183. 
Fractions    expressed     in     decimals, 

26, 
Fractured  surface  of  wrought  iron. 

324. 
Framing    and    connecting    of    steel 

beams,  545. 
Framing  for  fire-proof  floors,  stee 

799. 

computations  for,  801. 
Framing    of    wooden    floor    beams, 

679. 
Freezing  of    cement   mortars,    193, 

199. 

of  concrete,  203. 

Freight  cars,    capacity  of,  1474;  di- 
mensions of,  1473. 
Freight    rates    on    structural    steel, 

1451. 
Fuels,  value  of,  in  heat  units,  1107, 

1108. 

Furnaces,  hot-air,  1175. 
Furniture,  dimensions  of,  1470. 
Furniture  and  fittings,  metallic,  841. 
Furring     and     studding,      Berger's 

Economy,  824. 
Furring,  metal,  837. 

of  outside  walls,  835. 
Fuses,  1311. 


1644 


INDEX. 


G— Heat. 


Galvanized-iron  sheets,  size,  thick- 
ness, and  cost,  1443. 
Galvanized    ironwork,    painting   of, 

1405. 

Gas  generators,  1286. 
Gas,  illuminating  varieties  of,  1285. 

piping  a  house  for,  1287. 
Gas-pipe  columns,  strength  of,  465. 
dimensions  and  data,  1205;    rules 
and  table  for  proportioning  size 
of,  1291. 

Gate  valves,  1155. 
Gauge  of  railroad  tracks,  1474. 
Gauge  of  rivet-holes, 

for  angles,  T's  and  Z-bars,  552. 
for  channels,  551. 
in  steel  beams,  550. 
Gauge,  U.  S.  standard,  1438. 
Gauges,  wire,  see  Wire  gauges. 
Gears,  rules  to  determine  size  and 

speed  of,  1513. 
Geometrical  problems,  70. 
Geometrical  terms,  37. 
Geometry,  definitions,  37. 
Girder    and    column    protection    in 
fire-proofing  of  buildings,  739- 
744. 
Girders, 

arched  (cast  iron),  262. 

built-up  wooden,  579. 

,     compound  wooden,  579. 

continuous,  strength  and  stiffness 

of,  608. 

fire-proofing  of,  712. 
flitch-plate,  584. 
•for  brick  walls,  542. 
riveted  steel  plate  and  box,  618; 

tables,  644. 
trussed,  586. 

Gjrders  and  beams,  protection  of, 795. 
Girders,  beams,  and  slabs  in  rein- 
forced    concrete    construction, 
see  under  Reinforced  concrete. 
Glass 

cost  of  bending,  1418. 
of  rolled  glass,  1419. 
discount  on,  1416,  1417. 
figured,  rolled  glass,  1418. 
for  skylights,  1419. 
grades  and  qualities  of  sheet  glass, 

1416. 

polished  plate  glass,  1416. 
price-list  of  plate  glass,  1420. 

of  sheet  glass, '1417. 
weight  of  plate  glass,  1417. 

of  rough  glass,  1419. 
Glass  tiles,  1446. 
Glazed  bricks,  1380. 
Glazed  tiles,  1445. 
Globe  valves,  1155. 
Globes,  1297. 

Goetz  box  and  anchors,  714. 
Golding  bar  in   reinforced-concrete 

constnction,  864,  867. 
Government  buildings,  architects  of , 
1537;  description  of,  1533. 


Grading  of  slates,  1426. 
Grand  Opera   House,  Paris,  dimen- 
sions of,  1530. 
Granite, 

strength  of,  213,  225,  229 

weight  of,  1342. 
Granite  in  fire-proofing  of  buildings, 

730. 

Graphic  statics,  application  to  sim- 
ple triangular  frames,  968;  to 
roof  trusses,  970. 

Graphite  as  a  paint  for  metal,  1409. 
Gravel  for  concrete,  855. 
Gravel  roofing,  1432. 

cost  of,  1435. 

durability  and  fire-resisting  qual- 
ities, 1435. 

method  of  applying,  1432. 

specifications  for,  1433. 

weights  of  felt  and  pitch,  1434. 
Gravity,  Centre  of,  see  Centre. 
Gravity,  specific,  1345. 
Gray  columns,  description  of,  448. 

strength  of,  489.     • 
Grease  traps,  1271. 
Grillage  over  piles,  151. 
Grooved  steel,  see  Channels,  small. 
Grouting,  216. 
Guastavino    stairs    and    stairways. 

842. 

Guastavino  tile  arch  system,  770. 
Gutters,  proportioning  to  roof  sur- 

face,  1481. 

Gypsinite  partitions,  820. 
Gyration,  radius  of,  279. 

of  angles  in  pairs,  316. 

of  channels  in  pairs,  319. 

of  compound  shapes,  289. 

of  round  columns,  293. 

of  structural  shapes,  293,  296. 


H 

Hair,  for  plaster,  1390. 
Hammer-beam  truss,  the, 

description  and  examples,  903. 

stress  diagrams,  991. 
Hand  rail,  height  of,  1476. 
Hangers,    see    Joist    hangers,    Wall 

hangers,  etc. 
Hard-pine  beams,  table  of  stiffness, 

603;  tables  of  strength,  574. 
Hard  wall  plasters,  1391 
Hardness  of  woods,  relative,  1509. 
Haunches,  definition,  249. 
Haunches  of  segmental  arches,  fill- 
ing, 754. 

Hawsers,  see  Ropes. 
Headers,  strength  of,  664,  676. 
Heat, 

colors  of  iron  caused  by,  1119. 

how  measured,  1107. 

mechanical  equivalent  of,  1107. 

specific,  1117. 

units  in  steam,   1114;     in   water, 
*    1112. 


INDEX. 


1645 


Heating — Insulating. 


Heating, 

hot-air  and  steam,  1187. 
and  water,  1186. 
heating,  1174,  1187. 
hot-water  heating,  1168. 
Paul  system,  1150. 
specifications    for,    see    Specifica- 
tions. 

steam,  gravity  systems,  1121. 
non-gravity  systems,  1151. 
•ys.  hot  water,  1172. 
systems  of,  1121. 
Webster  system,  1152. 
Heating  and  Ventilation,  see  Venti- 
lation. 

Heating  effects  of  electricity,  1308. 
Heights  of 

columns,  domes,  spires,  and  tow- 
ers, 1525. 
tallest    buildings    in    the    U.    S., 

531. 
Hennebique  bar  in    reinforced-con- 

crete  construction,  864. 
Herculean   arch,  765. 
advantages,  766. 
span,  766. 
strength,  766. 
weight,  766. 

Herculean  fire-proof  floor,  the,  808. 
Herringbone  lath,  829. 
Hip   and    jack   rafters,    length   and 

bevels,  97. 
Hoists,  chain,  1365. 
Holding  power  of  lag  screws,  1371. 

of  nails,  1365. 
Hollow  tile.  214 
wetting,  751. 
Hollow  tiles,  moulded,  for  interior 

finish,  840. 

Hollow  tiles,  see  Terra-cotta  tiling. 
Hollow  walls,  189. 
Hooks,  proportions  of,  1518. 
Horse,  the,  strength  of,  1512. 
Horse-power,  electrical,  1308. 
in  machinery,  1512. 
of  boilers,  1145. 
required  to  raise  water,  1250. 
Horse-stalls,  dimensions  of,  1474. 
Hose-carriages,  dimensions  of,  1473. 
Hose-reels,  850. 

Hot-air  and  steam  heating,  1187. 
Hot-air  and  water  heating,  1186. 
Hot-air  engines,  1246. 
Hot-air  (furnace)  heating,  1174. 
cold-air  supply,  1177,  1181. 
forced-blast  system,  1218. 
furnaces  for,  1175. 
location  of  furnace,  1181. 

of  stacks  and  registers,  1182. 
pipes  and  registers,  1179. 
size  of  furnace,  pipes,  and  regis- 
ters, 1182. 

specifications  for,  1185. 
ventilation,  1180. 
Hot-air   pipes    and   registers,    1179, 

1183,  1197. 

Hot-blast   system  of  warming  and 
ventilation,  1153,  1216. 


Hot-water  heating,  1168,  1187. 

boilers  for,  1170. 

disadvantages  of,  1173. 

expansion  tank,  1169. 

proportioning    radiating    surface, 
rules  for,  1 162. 

rules  for  size  of  ajr  ducts,  indirect 
radiation,  1163. 

size  of  pipes,  rules  for,  1166;  ta- 
bles for,  1201. 

specifications  for,  1188. 

systems  of  piping,  1171. 
Howe  trusses, 

counter-braces  in,  1013. 

description  of,  892. 

stress  diagrams,  977,  982. 

stress  in  formulas,  963. 

table  of  dimensions  for,  896. 

unsymmetrically  loaded,  1009. 
H-shaped  columns,  details  of,  1419; 

strength  of,  427. 
Hydraulic  oemeiit  mortar,  734. 
Hydraulic  Cements,  see  Cement. 
Hydraulic  Ram,  the,  1244. 
Hydraulics,  . 

discharges  through  pipes,  1234. 

flow    of    water    in    house-service 
pioes,  1240. 

flow  of  water  in  pipes,  1232. 

friction  of  water  in  pipes,  1241. 

pressure  of  water,  1231. 

private  water-supply,  1244. 

velocity  of  discharge,  1233. 
Hyperbola,  to  describe  an,  85. 


I-beams, 

size  and  properties  of,  296. 

strength  of,  as  beams,  table,  515. 

as   columns,  471. 
Illuminants,  color  of,  1299. 
Illuminating-gas,  varieties  of,  1285. 
Illumination,  notes  on,  1294. 
Imperial  or  spiral  lath,  830. 
Incandescent  lamps,  1313. 
Inches  converted  into  millimetres, 
366. 

expressed  in  decimals  of  a  foot,  25. 

fractions  of,  expressed  in  decimals, 

26. 

Inclined  beams,  strength  of,  506. 
Incombustible   vs.   fire-proof   build- 
ings, 726. 
Inertia,  moment  of,  278,  279. 

for  compound  shapes,  282. 

of  rectangles,  291. 

of  round  columns,  293. 

of  square  columns,  293. 

of  structural  shapes,  296. 
Inside  painting,  1405. 
Inspection  of  concrete,  882n. 
Instantaneous  water  heaters,  1282. 
Insulating  quilts,  1402. 


1646 


INDEX. 


Interior — Lime. 


Interior   finish   of   fire-proof   build- 
ings, 839. 

cement  trim,  840. 

electroplated  trim,  839. 

kalamein,  839. 

metal-covered     door- jambs     and 
trim,  839. 

moulded  hollow  tiles,  840. 
Interior  surfaces,  painting  of,  1405. 

repainting  of,  1407. 

varnishing  of,  1406. 
Interlocking  rubber  tiling,  1447. 
Intrados,  definition  of,  249. 
Introduction  to  Part  II,  128. 
Inverted  arches,  183. 
Involution,  3. 
Ionic  Order,  the,  1500. 
Ionic  Volute,  to  describe,  1502. 
Iron   (see  also  Wrought  iron,  Cast 

iron.  Steel,  etc.). 
Iron  buildings,  cost  of,  1467. 
Iron,  colors  of,  caused  by  heat,  1119. 


Johnson  bar  in  reinforced-concrete 

construction,  862. 
data,  863. 
Johnson  long-span  flat  construction, 

766. 

advantages,  768. 
span,  767. 
strength,  768. 
weight,  767. 
Joints 

in  wooden  construction,  to  deter- 
mine the  strength  of,  338. 
of  steel  trusses,  1064. 
of  wooden  trusses,  1051. 
pin,  strength  of,  375. 
riveted,  strength  of,  363;    failure 

of,  365;  examples,  1066. 
Joist  hangers,  comparative  strength 

of,  684;  description  of,  681. 
Joule,  definition  of,  1308. 


K 


Kahn  bar  in  reinforced-concrete 
construction,  864,  865,  867. 

Kahn  hollow-tile  construction,  88 Ir. 

Kalamein,  839. 

Keene's  cement,  1391. 

Kenney  fiushometer,  1281. 

Keyed  beams,  581. 

Keys,  end-  and  side-construction,  in 
end-construction  arches,  760. 

Keystone,  definition  of,  249. 

Keystones,  depth  of,  rule  and  table, 
253. 


King  rod  trusses,  885;  stress  dia- 
grams, 970,  1027. 

Kirkaldy's  experiments  on  wrought 
iron  and  steel,  325. 


Ladder  wagons,  dimensions  of,  1473. 

Lafarge  cement,  197. 

Lag  screws,  sizes  and  holding  power 

of,  1371. 
Lamp,  Lamps, 
electric,  1313. 
the  Meridian,  1298. 
the  Nernst,  1299. 
Larimer  columns, 

description  and  details,  445. 
strength  of,  tables,  486. 
Lateral  strength  of  steel  beams,  509. 
Laterally     reinforced-concrete     col- 
umns, 881/1. 

Lath,  metal,  see  Metal  lath. 
Lath,  truss  metal,  825. 
Lath,  Laths, 

wooden,    size    and    quantity    re- 
quired, 1389. 
Lathing,  cost  of,  1393. 
Lattice  trusses, 

description  of,  897. 
stress  diagrams,  996. 
stresses  in,  898. 
table  of  dimensions  for,  899. 
Latticing  of  channel  columns,  439. 
Lead  pipes,    supply,    1275;     waste, 
1263;    weights  and  sizes,  1276. 
Leaders,  proportioning  to  roof  sur- 
face, 1481. 

Length  of  bridges,  1519. 
Lever,  the,  principle  of,  235. 
Libraries,  Architects  of,  1539. 
Library  stacks, 
capacity  of,  1495. 
dimensions  of,  1495. 
weight  of,  1495. 
License  Law,   Architects',  State  of 

Illin9is,  1558. 

Light,    diffusion    of,    through    win- 
dows, 1300. 

quantity  of,   required  for  illumi- 
nation, 1296. 
Lighting  and  illumination,  notes  on, 

1294. 
Lightning     Conductors,    rules     for, 

1505. 

Lights,  artificial,  color  of,  1299;   in- 
tensity of,  1295. 
Lime,  kinds  of,  1387. 
popping  of,  1387. 
quantity     required     for     mortar, 

1375,  1385,  1389. 

slaking  of,  1387. 

weight  of,  1387. 

Lime  mortar,  735. 

Lime  plaster,  735. 


INDEX. 


1647 


Limestones — Merchant . 


Limestones,  strength  of,   213,  226, 

229. 

Limestones    and    marbles    in    fire- 
proofing  of  buildings,  730. 
Line  of  Resistance  in  masonry,  245. 
Linseed-oil,  1403. 
Lintels,  cast-iron,  strength  of,  555. 
Liquid  measure,  28. 
List  of  b9oks,  1566. 

of  foreign  Architects,  1540. 

of    noted     American    Architects, 

1545. 

Lithophone,  1403. 
Live  load,  definition  of,  132. 
Load,  distinction  between  dead  and 

live,  132. 
Load     tests     in    concrete    erection 

work,  882p. 

Load  tests  of  fire-proof  floors,  805. 
Loads  on  columns,  method  of  com- 
puting, 459. 
eccentric,      upon     reinforced-con- 

crete  columns,  88 II. 
on  concrete  piles,  88 10. 
on  flooi-s,  654.      See  Floor  loads, 
on  roof  trusses,  see  Roof  loads. 
Lock-woven     fabric    for    reinforce- 
ment, 780. 

Locomotives,  dimensions  of,  1473. 
Longest  bridges  in  the  world,  1519. 
Loop<bars,  338. 
Lug* bar,  cold  twisted,  in  reinforced- 

concrete  construction,  855. 
data,  864. 
Lumber, 

finishing,  measurement  of,  1399. 
rough,    sizes   of,    1394;    measure- 
ment of,  1395. 

tables  of  board  measure,  1396. 
weight  of,  1509. 
Luxfer  prisms,  1302. 


M 


"M"  system  of  reinforced-concrete 
construction,  881r. 

McKelvey  concrete  mixer,  882h. 

Mackolite  hollow  blocks  for  parti- 
tions, 819. 

Madison  Square  Garden,  dimensions 
of,  1536. 

Magnesia     and     sulphuric    acid    in 
cement,  854. 

.Mail-chutes,  1491. 

Mansard  roofs,  fire-proof,  808. 

Marble,  strength  of,  tests,  226,  229. 

Marble  tiles,  1445. 

Marbleithic  tile  and  slabs,  1446. 

Masonry  (see  also  Brickwork,  Stone- 
work, Walls,  etc.). 
bond-stones,  216. 
brick  piers,  214. 

crushing  height  of  brick  and  stone, 
217. 


Masonry — continued . 
grouting  of,  216. 
maximum  loads  on,  from  bearing 

plates,  399. 
strength  of,  212. 
weight  of,  1343. 

Masonry  wells,  for  foundations,  171. 
Materials  in  reinforced-concrete  con- 
struction, see  under  Reinforced 
concrete. 

Materials    of    construction    in    fire- 
proofing  of  buildings,  730-739. 
asbestic  plaster,  735. 
brickwork,  730. 
cast  iron,  736. 
concrete,  733. 
cinder,  734. 
slag,  734. 
stone,  733. 
dense  tiling,  731. 
fire-proof  paint,  739. 
fire-proof  wood,  736. 
granite,  730. 

limestones  and  marbles,  733. 
metal  lath,  see  under  Partitions, 
mortars,  plasters,   and  plaster  of 

Paris,  734. 
sandstones,  731. 
steel  and  wrought  iron,  736. 
terra-cotta,  731. 
wire  glass,  739. 
Materials  of  fire-proof  construction, 

730-739. 
Maximum    span     of     ceiling-joists, 

floor-joists,  and  rafters,  671. 
Maze  glass,  1300,  1418. 
Measure,  Measures, 

circular  and  angular,  31. 
dry,  27. 
liquid,  28. 

metric  system,  the,  31. 
miscellaneous,  28. 
nautical,  27. 
of  length,  25. 
of  surface,  27. 
of  value,  30. 
of  volume,  27. 
of  weight,  28. 
Scripture  and  ancient,  36. 
Measurement  of 
brickwork,  1382. 
excavations,  1371. 
lumber,  1395. 
plasterer's  work,  1391. 
slater's  work,  1428. 
stonework,  1374. 
Mechanics,  definition,  130. 
Melting-point  of   metals,  1110. 
Men,  average  height  of,  1474. 
Mensuration,  37. 
areas,  40. 

areas  of  circles,  tables   44. 
circular  arcs,  56. 
surface  of  solids,  62. 
volume  of  solids,  65. 
Merchandise,  weight  of,  657. 
Merchant  steel,  base  price  and  ex- 
tras, 1455. 


1648 


INDEX. 


Meridian — Nuts. 


Meridian  lamp,  the,  1298. 
Merrick   system   of   floor   construc- 
tion, 795. 
Merrick   system   of   reinforced-con- 

crete  construction,  SSlt. 
fire  protection  of,  8826. 
Metal-core    columns    in    reinforced- 

concrete  construction,  881  j. 
Metal-covered  door-jambs  and  trim, 

839. 

Metal-covered  wood  doors,  846. 
Metal  fabric,  welded,  for  reinforce- 
ment, 779. 
Metal  furring,  837. 
Metal  lath, 

expanded  metal,  828. 
herringbone  lath,  829. 
Imperial  or  spiral  lath,  830. 
perforated  sheet-metal  laths,  831. 
truss  metal  lath.  825. 
wire  lathing,  826. 
stiffened  wire,  827. 

width,  828. 
Metal  lath,  truss,  825. 
Metal  window  frames  and  sash, 
material,  848. 
sheet,  847. 

wire-glass  sash  for,  847,  848. 
Metallic      furniture      and     fittings, 

841. 

Metals,  melting-point  of,   1110. 
Metric  conversion  tables,  34. 
Metric  system,  the,  31. 
Mill  buildings,   steel,  shop  cost  of, 

1453. 
Mill  construction, 

arrangement  of  stairways,  699. 
belt,  stairway,  and  elevator  tow- 
ers, 696. 
columns  in,  706. 

connection    of    floor-beams    and 
girders,    713;     of    girders    and 
columns,  718. 
cost  of,  723. 
description  of,  687. 
details  of,  712. 
doors  and  shutters  in,  708. 
one-story  shops,  704. 
partitions  in,  708. 
patented  systems  of,  708. 
reinforced-concrete,  88 lp. 
roofing  materials  for,  707. 
standard,  689. 
with  concrete  flooring,  722. 
with  self-sustaining  frame,  701. 
Mineral  wool,  1450. 
Mirrors,  1424. 
Moduli   of   elasticity   in   remforced- 

concrete  construction,  881. 
elastic  properties  of  broken-stone 

concrete.  881. 
Modulus  of  elasticity,  defined,  133; 

values  of  table,  597. 
of  rupture,  definition,  498;    table 

of,  499. 

Moments,  233. 
bendinp,  236. 
of  inertia,  278,  282,  296. 


Moments — cont  inued . 

of     resistance,     "definition,     498; 
tables  of,  for  structural  shapes, 
296. 
Mortar,  Mortars, 

for  setting  porous  hollow  tile,  751. 
quantity  required  for  brickwork, 

1385;   for  stonework,  1375. 
strength  of,  214,  221. 
Mortar  colors,  cost  of  and  quantity 

required,  1386. 
Mortars,    plasters,    and    plaster    of 

Paris,  733. 

fire-proof  qualities  of,  734,  735. 
Mortise  and  tenon  joints,  679. 
Motion,  definition  of,  130. 
Moulded    hollow    tiles    for    interior 

finish,  840. 

Mouldings,  classical,  1496. 
Multiplex  steel  plate,  Berger's,  792. 
Municipal  requirements,  see  Build- 
ing Laws. 

Mushroom    system    of    reinforced- 
concrete  construction,  88  Ir. 


N 

Nails, 

cement-coated,  1365. 
holding  power  of,  1365. 
kinds  and  varieties  of,  1365. 
quantities  of,  required  for  differ- 
ent kinds  of  work,  1366. 
size,  length,   and  number  to  the 
pound,  1367. 

National  Electrical  Code,  1335. 

Natural  rock  cements,  192. 

Natural    sines,     tangents,    secants, 
etc.,  103. 

Nautical  measure,  27. 

Neponset  building  papers,  1401. 

Nernst  lamp,  the,  1299. 

Neutral  axis,  definition  of,  497. 

New  York,  fire-proofing  of  buildings 
in,  727. 

New   York   formula   for  reinforced- 
concrete  columns,  88 If. 

Non-conductivity  of  concrete,  88 lit? . 

Non-fire-proof     buildings,     limiting 

areas  for,  728. 
limiting  heights  for,  729. 

Notable    buildings,    American,    de- 
scription  of,    1533;     Architects 
of,  1537. 
European,  dimensions  of,  1529. 

Noted  American  Architects,  list  of, 
1545. 

Noted    foreign    Architects,    list    of, 
1540. 

Novus  sanitary  glass,  1446. 

Nurick  column,  the,  44.8;    strength 
of,  488. 

Nuts,   dimensions   and  proportions, 
136,  1361. 


INDEX. 


1649 


O— Planks. 


Oak  beams,  table  of  stiffness,  607; 
table  of  strength,  576. 

Obelisks,  dimensions  of,  1528. 

Office  buildings,   cost  of  per  cubic 

foot,  1461. 

some  of  the  tallest,  and  name  of 
the  architect,  1531. 

Ohm,  definition  of,  1307. 

Oil  paint,  ingredients  of,  1403. 

Old  iron,  strength  of,  359. 

Opera  chairs,  1478. 

Opera  houses,  see  Theatres. 

Orders,  the  Five,  1497. 

Oregon  pine  beams,  table  of  stiff- 
ness, 604;  table  of  strength,  575. 

Outside  painting,  1404. 

Outside  walls,  furring  of,  837. 


P  and  B,  building  papers,  1401. 
Paddle  concrete  mixer,  882.?. 
Paint  and  varnishes,   1403, 
driers,  1404. 

ingredients  of  oil  paint,  1403. 
fire-proof,  739. 
inside  painting,  1405. 
kinds  of  paint,  1408. 
outside  painting,  1404. 
paint  for  structural  steel,  1408. 
priming  coat,  1404. 
repainting,  1407. 
varnish,  1405. 

Panelled  vs.  flat  ceilings,  761. 
Painting  of  structural  steel,  cost  of, 

1453. 

Parabola,  to  describe  a,  85. 
Paris,  Grand  Opera  House,  1530. 
Partitions,  fire-proof,  812. 
fire  tests,  813. 
metal  lath,  see  Metal  lath, 
plaster  boards,  832. 
requirements,  812. 
resistance    to    passage    of    sound 

through,  838. 
shaft  construction,  832. 
sound-deadenjng  qualities  of,  833. 
wall  board,  832. 
types, 

brick,  841. 

concrete,  817. 

plaster  block,  817. 

plaster  and  metal,  see  Plaster 

and  metal  partitions, 
terra-cotta,  see  Terra-cotta  par- 
titions. 

triangular  mesh  fabric,  826. 
truss  metal  lath,  826. 
Party  walls,  190. 
Paste  fillers,  in  painting,  1406. 
Patent-office   drawings,   dimensions 
of,  1474. 


Patent  plasters   in   fire-proofing  of 

buildings,  735. 

Paul  system  of  heating,  the,  1150. 
Paving  bricks,  1378. 
People,  average  weight  of,  1474. 
Perch,  number  of  cubic  feet  in,  1374. 
Perforated  sheet-metal  laths,  831. 
Philadelphia  City  Hall,  1535. 
Phoenix  columns, 

details,  etc.,  440. 

strength  of,  tables,  484. 
Pianos,  dimensions  of,  1471. 
Piers   and   buttresses,   stability  of, 

242. 
Piers,  brick, 

bond-stones  for,  216. 

bonding  of,  216. 

strength  of,  214. 
Pigments,  1403. 
Pile  foundations,  147. 

examples  of,  155. 

specifications  for,  155. 
Piles,  concrete,  177. 

See  Concrete  piles. 
Piles,  timber, 

bearing  power  of,  154. 

capping  of,  150. 

cost  of  driving,  157. 

driving  of,  148. 

loads  on  some,  actual,  156. 

materials  for,  148. 

spacing  of,  150. 

specifications  for,  153. 
Pin-connected  girder  frames  in  re- 
inforced-concrete  construction, 
870. 
Pine  beams, 

table    of    stiffness,    yellow,    603; 
white,  606. 

table    of    strength,    yellow,    574; 

white,  578. 
Pins,  for  bridge  and  truss  joints, 

bending   moment    in,    how    com- 
puted, 378. 

bending  moment  in,  table,  377. 

shearing  and   bearing  values  of, 
376. 

strength  of,  375. 

Pipe  (see  also  Gas-pipe,  Steam-pipe, 
etc.), 

block  tin,  1278. 

gas  and  steam,  1153,  1205. 

lead,  1276. 

seamless  drawn  nickel  silver,  1274. 

tin-lined,  1273,  1277. 

water,  1241. 

Pipe  areas,  equalization  of,  1203. 
Pipe  coverings,  1167. 
Pipes,  capacity  of,  1258. 

recesses    for,    in    fire-proofing    of 

buildings,  744. 

Pipes  for  hot  air,  1179,  1183,  1197. 
Piping  a  house  for  gas,  1287. 
Pitch  of  flat  roofs,  1435. 

of  rivets,  364. 

Pitched  roofs,  fire-proof,  806. 
Plank  flooring,  thickness  of,  667. 
Planks,  measurement  of,  1399. 


1650 


INDEX. 


Plaster — Pyramids . 


Plaster  and  metal  partitions,  821. 
Berger's   Economy  studding  and 

furring,  824. 
construction,  822. 
double  partitions,  823. 
truss  metal  lath,  825. 
weight,  822. 
See  also  Metal  lath. 
Plaster,  Plasters, 

hard  wall,  1391. 
Plaster  block  partitions,  817. 
gypsinite,  820. 
mackolite,  819. 
weight,  819. 
Plaster  boards,  832. 
Plaster    column    covering    in    fire- 
proofing  of  buildings,  743. 
Plaster  of  Paris, 
cost  of,  1393. 

fire-resisting  qualities  of?  735. 
Plastered  walls,  painting  of,  1406. 
Plastering, 

cost  of,  1393. 
description     of     operations,     terms 

used,  etc.,  1389. 
hair  for,  1390. 

improved  wall  plasters,  1391. 
machine-made  mortar,  1390. 
measurement  of  1391. 
quantities    of   materials   required 

for,  1392. 
Plasters,  fire-proof  qualities  of,  734, 

735. 

asbestic  plaster,  735. 
lime  plaster,  735. 
Plate   and    angle    columns,    details, 

440. 
Plate    girders,    riveted    steel,    618; 

tables  of,  644. 

Plate  glass,  1416;  price-list,  1420. 
Plenum      system      of     ventilation, 

1216. 
Plumbing,  1262. 

definitions  of  terms,  1262. 

drains,  1264. 

lead  waste-pipes,  1263,  1266. 

leaders,  1264. 

rules  and  regulations,  City  of  New 

York,  1262. 
testing  of,  1269. 
traps,  1267,  1269. 
Plumbing    fixtures,    dimensions    of, 

1471. 
Plumbing  specialties, 

Climax  cellar  drainer,  1282. 
filters,  1281. 

Kenney  flushometer,  the,  1281. 
water  heaters,  1282. 
Plunge  baths,  1283. 
Plunger  pumps,  1245;    capacity  of, 

1247. 
Polygons, 
areas  of,  40. 
definitions,  37. 
Porous   terra-cotta,    730.     See   also 

Terra-cotta. 

Portal    bracing    of      tall    buildings, 
1097. 


Portland  cement, 

amount  required  for  mortar,  etc., 

193,  199. 

properties  of,  197. 
strength   of,   for  anchoring  bolts, 

1507. 
Portland-cement  concrete,  202.    See 

also  Concrete. 
Post-caps,  719. 
Posts,  see  Columns. 
Pouring  of  concrete,  882k. 
Prary  improved   mill   construction, 

708;  cost  of,  723. 
Pratt   truss,    shape  of,   927;    stress 

diagram,  996. 
Pressure  of  water,  1231. 
Price,  see  Cost. 
Priming  coat,  1404. 
Principle  of  the  lever,  235. 
Principles  of  the  arch,  252. 
Prism  glass,  1302. 

Prismatic    glass,    list    of    Manufac- 
turers, 1419. 
Prisms,  volume  of,  65. 
Private  water-supply,  1244. 
Problems, 

geometrical,  70. 

of   the   eclipse,   parabola,    hyper- 
bola, and  cycloid,  81 
Professional  practice  of  architects, 

schedule  of  charges,  1552. 
Properties  of,  see  Article  in  question. 
Properties  of  structural  shapes,  296. 
Proportioning  gutters  and  conduc- 
tors to  roof  surface,  1481. 
Proportions  of  concrete,  201,  203. 
Proportions  of  mortar,  cement,  199; 
cement    and    lime,    200,    1375; 
lime  mortar,  1375,  1385,  1389. 
Protecting     devices      in     fire-proof 

buildings,  849. 
automatic  alarms,  849. 
automatic  sprinklers,  850. 
stand-pipes  and  hose  reels,  850. 
water  curtains,  848. 
Protection    of    girders    and    beams, 

795. 

concrete,  797. 
terra-cotta,  795. 

Protective  coverings  for  girders  and 
columns     in     fire-proofing     of 
buildings,  739-744. 
tests,  740. 
Prussian  regulations  for  reinforced- 

concrete  columns,  881h. 
Pulleys,  rules  to  determine  size  and 

speed  of,  1513. 

Public  buildings,  Architects  of,  1537. 
Pumps, 

air-lift  process,  1248. 
Climax  cellar  drainer,  1282. 
plunger    1245;  capacity  of,  1247. 
Purlin,  Purlins,  891,  943. 

connection  to  steel  roof  trusses, 

1073. 

Puzzolan,  slag  cement    195. 
Pyramids,  surface,  64;    volume  of, 
67. 


INDEX. 


1651 


Q — Reinforced. 


Quadrangular  truss, 

description  and  examples,  928. 
stress  diagrams,  997. 
Quantity,  Quantities  of, 

materials  for  concrete,  203,  205. 
for    mortar,    199,    1375,    1385, 

1389. 
for  top  coat,  cement  walks  and 

floors,  200. 

mortar  for  masonry  and  plaster- 
ing, 199. 
nails  required  for  different  kinds 

of  work,  1366. 

Queen-rod  trusses,  886;    stress  dia- 
grams, 974,  1030. 
Quilt,  cabots,  1402. 


Radial  block  chimneys,  1229. 
Radiating    surface,    rule  for,   1158, 

1163. 
Radiators  for  steam  or  hot  water, 

see  Steam  radiators. 
Radiators,  warm  air,  1180. 
Radius  of  gyration,  see  Gyration. 
Rafters,   hip    and   jack,   length   and 

bevel,  97. 

maximum  span,  table,  674. 
Ram,  hydraulic,  1244. 
Ramming  of  concrete,  882Z. 
Range  boilers,  diameter  of,  1473. 
Ransome  bar  in  reinforced-concrete 

construction,  861. 
Ransome  concrete  mixer,  882ft. 
Ready  roofings,  1436. 
Reciprocals,  table  of,  9. 
Rectangular    beams    in    reinforced- 
concrete  construction,  877. 
Red  lead,  1408. 
Refrigerators,  notes  on,  1492. 
Registers,  1183,   1198;    capacity  of, 

1200. 
Regulations  for  reinforced-concrete 

columns,  Brooklyn,  881/1. 
Prussian,  881ft. 
Reinforced  concrete,  851. 
definition,  851. 
design,  871. 
columns,  8810. 

amount  of  vertical  reinforce- 
ment, 8810. 

Brooklyn  regulations,  881ft. 
cast-iron,  88 11. 
eccentric  loads,  88 1Z. 
laterally  reinforced,  881ft. 
length  of,  881gr. 
limiting  conditions,  881z. 
metal-core  columns,  88 1/. 
New  York  formula,  88 If. 
Prussian  regulations,  881  h. 
steel,  881 Z. 


Reinforced  concrete — continued, 

strength    of   vertically    rein- 
forced, 8810. 
concrete,  piles,  881rc. 
connections,  881o. 
'  Chenoweth,  88 In. 
corrugated,  881n. 
loads,  88 lo. 

disposition  of  steel,  8816. 
footings,  881m. 

economy   of   reinforced   con- 
crete, 881m. 

girders,  beams,  and  slabs,  871. 
assumptions,  871. 
attached      shear      members, 

88  If. 
bending  moments  in  beams, 

881a. 
bending    moments    in   slabs, 

881a. 

breadth  of  beams,  88 If. 
check  formulae,  878. 
compression   rods   in  beams, 

88  If. 

Cummings  system,  870. 
formulae  of  beams,  872. 

tables,  837-7. 
moduli  of  elasticity,  881. 
elastic  properties  of  broken 

stone  concrete,  881. 
pin-connected  girder  frames, 

870. 
position  of  the  reinforcement, 

868. 

provision  against  shear,  881  e. 
rectangular  beams,  877. 
slabs,  878. 
tee  beams,  879. 

formula  for,  879. 
number  of  rods,  88 Ic. 
adhesion  required,  88  Id. 
separation  of  rods,  881rf. 
percentage     of     reinforcement, 

881c. 
shrinkage      and      temperature 

stresses,  8816. 
stairs,  881p. 
walls,  881m. 
erection,  852,  882/. 

concrete  mixing,  882ft. 

changing  the  mixers,  882/c. 
McKelvey  mixers,  882ft. 
paddle  mixer,  882/. 
Ransome  mixer,  882ft. 
Smith  mixer,  882j. 
wet  mixture,  882JL 
finish,  882m. 
floor  finish,  882m. 
forms,  882/. 
inspection,  882n. 
load  tests,  882p. 
pouring  the  concrete,  882/c. 
ramming,  SS21. 
removing  forms,  882n. 
fire  protection,  881iy. 
fire  tests,  SSly. 
actual  fire,  88 lz. 
Baltimore  fire,  881z. 


1652 


INDEX. 


Reinforced — Riveted. 


Reinforced  concrete — continued. 

San  Francisco  fire,  8812. 
Fire      Underwirters'      require- 
ments, 882. 
loss  of  strength,  881]!/. 

tables  of  tests,  881x-88ly. 
non-conductivity    of    concrete, 

88110. 
thickness  of  concrete  required, 

882. 
various    forms    of    protection, 

882a. 

history,  851. 
materials,  852. 
cement,  852. 

constancy  of  volume,  853. 

fineness,  853. 

specific  gravity,  853. 

sulphuric  acid  and  magnesia, 

tensile  strength,  853. 

time  of  setting,  853. 
cinders,  855. 
cold  twisted  lug  bar,  863. 

data,  864. 

concrete,    852.     See    also   Con- 
crete   in    reinforced-concrete 

construction, 
cup  bar,  864. 
deformed  bars,  861. 
De  Man  undulated  bar,  864. 
diamond  bar,  863. 
Golding  bar,  864,  867. 
gravel,  855. 
Hennebique  bar,  864. 
Johnson  bar,  862. 

data,  863. 

Kahn  bar,  864,  865,  867. 
Ransome  bar,  861. 
sand,  854. 

shear  members,  865. 
steel  in  compression,  868. 
steel  reinforcement,  869. 

mild  or  high  steel,  859. 

working  stresses,  860,  881. 
stirrups,  865. 
stone,  855. 

tension  members,  861. 
Thacher  bar,  862. 
Universal  type  corrugated  bar, 

864. 

protection  against  corrosion,  882d 
corrosion  in  cinder  concrete, 8S2d 
thickness  of  concrete  required, 

882d. 

types  of  construction,  88 lp. 
Faber,  881*. 

Hennebique  system,  864. 
Kahn  hollow-tile,  881r. 
Merrick  system,  881*. 

fire  protection  of,  8820. 
mill,  881p. 

mushroom  system,  881r. 
skeleton,  SSlq. 
system  "M,"  88 Ir. 
Reinforced  concrete,  advantages  of, 

for  floor  construction,  771. 
disadvantages,  772. 


Reinforced  concrete  floors,  see  Con- 
crete floors,  reinforced. 
Reinforced-concrete  stairs  and  stair- 
ways, 842. 

Reinforced  floors,  flat,  777. 
Reinforced  tile  arches,  765. 
Reinforcement,  forms  of,  772.  See 

also  Reinforced  concrete, 
lock-woven  fabric,  780. 
necessity    for    longitudinal    bars, 

773. 

welded  metal  fabric,  771. 
Reinforcement,   position   of,   in   re- 
inforced-concrete construction, 
868. 

percentage  of,  881c. 
Reinforcing  bars, 

cold  twisted  lug  bar,  863. 

data,  864. 
cup  bar,  864. 
deformed  bars,  861. 
De  Man  undulated  bar,  864. 
diamond  bar,  863. 
Golding  bar,  864,  867. 
Hennebique  bar,  864. 
Johnson  bar,  862. 

data,  863. 

Kahn  bar,  864,  865,  867. 
Ransome  bar,  861. 
Thacher  bar,  862. 
Universal    type    corrugated    bar 

864. 

sectional  systems,  863. 
steel  framing  for,  873. 
Relative  hardness  of  woods,  1509. 
Relative    strength     of     rectangular 

beams,  570. 
Repainting,  1407. 
Residence  heating.  1174,  1187,  1191; 

books  on,  1196. 

Resistance,  line  of,  in  piers  and  but- 
tresses, 245. 

Resistance,   moments  of,  278,   282; 

of  structural  shapes,  tables,  296. 

Resistance     (electrical)     of    copper 

wire,  1327. 

Resolution  of  forces.  231. 
Rest,  definition,  130. 
Retaining  walls,  206. 

of  reinforced  concrete,  210. 
thickness  of,  208. 
Revolving  doors,  1494. 
Rivets, 

bending  moment  in,  370. 

dimensions  of,  373. 

in  plate  and  box  girders,  620,  625. 

in  steel  columns,  432. 

length  of  shank  required  to  form 

head,  374. 
pitch  of,  364. 
shearing  and  bearing  value,  table, 

371. 

signs  for,  373. 
steel  for,  grade  of,  333. 
weight  of,  1364. 
Riveted  girders,  steel  plate  and  box, 

618. 
calculations  for,  620. 


INDEX. 


1653 


Riveted— Roof. 


Riveted  girders — continued, 
example  of,  627. 
splices,  632. 

strength  of  web  plates,  641. 
tables  of,  644. 

weight  of,  approximate,  626. 
Riveted  joints,  363;    failure  of,  365. 
in  steel  trusses,  1064. 
splicing  of  tie-bars,  367. 
Rock, 

bearing  power  of,  137. 
foundations  on,  144. 
Rock  asphalt,  1448;    cost  of,  1449. 
Rock- wall  plasters,  1391. 
Rods    in    reinforced-concrete    con- 
struction, adhesion  required  in, 
88  Id. 

number  of,  88  le. 
separation  of,  88 Id. 
Rods,    round,    tensile    strength    of, 

340. 

size  of  head  and  nut,  1362. 
upset,  340,  341. 

Roebling  arch  floor  system,  774. 
Roebling  flat  floor  construction,  784. 
adaptation,  786. 
strength,  786. 

Roman  measures  and  weights,  36. 
Roof,  Roofs   (see  also  Roofing  and 

Roof  trusses), 
fire-proof,  see  Fire-proof, 
method  of  supporting  from  trus- 
ses, 891,  942. 

Roof  coverings,  fire-proof,  844. 
Roof  loads  on  trusses, 
data  for  computing,  946. 
examples  of  computation  of,  952. 
method  of  computing,  944. 
snow  loads,  949. 
wind  pressure,  950. 
Roof  trusses, 

definition  of  terms,  883. 
details  of  steel  trusses,  1064. 
details  of  wooden  trusses,  1051. 
loading  of,   variations   for  which 
stresses  should  be  found,  951, 
1024. 

loads  on,  see  Roof  loads, 
proportioning  the  members  to  the 

stresses,  1037. 
spacing  of,  943. 
stress  diagrams,  970;  for  wind 

pressure,  1026. 
stresses  in,  determining  the,  957, 

970. 

N  supporting  forces,  967. 
unsyrnmetrically  loaded,  1004. 
weight  of,  947. 
wind  stress  diagrams,  1026. 
Roof  trusses,  steel, 

Arched    trusses,    932.     See    also 

Three-hinged  arch. 
Bowstring  trusses. 

description  and  examines,  931. 
stress  diagrams,  1003. 
Cantilever  trusses, 

advantages  and  disadvantages, 
939. 


Roof  trusses — continued. 

example  of,  940. 

principle  of,  936. 
stress  diagram,  1014. 
Cost  of,  1453. 
Fan  and  Fink  trusses, 

cambering  of,  920. 

depth  of,  920. 

description  of,  918. 

stress  diagrams,  984. 

stresses  in,  958. 

with  pin  joints,  923. 
for  flat  roofs,  923. 
for  pitch  roofs,  917. 
joints  of,  1064. 
Latti'ce  trusses,   stress  diagrams, 

996. 
Pratt  truss,  shape  of,  927. 

stress  diagram,  996. 
Proportioning    the    members    of, 

1044. 
Quadrangular  truss, 

description       and       examples, 
928. 

stress  diagrams,  997. 
Three-hinged  braced  arches, 

description    and    examples    of, 
993. 

horizontal  resistance,  1019. 

stress  diagrams,  1021. 
types  of,  917. 
weight  and  spacing  of  some  steel 

roofs  with  wide  span,  949. 
Roof  trusses,  wooden, 

arched  ribs,  with  iron  or  steel  ties, 

911. 
cantilever  trusses,  936. 

stress  diagrams,  1014. 
counter-braces,  object  of,  887. 
Fink  trusses,  with  wooden  rafters 

and  struts,  910. 
Hammer-beam  trusses, 

description  of,  903. 

examples  of,  905. 

stress  diagrams,  991. 
Howe  trusses, 

counter-braces  in,  1013. 

description  of,  892. 

joints  in,  1056. 

stress  diagrams,  977,  982. 

stresses  in,  formulas,  963. 

table  of  dimensions,  896. 

unsyrnmetrically  loaded,  1009. 
joints  of,  1051. 
King  and  Queen  trusses,  885. 

stress  diagrams,  970. 

wind  stress  diagrams,  1027. 
Lattice  trusses, 

description  of,  897. 

stresses  in,  898. 

table  of  dimensions,  899. 
proportioning    the    members    of, 

1037. 
Scissors  trusses, 

description  of,  900. 

joints  in,  903. 

stress  diagrams,  989. 
types  of,  884. 


1654 


INDEX, 


Roofing —  Side-construction. 


Roofing,  Roofing  materials  (see  also 
the  Kind  in  question), 

asphalt,  1435. 

canvas,  707. 

corrugated  iron,  1439. 

cost  of,  942. 
Roofing,  fire-proof,  844. 

for  fiat  roofs,  941. 

for  pitch  roofs,  941. 

gravel  or  slag,  1432. 

least  pitch  for,  941,  942. 

papers,  1401. 

ready,  1436. 

shingles,  1425. 

slates,  1426. 

tile,  1429. 

tin,  1430. 

weight  of,  946. 
Roofs  of  fire-proof  buildings,  806. 

flat,  806. 

mansard,  808. 

pitched,  808. 
Ropes, 

hemp  and  Manila,  353,  356. 

wire,  352,  355. 

Rosin-sized  building  papers,  1401. 
Rubber  tiling,  1446. 
Rubble  stonework,  1373. 


S 

Sackett's  wall  board,  832. 

Safe  loads  for  Columbian  floors,  790. 

Safe     loads     for     end-construction 
arches,  762. 

Saints,  the,  symbols  for,  1524. 

Salt  in  mortar,  199. 

Sand    and    gravel,    foundations   on, 
145. 

Sand  as  material  in  concrete,  854. 

Sand  finish,  1390. 

Sand,    number  of  yards   to  a  load, 
screening  weight,  etc.,  1388. 

Sand-lime  brick,  1379. 

Sandstones  in  fire-proofing  of  build- 
ings, 731. 

Sandstones,   strength  of,   213,  221, 
229. 

San  Francisco  fire,  test  of  reinforcecl- 
concrete  construction  in,  8810. 

Sash,  glazed,  weight  of,  1477. » 

Sash  weights,  1477. 

Scale  of  Architects'  charges,  1552. 

Scantlings   reduced  to  board  meas- 
ure, 1396. 

Scholarships,  travelling,  1565. 

Schoolrooms,  dimensions  of,  1475. 

School  seats,  1475. 

Schools  of  Architecture,  1562. 

Scissors  trusses, 

description  and  examples  of,  900. 
joints  of,  903,  1059. 
stress  diagrams,  989. 

Screw  ends,  upset,  338;    dimensions 
of,  341. 


Screw-geared  blocks,  1516. 
Screw  threads,  proportions  of,  1361. 
Screws,  kinds,  sizes,  etc.,  1370. 
Scripture  measure,  36. 
Seating  space  in  churches  and  the- 
atres, 1478. 
in  schools,  1475. 
Secants  table  of   natural,  123a. 
Section  modulus,  defined,  498. 

tables  for  structural  shapes,  296. 
Sectional  area  to  be  deducted  from 
plates    and     angles    for    round 
holes,  350,  640. 

Sectional  cast-iron  boilers,  1137. 
Sectional  coverings  for  steam-pipes, 

1167. 
Sectional  systems,  disadvantages  of, 

794. 

Segmental  concrete  arches,  773. 
Segmental  terra-cotta  arches,  753. 
filling  the  haunches,  754. 
rise  of  arch,  754. 

strength  of  segmental  arches,  755, 
thickness  of  webs,  754. 
tie-rods,  755. 

Self-sustaining  steel  chimneys,  1230. 
Semi-porous    tiling,    its  value   as   a 

fire-resistant,  732. 
Separators  for  steel  beams,  543. 
Sewer-pipe,  1279. 
Shaft  construction,  832. 
Shafting,   horse-power   capacity   of, 

1516. 

Shear  in  reinforced-concrete  con- 
struction, provision  against, 
881e. 

Shear   members    in    reinforced-con- 
crete construction,  865. 
Shear  members,   attached,  in  rein- 
forced-concrete    construction, 
881/. 
Shearing, 

examples  of,  361,  363. 
resistance  to.  360,  361. 
strength  of  rivets,  371. 
Sheathing,  cost  of  putting  on,  quan- 
tity required,  1400. 
Sheet  lead,  weights  and  thicknesses, 

1277. 

Sheet-metal  laths,  775. 
Sheet-metal  tiles,  1430. 
Sheet-metal  window  frames  and 

sash,  847. 
material,  848. 
wire-glass  sash,  847,  848. 
Shellac  varnish,  1406. 
Shingles,  staining  of,  1405. 
Shingles,  wood, 
C9st  of,  1426. 

kinds  and  dimensions  of,  1425. 
number  to  cover,  100  sq  ft.,  1425. 
Shrinkage  and  temperature  stresses 
in  reinforced-concrete  construc- 
tion, 8816. 

Shrinkage  in  castings,  1357. 
Sideboards,  dimensions  of,  1471. 
Side-construction  terra-cotta  arches, 
756.     See  also  Flat  arches. 


INDEX. 


1655 


Siding— Steam. 


Siding,  dimensions  of,  1399;    quan- 
tity required,  1400. 
Signs,  arithmetical.  3. 
Signs  for  rivets,  373. 
Silica-Portland  cement,  194. 
Sines,  table  of  natural,  103. 
Sinks,  dimensions  of,  1472. 
Size  of,  see  Dimensions  of  (see  also 

the  Article  in  question). 
Skeleton     reinforced-concrete     con- 
struction, SSlq. 
Skewback,  definition,  249. 
Skewbacks,      in      end-construction 
arches,  form  of,  758. 

raised,  760. 
Skylights, 

cost  of,  glass  for,  1419. 

Faboleum,  1424. 

in  courts,  1304. 

Slabs    in    reinforced-concrete    con- 
struction, see  under  Reinforced 
concrete. 
Slag    concrete    in    fire-proofing    of 

buildings,  733. 
Slag  roofing,  1432. 
Slate  tiles  and  slabs,  1446. 
Slates,  slater's  work,  etc., 

characteristics  and  color,  1426. 

cost  of,  1428. 

grading  of,  1426. 

laying  of,  1427. 

measurement  of,  1428, 

sizes  of,  1427. 

weight  of,  1429. 
Sleeve-nuts,  336, 338 ;  dimensions  of, 

346. 
Slow-burning      construction,      726. 

See  also  Mill  construction. 
Smith  concrete  mixer,  882/. 
Smoke  and  dirt  on  ceilings,  removal 

of,  1407. 

Smoke  prevention,  1207. 
Snow,   allowance   for  weight  of,  on 

roofs.  949. 

Soffit,  definition  of,  249. 
Soffit  of  segrnerital  arch,  rise  of,  754. 
Soil-pipe,  1262. 
Soils, 

bearing  power  of,  136. 

maximum  loads  on,   as  fixed  by 
municipal  laws,  139. 

testing  of,  136. 
Solid  built  beams,  579. 
Sound-deadening    qualities    of    fire- 
proof partitions,  833. 
Span,  definition  of,  249. 
Spar  varnish,  1406. 
Specific  gravity  of  substances,  1341. 
Specifications  for 

asphalt  roofing,  1436. 

electric  light  wiring,  1338. 

elevators,  1484. 

furnace  work,  1185. 

gravel  roofing,  1433. 

hot-water  heating,  1188. 

painting  structural  steel,  1413. 

steam  heating,  1192,  1194. 

structural  steel  work,  335. 


Specifications  governing  physical 
properties  of  structural  steel, 
331. 

Speed  of  elevators,  1483. 
Speed  of  gears  and  pulleys,  1513. 
Spheres, 

surface  of,  62. 

volume  of,  65. 
Spheroids,  surface  of,  63. 
Spikes,   sizes,   number  to  a  pound, 

etc.,  1367. 

Spires :  height  of,  1526. 
Spirit  varnish,  1405. 
Splices  in  riveted  girders,  632. 
Spread  foundations,  158. 

examples  of,  169. 
Sprinklers,  automatic,  850. 
Spruce  beams, 

table  of  stiffness,  605. 

table  of  strength,  577. 
Square  root,  4;  table  of;  8. 
Squares,  table  of,  8. 
St.  Peter's,  Rome,  1530. 
Stability,  definition  of,  131. 
Stability  of  arches,  256 

of  piers  and  butti  esses,  242. 
Stacks,  see  Library. 
Staff,  1394. 
Stainless  cement,  196. 
Stains,  1405. 
Stairs, 

notes  on,  and  rules  for,  1476. 

with  ferroinclave  treads  and  risers 

765. 
Stairs  and  stairways,  fire-proof,  841. 

brick,  842. 

cast  iron,  841,  842. 

clay  tiles,  842. 

ferroinclave,  843. 

Guastavino,  842. 

reinforced  concrete,  842. 
Stairs    in    reinforced-concrete    con- 
struction, 881p. 

Standard  building  contract,  1555. 
Standard      connections      for      steel 

beams,  546. 

Standard  steel  classification,  1455. 
Stand-pipes  and  hose  reels,  850. 
State      Capitol,    Hartford,      Conn., 

1535. 

State  Capitols,  architects  of,  1538. 
Statics,  definition  of,  130. 
Steam, 

definitions,  1111. 

drying  by,  1117. 

properties  of,  1114. 

sensible  and  latent  heat  of,  1111. 

superheated,  1111. 
Steam-boilers,  see  Boilers,  steam. 
Steam-hammers,    for   driving   piles, 

149. 
Steam  heating,  gravity  systems. 

boilers    for,     1133.      See    Boilers, 
steam. 

by  direct-indirect  radiation,  1127. 

by  direct  radiation,  1122. 

by  indirect  radiation,  1129. 

for  residences,  1191. 


1656 


INDEX. 


Steam — Strength. 


Steam  heating — continued. 

overhead    systems    of    radiation, 

1162. 
rules  for  proportioning  radiating 

surface,  1158. 

rules  for  size  of  air  ducts,  for  indi- 
rect radiation,  1163. 
size  of  pipes,  rules  for,  1165. 

tables  for,  1202. 
specifications  for,  1192,  1194. 
systems  of  piping,  1148. 
the  Paul  system,  1150. 
Steam  heating,  non-gravity  systems, 
distinction   between   gravity  and 

non-gravity  systems,  1146. 
hot-blast  system,  1153. 
return  of  water  to  boiler,  1151. 
the  Webster  system,  1152. 
Steam-pipe    columns,    strength    of, 

465. 
Steam-pipes,  1153;    dimensions  and 

data,  1205. 

Steam-piping,  in  heating  systems, 
covering  of,  1166. 
definition  of  terms,  1147. 
equalization  of  pipe  areas,  1203. 
fittings  for,  1153. 
systems  of,  for  hot  water,  1171. 

for  steam,  1148. 
valves  for,  1155. 
Steam-radiators, 
classes  of,  1122. 
direct,  1123;   heating  surface  and 

dimensions,  1127. 
direct-indirect,  1127. 
efficiency  of,  1122. 
indirect,  1130. 
measurement  of,  1122. 
pipe,  1124. 
Steam-valves,  1155. 
Steam  vs.  hot-water  heating,  1172. 
Steel, 

chimneys,  self-sustaining,  1230. 

constituents  of,  327. 

crushing  strength  of,  407,  454. 

elasticity  of,  329. 

expansion  of,  330. 

grades  of,  328,  333. 

rules    for    estimating    weight    of, 

1357. 

shearing  strength  of,  361. 
specifications  for,  331. 
standard  classification,  1455. 
tensile  strength  of,  329. 
transverse  strength  of,  569. 
weight  and  specific  gravity  of,  330 
working  strength  of,  321. 
Steel  and  concrete,   tests  on  adhe- 
sion between,  866. 
Steel-beam  box  girders,  safe  loads, 

537. 

Steel-beam  footings,   161;    calcula- 
tions for,  164. 
Steel    beams    (see    also   Beams,    I- 

beams,  etc.). 
connections  for,  545. 
framing  and  connecting  of,  543. 
separators  for,  543. 


Steel  beams — continued. 

standard  punching  for  connection 

angles,  550. 
strength  of,  formulas,  550;  tables, 

515. 

wall  anchors  for,  553. 
Steel    clips    for   fastening   tees    and 
angles  to  beams  and  channels, 
811. 

Steel  columns,  see  Columns. 
Steel,  disposition  of,  in  reinforced- 

concrete  construction,  8816. 
Steel  fire  doors  and  shutters,  864. 
Steel   framing  for  fire-proof  floors, 

799. 
Steel  in  compression  in  reinforced- 

cqncrete  construction,  868. 
Steel   in   fire-proofing  of  buildings, 

736. 

Steel     in     reinforced-concrete     col- 
umns, 88 11. 
Steel  mill  buildings,   shop  cost  of, 

and  cost  of  erecting,  1453. 
Steel,  paint  for  structural,  1408. 
Steel   plate    and    box   girders,    618. 

See  also  Riveted  girders. 
Steel  plate,  Berger's  multiplex,  792. 
Steel  reinforcement,  859. 
mild  or  high  steel,  859. 
working  stresses,  860,  881. 
Steel  trusses,  see  Roof  trusses,  steel. 
Steel-wire  reinforcement,  782. 
Stiffness  of  beams,  595,  598;   tables, 

603. 

of  continuous  girders,  608. 
of  steel  beams,  510. 
Stirrups  and  joist  hangers,  680,  713. 
Stirrups  in  concrete  steel-beams,  870. 
Stirrups  in  reinforced-concerte  con- 
struction, 865. 
Stirrups,  weakness  of,  when  exposed 

to  fire,  717. 
Stone  arches,  255. 
Stone  as  material  in  concrete,  855. 
Stone  beams,  strength  of,  573. 
Stone  footings,  178. 
Stone  piers,  strength  of,  217. 
Stones,  building, 
cost  of,  1375. 

crushing  strength  of,  221,  224,225. 
Stone  stairs,  842. 
Stones  in  fire-proofing  of  buildings, 

730. 

Stone  walls,  thickness  of,  189. 
Stonework, 
cost  of,  1375. 
crushing  height  of,  217. 
data  on,  1373. 
measurement  of,  1374. 
strength  of,  213,  214. 
Storehouse  construction,  697.     See 

also  Mill  construction. 
Strain,  definition  of,  131. 
Strains,  classification  of,  134. 

cross  or  breaking,  see  Beams. 
Street  cars,  dimensions  of,  1473. 
Strength, 

of  materials,  defined,  131. 


INDEX. 


1657 


Strength — Tension. 


Strength — continued . 

tensile,  safe  for  building  materials, 

322. 
transverse,  for  building  materials, 

499,  569. 
Strength  of  (see  also  the  Article  in 

question), 

angles  (tensile),  349. 
bolts  in  trusses  and  girders,  382. 
brick  piers,  214,  215,  219. 
bricks,  actual  tests,  218. 
cast  iron,  327. 

cast-iron  beams  and  lintels,  554. 
chain,  358. 

columns,  see  Columns, 
concrete,  214. 

concrete-steel  columns,  228. 
continuous  girders,  608. 
flat  bars  (tensile),  347. 
flat  bars  as  beams,  523. 
hollow  tile,  214. 
inclined  beams,  506. 
lead  pipe,  1278. 
masonry,  213. 
mortars,  214,  221,  224. 
old  iron,  359. 
posts,    struts,    and    columns    (see 

Columns),  407. 
rods,  340. 

ropes,  hawsers,  and  cables,  356. 
segmental  arches,  755. 
steel  beams,  formulas,  500. 

tables,  515. 

without  lateral  support,  509. 
stones,  actual  tests,  221. 
stonework,  213. 

structural  steel  (as  a  metal),  327. 
terra-cotta,      architectural,     228, 

230. 
terra-cotta  brackets  and  consoles, 

230. 
Strength    of    vertically    reinforced 

columns,  881gr. 
water-pipes,  1242. 
wire,  351. 

wire  ropes,  354,  355. 
wooden    beams,    formulas,    562; 

tables,  574. 

wooden  floors,  651,  675. 
wrought  iron,  323. 
Stress,  definition  of,  131.1 
Stress  diagrams  for  roof  trusses,  970. 
Stresses  in   roof  trusses,   957.     See 

also  Roof  trusses. 
Stresses,  temperature,  in  reinforced- 

concrete  construction,  8816. 
Structural  shapes,  properties  of,  296. 

See  also  I-beams,  Channels,  An- 
gles, etc. 

Structural  steel  (see  also  Steel), 
cost  of,   base  price,   and  extras, 

1451. 
cost  of  drafting,  1454. 

of  erecting,  1453. 

of  painting,  1453. 
data  for  approximating  weight  of 

in  buildings.  1454. 
paint  for,  1480, 


Structural  steel — continued. 

shapes  of,  296. 

specifications  for,  335. 
Structures,  definition  of,  130. 
Strut-beams, 

of  steel,  rules  for,  511. 

of  wood,  rules  for,  568. 
Struts,  steel,   strength  of,  formula, 

453;  tables,  466,  468. 
Struts  in  steel  trusses,  1047,  1050. 

in  woooen  trusses,  1039. 
Studding     and     furring,      Berger's 

Economy,  824. 
Styles,  see  Orders. 
Sulphur  for  anchoring  bolts,  1507. 
Sulphuric    acid    and    magnesia    in 

cement,  854. 

Supply-pipes,  1273;  size  of,  1275. 
Supporting  forces,  how  found,  274. 
Suspended  ceilings,  809. 
Switches,  electric,  1332. 
Symbols  for  the  apostles  and  saints, 
1524. 


Table,  Tables  of,  see  the  Article  in 

question. 

Tables,  dimensions  of,  1470. 
Tables  for  floor  beams,  82. 
Tacks,  length,  size  and  number  to 

the  pound,  1367,  1369. 
Tall  buildings, 

heights  of,  and  name  of  Architect, 

1531. 

wind  bracing  of,  1082. 
Tangents,  table  of  natural,  112. 
Tanks, 

cylindrical,  capacity  of,  1259. 
house,  1274. 

rectangular,  capacity  of,  1261. 
steel,  notes  on,  1257. 
wooden,  construction  of,  1252. 
Tee    beams    in    reinforced-concrete 

construction,  879. 
formulae  for,  879. 
Tees  and  angles,  clips  for  fastening, 

to  beams  and  channels,  811. 
Tees,  T-bars,  rolled  steel, 
size  and  properties  of,  313. 
small,  base  price  and  list  of  extras 

on,  1456. 

strength  of,  as  beams,  533. 
Temperature  of  fire,  1110. 

of  steam,  1114. 

Temperature  stresses  in  reinforced- 
concrete  construction,  8816. 
Tensile  strength  of  cement,  853. 
Tension  members  in  reinforced-con- 
crete construction,  861. 
Tension,  Tensile,  see  also  Strength, 
resistance  to,  321. 
safe  tensile  strength  of  materials, 

322. 
strength  of  rods,  table,  34<». 


1058 


INDEX. 


Terra-cotta — Trigonometry. 


Terra-cotta,  731. 
ornamental,  731. 
porous  and  semi-porous,  731. 
value    of,    in    fire-proofing    of 

buildings,  732,  733. 
strength  of,  732. 
structural,  731. 
Terra-cotta  arches,  see  Hollow  tile 

arches. 

Terra-cotta  arches,  749-770. 
advantages  of,  749. 
protection  from  stains  in  ceiling, 

753. 
types, 

flat  end-construction,  757.    See 

also  Flat  arches, 
flat  side-construction,  756.    See 

also  Flat  arches. 
Guastavino,  770. 
Herculean,  765. 
New  York  reinforced,  768. 
reinforced  tile,  765. 
segmental,  see  Segmental  terra- 
cotta arches. 
tile,  see  Tile  arches, 
weather  protection,  752. 
Terra-cotta,  architectural, 

brackets  and  consoles,  strength  of, 

230. 
weight     and     strength    of,    228, 

230. 
Terra-cotta    column    protection    in 

fire-proofing  of  buildings,  740. 
Terra-cotta  filling-blocks,  752. 
Terra-cotta  partitions,  814. 
height  and  length,  816. 
mortar,  816. 

porous  vs.  dense  material,  816. 
weight,  817. 
Terra-cotta  protection  of  girders  and 

beams    795. 

Test,   proposed   standard,   for   fire- 
proof floor  construction,  745. 
Tests,  fire,  of  concrete,  881^-8812. 
Tests  for  structural  steel,  332. 
Tests,    load,    in    concrete    erection 

work,  882p. 
Tests  on  adhesion  between  concrete 

and  steel,  866. 

Tests  of  fire-proof  floors,  805. 
Tests  of  protective  coverings,  740. 
Thacher  bar  in  reinforced-concrete 

construction,  862. 
Thacher  floor  unit,  793. 
Theatres, 
i  chairs  for,  1478. 
cost  of,  per  cubic  foot,  1466. 
dimensions  of  several,  1480. 
notes  on  dimensions  of,  1480. 
seating  capacity  of  several,  1479. 
space  required  for  seats,  1478. 
Thermometers,  comparison  of,  1118. 
Three-hinged  braced  arches, 
description  and  examples,  933. 
horizontal  resistance  of,  1019. 
stress  diagrams,  1021. 
Tie-bars,  description  and  data,  336; 
splicing  of,  367. 


Tie-beams, 

built-up  (wood),  385;  detail  of, 
1058. 

in  wooden  trusses,  1039,  1044. 

of  steel,  strength  of,  512. 

of  wood,  strength  of,  569. 
Tie-rods  for  arches,  formula  for,  252, 

263. 

Tie-rods  in  floor  construction,  802. 
Tie-rods  of  segmental  arches,  755. 
Ties,  wooden,  1042. 
Tiffany's  estimate  of  depreciation, 

1468. 
Tile  arches,  disadvantages  of,  750. 

cement  floors,  752. 

inspection,  750. 

filling  above,  752. 

mortar  for  setting,  751. 

reinforced,  765. 

setting  of,  750. 

terra-cotta  filling-blocks,  752. 

wetting  the  tile,  751. 

See  also  Terra-cotta  arches. 
Tile,  Tiles, 

enamelled,  1445;  cost  of,  1447. 

floor,  kinds  of,  1444;  cost  of,  1447. 

glass,  1446. 

marble,  1445. 

marbleithic,  1446. 

roofing,  1429 

rubber,  1447. 

terra-cotta,  see  Terra-cotta  tiling; 

also  Hollow  tile  arches. 
Tiles,  moulded  hollow,  for  interior 

finish,  840. 
Tiling,  dense,  731. 

semi-porous,  732. 
Timber,  reduced  to  board  measure, 

1396. 

Time,  measure  of,  30. 
Tin-covered  wood  doors  and  shut- 
ters, 844,  845. 
Tin,  Tin  roofs, 

cost  of,  1432. 

durability  of,  1432. 

laying  the  sheets,  1431. 

number  of  sheets  required,  1432. 

painting  of,  1405. 

size,  thickness,  weight,  methods 
of  manufacture,  etc.,  of  tin 
sheets,  1430. 

Tin-lined  pipe,  1273,  1277. 
Tower  clocks,   dimensions  of  dials, 

1494. 

Towers,  heights  of,  1525. 
Trade  references,  1570. 
Trao-rock  as  material  in  concrete, 

855. 
Transverse   strain   or  strength,   see 

Strength  of  beams. 
Traps,  for  plumbing,  1267. 
Travelling  fellowships  and  scholar- 
ships, 1565. 

Treads  and  risers,  rules  for,  1476. 
Triangle  of  forces,  232. 
Triangles,  definitions,  37;  area  of,  40. 
Trigonometry,  Trigonometrical, 

formulas,  99. 


INDEX. 


1659 


Trigonometry — Water. 


Trigonometry — continued. 

table    of   secants    and    cosecants, 
123a. 

table  of  sines  and  cosines,  103. 

table  of  tangents  and  cotangents, 

112. 
Trim,  cement,  840. 

electroplated,  839. 

metal-covered,  839. 

moulded  hollow  tiles,  840. 
Trimmers,  strength  of,  664,  677. 
Triplex  blocks,  1516. 
Truss  metal  lath,  825. 
Trussed  beams,  586. 
Trusses,  see  Roof  trusses, 

protection  of,  798. 
Tubular  boilers,    1133;    setting   of, 

1136. 
Turnbuckles,  336,  338;    dimensions 

of,  345. 

Tuscan  Order,  the,  1498. 
Types  of  steel  roof  trusses,  917. 

of  wooden  roof  trusses,  884. 


U 

U.   S.   Capitol,   the,   description  of, 
1533. 

U.  S.  Government  buildings,  archi- 
tects of,  1537;   cost  of,  1468. 

U.  S.  post-offices  and  court-houses, 
architects  of,  1537. 

U.  S.  standard  gauge  for  sheet  metal, 
1438. 

Ultimate  strength,  see  Strength, 
definition  of,  131. 

Uniform     contract,     the,     between 
owner  and  builder,  1555. 

Unit  stress,  definition  of,  132. 

Units,  electrical,  1308. 

Universal  type  corrugated  bar,  864. 

Upset  screw  ends,  338,  341. 

Urinals,  dimensions  of,  1472. 


Valleys,    distinction   between   open 

and  close,  1427. 
Valves,   for  steam  and  hot   water, 

1155. 

Varnish,  1405. 
Varnish  remover,  1407. 
Vault  walls,  210. 
Velocity  of  air  due  to  expansion  by 

heat,  1212. 

of  flow  of  water,  1232. 
Ventilation, 

amount  of  air  required  for,  1210. 
defined,  1209. 

diffusion    of    air    through    walls, 
1209. 


Ventilation — continued. 

ducts,  shape  and  material  of,  1213. 

fan  systems  of,  1215. 

fans  for,  1218. 

forced   blast   in   connection  with 
warm-air  furnaces,  1218. 

location  of  inlet  and  outlet,  1211. 

of  traps,  1270. 

plenum  or  hot-blast  system,  1216. 

size  of  flues,  1211. 

velocity  of  air  due  to  expansion  by 
heat,  1212. 

velocity  of  entering  air,  1210. 

with  furnace  heating,  1180. 
Vent-pipes,  1266,  1270. 
Vertical  reinforcement  of  columns, 
amount  of,  88  Ig. 

strength  of,  881gr. 
Volt,  definition  of,  1306. 
Volume  of  solids.  65. 
Voussoirs,  definition  of,  249. 


W 


Waite's  concrete  beam.  794.1 

Wall     anchors,     box,     for     wooden 

beams,  714. 

Wall  anchors,  for  steel  beams,  553. 
Wall  board,  Sackett's,  832. 
Wall  hangers,  for  floor  joists,  716. 
Walls, 

and    floors,    concrete,    finish    of, 
882m. 

breast,  210. 

brick  and  stone,  185. 

cement  block,  190. 

curtain,  190. 

faced  with  ashlar,  189. 

foundation,  183. 

furring  of  outside,  835. 

general  rule  for  thickness  of,  188. 

hollow,  189. 

in    reinforced-concrete    construc- 
tion, 881m. 

painting  of  plastered,  1406. 

party,  190. 

retaining,  206. 

stone,  thickness  of,  189. 

thickness  of  external,  186. 

vault,  210. 
Warehouse    construction,    see    Mill 

construction. 

Washers,  for  roof  trusses,  1062. 
Washington  Monument,  the,  1535. 
Waste-pipes,    1263;    least  diameter 

of,  1275. 
Water, 

amount  of,   required  for  various 
purposes,  1274. 

boiling-point  of,  1110. 

discharges  through  pipes,  1234. 

flow  of,  in  pipes,  1232. 

friction  of,  in  pipes,  1241. 

pressure  of,  1231. 


1660 


INDEX. 


Water— Wood. 


Water — -eon  t i  nued. 

several  conditions  of,  1110. 
specific  heat  of,  1113. 
weight  of,   at  different  tempera- 
tures, 1112. 
Water-closets,  N.  Y.  requirements, 

1268. 

Water  curtains  for  fronts  of  build- 
ings, 849. 

Water-heaters,  1282. 
Water-pipe,  1241. 
Water-proof  papers,  1401. 
Water-supply,  private,  1244. 
Wear  and  tear  of  building  materials, 

1469. 
Webster    system    of    heating,    the, 

1152. 
Webs  of  segment  tile,  thickness  of, 

754. 

Web,  thickness  of,  in  end-construc- 
tion flat  arches,  758. 
Weight,  measures  of,  28. 
Weight  of  (see  also  Article  in  ques- 
tion), 
air,     at     different     temperatures, 

1116. 
bars  of  brass,   copper,  and  lead, 

1348. 

bells,  1522. 
bolts,  1363. 
bricks,  1378. 
building  papers,  felts,  and  quilts, 

1401,  1403. 

cast-iron  column  bases,  1360. 
cast-iron  columns,  1358. 
cast-iron  plates,  1360. 
cast-iron  water-pipes,  1243. 
coal,  1342. 
coin,  30. 

copper  wire,  1327. 
corrugated  sheets,  1442. 
crowds,  653. 
earth,    sand,    and    gravel,    1373, 

1388. 

flat-rolled  steel  bars,  1353. 
glass,  1417,  1419. 
gravel  roofing,  1433. 
hay,  1342. 
lead  pipes,  1276. 
library  stacks  and  books,  1495. 
masonry,  1343. 
merchandise,  657. 
people,  1474;   in  crowds,  653. 
rafters,  table,  947. 
rivets,  1364. 
roofing  materials,  946. 
round  and  square  steel  bars,  1351. 
sheet  lead,  1277. 
sheets  of  brass,  copper,  iron,  lead, 

and  steel,  1347,  1358. 
slates,  for  roofing,  1492. 
square  and  round  steel  bars,  1350. 
steel,  330,  1357. 
steel   in   buildings,    approximate, 

1454. 

steel  wire,  1349. 
stones,  1341. 
substances,  table,  1341. 


Weight — continued. 

tin  roofing  sheets,  1431. 

trusses,  947. 

water,  at  different  temperatures, 

1112. 

Welded  metal  fabric  for  reinforce- 
ment, 779. 
Wells,  deep,  1244. 
Wet  concrete  mixture,  SS2k. 
White  lead,  1403,  1404. 
White  zinc,  1403,  1404. 
Wind, 

force  of,  1510. 

pressure    against    buildings    and 

towers,  1076,  1084. 
pressure  on  roofs,  950. 
stress  diagrams,  1026;  for  towers, 

1075. 
stresses,    in   buildings,    1085;     in 

towers,  1075. 
Wind     bracing    of    tall    buildings, 

1082. 
buildings  which  require  bracing, 

1082. 

computation  of  stresses,  1085. 
examples  of,  1085,  1092,  1100. 
intensity  of  wind  pressure,  1084. 
methods  of,  1083. 
portal  bracing,  1097. 
Windmills,  1248. 
Window  glass,  1415. 
Window   and   door  protection,    see 

Door  and  window  protection. 
Window  frames  and  sash,  fire-proof, 

728. 

metal,  847. 

wire-glass  sash,  847,  848. 
Window     protection     of     fire-proof 

buildings,  844. 

Wire,  copper,  tables  for,  1326. 
iron,  Trenton  Iron  Co.'s  list,  351. 
steel,  kinds  of,  1349. 
steel,  tables  for,  351,  1349. 
Wire  gauges,  1345. 

American  Steel  and    Wire    Co.'s, 

1349. 

Brown  and  Sharp,  1320. 
circular-mil,  1320. 
comparison  of,  1346. 
Trenton  Iron  Co.'s,  351. 
Wire  glass,  1418. 
Wire  glass   for  fire-proof  windows, 

738,  847,  848. 
Wire  lathing,  826. 
stiffened  wire,  827. 
width,  828. 
Wire  nails,  1368. 
Wire  reinforcement,  steel,  782. 
Wire  ropes, 

description  of,  352. 
strength  of,  354. 

Wiring  for  electric  lighting,  see  Elec- 
tric-light wiring. 
Wiring  tables,  electrical,  1328. 
Wood  doors  and  shutters,  tin-cov- 
ered, 844,  845. 
Wood,  Woods, 

crushing  resistance  of,  407. 


INDEX. 


1661 


Wood — Zinc-lead. 


Wood,  fire-proof,  736. 

hardness  of,  1509. 

shearing  strength  of,  361. 

staining  of,  1406. 

stiffness  of,  597. 

tensile  strength  of,  322. 

transverse  strength  of,  569. 

varnishing,  1406. 
Wooden  beams, 

built  up,  strength  of,  579. 

keyed  beams,  581. 

stiffness  of,  595;    tables,  603. 

strength    of,   formulas,    562;     ta- 
bles, 574. 

Wooden  columns,  see  Columns. 
Wooden  floors, 

chapter  on,  651. 

framing  of,  651,  679. 

live  loads,  654. 

maximum  span  of  joists,  tables, 
671. 

plank  flooring,  formulas  for  thick- 
ness of,  667. 

stirrups  and  joist  hangers,  680. 

strength  of,  to  determine,  675. 

to  find  size  of  joists,  girders,  etc., 
656. 

weight  of,  652. 
Wooden  girders,  see  Girders. 
Wooden  tanks,  construction  of,  1252. 
Wooden  trusses,  see  Roof  trusses. 
Working  head,  for  pumps,  1245. 


Working  strength  of, 

Manila  ropes,  357. 

masonry,  213. 

steel  ties,  331. 

terra-cotta,  230. 

wrought-iron  ties,  324. 
Wrought  iron, 

appearance  of  fractured  surface, 
324. 

in  fire-proofing  of  buildings,  736. 

Kirkaldy's  experiment  on,  325. 

old,  strength  of,  359. 

shearing  strength  of,  361. 

tensile  strength  and  quality,  323. 

transverse  strength  of,  569. 

weight  of,  rules,  1357. 

working  strength  of,  324. 


Z-bar  columns, 

constant  dimensions,  437,  483. 

description  and  details,  433. 

strength  of,  tables,  475. 
Z-bars, 

size  and  properties  of,  315. 

strength  of,  as  beams,  535. 
Zinc-lead,  1403,  1404. 


ALPHABETICAL  INDEX  TO  AOTERTISEMEHTS. 

PAGE 

American  Radiator  Co 14 

American  Steel  &  Wire  Co 2 

Art  Metal  Construction  Co 8 

Atlas  Portland  Cement  Co 6 

Barrett  Manufacturing  Co 9 

Brown  Hoisting  Machinery  Co •  5 

Clinton  Wire  Cloth  Co 5 

Contractor's  Supply  and  Equipment  Company 4 

Cutler  Manufacturing  Co 11 

Devoe&Co.,  F.  W 12 

Gamewell  Auxiliary  Fire  Alarm  Co 10 

Gurney  Heater  Manufacturing  Co 16 

Keuffe^  &  Esser  Co 18 

Lawrence  Cement  Co. •. 6 

Lord  &  Burnham  Co 10,  15 

Lorillard  Refrigerator  Co. ^  „ 16 

Maurer  &  Son,  Henry 2 

Mississippi  Wire  Glass  Co.  .  ^ 7 

National  Fire-Proofing  Co 1 

New  Jersey  Zinc  Co 13 

Randolph-Clowes  Co 14 

Ransome  Concrete  Machinery  Co 3 

Rapp,  John  W 17 

Rider-Ericsson  Engine  Co 15 

Roebling  Construction  Co 3 

Sackett  Plaster  Board  Co. 4 

Smith  &  Co..  Edward 12 

Scead  <fc  Co.,  Iron  Works 11 

Standard  Table  Oil  Cloth  Co 17 

Voigtmann  &  Co 7 

Wiley  &  Sons,  John .  18 

i 


CLASSIFIED  LIST  OF  ADVERTISEMEMTS. 

ARCHITECTS'  REQUISITES.  PAGE 

Devoe  &  Co.,  F.  W 12 

Keuffel  &  Esser  Co 18 

ART  METAL  WORK. 

Art  Metal  Construtcion  Co 8 

Snead  &  Co.,  Iron  Works 11 

ARTISTS'  MATERIALS  AND  MATHEMATICAL  INSTRUMENTS. 

Devoe  &  Co.,  F.  W 12 

Keuffel  &  Esser  Co 18 

ARCHES,  FIRE-PROOF. 

Brown  Hoisting  Machinery  Co 5 

Clinton  Wire  Cloth  Co 5 

Maurer  &  Son,  Henry 2 

National  Fire-Proofing  Co 1 

Ransome  Concrete  Machinery  Co 3 

Roebling  Construction  Co 3 

BOILERS,  RANGE.     Randolph-Clowes  Co 14 

CEMENT. 

(Portland)  Atlas  Portland  Cement  Co 6 

(Portland  and  Rosendale)  Lawrence  Cement  Co 6 

CONCRETE  MIXERS. 

Contractor's  Supply  and  Equipment  Co 4 

CONCRETE  REINFORCEMENT. 

American  Steel  &  Wire  Co 2 

CONTRACTOR'S  EQUIPMENT. 

Contractor's  Supply  and  Equipment  Co 4 

CUTLER  PATENT  MAILING  SYSTEM 11 

DOMESTIC  WATER  SUPPLV. 

Rider-Ericsson  Engine  Co 15 

ENGINEERS  AND  CONTRACTORS. 

Snead  &  Co.  Iron  Works 11 

ENGINEERING  INSTRUMENTS.     Keuffel  &  Esser  Co 18 

FILING  EQUIPMENT. 

Art  Metal  Construction  Co 8 

Snead  &  Co.  Iron  Works 11 

FIRE  ALARMS.     The  Gamewell  Auxiliary  Fire  Alarm  Co 10 

FIRE-PROOF  MATERIALS  AND  CONSTRUCTION. 

Art  Metal  Construction  Co 8 

Brown  Hoisting  Machinery  Co 5 

Clinton  Wire  Cloth  Co 5 

Maurer  &  Son,  Henry 2 

Mississippi  Wire  Glass  Co 7 

National  Fire-Proofing  Co 1 

Ransome  Concrete  Machinery  Co 3 

Rapp.  John  W 17 

Roebling  Construction  Co 3 

Sackett  Plaster  Board  Co 4 

Snead  &  Co.  Iron  Works 11 

Voietmann  &  Co 7 

GLASS,  WIRE. 

Mississippi  Wire  Glass  Co 7 

GREENHOUSES.     Lord  &  Burnham  Co 10,  15 

HEATING  AND  VENTILATING. 

American  Radiator  Co 14 

Gurney  Heater  Mfg.  Co 16 

jx>rd  &  Burnham  Co 10tJ15 


IV  CLASSIFIED  LIST  OF  ADVERTISEMENTS. 

MAILING  SYSTEM.     Cutler  Mfg.  Co H 

METAL,  COATINGS. 

Smith  &  Co.,  Edward 12 

METAL-COVERED  WOOD.     Rapp,  John  W 17 

OIL,  CLOTH.     Standard  Table  Oil  Cloth  Co 17 

PAINTS,  OILS,  LEAD,  ZINC,  ETC. 

Devoe  &  Co,,  F.  W 12 

New  Jersey  Zinc  Co 

Smith  <fe  Co.,  Edward , 12 

PLASTER  BOARD.  Sackett  Plaster  Board  Co 4 

PRESERVATIVE  COATINGS. 

Smith  &  Co.,  Edward 12 

PUMPING  ENGINES.  Rider-Ericsson  Engine  Co 15 

RADIATORS. 

American  Radiator  Co 14 

Gurney  Heater  Mfg.  Co 16 

RANGE  BOILERS.     Randolph-Clowes  Co 14 

REFRIGERATORS.     Lorillard  Refrigerator  Co 16 

ROOFING  MATERIALS. 

Barrett  Mfg.  Co .  . .  . 9 

Brown  Hoisting  Machinery  Co 5 

STEAM  AND  HOT- WATER  HEATING. 

American  Radiator  Co 14 

Gurney  Heater  Mfg.  Co 16 

Lord  &  Burnham  Co 10-15 

STEEL  AND  IRON — CONSTRUCTIONAL. 

Art  Metal  Construction  Co 8 

Brown  Hoisting  Machinery  Co 5 

Clinton  Wire  Cloth  Co. 5 

Ransome  Concrete  Machinery  Co 3 

Roebling  Construction  Co 3 

Snead  &  Co.  Iron  Works 11 

STEEL  WIRE.     American  Steel  &  Wire  Co 2 

VARNISH. 

Devoe  &  Co.,  F.  W.  .  . 12 

Smith  &  Co.,  Edward 12 

VENTILATION. 

Lord  &  Burnham  Co 10,  15 

WALL  COVERINGS.     Standard  Table  Oil  Cloth  Co 17 

WINDOWS,  FIRE-PROOF.     Voigtmann  $•  Co 7 

WIRE  CLOTH,  WIRE  LATH,  WELDED  WIRE.  ETC. 

Clinton  Wire  Cloth  Co 5 

WIRE  GLASS.     Mississippi  Wire  Glass  Co 7 

ZINC.     New  Jersey  Zinc  Co 13 


Decreasing 
i  Fireproof  ing  Cost 

Are  you  familiar  with 
the  new  methods  of  using 

Terra  CottaHollowTih 

in  connection  with  re-enforcld  concrete  structural  members? 

Are  you  familiar  with  the  economy,  efficiency  and 
strength  of  long  span  Hollow  Tile  Floors  (re-enforced) 
used  in  spans  up  to  25  feet? 

Are  you  aware  of  the  greatly  decreased  cost  of 
fireproof  construction  under  these  methods  ? 

How   can  you  be  sure  of  the  best  fire-proof  con- 
struction, or  the  lowest  cost,  or  either,  unless  you  figure 
with  the  largest,  fireproof  ing  organization  in  the  world? 
Send  us  your  plans  to  figure. 
Estimates  cheerfully  made. 

National  Fire  Proofing  Company 

Manufacturers  of 

Terra  Cotta  Hollow  Tile 

Contractors  for  Construction  of  Fireproof  Buildings 

The  largest  firm  in  the  world  devoted  exclu- 
sively to  the  business  of  fireproof  construction. 
Capital  Twelve  and  one-half  Million  Dollars. 

riTTSBURG.  F.llo.  Buiidioj  CHICAGO,  Com.crci.1  N.tio.J  B«A  BHf. 

PHILADELPHIA.  Land  Till.  Bullet        NFW  YORK.  Flttiron  Bmld,n< 

WASHINGTON.  D.  C..  Col.t.a.  B«ild«,f.  MINNEAPOLIS,  MINN.,  Lumttr  E.. 

BOSTON,  Old  South  BnUdiot       LOS  ANGELES.  CALIF,  Union  Tn»t  Buildup 

ST.  LOUIS.  MO.  LONDON.  ENG..  26  Cbaoctrr  lot 

SAN   FRANCISCO.  Monadnock  Building 

Twenly-six   factories  tKrou^out  the   United  States. 


H 


'Phoenix' 
Hollow  Wall  Construction 

(Patented) 

Red  Clay  and  Glass  Roofing 
Tiles 

"Herculean"    Flat   Arch 

(Terra.   cotteO  (Patented) 

Manufactured  by 

HENRY   MAURER    &   SON 

420  EAST  TWENTY-THIRD  STREET,  NEW  YORK,  N.  Y. 

WORKS:   MAURER,  N.  J. 
PHILADELPHIA    OFFICE,    PENNSYLVANIA    BUILDING 

0 


The  Roebling  System 

is  now  the  recognized  standard  of  fire=proof  con« 
struction.  It  has  been  used  in  over  twelve  hundred 
buildings.  It  is  the  only  system  that  has  withstood 
actual  conflagrations  without  injury  and  without 
the  necessity  of  repairing  the  construction.  It  has 
been  adopted  for  the  largest  department  stores, 
offices  and  apartment  hotels  in  the  world. 

72=PAGE  ILLUSTRATED  CATALOGUE 
ON  APPLICATION. 

THE  ROEBLING  CONSTRUCTION  CO. 

Fuller   Building,  Broadway  and   2jd  St.,   New  York 

-BRANCHES- 

Philadelphia.        Boston.         Buffalo.        Cleveland.        Pittsburg.        Chicafiau 
San  Francisco.  Seattle. 

~~~ TEST 

all  concrete  as  it  goes  into  your  building.  Structures 
where  this  machine  is  used  never  fall  down. 


THE 


Ransome  Concrete  Machinery  Co. 

DUNELLEN,    NEW   JERSEY 
11    and    1133    Broadway          ....          New  York 

3 


USE 

SACKETT  PLASTER  BOARD 

(WHICH  is  FIREPROOF) 
Instead  of  Inflammable  Wood  Lath 


SACKETT  PLASTER  BOARD  Co. 

NEW  YORK         CHICAGO 
FORT  DODGE    GRAND  RAPIDS    GARBUTT 


Everyone  in  the  Building  Line 

is  interested  in  concrete.     It    is    recognized  as  the  predominant  material 
for  building  purposes  of  the  future. 

Architects  are  being  called  upon  to  design  more  and  more  concrete 
buildings,  and  a  larger  part  of  these  buildings  will  be  made  of  concrete 
mixed  with  a 

SMITH   MIXER 

because  an  increasing  number  of    archi- 
tects are  writing  into  their  specifications: 

"  All  Concrete  must  be  mixed 
with  a  SMITH  MIXER." 

The  reason  for  this  is  their  discovery 
that  even  concrete  made  of  the  right 
proportions  and  quality  of  each  ingre- 
dient cannot  be  relied  upon  unless  it 
is  properly  mixed,  and  that,  further, 
the  "SMITH  MIXER"  is  one  of  the  few  which  may  be  relied  upon. 

CONTRACTOR'S    SUPPLY    AND    EQUIPMENT   CO. 
OLD   COLONY  BUILDING,   CHICAGO,   ILL. 


REINFORCED    CONCRETE 
CONSTRUCTION 

using  a  special  corrugated  iron;   attached  to  buildings  In 

the   ordinary  way  and  plastered  with  Portland  cement, 

making   a  light,  strong,  fire-proof  construction  for  roofe, 

walls,  floors,  etc* 

THE  BROWN  HOISTING  MACHINERY  CO., 

Engineers,   Designers,  and  Builders    of 
Hoisting  Machinery  of  Every  Description. 

Main  Office  and  Works,   CLEVELAND,  OHIO. 

Branch  Offices,  NEW  YORK  and  PITTSBURG- 


CLI 

WELDED 

F 

ICONCRETE 

CONS' 


TON 

IIFABRICS 

FIRE-PROOF 
AUCTION, 


A 

WIPE 
PLAIN  AN 

CLINTON 

CUNT 


o 

LATH 

STIFFENED. 

RECIOTHCO 

,MASS. 


BOSTON,  NEW  YORK,  CHIC  AGO,  SAN  FRANCISCO 


'DRAGON' 

PORTLAND  CEMENT. 


FOR  SALE  BY 

THE  LAWRENCE  CEMENT  CO, 

nakers  oc  nnn  nnn  RSRRFK  Nat^i  and 

and  Shippers  of  flUjUVUjUl/l/    DrillRjjljO  Portland  Cements 

HAIN  OFFICE,  i  BROADWAY,  NEW  YORK. 


ATLAS 

PORTLAND 

CEMENT 

Is  the  Standard  American  Brand. 

Used  by  all  the  leading  Engineers  and 
Contractors  throughout  the  United  States, 
and  preferred  by  the  U.  5.  Government 

ATLAS  PORTLAND  CEMENT  CO., 

30  BROAD  STREET,  NEW  YORK, 


"flississippi  Wire  Glass" 

The  Approved  Fire  Stop 

For  Skylights,  Elevator  Doors,  Shaft  Openings,  Fire  Doors,  Fire  Windows 
and  all  Roof,  Floor  and  Wall  Openings  Exposed  to  Fire  Hazard, 
Recommended  by  the 

NATIONAL  BO  iRD  OF  FIRE  UNDERWRITERS 
NATIONAL  FVE   PROTECTION   ASSOCIATION 
INSURANCE  ENGINEERING   EXPERIHF.NT  STATION 
BRITISH   rIRE  PREVENTION  COMIV   »     EE 
INTERNATIONAL   ASSOCIATION    V          'RE    ENGINEERS 
and  BUILDING,  INSPECTION  AND  RATT-       BUREAUS 
(From  The  Many  Testimonials  Addressed  Us) 

FIXED    VALUES 

"  It  retards  fire  withoutitiiding  it— permits  the  blaze  to  declare  itself." 

"  It  can  be  cracked,  but  it  cannot  be  scattered.     If  fractured  it  retains 

its  place."  EDWARD  F.  CROKER, 

Chief,  Fire  Department,  New  York. 

"  The  Most  Satisfactory  Fire  Protection  in  Windows." 

D.  H.  BURNHAM  &  CO., 

Architects,  Chicago,  San  Francisco,  Philadelphia,  Buffalo,  New  Orleans. 
THICKNESSES-i=4,  3-8  and  1=2  inch 
SIZES— Up  to  40  inches  wide  and  100  inches  (and  over)  long 

"  The  buildings  found  standing,  after  the  fire,  in  which  business  could  be 
transacted,  were  the  buildings  in  which  wire  glass  had  been  employed  to  protect 
openings  in  roofs  and  walls." 

"Architect  and  Builders'  Journal,  Baltimore.** 

For  additional  information  address 

MISSISSIPPI  WIRE  GLASS  CO., 

1 15  Broadway,  flew  York. 


Increases 

Rent 

Values 

Fire  Barriers 
Affording  Light 
and  Ventilation 

Decreases  ^ 

Fire 

Premiums 


The  Voigtmann  Standard  Automatic  Clos- 
ing and  Locking  Windows  a  Specialty 


The  Voigtmann  Adjustable  Weather  Guide  Win- 
dow^     Interior  View  Showing  Sash  Weights. 


METALLIC 


VOIGTMANN  &  COMPANY 

Manufacturers  under  Patents  of  THEIR   SPECIALTIES    IN 

WINDOW  FRAMES 
AND  SASHES      :      : 
For  Carrying  Wire  and  Plate  Glass 

TESTED  AND  APPROVED  BY   THE 
NATIONAL  BOARD  OF  FIR 8  UNDERWRITERS'  LABORATORIES 

42-54  East  Erie  Street,  CHICAGO 

430  WEST  14TH   STREET!  TVJPW     VOT?  V     I     Telephone 

427  WEST  13TH  STREET/1^11™        I  VJlXJV    |  fo  Ghe!sea 


Metallic  Furniture  and  Fixtures  make 
possible  incombustible  interiors.  These 
furnishings  are  artistic,  durable,  con- 
venient and  sanitary.  We  manufacture 
in  Steel  and  Bronze:  Counters,  Partitions, 
Desks,  Tables  and  Cases  ;  also  Library 
Shelving,  Fixtures  for  Vaults  and  all  kinds 
of  Metallic  Filing  Devices.  Vertical  Files 
for  Architectural  Plates  a  specialty.  Com- 
plete Equipments  furnished  for  Banks. 
Our  work  is  pure  Cabinet  Work  in  Metal, 
and  particular  attention  is  paid  to 
architectural  detail.  Plans  and  estimates 
furnished  on  request. 

ART  METAL  CONSTRUCTION  CO. 
Jamestown,  N.  Y.          12  Branch  Offices. 


JOHN  W.  RAPP 


MANUFACTURER   OF 


ALL    STEEL 

DOORS,  WINDOWS  %  TRIM 

OF  THE   HIGHEST  GRADE 

OFFICES    AND    SHOWROOMS 

Metropolitan    Life    Building 

1    MADISON    AVENUE,    NEW   YORK 


For  Roofing  and  Waterproofing^ 

For  roofing  and  waterproofing  purposes  we  recommend  our  SPECIFI- 
CATION BRANDS  of  Pitch  and  Felt,  because  we  believe  they  represent 
the  highest  quality  manufactured. 

The  Felt  weighs  from  14  to   15  pounds  per  one  hundred  square  feet, 

single  thickness. 
The  Pitch  is  the 
very  best  grade 
of  straight  -  run 
American  coal 
tar  pitch. 

The  record  of 
Coal  Tar  Materi- 
als for  roofing 
and  waterproof- 
ing purposes  cov- 
ers a  period  of 
over  50  years, 
and  their  use  is 
steadily  increas- 
ing. 

We  can  point 
to  buildings  of  all 
kinds  over  the 
country,  includ- 
ing the  largest 
manuf  a  c  t  u  r  i  n  g 
plants  and  sky 
scrapers,  which 
have  been  roofed 
with  coal  tar 
materials  in  the 
form  of  what  is 
commonly 
known  as  "Slag 
and  Gravel 

roofs."  All  of  these  have  given  the  utmost  satisfaction,  -many  for 
upwards  of  30  years,  at  a  cost  not  exceeding  i  of  a  cent  per  foot  per  year 
of  service. 

A  very  large  proportion  of  the  waterproofing  work  of  the  country  has 
also  been 
done  with 
Coal  Tar  Ma- 
terials, and 
no  other  form 
of  water- 
proofing  has 
proven  as 
economical 
and  satisfac- 
tory. 

We  should 
be  glad  to 
send  any  ar- 
chitect, engi- 
neer, or  any 
one  interest- 
ed, a  sample 
of  BARKETT 

SPECIFIC A- 

TIOV  Felt  and  full  information  covering  the  use  of  these  materials  for 
either  of  the  purposes  mentioned. 

BARRETT    MANUFACTURING    CO. 

New  York        Chicago        Philadelphia        Boston        Cleveland        Cincinnati        Minneapolis 
Kansas  City         St.  Louis         New  Orleans          Pittsburg         London,  Eng. 


TARRED  FELT 


The  Gamewell  Auxiliary  Fire  Alarm  Service 

Furnishes  any  desired  number  of  interior  stations 
from  which  Fire  Alarms  can  be  instantaneously 
transmitted  to  Fire  Department  Headquarters. 

This  service  is  installed  in  thousands  of  Hotels, 
Hospitals,  Theatres,  Office  Buildings  as  well  as  in 
Mercantile  and  Manufacturing  concerns  in  New  York 
and  many  other  cities. 

For  particulars  address 

THE  GAMEWELL  AUXILIARY  FIRE  ALARM  CO., 
19  Barclay  Street, 

New  York  City. 


SASH    OPERATING    APPARATUS 

For  all  propositions  where  long  or  short  runs  of  sash  are 
to  be  operated.  Adapted  to  fine  work  or  for  factories, 
mills,  etc.  :  :  :  :  :  Send  for  Catalogue. 

LORD   &    BURNHAM    CO. 

1133  Broadway        -  New  York 

10 


THE  CUTLER  PATENT 

MAILING   SYSTEM 

U.  S.  MAIL  CHUTE 

affords  the  only  means  of  posting  letters 
in  the  upper  stories  of  buildings.  A  let- 
ter once  in  the  chute  is  officially  "mailed." 

INSTALLED  IN  CONNECTION  WITH 
THE  U.  S.  FREE  COLLECTION  SER- 
VICE ONLY  BY  THE  SOLE  MAKERS, 

THE  CUTLER  MFG.  Co., 

ROCHESTER,  N.  Y. 

The  Double  Chute  equipment,  as  installed  in  the  more  important 
buildings,  makes  cleaning  and  repairs  possible  without  interruption 
of  the  Mail  Service. 


THESNtAD&CO.IR'JiN  WORKS, 


MANUFACTURERS  OF 


Structural  and  Ornamental  Iron  and 
Bronze  Work  for  Buildings, 

METAL  BOOKSTACKS  for  LIBRARIES. 


Office  and  Works:        Pacific  Avenue  Station 
Foot  of  Pine  Street,         C.  R.  R.  of  N.  J. 

JERSEY   CITY.  N.  J. 


P.  CU.  DEVOE  &  CO. 

(ESTABLISHED  1754.) 
The  Oldest  and  Largest  Paint  Manufacturing  Concern  in  the  United  States. 

PURE  PAINTS,  for  all  purposes. 
FINE  VARNISHES,  for  all  purposes. 

"ATRAMENT"  RUST  PREYEMTATIYE  PAINT, 

HOUSE  PAINTS, 

FACTORY   PAINTS, 

BRIDGE    PAINTS, 

MACHINERY    PAINTS. 

ARTISTS'    MATERIALS    of    all    kinds. 

MATHEMATICAL   INSTRUMENTS,  PAPERS,  ETC. 

CATALOGUES  SENT.  CORRESPONDENCE  INVITED. 

NEW    YORK   AND   CHICAGO. 
OUR 

Durable  Metal  Coating 

protects  iron  and  steel  in  the  best  pos- 
sible manner  from  rust,  corrosion,  weather, 
dampness,  etc.,  etc.  Our 

Preservative  Coatings 

accomplish  the  same  results  for  interior 
and  exterior  woodwork,  and  greatly 
improve  the  beauty  of  the  structure  at 
the  same  time. 

EDWARD  SMITH  &  CO. 

VARNISH    MAKERS   AND   COLOR   GRINDERC 

59  Market  St.,  Chicago  45  Broadway,  New  York 

12 


IN  SPECIFICATIONS 

When    oxide    of   zinc    made    from    the    metal 
is  required,  architects  should  specify 

Florence    Brand    Zinc    Oxide 

GREEN    SEAL RED    SEAL 

Always  uniform  in  color  and  quality. 

For  interior  work  Oxide  of  Zinc  is  the  only 
white  pigment  that  holds  its  color. 

For  exterior  painting  Oxide  of  Zinc  adds  to 
the  beauty  and  durability  of  the  work;  and  the 
spreading  Dualities  of  paints  based  on  it  makes 
them  more  economical  than  any  other  type  of 
paint. 


FREE: 

Our  Practical   Pamphlets :    "  Paints   in  Architecture,"  "  Specifications 
for  Architects,"  "  French  Government  Decrees," 
"  Paint :   Why,  How  and  When." 


THE  NEW  JERSEY  ZING  Co. 

71    BROADWAY        -        -        NEW   YORK 


WE  DO  NOT  GRIND  ZINC  IN  OIL 

A  LIST  OF  MANUFACTURERS  OF  ZINC  PAINTS  MAILED 
ON  REQUEST 


13 


Makers  of  the 


AMERICANxlDEAL 

/I  RADIATORS  ^(BOILERS 


20  Branch  Offices  and  30  Warehouses   at   prom* 
inent  shipping  points  throughout  the 
United  States 


General  Offices 


282-286  Michigan  Ave.,  CHICAGO 


RANDOLPH-CLOWES    CO., 

WATERBURY,   CONNECTICUT, 
SOLE     MANUFACTURERS    OF 


SEAMLESS    DRAWN    COPPER 
RANGE  BOILER. 

The  only  boiler  which  has  no  longitudinal  seam. 


14 


CONCERNING  GREENHOUSES 


We  manufacture 
and  erect  Green- 
houses, Conserva- 
tories, etc. 

Make  complete 
designs  or  carry  for- 
ward  architects' 
sketches. 


72    PAGE.    CATALOGUE 
OW     REQUEST 


LORD    &   BURNHAM  CO. 

1  1 33  Broadway  New  York 

DOMESTIC  WATER-SUPPLY 

Without  Depending  on  the  Wind. 

THE  "REECO-RIDER" 

AND  "REECO-ERICSSON" 

HOT-AIR  PUMPING- 

ENGINES 

In  use  for  thirty-five  years. 
More  than  40,000  sold. 

Specified  by  the  Leading  Engi- 
neers of  the  World. 

Catalogue  on  application  to  near- 
est store. 

RIDER-ERICSSON  ENGINE  Co., 

NEW  YORK,  BOSTON,  PHILADELPHIA,  CHICAGO. 

15 


THB  "LORILLARD" 

—. REFRIQERA  TOR 


Is  the  Standard. 


Established  1877. 


FOR  FAfHLIES,  HOTELS, 

CLUBS,   INSTITUTIONS, 
STEAflSHIPS,  ETC. 

Drawings,  Estimates  and  Specifications  given  on  receipt  of  plans 
and  statement  of  requirements. 


SEND   FOR   CATALOGUE    AND    INFORMATION. 


THE    LORILLARD     REFRIGERATOR    COMPANY, 
25  West  32nd  Street,  New  York. 


ALWAYS 
RELIABLE 

HEATERS 

Gurney  Heater  Manufacturing  Go. 

188-200    FRANKLIN    STREET,   BOSTON,   MASS 
New  York  Branch:     12  East  42nd  Street 

16 


S  ANITAS 

The     Washable     Wall     Covering 

When  you  have  a  house  to  build  specify  SANITAS  for  the  walls. 

It  is  a  wall  covering  which  will  satisfy  your  clie  nt      It  is  made  on 

cloth  and  printed  in  non-fading  oil  colors.   It  is  beautiful,  durable 

and  absolutely  cleanly.     Send  for  Booklet  16. 

STANDARD  TABLE  OIL  CLOTH  CO. 

320    BroeLdwsxy  New    York 


S  P  EC  I  F  Y 

S  AN  A  T I L  E 

An  Ideal  Substitute  for  Porcelain  Tiling 


Send  for  Samples  and  Circulars 


Standard  Table  Oil  Cloth   Co. 

320  BROADWAY,   NEW   YORK 


OF  THE 


KEUFFEL  &  ESSER  GO. 

127  FULTON  ST. ,  N.  Y.     General  Offices  and  Factories,  HOBOKEN,  N.  J. 
CHICAGO — ST.    LOUIS — SAN    FRANCISCO 

DRAWING    MATERIALS.      MATHEMATICAL    AND   SURVEYING) 
iNSTRUMENTS.     MEASURING   TAPES 

Our  Paragon  Drawing  Instruments  enjoy 
an  excellent  and  wide  reputation.  They  are 
of  the  most  precise  workmanship,  the  finest 
finish,  the  most  practical  design,  and  are  made 
in  the  greatest  variety.  We  also  have  Key 
Excelsior  and  other  brands  of  instruments 

We  carry    the   largest  and   most  complete 
assortment  of  Drawing  Papers, Tracing  Cloths 
and  Papers,  Blueprint,  Blackprint  and  Brown- 
print  Papers,  Profile  Papers. 

K  &  E  Measuring  Tapes,  Steel,  Metallic,  Linen. 
Most  accurate.  Best  quafity.  Largest  assortment. 
We  make  the  greatest  variety  of  engine-divided 
Slide  Rules,  and  call  especial  at  tentiontoour  Patented 
Adjustment,  which  insures  permanent,  smooth  work- 
ing of  the  slide.  Some  of  our  other  well-known  cal- 
culating instruments  are  the  Reckoning  Machine, 
Fuller's  Slide  Rule,Thacher's  Calculating  Instrument, 
Spery's  Pocket  Calculator,  etc. 

Our  complete 

(550  page)  catalogue 
on  request 


Analysis    of    Mixed    Paints,    Goloi 
Pigments,    and    Varnishes 

By  CLIFFORD   DYER  HOLLEY,  M.S.,  Ph.D. 

Formerly  Professor  of  Industrial  Chemistry,  North  Dakota  Agricultural  Col  eg 

AND 

E.    F.    LADD,    B.S. 

Professor  of  Chemistry,  North  Dakota  Agricultural  Collet  e 

Large  I2mo,  xi  +  235  pages,  illustrated.     Cloth,  $2.50 


Modern  Pigments  and  their  Vehicles 

Their  Properties  and  Uses,  Considered  Mainly  from 
the  Practical  Side,  and  How  to  Make  Tints*  from  Then 


By  FREDERICK  MAIRE 

Ex-editor  of  *  Painting  and  Decorating" 


I2mo,  xi  +  266  pages 


Cloth,  $2.o( 


JOHN   WILEY    &    SONS,    NEW   YORK 


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GENERAL  LIBRARY -U.C.  BERKELEY 


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THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


